Loudspeakers For Music Recording and Reproduction

Loudspeakers For Music Recording and Reproduction
Loudspeakers
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Loudspeakers
For Music Recording and Reproduction
Philip Newell and Keith Holland
AMSTERDAM • BOSTON • HEIDELBERG • LONDON
NEW YORK • OXFORD • PARIS • SAN DIEGO
SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO
Focal Press is an imprint of Elsevier
Focal Press is an imprint of Elsevier
Linacre House, Jordan Hill, Oxford OX2 8DP, UK
30 Corporate Drive, Suite 400, Burlington, MA 01803, USA
First edition 2007
Copyright © 2007, Philip Newell and Keith Holland.
Published by Elsevier Ltd. All rights reserved.
The right of Philip Newell and Keith Holland to be identified as the authors of this work
has been asserted in accordance with the Copyright, Designs and Patents Act 1988
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ISBN-10: 0-2405-2014-9
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Contents
About the authors
Acknowledgements
Preface
Introduction
xi
xv
xvii
xix
Chapter 1 What is a loudspeaker?
1.1
A brief look at the concept
1.2
A little history and some background
1.3
Some other problems
1.4
Some basic facts
1.4.1 Acoustic wave propagation
1.4.2 Mechanical and acoustic impedance
1.4.3 Impedance in loudspeakers
1.5
The practical moving-coil cone loudspeaker
1.5.1 The combined response
1.6
Resistive and reactive loads
1.7
The bigger picture
References
Bibliography
1
1
2
4
5
5
7
9
9
12
14
20
20
21
Chapter 2 Diversity of design
2.1
Moving-coil cone loudspeakers
2.1.1 Cones
2.1.2 Surrounds
2.1.3 Rear suspensions
2.1.4 The chassis
2.1.5 The voice-coil assembly
2.1.6 Magnet systems
2.1.7 Ferrofluids
2.1.8 The complete system
2.2
Dome loudspeakers
2.2.1 Hard and soft domes
2.3
Compression drivers
2.4
Ribbon loudspeakers
2.5
Heil air-motion transformers
2.6
Distributed mode loudspeakers
2.6.1 Panel/piston combinations
2.7
Beyond magnetics
2.7.1 Piezoelectric devices
2.7.2 Ionic loudspeakers
2.8
Electrostatic loudspeakers
22
22
23
30
32
34
35
36
39
39
40
43
45
48
50
51
55
56
57
57
58
vi Contents
2.9
2.10
Electromagnetic planar loudspeakers
Summary
References
Bibliography
63
63
64
64
Chapter 3 Loudspeaker cabinets
3.1
The concept of the infinite baffle
3.2
The sealed box
3.2.1 Acoustic suspensions
3.3
Reflex enclosures
3.4
Acoustic labyrinths
3.4.1 Modern transmission lines
3.5
ABR systems
3.6
Bandpass cabinets
3.7
Series driver operation and isobaric loudspeakers
3.8
General discussion
3.9
Cabinet lining materials
3.10 Cabinet constructions
3.11 Cabinet shapes and diffraction effects
3.12 Front grilles
3.13 Cabinet mounting
References
65
65
67
71
71
76
78
81
82
84
85
86
87
88
92
93
95
Chapter 4 Horns
4.1
The horn as a transformer
4.2
Directivity control
4.3
Horn design compromises
4.4
Non-linear acoustics
4.5
Examples of non-linear acoustics in loudspeakers
4.6
Practical horns in studios and homes
4.7
Implications for practical horn design parameters
4.8
Summary of results
4.9
General horn characteristics
4.10 Phasing plugs
4.11 Acoustics lenses
4.12 Horn types
4.13 Materials of construction
4.14 Vestigial horns and ‘waveguides’
4.15 Flare rates
References
96
96
102
103
104
105
107
108
112
113
115
117
118
119
120
121
123
Chapter 5 Crossovers
5.1
What is a crossover?
5.2
Reconstruction problems
5.3
Orders, slopes and shapes
5.4
Filter shapes
5.5
Target functions
5.5.1 Minimum and non-minimum phase effects
5.5.2 Corrective measures and side-effects
5.6
Active versus passive crossovers
124
124
125
129
137
139
140
141
142
Contents vii
5.7
5.8
Physical derivation of crossover delay
Digital crossovers
References
Bibliography
146
147
150
150
Chapter 6 Effects of amplifiers and cables
6.1
Amplifiers – an over-view
6.2
Basic requirements for current and voltage output
6.3
Transient response
6.4
Non-linear distortions
6.5
Amplifier classes and modes of operation
6.5.1 Class A amplifiers
6.5.2 Class A derivatives
6.5.3 Class AB
6.5.4 Class D
6.5.5 Class G and H
6.6
MOSFET or BJT?
6.7
Choosing an amplifier
6.8
Loudspeaker cables and their effect on system
performance
6.8.1 The bare minimum
6.8.2 The status quo
6.8.3 Cable designs for loudspeaker use
6.9
The amplifier/loudspeaker interface
6.10 Some provable characteristics of cable performance
6.11 Some passing comments
6.12 Multi-cabling
6.13 Polyamplification and multiamplification
6.14 System design
References
Bibliography
151
151
153
154
157
158
159
160
161
161
163
163
164
166
166
168
169
170
174
188
191
192
193
194
195
Chapter 7 Loudspeaker behaviour in rooms
7.1
The anechoic and reverberation chambers
7.2
Boundary loading and room gain
7.2.1 Restriction of radiating space
7.2.2 The mirrored room and mutual coupling
7.3
Room reflexions
7.3.1 Resonant modes
7.4
Flush-mounting
7.5
Multichannel considerations and phantom imaging
7.6
Stereo perception in rooms
7.7
Rooms for critical listening
7.8
Electronic, digitally adaptive response correction
7.9
Minimum and non-minimum phase responses
References
Bibliography
196
196
198
202
205
206
209
211
212
216
217
220
225
227
227
Chapter 8 Form follows function
8.1
The chain
8.2
Recording monitors
229
229
230
viii Contents
8.2.1
8.2.2
8.2.3
8.2.4
8.2.5
8.2.6
8.2.7
8.3
8.3.1
8.4
8.5
8.6
8.6.1
Basic requirements
Proportional costs
Different approaches
Crossover points
Power consideration
Interfacing with the rooms
A word about listening levels
Mixing monitors
Location dilemmas
Mastering loudspeakers
Domestic loudspeakers
Musical instrument loudspeakers
Cabinet designs
Summary
References
Bibliography
233
237
238
241
245
248
250
250
258
258
263
264
267
269
269
270
Chapter 9 Subjective and objective assessment
9.1
The general situation
9.2
Test signals and analysis
9.2.1
Frequency response plots
9.2.2
Waterfall plots
9.2.3
Harmonic distortion
9.2.4
Intermodulation distortion
9.2.5
Delta-functions and step-functions
9.2.6
Acoustic source plots
9.2.7
Cepstrum analysis
9.2.8
Modulation transfer functions
9.2.8.1 Application of room equalisation
9.2.8.2 A D-to-A dilemma
9.3
Sound fields and human perception
9.3.1
Further perceptual considerations
References
Bibliography
271
271
272
275
277
281
283
288
292
295
297
298
301
302
305
309
310
Chapter 10 The
10.1
10.2
10.2.1
10.3
311
311
312
314
314
319
mix, the music and the monitors
Physics or psychology?
The musical dependence of compatibility
Sine waves and pink noise
Real responses vs. preconceived ideas
Acknowledgement
Chapter 11 Low frequency and transient response dilemmas
11.1
The great low frequency deception
11.1.1 The air spring
11.1.2 Size, weight and sensitivity
11.1.3 Further consequences of small size
11.2
Commercial solutions
11.2.1 The time penalty
11.2.2 The transient trade-off
320
320
321
324
326
326
327
330
Contents ix
11.3
11.4
11.5
11.6
11.7
11.8
11.9
Chapter 12 The
12.1
12.2
12.3
12.4
12.5
12.6
12.7
The evolution of the desk-top monitor
The great time deception
Resonant tails and one-note bass
The masking of detail
Theoretical equalisation and excess phase
Modulation transfer-function and a new type
of frequency response plot
Summing-up
References
333
339
339
342
343
challenges of surround sound
Surround sound in professional studios
Cinema sound
Music mixing
Sub-woofers – discrete and managed
Size versus performance compromises
Compound sub-woofers and electronic control
System considerations
References
352
352
357
360
362
364
368
372
375
Glossary of terms
Index
345
350
351
376
395
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About the authors
Philip Newell began working professionally with loudspeakers in 1966, in
the maintenance department of a shop selling high fidelity sound reproduction equipment in the town of his birth, Blackburn, England. Within
a year he had begun to work for the Mecca chain of dance halls as a
live-sound engineer. By 1970 he was working at a recording studio in
south London, where he designed his first studio monitoring system. Philip
moved to Pye Records in late 1970, when Pye was one of the UK’s premier
record companies with a large recording complex near Marble Arch, in
central London. He worked primarily as a studio maintenance engineer,
but was also involved in many recordings, and then moved to a fledgling
Virgin Records organisation in late 1971 as chief recording engineer. In
1973 Philip co-founded The Manor Mobile with partners Richard Branson
and Nik Powell, putting on the road what was probably at the time the
world’s most advanced mobile recording studio. From 1974 to 1982 he was
technical director of the whole recording divisions of Virgin, but remained
working as a recording engineer and record producer during the entire
period, feeling that it was better to keep in practice than to concentrate
solely on administration if the most balanced decisions were to be made.
After selling his shares in Virgin in 1982, to concentrate on flying seaplanes, a chance meeting in London in 1983 with Alex Weeks, the then
owner of Reflexion Arts, led them to deciding to start an acoustics and
monitoring branch of the company, for which Philip designed a series of
studio monitor loudspeakers during a period of building many recording
studios. It was during this time that he met Keith Holland at the Institute
of Sound and Vibration Research (ISVR), a department of Southampton
University, in the UK. Together they worked on the design of improved
mid-range horn loudspeakers for studio monitoring systems. Although
Philip left Reflexion Arts in 1988 to pursue a free-lance career, his collaboration with them and Keith Holland and the ISVR has lasted the twenty
years to the publication of this book.
Philip Newell’s 40 year career with loudspeakers has encompassed
their use in domestic hi-fi, live sound, musical instrument amplification,
music recording and mixing, film studios, television studios, video postproduction rooms and many other uses. He has worked with them as a live
sound engineer, recording and mixing engineer and record producer. The
majority of his work since leaving Virgin has been as a designer of music
recording studios, cinema mixing theatres and live performance spaces,
and he is still involved in the design and development of high performance
loudspeaker systems.
Philip is a Fellow if the Institute of Acoustics, a Member of the Audio
Engineering Society, a member of the Seaplane Pilot’s Association and
xii About the authors
British Mensa. He has written five books on acoustics and electro-acoustics,
and has published over 100 related articles, journal papers and conference
papers. Since 1992 he has lived in Spain, and during the course of his
work, he has travelled to over 30 countries. His recording career was very
musically varied, from the Duke Ellington Orchestra to Queen; from The
Who to The Warsaw Philharmonic Orchestra; from Mike Oldfield to John
Cale; to English brass bands and Welsh choirs.
Dr Keith Holland is currently a Lecturer at the Institute of Sound and
Vibration Research (ISVR), University of Southampton, UK, where he
has been in full-time employment since 1993, and from where he obtaining
a BSc in Engineering Acoustics and Vibration in 1987, and a PhD on horn
loudspeakers in 1993. Since 1990, Keith has taught Electroacoustics and
Audio Systems to under- and post-graduate students at the ISVR, and for
ten of those years, also to the Tonmeister students at the University of
Surrey.
As a researcher and academic at the ISVR, Keith has been involved in
a large number of acoustic research projects on a wide variety of topics,
which include: acoustic source location, advanced measurement techniques,
aircraft cabin noise, cathedral acoustics, crossovers, drive-unit characterisation, duct acoustics, engine exhaust noise, fluid dynamics, guitar amplifiers, horn loudspeakers, inverse methods, jet noise, loudspeaker arrays,
loudspeaker cables, loudspeaker directivity, microphone array processing, musical acoustics, nonlinear acoustics, numerical acoustic modelling,
psychoacoustics, recording studio acoustics, room acoustic measurement,
sound absorption, spacial imaging, tyre noise, vibration transducer development, vibroacoustic reciprocity and virtual audio. He is the author/
co-author of over 60 papers, of which more than 30 are audio-related, and
was the author of a series of 36 monthly objective monitor loudspeaker
reviews published in Studio Sound magazine.
A healthy interest in all things audio, and loudspeakers in particular, was
inherited from his father, Peter Holland, who, throughout the 1950s, 60s
and beyond, spent many hours tinkering and experimenting with valves,
transistors, tape recorders, loudspeakers and a lot of wire - with sometimes
remarkable results! Keith followed suit, and built his first complete audio
system in about 1967, using a Garrard turntable, home-made amplifiers
(3 watts per channel) and speakers based around 9 inch × 5 inch elliptical
drivers which came out of an old radiogram. By the early 1970s, this system had evolved into a room-dominating monster, including a 9 cubic foot
sand-filled corner cabinet from a book by Gilbert Briggs (the founder of
Wharfedale). While experimenting with crossovers for the giant woofer,
it became very obvious that the more components that were used in
the crossover, the worse the bass sounded. Using a 10-channel graphic
equaliser, with the 30 and 60 Hz sliders fully up and the rest down on
the left channel, and the opposite on the right, a makeshift mono active
system was created. The benefits of active crossovers were immediately
heard as the sound quality of this system was vastly superior to that from
any attempt to use passive crossovers.
A few years later, a chance meeting with Ian Piper of ICP Electronics
resulted in a collaboration on the design and construction of an activelydriven PA loudspeaker system which, to the amazement of many clients,
About the authors xiii
delivered a sound quality and level far beyond what was expected using
such apparently modest components. This system evolved over a period
of about 10 years, during which time Ian taught Keith a great deal about
the skills of live sound mixing, and between them they set up and mixed
hundreds of live acts, some very good, some awful, and some were even
quite famous!
By 1984, Keith had spent six years working in the manufacturing industry
since being awarded a HND in Mechanical Engineering at (the then)
Bournemouth College of Technology in 1978. He had become a skilled
machinist, but his strong interest and curiosity about all things acoustic
drew him to leave a well-paid job and go back to school at the ISVR
to learn more. Three years later he was awarded a BSc in Engineering
Acoustics and Vibration and received the prize for academic performance
in his final year. It was during this year that Keith first met Philip Newell.
Keith had mentioned to his academic supervisor, Professor Frank Fahy,
that he was interested in horn loudspeakers, and, quite by chance, Philip
Newell was developing monitor loudspeaker systems and had been making enquiries at Southampton University to find out if anyone was doing
research into horns. Philip was put in touch with Frank, and within a very
short time Keith was beginning a three-year doctoral research project on
horn loudspeakers, sponsored by Philip. A key result of the research is
the AX2 horn used in the current Reflexion Arts monitor loudspeakers.
To date, the work has produced, or inspired a total of 26 papers jointly
authored by Philip Newell and Keith Holland, and, as this book proves,
their collaboration is still as strong as ever.
Keith is a Member of the Institute of Acoustics and is a regular contributor to the Institute’s Reproduced Sound series of conferences. He is also
a member of the Audio Engineering Society. He continues to maintain
and build on his interest in loudspeakers through many teaching, research,
consultancy and hobby activities.
Keith is married to Sharon, whom he met in 1984. They live in their
native southern England, and together they have two children, Bethany
and Thomas. As a family, they enjoy camping, boating, walking and, of
course, listening to music.
Sergio Castro, who orchestrated all the figures for this book, was born
in 1955, in Oporto, Portugal and soon found his great interest in music. At
the age of 12 he bought his first acoustic guitar and a few months later,
with a turntable ceramic cartridge, he added electric amplification to the
instrument through an old Telefunken radio set.
When he was 13, he was playing drums professionally with a local rock
band and from then on, and simultaneously with his high school and his
university studies later, he has been a full time professional musician,
playing bass and guitar with some of the most relevant bands both in
Portugal and in Spain until the early 90s.
During 1983 he built and operated the first multitrack recording studio
in Oporto, and in 1985 he initiated the Planta Sonica Studios project, later
to be designed and built by Philip Newell. During the following years, in
this studio, he recorded and/or produced most of the Pop, Folk and Rock
acts in the region (Galicia).
xiv About the authors
His interest in loudspeakers goes back to the time he had to choose his
bass and guitar amplification, when he started experimenting with different
driver types in order to tailor the timbre of the instruments he played.
Modifying some of the off-the-shelf available amplifiers, and experimenting
with bigger speaker boxes in order to achieve extended bass, he attempted
to understand more about loudspeaker behaviour, aiming to improve his
live gear without huge money investment.
In the late 70s he contributed to the PA loudspeaker designs at SEC,
one of the pioneering pro-audio systems manufacturers in Portugal.
His involvement in the studio business, both as a producer and as a
recording engineer, led him to investigate further the concept of studio
monitors, trying to understand the audible differences he could then
find when travelling among different studios and different listening
environments.
Since then, his interest in the matter has grown and he became an
Associate Member of the Institute of Acoustics in the UK and a member
of the AES (currently a Member of the Board of Directors of the Spanish
section). He studied acoustics at Vigo University, Spain, where he took
a degree in Applied Acoustics.
Today he shares his time between being the head designer and co-owner
of Artesania de BluesBox, the manufacturer of the recently introduced
and successful brand of guitar, bass and installation PA speakers cabinets,
as well as being the managing director of Reflexion Arts. Reflexion Arts
is a company dedicated to the acoustic design and installation of musicrelated spaces, who also manufacture one of the highest definition range
of studio monitor loudspeakers. Apart from that he keeps playing guitar
live and in the studio through excellent amplifiers and loudspeakers.
Acknowledgements
Special thanks to Janet Payne, who assembled all the text of this book
from the thousands of pages of manuscript.
Many thanks to Christian Haselev, at Middle Tennessee State University,
for many helpful comments after reading the first draught of the book.
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Preface
I was building a studio, some years ago, in the Basque region of Spain,
close to Bilbao. We were using local labour, but I used a Portuguese
foreman who had previously worked with me on other constructions in
order to provide some experienced guidance on the specialised day-to-day
work. He understood Castilian Spanish quite well, but many of the people
working on the construction were speaking Euskera, the Basque national
language. After a few days, the foreman said to me, “This language is very
similar to Arabic” (In fact, apart from ‘Coca Cola’ and ‘Windows’ there
are probably no other words or structures in common), I asked how he
came to this conclusion, and he replied, “A few years ago I was working
in Morocco, where they speak Arabic, and I couldn’t understand anything.
Well, I can’t understand anything when they speak Basque either, so the
two languages must be very similar”.
It must have taken a full week for my brain to recover from the intellectual offence which it had suffered, and yet, at times, within the recording
industry I am assaulted by opinions and reasoning about loudspeakers
which bear little more logic than the aforementioned foreman’s linguistic
conclusions. In an attempt to throw some more light on these matters,
Dr Keith Holland and I therefore decided that we should write a book
on the subject of the fundamental differences between the Basque and
Arabic languages. However, once we realised that we knew no more than
half a dozen words between us (‘Coca Cola’ and ‘Windows’ included) we
resolved to write a book on loudspeakers, instead.
Philip Newell
Moaña
Spain
2006
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Introduction
Every day, around the world, millions of people use loudspeakers as some
sort of reference in their place of work. These people include those who
work in film studios, radio stations, live sound events, discothèques, clubs,
music recording studios, television studios, theatres, cinemas and many
other associated professions. For many musicians who play electrified or
electronic instruments, their loudspeakers are an integral part of their
instruments, and as such can significantly affect the interpretation of a
performance, as well as its sound. Amongst all of the professionals there
are only a very few who actually know much about how loudspeakers
work, other than a little knowledge gained in a cursory way that can be
as deceiving as it is revealing. They rely on loudspeakers as ‘black-boxes’
which somehow transform electrical signals into sound. Upon opening a
box, they see very little inside, except a metal or plastic chassis, cardboard
of plastic diaphragms, a magnet, some fluffy material, and perhaps a few
simple electronic components and wires that may make up a crossover
circuit.
It is often a source of frustration to these people – and to countless
millions more of domestic hi-fi enthusiasts – that these simple little boxes
fail to deliver an accurate and repeatable sound in a variety of circumstances. It is a further source of frustration that they all seem to sound
different, because it seriously complicates the compatibility problems when
their work travels from system to system, or room to room. They feel frustrated because it seems that surely the knowledge exists to sort out such
uncomplicated devices. This situation is often exacerbated by the powers of
marketing, when so many advertisements from so many manufacturers all
claim that their loudspeakers have the ability to tell the truth; but obviously
the reality cannot be quite so simple. In fact, loudspeakers are electromechanico-acoustic systems whose behaviour is complex to a degree that
seems totally disproportionate to the simplicity of their appearance.
Drivers of racing cars, helicopter pilots or submarine captains are people
who we cannot imagine as not having a through knowledge of the vehicles
that they command. It almost goes without saying that when they return to
base they would be able to communicate to the technicians, mechanics and
engineers in a way that was clear and concise about any technical failings
or handling difficulties that had occurred. Conversely, many people who
use loudspeakers, professionally, have remarkably little insight into what
is going on inside the equipment, and when problems arise with the sound,
they are at a total loss to explain either what the symptoms are or what the
problem might be. They work by trial and error, and often try to restrict
themselves to working in familiar environments where any problems, even
if not understood, are at least known.
xx Introduction
In all fairness, some professional users of loudspeakers do try to learn
something more about the devices which are so important to their daily
work, but they are often faced with a choice of two equally blind alleys. The
first is to look at some text books on the subject, and the other is to search
through popular magazines which publish articles about loudspeakers, such
as the hi-fi and home recording publications. The text book approach often
grinds to a halt somewhere before the end of page 1 as they become overwhelmed by the complexity of the electro-acoustic theory which, even for
specialised loudspeaker engineers, is not always entirely straightforward.
[In fact, one of the most authoritative books on loudspeaker theory and
application was written by fourteen different people, because such a work
would almost certainly be beyond the ability of any, one person1 .] The
popular press, on the other hand, is largely concerned with filling pages
with text and selling advertising space, which is perfectly understandable
because their primary raison d’être is to entertain the readers. However,
conjecture and opinions are often passed off as authoritative fact, and
contradictions are commonplace. It can thus become very difficult for the
non-specialist to separate the fact from the fiction, so the avid reading of
such publications is liable to result in an information overload, but with no
clear facts being apparent in any unequivocal manner.
The object of this book therefore is to try to fill the gap which currently
exists between the text books and the popular press. It will try to describe
the theory behind, and application of, the loudspeakers which are used
for music recording and reproduction in a way that is accessible to those
who would benefit from a greater understanding of the concepts, but
who do not have anything more than a basic understanding of general
science. Nevertheless it is intended that the facts and descriptions will be
both accurate and thorough, and where subjective aspects of loudspeaker
performance is discussed, it will be backed up with objective and perceptual
justification.
It is inevitable that subjective perceptions must be discussed, because
ultimately it is the ear of each individual listener which acts as judge
and jury, despite what the measurement may say, but recent research
has shown that subjective assessments can be reliable and quite precise
as long as the variable peripheral factors are minimised and understood.
The authors are very aware of the pitfalls, and have had a great deal
of experience in dealing with them. One of the authors is a designer of
recording studios, film dubbing theatres, television studios and concert
halls, who for many years was a recording engineer, live sound engineer,
record producer and monitor system designer. The other is a Doctor of
Acoustics, and a university lecturer in electro-acoustics who has had much
experience in live sound as a front of house engineer. Both are members
of the UK’s Institute of Acoustics and the Audio Engineering Society, and
both are experienced at teaching audio technology from very basic levels.
Hopefully, therefore, ways will be found to explain complex ideas via
understandable but nevertheless accurate analogies, which should enable
the readers to grasp an intuitive feel for the subject, especially where
mathematical explanations would elude them.
Whilst it has to be accepted that the majority of loudspeaker users
neither have the time nor the inclination to formally study electro-acoustics,
Introduction xxi
it is still extremely useful for them to understand much more than most of
them currently do, in order to help them make more informed decisions
about matters which affect their working lives. People beginning to work in
the recording world or people with a keen interest in sound reproduction
will also probably find this book useful. Inevitably, from time to time, things
may need to get a little deep. This will be essential when the discussion
requires it, but hopefully it can be done in a series of steps which will not
leave the less technical readers too isolated.
The book will begin with a brief history of loudspeaker development in
the early days, and will look at the basic concepts of just what a loudspeaker
is, and what it must do. Some basic principles of sound radiation will then
be introduced, in order to give a better understanding of the principles
before looking at the wide range of motor systems technologies that are
available, such as moving coil, electrostatic, piezoelectric, ionic, magnaplanar and various other concepts. The pros and cons of different diaphragm
technologies will be discussed, as will those of the loading techniques, such
as with horns and various cabinets and baffles.
Loudspeakers, of course, require an electrical drive signal, so Chapter 5
will look at the whole concept of crossovers, discussing why they are needed
and how they can be realised in practice. Active and passive designs will
be investigated, as will various slopes, shapes, phase effects and reconstruction difficulties. The electrical, acoustical and mechanical (physical)
factors which affect crossover performance will be dealt with in a thorough, yet understandable way, before the following chapter discusses the
amplifiers and cables which are necessary to complete any monitoring system. Different amplifier topologies will be discussed, and their suitability
for different specialised uses will be indicated. Without getting into the
subjective minefield of loudspeaker cable audibility, an objective presentation will be made of the ways in which it has been shown that cables can,
and do, affect system performance. There is no point in paying ten times
more than necessary for a special loudspeaker cable if a standard cable
will sound exactly the same, but in sensitive circumstances a more esoteric
cable may be beneficial. It is the first time that most of this work has
been published outside of the proceedings of international electro-acoustic
conferences.
The book will then go on to discuss the consequences of the interaction
between the loudspeaker systems and the rooms in which they are sited,
and how, in so many cases, the rooms can dominate the overall response.
Guidance will be given as to where to find out more about the room
acoustics, but the consequences of different mounting regimes will be dealt
with, here.
Chapter 8 is a wide-ranging analysis of the reasons why different
loudspeakers appear to be more appropriate during different phases of
the recording/mixing/mastering/listening process. Many concepts of loudspeaker system design will be analysed, and their application to the environments in which they are most likely to be used will be assessed. Motor
systems and cabinet options will be brought together in ways that they can
be applied to the physical, electro-acoustic and psychoacoustic requirements of each stage of the work. With the introduction of the question of
perception, highlighted by the fact that different loudspeakers tend to be
xxii Introduction
chosen for different phases of the work, Chapter 9 analyses the different
measurements which can be used to define the performance of a loudspeaker system, and how the objective measurements relate to different
aspects of the subjective perception of the music. Chapter 10 will then
reverse the concept, and will discuss how the musical arrangements can be
the culprits for many system-to-system compatibility problems for which
the loudspeakers usually take the blame. This is a crucial subject, but one
which one very rarely sees discussed in print.
The final two chapters will deal with subjects which are, in general,
very poorly understood by the vast majority of people who work with
loudspeakers. Chapter 11 discusses the fundamental requirements of the
low frequency radiation from small loudspeakers. It explains why, in accuracy terms, loudspeaker designers compromise the performance in order
to reduce box sizes and/or extend the responses. Brand new measurement concepts will be introduced which demonstrate the degree to which
these performance enhancements reduce the reproduction accuracy in an
exchange of quantity for quality. The chapter then goes on to look at the
transient performances, which are so important for the realistic perception of music, but which are consistently ignored by many loudspeaker
manufactures, partly because they do not feature in most performance
specifications which are used for publicity purposes. They are often compromised for the betterment of some less significant responses benefits
which do carry more weight in terms of advertising.
The book concludes with a chapter on surround-sound application; not
only in the more physical realms of room interfacing that were discussed
in Chapter 7, but also in terms of the application problem that confound
the day-to-day use of surround sound, such as format compatibility, the
suitability of certain loudspeaker radiation patterns to specific mounting
conditions, and the appropriateness of loudspeaker choices for different
musical programme.
Hopefully, therefore, this book will fill the gap left between the textbooks and the magazines. It deals with the application and use of the
technology and science, justifying ideas with hard facts rather than conjecture, and in a way that should be accessible to anybody with a general
level of experience in the use of loudspeakers, whether for work or leisure
purposes.
Reference
1 Borwick, J., ‘Loudspeaker and Headphone Handbook’, Third Edition, Focal
Press, Oxford, UK (2001)
Chapter 1
What is a loudspeaker?
1.1 A brief look at the concept
Before answering the question posed by the title of this chapter, perhaps we
had better begin with the question “What is sound?” According to Fahy 1
“sound may be defined as a time-varying disturbance of the density of a
fluid from its equilibrium value, which is accompanied by a proportional
local pressure, and is associated with small oscillatory movements of the
fluid particles”. The difference between the equilibrium (static) pressure
and the local, oscillating pressure is known as the sound pressure.
Normally, for human beings, the fluid in which sound propagates is air,
which is heavier than most people think – it has a mass of about 1.2 kg
per cubic metre at a temperature of 20 degrees C at sea level. It is also
interesting to note that sound propagation in air is by no means typical of
its propagation in all substances, especially in that the speed that sound
propagates in air is relatively slow, and is constant for all frequencies. For
music lovers, this latter fact is quite fortunate, because it would be hard
to enjoy a musical performance at the back of a concert hall if the notes
arrived jumbled-up, with the harmonics arriving before the fundamentals,
or vice versa. Conversely, as we shall see later, most of the materials from
which loudspeakers are made do not pass all frequencies at the same speed
of sound, a fact which can, at times, make design work rather complicated.
The speed of sound in air is about 343 metres per second (m/s or ms−1 )
at 20 degrees C and varies proportionally with temperature at the rate
of about 0.6 m/s for every degree Kelvin. (In fact, the speed of sound in
air is only dependent upon temperature, because the changes that would
occur due to changes in atmospheric pressure are equal and opposite to the
accompanying changes in density, and the two serve to cancel each other
out). Air therefore has some clearly defined characteristic properties, and
our perception of sound in general, and music in particular, has developed
around these characteristic properties.
The job of a loudspeaker is to set up vibrations in the air which are
acoustic representations of the waveforms of the electrical signals that
are being supplied to the input terminals. A loudspeaker is therefore an
electro-mechanico-acoustic transducer. Loudspeakers transform the electrical drive signals into mechanical movements which, normally via a
vibrating diaphragm, couple those vibrations to the air and thus propagate
acoustic waves. Once these acoustic waves are perceived by the ear, we
experience a sensation of sound.
2 Loudspeakers
To a casual observer, a typical moving coil loudspeaker (or ‘driver’ if
you wish to restrict the use of ‘loudspeaker’ to an entire system) seems
to be a simple enough device. There is a wire ‘voice-coil’ in a magnetic
field. The coil is wound on a cylindrical former which is connected to a
cardboard cone, and the whole thing is held together by a metal or plastic
chassis. The varying electrical input gives rise to vibrations in the cone as
the electromagnetic field in the voice coil interacts with the static field of
the (usually) permanent magnet. The cone thus responds to the electrical
input, and there you have it, sound! It is all as simple as that! Or
is it?
Well, if the aim is to make a sound from a small, portable radio that fits
into your pocket, then maybe that concept will just about suffice, but if full
frequency range, high fidelity sound is the object of the exercise, then things
become fiendishly complicated at an alarming speed. In reality, in order
to be able to reproduce the subtle structures of fine musical instruments,
loudspeakers have a very difficult task to perform.
1.2 A little history and some background
When Rice and Kellogg 2 developed the moving coil cone loudspeaker in
the early 1920s, [and no; they did not also invent Kellogg’s Rice Krispies!]
they were already well aware of the complexity of radiating an even frequency balance of sound from such a device. Although Sir Oliver Lodge
had patented the concept in 1898 (following on from earlier work by Ernst
Werner Siemens in the 1870s at the Siemens company in Germany), it
was not until Rice and Kellogg that practical devices began to evolve. Sir
Oliver had had no means of electrical amplification – the thermionic valve
(or vacuum tube) had still not been invented, and the transistor was not to
follow for 50 years. Remarkably, the concept of loudspeakers was worked
out from fundamental principles; it was not a case of men playing with bits
of wire and cardboard and developing things by trial and error. Indeed,
what Rice and Kellogg developed is still the essence of the modern moving
coil loudspeaker. Although they lacked the benefit of modern materials
and technology, they had the basic principles very well within their understanding, but their goals at the time were not involved with achieving a flat
frequency response from below 20 Hz to above 20 kHz at sound pressure
levels in excess of 110 dB SPL. Such responses were not required because
they did not even have signal sources of such wide bandwidth or dynamic
range. It was not until the 1940s that microphones could capture the full
frequency range, and the 1950s before it could be delivered commercially
to the public via the microgroove, vinyl record.
Prior to 1925, the maximum output available from a radio set was in the
order of milliwatts, normally only used for listening via earphones, so the
earliest ‘speakers’ only needed to handle a limited frequency range at low
power levels. The six inch, rubber surround device of Rice and Kellogg
used a powerful electro-magnet (not a permanent magnet), and as it could
‘speak’ to a whole room-full of people, as opposed to just one person at
a time via an earpiece, it became known as a loud speaker. The inventers
were employed by the General Electric Company, in the USA, and they
What is a loudspeaker? 3
began by building a mains-driven power amplifier which could supply
the then huge power of one watt. This massive increase in the available
drive power meant that they no longer needed to rely on resonances and
rudimentary horn loading, which typically gave very coloured responses.
With a whole watt of amplified power, the stage was set to go for a flatter,
cleaner response. The result became the Radiola Model 104, which with its
built in power amplifier sold for the then enormous price of 250 US dollars.
[So there is nothing new about the concept of self-powered loudspeakers:
they began that way!] Marconi later patented the idea of passing the DC
supply current through the energising coil of the loudspeaker, to use it
instead of the usual, separate smoothing choke to filter out the mains hum
from the amplifier. Therefore right from the early days it made sense to
put the amplifier and loudspeaker in the same box.
Concurrently with the work going on at General Electric, Paul Voight
was busy developing somewhat similar systems at the Edison Bell company.
By 1924 he had developed a huge electro-magnet assembly weighing over
35 kg and using 250 watts of energising power. By 1926 he had coupled
this to his Tractrix horn, which rejuvenated interest in horn loudspeakers
because it enormously improved the sensitivity and acoustic output of the
moving coil loudspeakers, and when properly designed did not produce
the ‘honk’ sound associated with the older horns. Voight then moved on to
use permanent magnets, with up to 3.5 kg of Ticonal and 9 kg of soft iron,
paving the way for the permanent magnet devices and the much higher
acoustic outputs that we have today.
Gilbert Briggs, the founder of Wharfedale loudspeakers, wrote in his
book of 19553 “It is fairly easy to make a moving-coil loudspeaker to cover
80 to 8,000 cycles [Hz] without serious loss, but to extend the range to
30 cycles in the bass and 15,000 cycles in the extreme top presents quite
a few problems. Inefficiency in the bass is due mainly to low radiation
resistance, whilst the mass of the vibrating system reduces efficiency in the
extreme top”. The problem in the bass was, and still is, that with the cone
moving so relatively slowly, the air in contact with it simply keeps moving
out of the way, and then returning when the cone direction reverses, so
only relatively weak, low efficiency pressure waves are being propagated.
The only way to efficiently couple the air to a cone at low frequencies
is to either make the cone very big, so that the air cannot get out of the
way so easily, or to constrain the air in a gradually flaring horn, mounted
directly in front of the diaphragm. Unfortunately, both of these methods
can have highly detrimental effects on the high frequency response of the
loudspeakers. For a loudspeaker cone to vibrate at 20 kHz it must change
direction forty thousand times a second. If the cone has the mass of a big
diaphragm needed for the low frequencies, its momentum would be too
great to respond to so many rapid accelerations and decelerations without
enormous electrical input power – hence the loss of efficiency alluded to
by Briggs. Large surfaces are also problematical in terms of the directivity
of the high frequency response, but we will come to that later. So, we can
now begin to see how life becomes more complicated once we begin to
extend the frequency range from 20 Hz to 20 kHz – the requirements for
effective radiation become conflicting at the opposing frequency extremes.
4 Loudspeakers
The wavelength of a 20 Hz tone in air is about 17 metres, whereas the
wavelength at 20 kHz is only 1.7 centimetres, a ratio of 1000 to 1, and
for high quality audio applications we want our loudspeakers to produce
all the frequencies in-between at a uniform level. We also need them to
radiate the same waveforms, differing only in size (but not shape) over a
power range of at least 10,000,000,000 to 1 and with no more than one part
in a hundred of spurious signals (non-linear distortion). It is a tall order!
Indeed, for a single drive unit, it still cannot be achieved at any realistic
SPL (sound pressure level) if the full frequency range is required.
1.3 Some other problems
There are also many mechanical concepts which must be considered in
loudspeaker design. For example, the more that one pushes on a spring, the
more one needs to push in order to make the same change in length. If the
force is limited to less than what is necessary to fully compress the spring,
equilibrium will be reached where the applied force and the reaction of
the spring balance each other. This is useful when we go to bed, because
it prevents the suitably chosen springs from bottoming out, and allows the
mattress to adapt to our shape yet retain its springiness. The suspension
systems of loudspeaker diaphragms are also springs, but they must try to
maintain a consistent opposition to movement or they would compress
the acoustical output. If, for example, the first volt of input moved the
diaphragm x millimetres, and a second volt moved it only 0.8 x mm further,
this would be no good for high fidelity, because when we double the voltage
we expect to see the same linear increase in motion. Otherwise, the acoustic
output would not be linearly following the electrical input signal, and the
non-linear movement would introduce distortion. Therefore, to keep the
diaphragm well centred, but to still allow it to move linearly with the input
signal, suspension systems must be used which do not exhibit a nonlinear
restorative force as the drive signal increases, at least not until the rated
excursion limit is reached. (However, as we shall see in Chapter 8, certain
non-linear loudspeaker characteristics may actually be desirable for musical
instrument amplification.) We tend complicate this suspension problem
further when we put a loudspeaker drive unit into a box, because the air
in the box acts as an additional spring which is also not entirely linear.
Electrically we can also run into similar problems. Whenever an electric
current flows through a wire, the wire will heat up. It is also a property of voice coil wires that as they heat up their resistance increases. As
the resistance increases, the signal voltage supplied by the amplifier will
proportionally drive less current through the coil. So, as the drive force
depends on the current flowing through the wire which is immersed in the
magnetic field, if that current reduces, the movement of the diaphragm
will reduce correspondingly. We therefore can encounter a situation where
the amplifier sends out an accurate drive signal voltage, but how the loudspeaker diaphragm responds to it can, depending on level, change with the
voice coil temperature and the springiness of both the air and the suspension system. Even the very magnetic field of the permanent magnet, against
which the drive force is developed, can be modulated by the magnetic field
What is a loudspeaker? 5
given rise to by the signal in the voice coil. Notwithstanding, all of these
effects, we still need our diaphragm to move exactly as instructed by the
drive voltage from the amplifier, because in reality modern amplifiers are
usually voltage sources. This is despite the fact that the loudspeaker motor
is current driven, and that the voice coil resistance and reactance (together
they form the impedance) will not remain constant over the whole of the
frequency range.
Clearly, things are beginning to get complicated, and already we have
seen problems begin to pile up on each other. The concept of a loudspeaker
being simply an electromagnet, coupled to a moveable cone and placed into
a box is obviously not going to produce the high fidelity sounds needed for
music recording and reproduction. Good loudspeakers are complex devices
which depend on the thorough application of some very rigid principles of
electroacoustics in order to perform their very complex tasks. In the minds
of most people the concept of a loudspeaker, if it exists at all, is usually
grossly over-simplified, and unfortunately this is the case even with most
professional users of loudspeakers.
Typical loudspeaker systems consisting of one or more vibrating
diaphragms, either on one side of a rectangular cabinet or flush mounted
into a wall, represent physical systems of sufficient complexity that accurate and reliable predictions of their sound radiation are rare, if not nonexistent, even with the aid of modern computer technology. Despite the
fact that we inevitably have to deal with a degree of artistry and subjectivism in the final assessment, at the design and development stages
we must stick close to the objective facts. So, to begin to understand the
mechanisms of sound radiation it is necessary to establish the means by
which a sound ‘signal’ is transported from a source, through the air, and
to our ears.
1.4 Some basic facts
As explained in the opening paragraphs of this chapter, acoustic waves are
essentially small local changes in the physical properties of the air which
propagate through it at a finite speed. The mechanisms involved in the
propagation of acoustic waves can be described in a number of different
ways, depending upon the particular cause or source of the sound. With
conventional loudspeakers that source is the movement of a diaphragm,
so it is appropriate here to begin with a description of sound propagation
away from a simple moving diaphragm.
1.4.1 Acoustic wave propagation
The process of sound propagation is illustrated in Figure 1.1. For simplicity,
the figure depicts a diaphragm mounted in the end of a uniform pipe, the
walls of which constrain the acoustic waves to propagate in one dimension
only. Before the diaphragm moves (Figure 1.1(a)), the pressure in the pipe
is the same everywhere and equal to the static (atmospheric) pressure
P0 . As the diaphragm moves forwards (Figure 1.1(b)), it causes the air in
6 Loudspeakers
a)
Diaphragm
at rest
Uniform pipe
Pressure is uniform
everywhere in the
pipe
Pressure
P0
Distance
b)
Diaphragm
moves
forward
Pressure increases
in front of the moving
diaphragm
Pressure
P0
Distance
c)
Acoustic wave
propagates away
from diaphragm at
speed of sound,
even though the
diaphragm has
stopped.
Pressure
c
P0
X = ct
Distance
Figure 1.1 The generation and propagation of an acoustic wave in a uniform pipe
contact with it to move, compressing the air adjacent to it and bringing
about an increase in the local air pressure and density. The difference
between the pressure in the disturbed air and that of the still air in the rest
of the pipe gives rise to a force which causes the air to move from the region
of high pressure towards the region of low pressure. This process then
continues forwards, and the disturbance is seen to propagate away from
the source in the form of an acoustic wave. Because air has mass, and hence
inertia, it takes a finite time for the disturbance to propagate through the
air; a disturbance ‘leaves’ a source and ‘arrives’ at another point in space
some time later (Figure 1.1(c)). The rate at which disturbances propagate
through the air is known as the speed of sound, which has the symbol ‘c’,
What is a loudspeaker? 7
and after a time of t seconds, the wave has propagated a distance of x = ct
metres. Note, though, that the speed of propagation is not related to the
velocity of the diaphragm. In the great tsunami of December 2004, a five
metre displacement of the ocean floor caused a tidal wave to travel at
over 500 kilometres per hour, a speed much more rapid than that of the
displacement which caused it. For most purposes, the speed of sound in
air can be considered to be constant, and independent of the particular
nature of the disturbance, although as previously stated it does vary with
temperature. A one-dimensional wave, such as that shown in Figure 1.1,
is known as a plane wave. A wave propagating in one direction only (e.g.
left-to-right) is known as a progressive wave.
1.4.2 Mechanical and acoustic impedance
The description of sound propagation in Section 1.4.1 mentioned the
motion of the air in response to local pressure differences. This localised
motion is often described in terms of acoustic particle velocity, where the
term ‘particle’ here refers to a small quantity of air that is assumed to move
as a whole. Although we tend to think of a sound field as a distribution
of pressure fluctuations, any sound field may be equally well described
in terms of a distribution of particle velocity, and there is a relationship
between the distribution of pressure in a sound field and the distribution
of particle velocity. At a given frequency, the ratio of pressure to particle
velocity at any point (and direction) in a sound field is known as acoustic impedance (strictly specific acoustic impedance), Za = p/u, and it is
very important when considering the sound power radiated by a source.
Acoustic impedance can be thought of as a quantity that expresses how
difficult the air is to move. A low value of impedance tells us that the
air moves easily in response to an applied pressure (low pressure, high
velocity), and a high value of impedance tells us that it is hard to move
(high pressure, low velocity). Mechanical impedance is directly equivalent
to acoustic impedance, but with pressure replaced by force (pressure is
force per unit area) and particle velocity replaced by velocity: Zm = F/u.
With acoustic radiators, as well as electrical circuits and mechanical systems, there is a need to match impedances for good energy transfer. If a
microphone needs to be connected to a 600 ohm input, then it will not
sound as intended by its designers or exhibit its quoted sensitivity if connected to a 30 ohm or 10,000 ohm input. An amplifier which is optimised
to function into a 4 ohm load will not produce its maximum power output
capability into a load of 16 ohms. Loudspeakers are effectively ‘plugged
into’ the air, so if the air load impedance does not match the electromechanical output impedance of the loudspeaker, the radiated power will
be less than optimal. Impedance changes with frequency, so, for example,
a resistor and capacitor in parallel have a frequency dependent impedance
which is the combination of the purely resistive, frequency independent
characteristic of the resistor, and the reactive, frequency dependent characteristic of the capacitor. This is the basis of electrical filter design.
Impedance (Z), whether it be electrical, mechanical or acoustic, can be
divided into two components, resistance (R) and reactance (X). Reactive
impedances represent systems which store input energy, but which later
8 Loudspeakers
large, rigid panel (diaphragm)
a) air loading on diaphragm
(reactive)
air acting as a spring
The person pushes on the
spring and it compresses.
When the force is stopped,
the spring returns to its
original length: no net energy
has been transferred from
person to spring.
b) inertia and momentum
of diaphragm and coil
assembly (reactive)
The person pushes on the
mass and it acelerates. When
the force is stopped, the mass
pulls back on the person to
slow itself down: again, no net
transfer of energy.
c) mechanical friction and
electrical resistance
(resistive)
The person pushes on the
block, overcomes friction and
the block moves. This time,
when the force stops, the
block stops moving: all of the
energy transferred to the
block is lost as heat, due to
friction, between the block
and the surface on which it is
sliding.
input force
reactive force
heat
Figure 1.2 Three characteristic properties of a moving coil loudspeaker depicted as three components of its impedance. In electrical terms, these can be related to capacitance, inductance
and resistance
give it back, whereas resistive impedances represent systems which transfer energy away from the input, never to return. Figure 1.2 shows three
mechanical systems which can be used to demonstrate the three different
components of mechanical impedance and the way in which they relate to
What is a loudspeaker? 9
conventional loudspeakers. In Figure 1.2(a), the person applies a force to
compress a spring. When the applied force is stopped, the spring returns
to its original length and all of the (potential) energy applied to the spring
is returned to the person as the spring pushes back. If the person pushes
back and forth on the spring in an oscillatory manner, the energy flows
from person to spring and back again in each half-cycle with an overall
zero transfer of energy. A spring represents a purely reactive mechanical
impedance. Figure 1.2(b) shows the person applying a force to a mass on a
trolley. The force acts to accelerate the mass from rest, but when the force
is stopped the mass tries to continue moving at a steady velocity. If the
person then applies a force to slow the mass down, the (kinetic) energy
possessed by the mass is returned as the mass pulls back on the person.
Again, if the force is applied in an oscillatory manner, there is zero overall
transfer of energy from the person to the mass. A mass also represents a
purely reactive mechanical impedance, but with the opposite sign to that
of a spring. (Note the different direction of the reactive force arrows in the
figure.) Figure 1.2 c) shows the person pushing a block along a table. The
applied force overcomes the friction between the block and the table and
the block moves with a constant velocity. When the force is stopped the
block also stops, and none of the energy supplied to the block is returned
to the person. If the force is applied in an oscillatory manner in this case,
the flow of energy is always from person to block, regardless of the direction of motion. All of the energy is ‘lost’ to friction as heat, and none is
returned to the person. The friction block represents a resistive mechanical
impedance which is the mechanism by which power can be transferred
from one system to another (in this case, from the person to heat). There
are acoustic counterparts to each of these mechanical components, for
example, a small sealed cavity driven by a piston is an acoustic spring. The
electrical counterparts will be further discussed in Section 1.6.
1.4.3 Impedance in loudspeakers
In a cone loudspeaker, we have all of these forms of impedance present
at the same time. The diaphragm radiates useful sound power through
its motion via an acoustic radiation resistance. The mass of the voice coil
and diaphragm, together with the stiffness of the suspension, produce a
reactive impedance which merely serves to reduce the diaphragm motion.
The reactive inductance of the voice coil reduces the current, and hence
the applied force, at higher frequencies. And finally, the resistive frictional
losses in the suspension and the electrical resistance of the voice coil simply
waste power by turning it into heat.
1.5 The practical moving-coil cone loudspeaker
The majority of all loudspeakers are moving coil devices employing a
cone-shaped radiating diaphragm, but the mechanisms of sound radiation
from these devices are not as straightforward as they may initially seem
to the casual onlooker. This type of loudspeaker is essentially a ‘volume
10 Loudspeakers
velocity’ source. In other words it creates a pressure wave equivalent to
injecting air from a point source at a rate of injection measured in cubic
metres per second (or extracting the air on the rarefaction half cycle).
However, unlike the piston shown in Figure 1.1, most cabinet-mounted
cone loudspeakers, direct radiating into a room (i.e. not radiating via a
horn), do not couple effectively with the air. Instead, the cone finds itself
punching into thin air, with much of the potential load being lost as most
of the air adjacent to it simply moves out of the way, then returns when
the direction of the cone movement reverses. Efficiency is therefore often
extremely low, with less than 1% of the energy being supplied to the voice
coil resulting in the radiation of sound. The remaining energy either gets
lost by friction in the moving system, or by being burned up as heat by the
resistance of the voice coil, or even by being reflected back into the output
stages of the power amplifier. To complicate matters, many of these things
are frequency dependent, so, it is little wonder that many things must be
considered and balanced before there is any chance of such a device having
a flat frequency response.
As long as the circumference of the diaphragm remains small with
respect to the wavelength, the radiation will be omnidirectional, but when
the wavelength starts to become small compared to the circumference of
the source, the radiation begins to beam directly ahead. [The wavelength,
in metres, can be calculated simply by dividing the speed of sound in metres
per second by the frequency in hertz.] This is a result of the interference
field where the different parts of the diaphragm, radiating in phase, become
significantly different in their path lengths to an off axis listening position.
The cause is depicted in Figure 1.3, and the effect is shown in Figure 1.4.
The ka values referred to in the latter figure are derived from the wave
number k, which is simply 2 divided by the wavelength () in metres, and
a, which is the radius of the radiating surface. In practice we can think of
ka as being the number of wavelengths around the circumference of the
diaphragm: ka = 2a/.
Sounds from different
parts of the piston arrive
substantially in phase to
point A on-axis.
Vibrating piston
A
B
Here, the path lengths to
point B, off-axis, differ
considerably
Figure 1.3 The cause of the off-axis interference effects that give rise to the directivity shown
in Figure 1.4
What is a loudspeaker? 11
Figure 1.4 The directivity of a vibrating piston due to off-axis interference effects at different
frequencies. Note the narrowing of the main lobe as the frequency increases
We would tend instinctively to think of the whole diaphragm as being the
radiating surface, however, this is often not the case, and a large diaphragm
driven at high frequencies will almost certainly not move uniformly. The
outer parts would lag with respect to the movement of the central area, in
which case the outer parts would radiate with a phase shift relative to the
central area of the diaphragm. In fact they may even simply stay still, in
which case they would not radiate at all. In either case the radiation may
not correspond with the ka value taken from the physical measurements
of the diaphragm.
Over the years, many ‘solutions’ have been tried in the search for perfect
pistonic motion in a diaphragm, such as using ultra-rigid cone materials,
or solid, conical ‘plugs’ as diaphragms, but internal losses and differential
sound speeds within the materials have tended to confound all efforts.
Remember, it was stated at the beginning of this chapter that air was not
typical of all materials in terms of the speed with which sound propagates
though it being equal for all frequencies. Many types of solid materials
propagate high frequencies faster than low frequencies, a property known
as phase dispersions, and exhibit sound speeds very different from that
in air.
When the sound propagates from the voice coil through the material of
the cone, in a radially outward direction, the different sound speeds may
give rise to interference between the sound waves travelling to the edge
12 Loudspeakers
of the cone and the forward radiation into the air by the pistonic action
of the whole cone being driven by the voice coil. Resonances can also
be set up within the cone itself, and one job of the cone surround is to
absorb as much as possible of the waves propagating radially through the
cone material, to prevent them from being reflected back and causing even
more interference. Complex cone surrounds are often as much to do with
suppressing these waves as with linearly suspending the cone itself.
1.5.1 The combined response
It was stated earlier that a loudspeaker was an electro-mechanico-acoustic
transducer. Well, we have just looked at a few of the acoustic properties,
but the electrical and mechanical aspects also present their own complications. The voice coil is a mixture of resistance and inductance, the latter
being a form of frequency dependent reactance. The reactance, in ohms,
of an inductor is given by 2f L, where f is the frequency in hertz and L is
the inductance in henries. An 8 ohm voice coil is only nominally 8 ohms,
and approximates that value only over a limited band of frequencies. The
inductive part of the impedance (impedance here being resistance plus
reactance) rises with frequency, whereas any capacitive reactance effects
decrease with frequency. The reactance(c) of a capacitor, in ohms, is given
by 1/ 2f c, so the frequency component, being in the denominator in this
case, reduces the reactance as it rises. An overall impedance plot of a typical
low frequency loudspeaker with respect to frequency is shown in Figure 1.5.
Fortunately, however, some effects counterbalance each other. Figure 1.6
shows how a flat frequency response can be achieved above the resonance
frequency of a cone driver, mounted on a theoretical infinite baffle, where
the roll-off in the diaphragm velocity compensates for its rising relationship
with the pressure radiated to a point far away on the cone axis. However,
at very close distances some rather more complex relationships manifest
themselves. Academically speaking, this region is known as the near-field,
Low frequency driver
Impedance (ohms)
316
100
31.6
10
3.16
20
8 Ω nominal
30 40 50 70 100
200 300 400 500 700 1k
2k
3k 4k 5k 7k 10k
Frequency (Hz)
Figure 1.5 Magnitude of electrical impedance of a typical loudspeaker drive unit
20k
What is a loudspeaker? 13
Diaphragm velocity
×
On-axis pressure per unit velocity
=
Overall on-axis pressure
Fundamental
resonant
frequency
Frequency
Figure 1.6 How a flat frequency response results from a falling velocity and a rising radiated
sound pressure
but it should not be confused with the more colloquial ‘near-field’ that
many recording personnel speak of. In fact, it is better to use the term
‘close-field’ for desk-top monitors, because the true near-fields are not
good distances to listen within as the frequency balance can be strange in
those regions.
For people conversant with electrical circuit diagrams, equivalent circuits can be devised which represent the electrical, mechanical and acoustic
properties of a loudspeaker as a single electric circuit. This type of representation is very common in traditional text books on electroacoustics.
In these circuits, the mechanical and acoustic components such as springs
and masses are replaced by their electrical equivalents. One way in which
this can be realised is to replace mechanical forces (and acoustic pressures)
with electrical currents, and mechanical velocities with electrical voltages.
It follows then that mechanical springs are replaced by electrical inductors,
masses are replaced by capacitors, and mechanical resistances are replaced
by resistors. This arrangement is known as the mobility analogy, although
it should be noted that a different, but equally valid, impedance analogy
exists, where voltages replace forces and currents replace velocities. Each
analogy has its strengths and weaknesses and may better suit different
aspects of loudspeaker analysis. The equivalent mobility analogy circuit of
a typical moving coil loudspeaker is shown in Figure 1.7. The transformers represent the coupling between the electrical and mechanical, and the
mechanical and acoustical domains. This type of circuit is what an amplifier
14 Loudspeakers
current voice coil
voice coil
resistance
reactance
Voltage
source
force
stiffness
mass
Bl:1
ELECTRICAL
DOMAIN
pressure
resistance
1:S
MECHANICAL
DOMAIN
radiation
load
ACOUSTICAL
DOMAIN
Figure 1.7 The equivalent electrical circuit of a moving coil loudspeaker drive unit (mobility
analogy): Bl = the product of the magnetic flux density and the length of wire in the magnetic
field – the force factor – Tm (tesla × metres): S = area of the cone
really ‘sees’ when terminated by a typical moving coil loudspeaker, which
is a far cry from a resistive 8 ohm load.
Getting a frequency-independent acoustic output from such a combination of components is no simple task. It can only be achieved by very
careful balancing of the values of the components, and even then the
perfect balance is usually only achievable over a limited bandwidth. It is
apparent that any extra series resistance increase, or any parallel resistance
decrease, will serve to reduce the power supplied to the load for any given
input power, and so will reduce the efficiency of the system. What is more,
with such a finely balanced system, any change to any component part(s)
may require a counterbalancing change to many other component parts.
As true perfection can never be achieved, there are an infinite number of
close approximations which are possible, and this fact contributes to the
diversity of loudspeaker designs that we have available in the marketplace.
1.6 Resistive and reactive loads
Before ending this introductory chapter, it may be worth looking a little
more closely at the concepts of resistive and reactive loading. Figure 1.8
shows three potential-divider networks. If we consider a constant voltage
source to be applied between terminals A and C we can consider what
voltages occur between points B and C, and how much power will be
dissipated in each component. In the case of the resistor-resistor network
shown in Figure 1.8 (a), the resistance of the two components R1 and
R2 is equal. In a resistor, as the voltage is increased across its terminals
the current will also increase in direct proportion, as given by Ohm’s law,
which may be written in the following ways:
V
R
(1.1)
V = IR
(1.2)
V
I
(1.3)
I=
R=
What is a loudspeaker? 15
a)
A
A
10 V
AC or DC
100 Ω
200 Ω
W=
V2 25
= 0.25 watts
=
R 100
5V
W=
V2
= 25 = 0.25 watts
100
R
7V
W=
49
V2
cos 0° =
× 1 = 0.5 watts
R
100
3V
W=
V2 cos 90° 9
=
× 0 = 0 watts
X
100
7V
W=
49
V2
cos 0° =
× 1 = 0.5 watts
R
100
3V
W=
9
V2
cos 90° =
× 0 = 0 watts
X
100
B
100 Ω
C
5V
C
b)
A
A
10 V
1 kHz
100 Ω
141 Ω
B
1.6 μF
C
C
c)
A
A
10 V
1 kHz
100 Ω
141 Ω
B
16 mH
C
(X = 100 Ω)
C
Figure 1.8 Three potential divider networks. W = watts, V = volts, R = resistance (ohms),
X = reactance (ohms), Cos 0 degrees = 1, Cos 90 degrees = 0. In each case the total power
dissipation is the same, at 0.5 watts, but it is only dissipated in the resistors. The inductors
and capacitors merely store the energy then release it into the resistors. Note that a total of
0.5 watts is dissipated in each case
Where I = current in amps
V = voltage in volts
R = resistance in ohms
The voltage and current are always in phase, so they will produce power,
in watts (W), according to a simple multiplication:
V×I = W
(1.4)
16 Loudspeakers
Strictly speaking, this should be multiplied by the cosine of the phase angle,
but as this is 0 degrees in resistive circuits, and the cosine of 0 degrees is 1,
then a multiplication by one has no effect, so it is traditionally omitted.
Whether the current is direct or alternating is also of no consequence in
resistors, and the resistance remains the same irrespective of frequency.
In the case of capacitors, there is a frequency dependent effect. Capacitors will not pass DC, because the impedance (reactance in this case) at
0 Hz is infinite, but as the frequency rises, the reactance lowers. Reactance (X), like impedance (Z) and resistance (R), is measured in ohms, but
unlike resistance it is frequency dependent. In the case of capacitors, the
reactance is inversely proportional to the frequency: as the frequency rises
the reactance lowers. The formula for the reactance (X) of a capacitor is
given by:
X=
1
2fc
(1.5)
where f = frequency in hertz
c = capacitance in farads
= 3142
or,
X=
1000000
2fc
(1.6)
where c is in microfarads
In capacitors, the current and voltage are not in phase, but are shifted
by 90 degrees. In the case of Figure 1.8(b) an application of a DC voltage
across A-C will initially see an uncharged capacitor behaving like a short
circuit (zero ohms). A current will then flow through R and the plates of
the capacitor will begin to charge. As the voltage rises across B-C, the
current will reduce until, once the plates are fully charged, the voltage will
rise to a maximum (as across A-C) and the current will reduce to zero.
All conduction will then cease. Thus it can be seen how the current leads
the voltage: the current flows first, then it falls as the voltage rises. The
electrostatic charge is a voltage effect.
In the case of Figure 1.8(c) the effect is the reverse. Inductors work on
an electromagnetic principle, which is a current effect. The formula for the
reactance (X) of an inductor is given by:
X = 2fL
(1.7)
Where: f = frequency in hertz (Hz)
L = inductance in henries (L)
In this case, the reactance is directly proportional to the frequency.
As the frequency rises, so does the reactance, and the voltage leads the
current. In the cases of both the capacitor and the inductor, the voltage and
current are 90 degrees out of phase. Equation 1.4 showed the formula for
What is a loudspeaker? 17
calculating the power from the voltage and the current, and it was noted
that for AC currents and voltages there should be a phase angle multiplier,
cos (theta). The cosine of 90 degrees is zero, therefore whatever values
of voltage and current exist in the circuit, the power dissipation (heating
effect) in inductors and capacitors is always zero, (except for losses due to
imperfections). This is wattless power, and is why AC power circuits are
measured in VA (volt-amps) and not in watts. Electricity meters measure
kVA because in heavily inductive loads, such as electrical motors and
machinery, the kW value would be less, and the electricity company would
not be charging for all the current and voltage that they were supplying.
In Figure 1.8(a), a 10 volt, 1 kHz voltage at terminals A-C would give
rise to a voltage of 5 volts across B-C if R2 was equal to R1 , at say 100 ohms
each, and the resistors would heat up with the power dissipation. In the
case of Figure 1.8(b), we could select a capacitor to have a reactance of
100 ohms at 1 kHz, but the circuit would not behave in the same way. The
capacitor would be selected from the formula
X=
1000000
2fc
which transposes to
so for 100 ohms at 1 kHz
1000000
2fx
1000000
c=
62842 × 1000 × 100
1000000
c=
628400
c = 16 microfarads (
F)
c=
However, despite the resistance and reactance in the circuit both being
equal at 100 ohms, the total impedance (resistance plus reactance) would
not be 200 ohms. The same current would flow through both components,
but whereas the voltage across the resistor would be in phase with the
current, the voltage across the capacitor would be 90 degrees out of phase
with the current. We can draw a right-angled triangle, as in Figure 1.9, with
one side representing the resistance and the other side, at 90 degrees, representing the reactance. The total impedance (Z) would be represented by
the hypotenuse. From Pythagorus’ theorem, the square of the hypotenuse
is equal to the sum of the squares of the other two sides. Therefore:
1002 + 1002 = 10000 + 10000 = 20000
Z2 = 20000
Z = 20000
Z = 141
total impedance = 141 ohms
The resistor would dissipate power in the form of heat, but the capacitor would dissipate no power, and would not heat up. The inductive circuit
18 Loudspeakers
100
ohms in
resistor
(resistance R)
Millimetres represent ohms
100 mm
impedance (Z)
of total circuit
141 mm
(141 ohms)
90°
100 mm
0
ohms in
capacitor or inductor
(reactance X)
100
Figure 1.9 Phase angle vector triangle, using 1 mm to represent 1 ohm
in Figure 1.8(c) would behave similarly, except that the phase of the voltage across the inductor would be 90 degrees out with the voltage across
the resistor in the opposite direction to the phase shift across the capacitor. The 90 degree differences in opposite directions leads to the 180 degree
phase shift between capacitors and inductors, which gives rise to the resonance in tuned circuits. A capacitor and inductor in series are the electrical
equivalent to the mass and the spring shown in Figure 1.10. Both are tuned
circuits, and both work in the same way, by transferring energy backwards
and forwards and dissipating very little of it. The mass takes in energy when
one tries to move it, but releases it again when one tries to stop it – this is
why the brakes get hot when a car stops. A spring takes in energy when it is
stretched or compressed, but releases it when it is released. A mass, basically,
‘wants’ to stay free of accelerations and decelerations. A spring, basically,
does not ‘want’ to change its length. The two together, given their different
phase relationships, take in and release energy alternately, and so remain
in oscillation until frictional losses eventually turn the energy into heat.
At the risk of labouring the point (but it is really not well understood
by most loudspeaker users) if we have a mass and a spring as shown in
Figure 1.10 (a) at equilibrium, the spring is ‘happy’ because it is at its
equilibrium length given the forces acting upon it. The mass is also ‘happy’
because it is at rest; it is neither accelerating nor decelerating. If somebody
then pulls down on the mass, and holds it there, the mass is still happy,
but the spring is not, because it is stretched as in Figure 1.10(b). If the
mass is released, the spring will act to overcome the inertia of the mass
so that it can return to its equilibrium length. When the spring reaches its
equilibrium length the mass is in motion, so the mass times velocity gives it
momentum, which will carry it through the rest position of the spring, and
will begin to compress it, as shown in Figure 1.10(c). The ‘unhappy’ spring
What is a loudspeaker? 19
a)
b)
Equilibrium
Equilibrium
kg
kg
c)
d)
kg
Equilibrium
kg
h
e
a
t
Figure 1.10 Masses, springs and resistances vis-à-vis inductors, capacitors and resistors
therefore begins to slow the mass, so that it (the spring) can once again
return to its ‘happy’ equilibrium position, but it overshoots once again,
and the oscillation continues. This is a reactive system like a capacitor and
inductor, and the only energy loss is due to its imperfection; which in the
mechanical case is friction and air resistance, and in the electrical system
is electrical resistance due to the less than perfect conductors – the coil of
an inductor will always have a small resistance due to the wire.
Now, if we add some resistance to the mechanical system, we can make
it do some work, like moving the hands of a clock, as in Figure 1.10(d), but
the work takes energy, so the oscillations will be reduced more rapidly –
the oscillations will be damped. The electrical circuit equivalent would be
to put a resistor in series with the inductor and the capacitor, so that the
current flowing through the circuit will produce some heat, and damp the
electrical oscillation.
When we load a loudspeaker diaphragm with a horn, the air in front
of the loudspeaker cannot escape to the side of the diaphragm, and the
stretching pressure due to the sideways component of the wave is restricted.
The reactive conditions are therefore minimised, and the air load in the
horn provides a substantially resistive load, with the particle velocity and
pressure in phase, so more useful work can be done by the diaphragm,
such as producing sound instead of just flapping backwards and forwards.
20 Loudspeakers
These concepts are relative to horns and direct radiators with their
predominantly resistive and reactive loadings respectively. The resistive
horn loading tends to be efficient because it gives rise to acoustic power
being radiated. The largely reactive loading on a direct radiator gives rise
to little power being radiated, just as little heat is produced in a capacitor
or an inductor.
1.7 The bigger picture
This chapter has tried to set out the fundamental characteristics of sound
radiation from moving coil loudspeakers, which represent 99% of all drive
units manufactured, but up to now we have only been referring to single
drive-units, which as we have previously discussed cannot be realistically
expected to cover the full frequency range. Once we are forced to consider
multi-driver systems with their obligatory crossover filters, the combined
system can take on a further considerable degree of complexity. Many
entire loudspeaker systems, some of great complexity, are made only from
drivers using this motor technique. However, there are many other types of
drive systems which will be discussed in the following chapter, and which
we will need to look at in order to get a better appreciation of the characteristics which they can offer. Chapter 3 will then discuss the enclosures
in which we must mount them, because the cabinets give rise to their own,
extra complications as they affect the air loading on the diaphragms of
open-framed drive units. Once we put the whole loudspeaker assemblies
into rooms, as described in Chapter 7, a further set of complications arise.
As all of these aspects of loudspeaker design and use compound each
other, achieving a uniform response in all cases is not possible. For this
reason, as perfection is not possible, much of this book will discuss the
aspects of what we hear and what we may need to hear at various different
stages of the music recording process; and, of course during the ultimate
objective of domestic listening enjoyment. It will become apparent that it
is all about compromise, but the optimum compromise points cannot be
chosen without a thorough understanding of the overriding priorities at
each stage of the process. A single driver is only a very small component
part of a complex system that takes a musical signal from the amplifier to
the ear.
References
1 Fahy, F., Walker, J., ‘Fundamentals of Noise and Vibration’, Chapter 5, Spon
Press, London, UK, (1998)
2 Rice, C., Kellogg, E., ‘Notes on the Development of a New Type of Hornless
Loudspeaker’, Transactions, American Institute of Electrical Engineers, Vol 44,
pp 461–475, (1925)
3 Briggs, G., ‘Loudspeakers’ Fourth Edition, Wharfedale Wireless Works Ltd,
Bradford, England (1955) – Reprinted by Audio Amateur Publications Inc,
Peterborough, NH, USA (1990)
What is a loudspeaker? 21
Bibliography
1 Borwick, J., ‘Loudspeaker and Headphone Handbook’, Third Edition, Focal
Press, Oxford, UK (2001)
2 Colloms, M., ‘High Performance Loudspeakers’, 6th Edition, John Wiley and
Sons, Chichester, UK (2005)
3 Eargle, J. M., ‘Loudspeaker Handbook’, Chapman and Hall, New York, USA
(1997)
4 Briggs, G. A., ‘Loudspeakers’, Fifth Edition, Rank Wharfedale Ltd, Bradford,
UK (1958) – Reprinted until 1972
5 Jordan, E., ‘Loudspeakers’, Focal Press, Oxford, UK (1963)
6 Borwick, J., ‘Loudspeaker and Headphone Handbook’, Second Edition, Focal
Press, Oxford, UK (1994) (significantly different in content from the aforementioned Third Edition.)
Chapter 2
Diversity of design
Although the original moving-coil, cone loudspeaker of Rice and Kellogg
was the first true loudspeaker of a type that we know today, it was, itself,
a development of ideas which had gone before, principally relating to the
design of telephone earpieces, which were not very loud speakers. The
moving coil direct radiator, along with amplifiers as great as 15 watts
output – which was then huge – soon opened a door to room-filling sound
levels, and, within only a couple of years, talking pictures at the cinema. The
need to fill larger and larger theatres with sound led to horn designs, and
the need for greater bandwidth led to the separation of the drive units into
frequency ranges where they could operate more efficiently. Thus began
a refinement and specialisation of designs which continues to this day,
with ever more ideas, magnet materials, diaphragm materials and radiator
concepts all designed essentially to do the same thing – convert electrical
energy into sound waves. What follows in this chapter is a discussion of
some of the various ways in which this conversion can be made to take
place, and the strengths and weaknesses of the various approaches.
2.1 Moving-coil cone loudspeakers
Of all types of drive units, there is probably none so varied in size, shape,
materials of construction or performance as the moving coil cone loudspeaker. They basically all follow the concept shown in Figure 2.1, and
little has changed in the underlying principles of their operation in the
80 years of existence so far. They all need a magnet, which was often an
electro-magnet in the early years before permanent magnets of sufficient
strength were developed. In this case, a ‘field coil’ was supplied with a DC
current sufficient to generate the required strength of magnetic field for
the ‘voice coil’ (which was fed with the output signal from the amplifier),
to drive the cone with the required level of sensitivity. Early permanent
magnets were often made from iron and chromium. Aluminium, nickel
and cobalt were variously used in the early 1930s, alloyed with iron in different combinations, and the three together gave rise to the name Alnico.
In the 1970s, the civil war in the Congo (then Zaire) created a big hole in
the production of cobalt, whose price rose astronomically in a very short
period of time. This led to the use of ferrite materials, known as ceramic
magnets, which had their strengths and weaknesses which will be discussed
in Section 2.1.6. More recently, ‘rare earth’ magnets, principally made from
Diversity of design 23
Surround
Cone
Dust
cap
Spider
Chassis or
basket
Coil
former
Annular pole
Magnet
Coil
Centre pole
Figure 2.1 The components of a moving coil loudspeaker
neodymium and samarium based alloys, such as neodymium with iron and
boron, or samarium and cobalt, have led to very light weight magnets, and
opened a door to new magnet shapes and magnetic field designs. The basic
concept of two different magnet structures is shown in Figure 2.2.
The magnetic circuits are designed to concentrate the magnetic field in
a circular gap, as shown in Figure 2.3. In this gap is inserted the voice
coil, which receives the electrical drive current from the power amplifier.
This current produces its own, alternating magnetic field, whose phase and
amplitude depend on the drive signal. The variable field interacts with the
static field in the circular gap, and creates a force which either causes the
voice coil to move into or out of the gap. Of course, a means is required
to maintain the coil centralised in the gap, and this is achieved by the use
of centring device, or inner suspension, which is still often referred to as a
spider for reasons which should be clear from an inspection of Figure 2.4.
A more typical modern device is shown in Figure 2.5. A chassis, also known
as a frame or basket, supports the whole assembly and enables it to be
mounted on a front baffle. The cone is connected rigidly to the former
upon which the voice coils is wound, and is also connected more or less
at the same point to the inner suspension. At the chassis’ outer edge the
cone is attached via a flexible outer suspension, or surround, which may
take the form of half-rolls, corrugations, or pleats. These will be discussed
in more detail in Section 2.1.2. A dust cap is then normally placed in the
apex of the cone in order to prevent the ingress of dust and any abrasive
dirt, and may also be used as an air pump to cool the voice coil and gap
when the cone assembly moves in and out.
2.1.1 Cones
A three-way loudspeaker system consisting entirely of cone drivers is
shown in Figure 2.6. Although the cone drivers all follow the above principles of construction, their designs are very different. In Chapter 1 it was
explained how, at low frequencies, the electro-acoustic conversion efficiency is low, because the air tends to move out of the way of the vibrating
24 Loudspeakers
Force
Current in
voice-coil
Diaphragm
Front plate
(mild steel)
Voice-coil
on former
S
N S
S N
N
S
N
Ceramic
magnet
Powerful external
magnetic field
Back plate
(mild steel)
Centre pole
(mild steel)
Path of
magnetic
circuit
Magnetic gap
in which field
is concentrated
Ceramic ring magnet geometry
Magnetic field
concentrated
in gap
S
No appreciable
external magnetic
field
Optional copper ring
for inductance control
External pole piece
(mild steel)
N Plug
N
S
magnet
(Alnico,
etc)
Magnetic
circuit
Back plate
(mild steel)
Metal plug-magnet geometry
Figure 2.2 Typical motor topologies
cone. The result of this is that for a reasonable on-axis sensitivity, the cone
needs to be quite large. In the loudspeaker shown in Figure 2.6, the low
frequency cone is of nominally 12 inch diameter (300 mm), although the
effective radiating area is only just over 10 inches because the surround
does not contribute much to the radiation. The cone needs to be rigid,
because if it breaks up into non-uniform movement, phase cancellations
will occur at some frequencies and the subsequent frequency response
will not be flat. In some cases, cone break up can be used to extend the
frequency response, and can be used in musical instrument loudspeakers
to create desirable colouration in the sound, but for flat, uncoloured lowfrequency responses, the piston which is pumping the air needs to maintain
its rigidity. Some of the ways in which a cone can break up are shown in
Figure 2.7.
Diversity of design 25
a)
Top plate Pole piece
Symmetrical
magnetic field
Ferrite
magnet
Vent
Flux
stabilizing
ring
Cast back plate
Magnet geometry for concentrating the flux in the voice-coil
gap – section view (courtesy JBL inc.)
b)
The circular voice-coil gap – perspective view
Figure 2.3 The voice-coil gap
Figure 2.4 An early centring device – a ‘spider’, some of which had more legs than the one
shown
Once cones exceed a diameter of about 18 inches (460 mm) it can become
difficult to maintain their rigidity. The gain in efficiency due to the large
radiating areas of big drivers can rapidly be offset by the greater proportional weight needed to keep them rigid. Many designers favour multiple,
smaller drivers to the use of single larger drivers partly because they feel
26 Loudspeakers
Centring devices
Typical centring device in corrugated paper or fabric
Figure 2.5 A typical, modern centring device, or inner suspension
Figure 2.6 A full-range, all cone driver loudspeaker system – the JBL L100
that they can keep these better controlled. It is unusual to see drivers
of greater than 18 inch diameter, although they do exist, as shown in
Figure 2.8. Sandwich cones, honeycomb cones and Kevlar and carbon fibre
and metal cones have all been employed in attempts to maintain cone
rigidity, and consequently the pistonic movement. In each case, the cones
exhibit different characteristics above certain frequencies, so the suitability
of each material or construction may depend upon the upper frequency
limit to which a driver will be used. Solid cones have also been used,
but they can introduce as many problems as they solve, and they are not
so obviously beneficial as they may at first appear to be. One problem
with many of these approaches has been that the near-perfect rigidity has
improved matters at low frequencies but has only pushed the resonances
up in frequency, rather than eliminating them. When stiff structures do
Diversity of design 27
Rim flexure
+
–
–
+
First order
Perspective view
Plan views
of cone
+
–
–
+
+
–
–
+
–
+
+
Second order
–
Higher modes
± direction of motion
Figure 2.7 Bell-mode break-up in cones
FW800N
Figure 2.8 A very large loudspeaker – a 30 inch (800 mm) low frequency loudspeaker with
radial reinforcing ribs to augment the cone rigidity
break up they tend to do so much more severely, so crossover frequencies
must be chosen well away from the break-up frequencies if colouration
is to be avoided. It has proved difficult to achieve uncoloured mid-range
responses from highly rigid low frequency driver cones, so they are often
best restricted to use at low frequencies only.
Bextrene, a mixture of polystyrene and neoprene, was pioneered as a
cone material by the BBC, in the UK, as far back as the 1960s. This was
originally researched largely to find a solution to the inconsistency problems encountered in the manufacture of paper pulp (cardboard) cones.
28 Loudspeakers
Paper, being made from wood, which is a natural material, can suffer
from the problem of all natural organic materials; they are not homogeneous substances so they tend to vary from batch to batch. Bextrene
was well-damped and resisted break-up to relatively high frequencies.
Designs have been employed using Bextrene cones which have used 12 inch
(300 mm) bass drivers up to crossover frequencies beyond 1.5 kHz with
little mid-range colouration. Polypropylene has since been developed for
use as a cone material, offering even more consistency, long term stability and sensitivity. However, opinions vary about the sonic neutrality of
polypropylene-coned drivers.
The original loudspeaker of Rice and Kellogg used a paper cone. Quite
remarkably, despite all of the modern developments in materials and construction, paper pulp cones, and even folded and seamed paper cones, are
still in use in all levels of performance ranges. Paper pulp cones are made
by drawing a slurry (wet mix) of paper fibres through a fine screen in the
required shape. The resulting cone is then cured and dried before being cut
to the exact size required. This ‘old fashioned’ material still exhibits excellent characteristics of high rigidity and high internal damping, and these
are two things which normally are contradictory inasmuch as the augmentation of either one usually tends to reduce the other. At low frequencies
the rigidity is necessary to maintain piston action, but once any break-up
does begin, the internal damping of the cone material needs to suppress the
waves which travel as shown in Figure 2.9, which would cause peaks and
dips in the frequency response. The bass cone shown in Figure 2.6 has been
further treated on both sides with a damping material known as Aquaplas,
which also adds some mass, and this lowers the free-air resonance of the
driver.
Despite the fact that many drive units of similar specification which
employ different cone materials may perform very closely in objective
measurement, there is strong evidence that some very similarly performing
drivers do not sound the same. In very high quality loudspeakers, paper
pulp is still a favoured material, despite its sensitivity to humidity and batchto-batch variation. Colloms1 refers to the well-balanced characteristics of
paper pulp, together with the fact that its properties and manufacturing
techniques are well-understood, as strong justification for its continued
use. He notes how some high-loss materials also may tend to lose, or
mask, fine musical detail. The authors of this book have noticed a loss
of reverberation detail when substituting some synthetic cones for paper
cones used up to 1 kHz, and have received comments from professional
users about guitar strings not sounding as new when heard via the synthetic
cones as when heard via high quality paper pulp cones. The Celestion
loudspeakers company still produce the exact model of guitar loudspeaker
which was made famous in the Vox AC30 guitar amplifier of the 1960s.
This blue-chassised driver has resisted all efforts to update its construction,
yet still maintain its highly desirable sound qualities. A great number of
musicians claim to hear their guitars more ‘clearly’ via paper cones.
The observations about guitar strings could suggest a harmonic enhancement due to non-linear distortion products enriching the sound, but harmonic distortion could not explain the increased sensation of low-level
detail and reverberation. Synthesising natural sounding reverberation is
Diversity of design 29
a) Progressive, concentric break-up of a cone
B
C
B
A
A
4
5
940 Hz
6
1100 Hz
7
2150 Hz
8
2700 Hz
3900 Hz
b) Response peaks and dips numbered according to the corresponding
break-up modes as shown in (a)
24
20
6
8
16
4
12
SPL
(dB)
8
7
4
0
5
–4
–8
–12
0.03 0.04 0.06 0.08 0.1
0.2
0.3 0.4
0.6 0.8 1
2
3
4
6
8
Frequency (kHz)
Figure 2.9 Concentric modes in loudspeaker cones
not something which one would expect from the addition of harmonic distortion. It seems probable that the guitar strings are benefiting from the
same characteristics which are enabling the greater resolution of reverberation and room effects, and paper-pulp seems to be a good performer in
this respect. Work is currently under way to investigate the possibility of
intermodulation distortion contributing to the low level detail loss with certain materials, given rise to by non-linear hysteresis effects connected with
the damping action. Intermodulation distortions will be discussed in more
detail in Chapter 9, but it results in harmonically and non-harmonically
related products which together tend to produce a noise signal below the
music.
As the frequency rises, two things begin to affect the performance of a
cone driver. It was shown in Figures 1.3. and 1.4 how the directivity of a
cone, or any pistonic radiating surface, narrows as the wavelength become
30 Loudspeakers
small compared to the circumference of the radiating area. However, as frequencies rise, the mass of the moving assembly gradually tends to oppose
more strongly the force which is trying to move it. There comes a point
where the increasing efficiency of radiation due to the greater radiation
resistance provided by the air as the frequency rises can no longer compensate for the mass effects of the moving parts, and the power response
of the driver begins to roll off. For a 15 inch (380 mm) loudspeaker, 1 kHz
is about the upper limit of either its flat response range or the acceptability
of its narrowing directivity. Nevertheless, the directivity narrowing may
not be too severe if the centre section of the cone begins to decouple itself
from the outer section, as often happens – either by design or accident.
Eight inch loudspeakers (200 mm) can work well up to 2 kHz, or more,
but the compromises which must be made if their responses are to be
extended at the bottom end may begin to degrade the higher frequency
performance. In the loudspeaker shown in Figure 2.6, the 12 inch (300 mm)
low frequency driver, having a free-air resonance of 25 Hz, is used up to a
frequency of around 1 kHz, at which point the crossover begins to divert
the signal towards the 5 inch (125 mm) cone. Five octaves is just about the
limit of the bandwidth of a cone driver if very high quality, wide directivity,
minimum-compromise sonic performance is required.
In smaller loudspeakers, cone rigidity is much easier to achieve, therefore much lighter moving assemblies can be employed which can exhibit
good efficiency without the massive magnet assemblies needed for the
low frequency drivers. The low frequency driver shown in Figure 2.6 has
a sensitivity of 89 dB for 1 watt input at 1 metre distance, yet with a
much smaller magnet but a lighter moving assembly, the 5 inch mid-range
driver has a corresponding sensitivity of 94 dB. This sensitivity increase
can be important, because smaller loudspeakers cannot lose the waste heat
as easily as can large loudspeakers, which was one driving force behind
the developments of domes, as will be discussed in Section 2.2. The tiny
tweeter cone shown in Figure 2.6 is only 11/2 inches (38 mm) in diameter,
but handles frequencies from 4 kHz to almost 20 kHz, so in this design of
loudspeaker cabinet all frequencies from below 40 Hz to almost 20 kHz
are handled by paper cones.
2.1.2 Surrounds
The outer suspension, or cone surround, serves two functions. The most
obvious is to maintain the outer edge of the cone stable during the rapid
movements along the front-back axis, but surrounds also serve to absorb
vibrational waves which propagate from the voice coil in the manner shown
in Figure 2.9. A selection of surround designs are shown in Figure 2.10. The
surrounds are variously formed from a continuation of the cone material
or from separate materials attached with adhesives. Polyurethane foam,
butyl rubber, nitryl rubber, cambric (pronounced Kāymbrik - a woven
linen or cotton fabric), or other treated fabrics are frequently used as cone
surround materials. PVC is also sometimes used. Figure 2.10(a) shows a
half-roll surround. These are usually made from synthetic foams or rubbers. They allow long travel because they tend to stretch in an elastic
manner over a considerable range of movement, and hence give rise to
Diversity of design 31
a)
b)
c)
d)
Figure 2.10 Cone surround variants. a) Half-roll of polyurethane foam – low stiffness (high
compliance) for long travel, but requires precise choice of centring device for controlled
linearity. b) Double half-roll cloth – shape of rolls can precisely tune the stiffness characteristic. c) Multiple-roll accordion pleat – long travel but prone to rim-resonance response dip
problems (see Figure 2.11). d) One piece cone/surround with treated edge – stiff, non linear
suspension, provides HF resonance peak. Principally used for musical instrument loudspeakers to prevent over-excursions of the cone
little distortion which would be caused by restraining the cone travel. When
the materials are carefully chosen they can effectively absorb the resonant
modes which pass radially along the cone, thus avoiding standing waves
within the materials of the cones. The double half-roll surrounds, shown
in Figure 2.10(b) are usually made from treated cloths. They are more
rugged than the single half-rolls, and find much use in sound reinforcement
and musical instrument amplification, but tend in general to be used in
less long-throw loudspeakers with higher resonant frequencies than those
which usually employ the single half-rolls. The extra stiffness of the double
half-roll surrounds both adds to their ruggedness and increases the resonant
frequency of the moving system as compared to single half-roll devices.
Figure 2.10(c) shows a concertina (accordion) surround. These are often
pressed or moulded as part of the cone. They can allow extended travel,
but unless very carefully damped can give rise to resonance problems.
They also tend to be stiffer than the single or double half-roll surrounds,
and are therefore not often found on low-resonance designs.
Surround materials are also a specialised subject. Some of the foams
which are commonly used can deteriorate much quicker than expected in
sunlight or polluted atmospheres, and can also suffer from insect damage.
Nevertheless, in clean, temperature-controlled environments such as exist
in many sound control rooms they can easily last for 20 years or more,
and can be replaced by skilled artisans without removing the cone from
the chassis. Plasticised PVC is another material which has been employed
with success, and is found on some mid-range cones where its properties
efficiently absorb the waves reaching the cone edges. In sealed cabinets,
the surrounds must also resist the differential pressures between the inside
32 Loudspeakers
surround dip
15
dB
10
5
0
200
500
1K
2k
5k
10 k
hertz
Figure 2.11 Response dip due to a surround resonance
and the outside of the cabinet, and this fact can preclude the use of some
foams in certain cases. In order to fulfil all of the demands made of them,
surrounds are quite specialised devices. The surrounds not only need to
be selected according to the density of the cone material, but also the
principal frequency ranges over which a driver will work, and the excursion
limits within which they must allow relatively unrestricted movement. For
wide-range drive units, the compromise choices are not simple. Figure 2.11
shows a response dip due to an antiphase movement of a surround. The
fact that the dip exists in the response of such a high quality driver suggests
that solutions to the dip problem would have compromised the overall
response to a greater degree.
2.1.3 Rear suspensions
The prime function of the rear suspension, or spider, is to maintain the
coil centralised in the magnetic gap. On its inner edge it is connected to
the voice coil former, and at its outer edge it is glued to the chassis. Modern suspensions, such as the one shown in Figure 2.5, are usually made
from phenolic resin impregnated cloth, hot pressed into shape. Care has
to be taken in the design of the corrugations to ensure that movement in
one direction is not favoured over the other direction, because an asymmetrical movement would give rise to non-linear distortion. Some designs
Diversity of design 33
have employed double spiders, mirror imaged, in order to ensure symmetrical linear travel of the cone. A double spider arrangement is shown in
Figure 2.12. These are fine in vented magnet designs, but a complication
in double suspension designs arises if they must allow air to pass through
to cool the voice coil in designs that do not have vented magnet systems.
As with the corrugated, concertina surrounds, the corrugated inner suspensions can suffer from resonance problems unless they are carefully
‘tuned’.
The stability of the inner suspensions needs to be very good because
the gap between the voice coil and the magnet can be less than half a
millimetre, even with a relatively large cone and coil. With large, heavy
cone/coil assemblies, the suspensions can become stretched if the drivers
are stored in a horizontal position without adequate support for the cone
(which effectively means in the manufacturers’ shipping boxes). Likewise,
complete loudspeaker systems should not be stored on their backs or ‘cone
sag’ is likely to result. Once mounted vertical again, the suspension may
have ‘set’ to a new equilibrium position which is not in the centre of the
cone’s axial travel, hence the cone excursion will be prematurely limited
in one direction. In many cases, this cone sag cannot be corrected by any
simple means, and so storage conditions likely to give rise to it should be
avoided.
The inner suspension is very critical because it usually provides the
main restoring force for centralising the cone in the axial as well as the
radial directions. Over 50 years ago, Briggs recognised not only the thirdharmonic distortion-producing mechanisms of badly designed suspensions,
but also the fact that inadequate suspensions could give rise to distorted
transient responses2 . Over 40 years later, Colloms wrote about work done
at KEF which correlated well with his own experiences that some inner
suspensions could give excellent, low distortion results on sine waves and
the more open bass waveforms of orchestral music, but could be slow in
responding to the more percussive bass sounds found in much modern
Figure 2.12 Cut-away view of a 380 mm loudspeaker with double spider (centring device)
construction (Cetec-Gauss Inc)
34 Loudspeakers
music1 . The KEF findings had emerged from investigations into the different low frequency measurements obtained via the use of steady state
or impulsive signal sources. [These test methods are described further in
Chapter 9.] The differences have been attributed to hysteresis in the suspensions, shown diagrammatically in Figure 2.13.
In some very small cone loudspeakers, designed only for high frequency
use, the additional complexity of the use of an inner suspension can often
be omitted, the external surround being sufficient to maintain the cone
in a central position, and thus avoiding all the inner-suspension-related
problems which larger, heavier cones must endure.
Although the suspension systems, both surrounds and spiders, are
mechanically essential in low and mid frequency cone loudspeakers,
towards their excursion limits they all begin to give rise to third harmonic
distortion due to the approaching elasticity limits where they become
less compliant (i.e. more stiff). Once they no longer obey Hooke’s Law
(the law governing the relationship between force and compression [or
expansion] of a simple spring) they can produce quite a number of undesirable artefacts.
2.1.4 The chassis
Loudspeaker chassis provide a frame for the mounting of the magnet
system and inner and outer suspensions. They can be made of plastic,
or pressed or cast metal. Metal is preferred when power levels are high
because it helps to conduct the heat away from the magnet assembly. Cast
Out
(mm)
In
(newtons)
Figure 2.13 Hysteresis curves – the hysteresis curves represent processes which are cyclic but
where the forward and backward processes do not follow the same path. ‘Hysteresis’ is from
the Greek word meaning ‘to lag behind’
Diversity of design 35
metal is usually preferable to pressed metal on grounds of stability and
dimensional accuracy; cast aluminium being the material of choice for most
large professional bass units. With magnet assemblies weighing 10 kg or
more on some 18 inch loudspeakers, the chassis (‘frames’, ‘baskets’) need to
be strong to withstand shipping shocks without disturbing the centralisation
of the sub-half-millimetre coil clearances. Also, coil temperatures of 250
degrees C, or over, need to be withstood and dissipated without warping.
Unfortunately, there is a conflicting requirement between the strength of
the chassis and the need not to impede the free movement of air between
the cone and the inside of the box (or outside the box in the case of external
chassis designs, as shown in Figure 2.14). The chassis therefore needs to
be as strong as necessary for support, whilst being as open as required
for non obstruction of the air adjacent to the cone. It is also important
that it should not suffer from resonance problems, and so needs to be well
acoustically damped.
Once a cone and coil assembly is mounted in a chassis at the surround
and the inner suppression attachment points, its mass will resonate with the
compliance of the suspension systems to determine the free air resonance
of the driver. The free air resonance normally defines the lower response
limit of a loudspeaker system in any given volume or design of cabinet.
However, there do exist some special designs of loudspeaker systems which
drive the bass units through their resonances, but they are rare, and need
electronic compensation.
2.1.5 The voice-coil assembly
The voice-coil former is normally attached to a cone at some point
between its apex and a point mid-way between the apex and the perimeter.
The coil former, of cylindrical design, must be mechanically stable
under high degrees of vibration and temperature changes, neither deforming
in circularity nor expanding or contracting to any significant degree. Without the required stability, the coil or the former could rub on the sides of
Figure 2.14 A 15 inch (380 mm) loudspeaker manufactured by the British company Volt
Loudspeakers Ltd, employing an external chassis for improved heat dissipation
36 Loudspeakers
the magnetic gap and make undesirable scraping noises. Although paper
was used to great effect on early, low-power loudspeakers, modern day, hightemperature voice coils need to be bonded to thermally stable formers with
thermally stable adhesives. Glass fibre has been used as a former material,
but polyamides are now more normal, (Nomex, Kapton etc). Aluminium has
also been used, but metal formers can suffer from eddy current problems
by acting as a shorted turn in the alternating magnetic field, and can also
conduct very high temperatures to the necks of the cones, where charring,
melting or softening can occur, and adhesives may also be caused to fail.
The coils are almost exclusively made from copper or aluminium,
although silver has also been used, reportedly to some sonic benefit1 . Copper offers lower resistance, but aluminium offers lighter weight. Which one
is the most appropriate depends on many other design factors, but both
materials have been used at either frequency extreme – there are no hard
and fast rules. Copper clad aluminium is another option, which simplifies
the soldering problems which may be encountered with pure aluminium.
Round wire and rectangular section (ribbon) wire are also options. The
ribbon wire packs more densely, eliminating the gaps between the adjacent
round wires, but round wires offer much simpler winding processes. To
prevent short circuits between turns, the copper wire is insulated with a
heat resistant lacquer, and aluminium wires are anodised, which creates a
layer of non-conducting aluminium oxide on the surface. In either case, the
wires may also be coated with a thermosetting adhesive before winding,
which, after curing, helps to render the entire assembly more rigid.
The most appropriate diameter of a voice coil is also the subject of compromise. Larger diameter voice coils have more surface area for any given
length of wire than coils of less diameter, at least for any given gap depth,
and can therefore lose heat more easily. They can also help to stiffen a cone
by driving it in a more evenly distributed manner. However, if the coil is
too big in diameter, the centre of the cone can begin to decouple from the
coil, which can cause strange frequency response and directivity problems.
Proponents of small diameter voice coils cite advantages of deeper coils in
longer gaps giving them design advantages such as deeper gaps with less
magnetic material at no thermal dissipation cost. As with so many things in
loudspeaker design, the art of the science is finding the best compromise
for any given situation. Low frequency efficiency versus high frequency
extension, for example, can dictate the optimum choice of coil material
as copper or aluminium. Some manufacturers have also great expertise
in using particular design concepts or manufacturing processes which suit
certain ways of doing things better than others. Electro-Voice, for decades,
continued to make excellent 15 inch (380 mm) loudspeakers with 21/2 inch
(62 mm) voice coils, whilst JBL had long since moved to 4 inch (100 mm)
coils for their equivalent designs, but using different magnet topologies.
2.1.6 Magnet systems
The voice coil and the magnet form the motor system of a moving-coil
loudspeaker. As mentioned above, either one depends on the other in
order to produce the required force to drive the cone in the required
direction at the required speed, as instructed by the electrical input signal.
Diversity of design 37
Magnets are a huge and complex subject in themselves, so only some of
the more fundamental aspects of their behaviour can be dealt with here,
but the Bibliography at the end of this chapter gives references to some
excellent further reading. Cost, however, perhaps plays a bigger part in
the choice of magnet systems than in any other aspect of the design of
cone loudspeakers. Some of the best magnetic materials ever developed
for loudspeaker use used cobalt, which, as mentioned in Section 2.1, rose
in price by over 2000% in a very short period of time when the civil war
in Zaire (the former Belgian Congo) began in the 1970s, because Zaire
was the world’s largest producer of cobalt. This drove many manufacturers
to use ferrite materials, predominantly barium ferrite, which had been
developed for deriving the static magnetic fields necessary around cathode
ray tubes in television sets.
The design of typical Alnico (Aluminium, nickel, cobalt and iron), Ferrite (ceramic), neodymium and Alcomax magnets are shown in Figure 2.15,
from which the geometrical differences are obvious, (although the Alcomax and Alnico geometries shown are interchangeable). Many modern
loudspeakers use neodymium alloys, and an alloy of samarium and cobalt
is also finding use in loudspeaker designs. These materials give enormous
magnetic strength for their weight, and they have given rise to further
changes in magnetic geometry. The ferrite materials are very resistant to
loss of magnetism due to time or heat stresses, but they exhibit powerful stray magnetic fields and can pose some difficulties in achieving the
desired magnetic field geometries. Alnico is somewhat less durable, but
can allow designs enabling very compact and concentrated magnetic fields.
Strength for strength, neodymium magnets are much lighter than either
ferrite or cobalt alloy magnets, but can be relatively easily demagnetised at
relatively low temperatures, and cannot withstand 250 degrees C voice coil
temperatures without permanently losing some of their magnetic strength.
The metal magnets are good conductors of electricity, but the ferrite magnets are ceramic materials, and hence are electrically non-conductive. The
non-conducting nature of the ferrite materials can be a problem unless
careful measures are taken to use other means to avoid unnecessary and
undesirable flux modulation effects. Iron of high magnetic permeability
is used in the magnetic structures shown in Figure 2.15 to complete the
magnetic circuit, and to achieve the correct shape of field and density of
magnetic flux in the gap in which the coil is positioned. The type of iron
used is normally a mild steel of low carbon content, but when very high
flux densities are required, a material known as Permendur is often used,
especially in compression drivers. Permendur is an iron-cobalt-vanadium
alloy, which is very hard and difficult to work, but its magnetic properties,
when required, may demand its use.
There are many people who consider the metal magnets to be capable of
better sonic performance than the ferrite magnets, citing better resolution
of fine detail with materials such as Alnico and the neodymium alloys. It
is hard to find evidence of tests which rigorously compare the differences
in the magnetic materials only, because the required structural differences
needed to get exactly the same magnetic field in the same gap can lead to
other changes being necessary. Nevertheless, there is a tendency for many
of the highest resolution devices to use metal magnets, and explanations
38 Loudspeakers
a)
Magnetic
return path
Pole piece
Alnico ring
magnet
Centre vent path
b)
Front/top plate
Pole piece
Ferrite
magnet
Back plate
Centre vent path
c)
Radial
magnet
One-piece
magnet return
path
Centre vent path
The centre vent paths do not
exist in all magnet structures
d)
Central
plug magnet
Figure 2.15 Basic magnet structures. a) Alnico ring magnet. b) Ferrite ring magnet. c) Radial,
high energy magnet (neodymium etc). d) Alcomax plug magnet a), c) and d) do not have any
appreciable external magnetic fields
Diversity of design 39
have been put forward to suggest that the magnetic domain jumps which
take place in non-conducting materials can give rise to effects not dissimilar to digital quantising distortion. These jumps are smoothed out by large
eddy currents flowing in the electrically conducting magnets. In some loudspeaker designs the central pole-piece of the magnetic assembly is fitted
with a copper ring to provide a very low electrical resistance – less than
that of steel – to effectively short out any flux-modulation currents.
As shown in Figure 2.15(a), (b) and (c), the entire magnet assemblies
in many high-power, low-frequency drivers have cylindrical holes through
their central axes to allow air to be pumped through by the dust cover
(dome) which caps the voice-coil former on the outer face of the cone. In
some other designs, the spider (inner suspension) and the dust cover are of
an open weave nature, to allow hot air to pass to the outside of the cabinet.
As mentioned earlier, the voice coils can get to temperatures above 250
degrees C in some cases, and this heat needs to be dissipated as quickly
as possible, not only to prevent the burn-out of the coil but also to avoid
overheating and weakening of the magnet. Furthermore, the resistance of
a copper wire rises by about 0.6% for every degree of temperature rise,
so a changing voice coil resistance will affect the sensitivity of the motor
system and may lead to signal compression.
2.1.7 Ferrofluids
The problem of the conduction of heat from the voice coil to the pole
piece of the magnet assembly can, in some instances, be augmented by the
use of a ferrofluid. Air is not a good conductor of heat, so much of the
heat is transferred from the voice-coil to the magnet assembly by radiation
alone. In the 1970s, ferrofluids began to be introduced which were liquids
with magnetic particles in colloidal suspension. The magnetic field holds
the ferrofluid in the gap, and the good heat-conduction properties of the
ferrofluids aids the cooling of the voice-coil by means of a thermal bridge
to the magnet assembly. The viscosities of the ferrofluids can be adjusted
according to the circumstances of use, a fast-moving tweeter needing lower
viscosity than a mid-range driver if viscous damping effects are to be
avoided. However, ferrofluids are rarely used in high-excursion low frequency drivers, because the shearing effects of the large axial movements
of the coil tend to create non-linear movement due to the non-laminar
flow of the fluids. In high frequency drive units, the ferrofluids can be
advantageous in damping some mechanical resonances if the viscosities are
chosen appropriately.
2.1.8 The complete system
The moving coil cone loudspeaker is quite remarkable in its degree of
versatility of application, and has formed the backbone of loudspeaker
system design since its first application in 1925. Despite all the technological
developments and improvements in materials, Rice and Kellogg, if still
alive today, would almost certainly be able to explain the workings of any
modern moving coil loudspeakers from simple inspection. When they filed
40 Loudspeakers
their patent, they already had described, in principle, almost everything
that we can find in a modern driver. Loudspeaker design is a science; but
there is art in deciding about the best compromise points for what are
imperfect devices. For example, whether a complete system should use
wider range drivers and fewer crossover points, or narrow range drivers
and more crossover points, is a question that may depend more on the
circumstances of use than any single measurement at a fixed position.
Things such as the room acoustics, the music, the required timbral fidelity
and the listening distance may all influence a design, but these things will
all be discussed later.
2.2 Dome loudspeakers
In general principle, a dome loudspeaker is a cone loudspeaker with the
voice coil having the same diameter as the diaphragm. The diaphragm is
also usually inverted, to be convex rather than concave to the exterior.
A mid-range dome loudspeaker is shown in Figure 2.16. The development
of dome loudspeakers largely grew out of the problems surrounding how
to lose heat from the small voice coils of mid and high frequency drivers
at high power levels. A 11/2 inch (38 mm) cone tweeter, with a coil of only
12 mm diameter simply cannot lose heat quickly enough to prevent itself
from burning up at power levels much above 10 watts, because the heat
production is all confined in a small space. However, if the coil were to be
made the same diameter as the diaphragm, a much greater surface area
would be available for heat loss. As light weight is important for sensitivity,
the coil former can be kept to a minimum length if the dome diaphragm
is convex because it will remain clear of the pole piece of the magnet
assembly, as shown in Figure 2.17.
Despite the ‘common sense’ belief of many people that domes radiate
over a wider angle than cones, this is not so. It is important not to confuse
Figure 2.16 A cut-away view of an ATC 3 inch (75 mm) soft dome driver. The British company
ATC pioneered the development of this type of high-output mid-range dome
Diversity of design 41
a) Conventional dome
Dome
Surround
Coil
Dome shape keeps the
diaphragm away from
the pole piece
Magnetic gap
Central plug magnet
Optional tapered vent to
couple the diaphragm to an
absorbent rear chamber
b) Inverted dome
Figure 2.17 A dome as a piston – in principle, if the voice-coil former were to be extended,
and the dome inverted (as in b) the sensitivity would drop due to the extra weight, but no
material change would take place in terms of the radiation pattern (directivity)
domes with pulsating spheres. As shown in Figure 2.18, a pulsating sphere,
which would radiate radially, moves by expanding and contracting in three
dimensions, whereas a dome simply radiates as a piston, because it moves
in one direction only – along its axis of movement. What is more, when a
cone begins to decouple from its voice coil, it does so from the outer parts
first. The central part, nearest to the voice coil, always remains under the
control of the coil, so the radiating area concentrates towards the centre
42 Loudspeakers
a) The pulsating sphere
Compression wave expands spherically
Diaphragm rest
position
Sphere expands
to make
compression wave
Sphere shrinks
on rarefaction
b) The pistonic dome radiator
Radiation propagates largely
in forward direction
Diaphragm moves
forward to make
compression wave
Diaphragm rest
position
Diaphragm moves
backwards to make
rarefaction wave
Figure 2.18 Comparison of radiation from pulsating spheres and domes
of the diaphragm as the frequency rises, which is exactly what is needed
to maintain its directivity. That is, the radiating area reduces in diameter
as the frequency rises, which can be desirable. Conversely, with a dome, it
is the centre of the radiating area which is furthest from the coil, so as the
frequency rises the tendency is for the voice coil to keep control over the
outer perimeter of the radiating area, whilst the centre of the diaphragm
decouples itself, as shown in Figure 2.19. This leads to a ring radiator,
which has very peculiar directivity properties, so domes, if not applied
Diversity of design 43
a)
b)
c)
Figure 2.19 A dome in break-up. a) Radiation equal in phase and amplitude from all parts of
the dome. b) First bending begins. The radiation amplitude increased from the dome edges
and begins to reduce from the centre. c) The dome breaks up. Radiation from the centre
becomes out of phase with the edge radiation
very carefully and below their break-up frequencies can actually have less
smooth directivity than cones.
2.2.1 Hard and soft domes
The diaphragms of hard domes are usually either made from phenolic-resin
impregnated cloth, aluminium, titanium, beryllium, carbon fibre or other,
similar materials with very high strength to weight ratios. Soft domes are
typically made from moulded cloth which has been treated with a viscous
damping material, usually a synthetic rubber. Other types of domes are also
sometimes used, as shown in Figure 8.8. Here, a rigid 7 inch (175 mm) dome
of polyurethane is used in the lower mid-frequency range. Hard domes are
usually restricted to use at high frequencies, above 3 or 4 kHz, because their
resonances are difficult to control in diaphragms of sufficient diameter to
radiate useful power at much lower frequencies. In rare cases, hard domes
of 3 inch (75 cm) or more can be found operating down to frequencies as low
as 800 Hz, but in order to maintain piston action up to very high frequencies
before the first break-up modes occur, materials such as titanium or beryllium
need to be employed. As beryllium is difficult to work with and its vapour is
highly toxic, the production of diaphragms out of this metal is an expensive
process. Such units have found favour in the design of domestic high-fidelity
loudspeakers, but are rarely to be seen in studios. At higher SPL, when they
do break up into separately radiating sections, they tend to do so suddenly
and in a sonically most unpleasant manner, and produce non-linear distortion
products quite differently from soft domes.
Soft domes, on the other hand, can be used down to around 400 Hz, but
many exhibit a hysteresis type of response, as discussed in Section 2.1.3
dealing with suspensions, and the same comments apply. The lagging
response shown in Figure 2.14 can tend to mask low level detail. The ‘rigid’
domes have been developed partly in response to this problem.
Because of their nature, domes only have an outer suspension. The
surround may be formed from the material of the dome in the case of soft
diaphragms, but hard domes often employ a separate, bonded suspension
44 Loudspeakers
material. Rocking motion can be a problem in some designs, and solutions
to remedy this are not always practical if they add weight to the moving
system, and hence lower the sensitivity, because they may introduce other
problems as a result. Lower sensitivity, for example, means more heat in
the coil for the same SPL, and can lead to various problems. Ferrofluids
can be beneficial in some cases by damping the rocking modes. On rare
occasions, double outer suspensions are used. A cross-section of such a
construction is shown in Figure 2.20. The choice of material for surrounds
can be quite an arduous task in the mid frequencies because the ideal
damping properties and compliance (the reciprocal of stiffness) may be
conflicting for frequencies two or three octaves apart, yet which must
all be radiated by the same diaphragm. At low mid frequencies, where
the diaphragm excursion may still be considerable, a cone driver may
need to be in a separate enclosure with at least half a litre of air. Dome
diaphragms are no different, but the magnetic assembly is an obstruction
to the air that is trapped behind the diaphragm, and which tends to push
up the resonant frequency. The hollow cavity between the diaphragm and
the magnet centre pole, clearly visible in Figure 2.20, is often filled with
absorbent material to reduce the cavity resonances. However, if this cavity
is too small, it can create problems by way of excessive back-pressure on
the diaphragm. Relieving the back pressure may require quite complex
boring of the magnetic system if resonances in the tubes and cavities are
to be kept out of the working range of the drivers. At high frequencies,
these problems are less complex because low resonance frequencies are
not required, so neither are such large air cavities required.
Dome tweeters have become very widespread in use, and now probably
account for the majority of high frequency drivers. Composite diaphragms
are also not uncommon, such as polyester bonded to PVC. Unfortunately,
dome tweeters tend to be rather low in sensitivity. This in some ways is
ironic, because one of the driving forces behind the development of domes
was to overcome the thermal failure problems due to the very small coil
surface area in small cone loudspeakers when used at high SPLs. The lower
Figure 2.20 Sectional view of an ATC soft-dome driver showing the double suspension which
helps to eliminate rocking motion
Diversity of design 45
sensitivity of an equivalent dome driver needs more power to drive it, and
hence produces more heat. Nevertheless, in many cases, the balance is still
in favour of the dome.
2.3 Compression drivers
Compression drivers are almost always used with horns, except in some
rare cases where their internal throats are sufficient to act as horns for
very high frequency use. Essentially, the diaphragm, coil and surround
assemblies of compression drivers are rather similar to those of dome
drivers. The principle difference lies in the way in which the diaphragm
couples to the outside air. In the case of the compression driver, the acoustic
radiation passes through a restricted aperture, the ratio of its area to the
area of the diaphragm being known as the compression ratio. This puts a
highly resistive air load on the diaphragm, which is then passed through a
horn of roughly exponential flare rate which prevents the air from moving
out of the way of the gradually expanding radiated sound wave. Figure 2.21
shows the cross-section of a typical compression driver, and due to the very
resistive load, electro-acoustic efficiencies of up to 50% can be achieved.
This means that for every watt of electrical input, only half a watt will be
dissipated as heat, and the other half a watt will be radiated as sound. It
is thus not unusual for mid and high frequency compression driver/horn
combinations to reach sensitivities of over 110 dB SPL for one watt input
at one metre distance. Domes, on the other hand, can rarely convert more
than 5% of the electrical input into radiated sound, so the other 95%
serves only to heat up the voice coil.
Horns are often shunned by many people who have not heard the
best examples. Much of this negative attitude has arisen from the days
when studio loudspeakers using compression drivers and horns were virtual transplants from the world of sound reinforcement and public address,
and once a bad reputation sticks it can be very difficult to lose. To far too
many people, because they have heard some bad horns, all horns must be
bad. This is the absolute opposite to the general perception of soft dome
mid-range drivers, where many people have heard some excellent ones
and thus think that they all must be excellent. It is sometimes difficult
to understand human reactions to these situations. In neither case is the
point of view either logical or correct. It is also worth noting how so many
people who state that they do not like horn loudspeakers in the mid range
will also say how they like the classic Tannoy Dual Concentric loudspeakers (shown cross-section in Figure 8.7) which, above 1 kHz, are exactly no
more and no less than compression drivers and horns.
One problem which does always plague compression drivers is that the
sound pressure levels within their throats can reach levels where the air
itself cannot linearly propagate sound waves. Air at these SPLs does not
compress and rarefy to the same degree under the same applied force
in each direction, and so gives rise to harmonic distortion. However, at
recording studio SPLs, which are way below live sound and cinema SPLs
because of the much closer listening distances, air overload often does
not become a problem until levels where direct radiating loudspeakers are
46 Loudspeakers
a)
Magnet
Moving mass, MMS
(diaphragm plus
voice coil)
Magnetic gap
(flux density B)
Pole piece
Phasing plug
Driver
exit
Compliance, C
Voice coil (length, l,
in metres; resistance,
RE, in ohms)
b)
Top
plate
Projected area of
phasing plug, SD, in
square metres
Area of annular slits
on phasing plug, ST,
in square metres
ST
= 0.1
SD
(Data courtesy of JBL inc.)
Figure 2.21 A high frequency compression driver (Data courtesy of JBL Inc). a) Section
view of a JBL high-frequency compression driver. b) Plan view of the diaphragm side of the
phasing plug
Diversity of design 47
suffering from mechanical and thermal non-linearities of their own. When
a compression driver made from 5 kg of metal is dissipating half a watt of
heat and producing 100 dB SPL for the people behind the mixing console,
thermal problems absolutely do not exist, and neither do mechanical stress
problems because the diaphragms are moving over such short distances.
Non-linear distortions can remain remarkably low, and transient attack
can be second to none. The problems with compression driver/horn combinations usually arise when designers fail to respect the physical realities
of how to couple the horn to the air, but that will be discussed further
in Chapter 4. High sensitivity loudspeakers, in general, also enjoy another
benefit in that the lower current in the voice coil for any given output SPL
gives rise to much less disturbance of the static magnetic field in the gap,
and thus avoid some intermodulation distortion products that are largely
unavoidable in less sensitive drive systems when passing high currents
through their voice coils.
Unfortunately, good compression drivers are not cheap to manufacture,
because they require precision, low tolerance engineering. It is therefore futile judging compression drivers in general by listening to cheap
examples. Tolerances of less than 50 micrometres are not unusual in
manufacturing specifications, and the magnetic flux density required in the
gap can be so high that special materials may be needed which are difficult
to cut and need heat treatment afterwards. Diaphragms also need to be
made to very high standards of uniformity whilst often only being about
50 micrometres in thickness. Some of the finest diaphragms are made out
of beryllium, because of its enormous strength-to-weight ratio, but its melting point of 1600 degrees C is too high to be accurately moulded in any
practicable manner, and rigidity is such that it would shatter like glass if
stamped to shape in a press. Some diaphragms are therefore made by a
time-consuming and laborious in-vacuo vapour deposition process which
is definitely not suited to mass production and is obviously expensive, but
2 inch (50 mm) diameter diaphragms can be made in this manner weighing
less than 0.15 grammes, and with frequency responses from 500 Hz to well
over 20 kHz.
In order to avoid phase cancellations at high frequencies in compression
drivers, a phasing plug is usually incorporated which guides the pressure
from different parts of the diaphragm down a series of tubes or concentric
slits (as can be seen in Figure 2.21), in order to bring a phase-coherent
wavefront to the driver exit, even at the highest frequencies of use. Alternatively, for very high frequency horns used largely only above about 5 kHz,
ring diaphragms may be used, as shown in Figure 2.22. These drivers also
usually incorporate a short exponential horn as a part of the driver itself,
and hence require no external horn. The diaphragms are clamped at the
outer and inner edges, and radiate into a ring-shaped aperture which gradually flares into a single exit by means of some sort of central ‘nose’. The
sensitivities of these devices range up to about 108 dB SPL for 1 watt input
at one metre distance. With a typical power handling capacity of 40 watts,
they are virtually indestructible in recording studio or domestic playback
use when operating only above about 7 kHz.
Compression drivers tend to work best from about 500 Hz upwards.
Below that frequency they can be used, but the horns required to couple
48 Loudspeakers
a)
b)
Figure 2.22 Ring diaphragm drivers. a) Section view of a JBL high-frequency compression
driver employing a centrally and peripherally clamped ring diaphragm (Drawing courtesy of
JBL Inc). b) Photograph of a ring diaphragm
them optimally to the outside air tend to become impractically large. The
horn shown in Figure 8.2(a) uses a 4 inch (100 mm) diaphragm driving
into a 2 inch (50 mm) throat, and is used from around 300 Hz to 20 kHz.
This is an exceptionally wide frequency range, although stress loads on the
diaphragms can be high at high SPLs. The designer, Shozo Kinoshita, cites
smooth directivity and lack of crossover points in the sensitive range of
hearing to be great benefits. Certainly the subjective impression from the
loudspeakers is one of great low level detail and a rapid transient response
which is effortless even at high levels.
One of the principal differences between the design of compression
drivers and dome loudspeakers is that a soft diaphragm is not an option
for compression devices. The diaphragms must be light and they must be
rigid if high sensitivity and low distortion are required. The rear cavities in
compression drivers are small, and the space between the diaphragm and the
phasing plug is so small that any flexing of the diaphragm would be likely
to make contact with the plug. Leaving more space between the diaphragm
and the phasing plug would lead to a loss of sensitivity at high frequencies.
More will be said about horn/driver applications in Chapter 4, because
many of the relevant points relate more to the horns than they do to the
driver.
2.4 Ribbon loudspeakers
The origin of the ribbon loudspeaker actually predates the moving coil
cone loudspeaker, with Schottky and Gerlack filing their patent two years
before the moving coil loudspeaker patent application. However, in practice it was rather disastrous, with a response of about two octaves between
Diversity of design 49
250 Hz and 1000 Hz. Eight years later, Olson and Massa made use of
the concept when they reversed it and turned it into a ribbon microphone. Nevertheless, the concept of a ‘current sheet’ had emerged, with
the diaphragm being suspended between the extended poles of a magnet system, and with the diaphragm itself passing the current. The idea is
shown graphically in Figure 2.23. Stanley Kelly patented a much superior
device in the 1950s, and, in his own words; “The ideal radiator is one which
a)
Current
I
S
N
Direction
of motion
Magnetic
field
B
F
b)
Terminal
Clamps
Powerful
magnet
poles
S
N
Terminal
Pleated metal foil
or metallised film
Axis of
motion
Figure 2.23 The ribbon driver. a) The basic concept of a ribbon driver. The current flowing
through the diaphragm reacts with the static magnetic field between the north (N) and south
(S) poles, and gives rise to a force, and hence a movement of the diaphragm in the direction
shown. b) A more practical realisation
50 Loudspeakers
a) vibrates in phase over its whole surface, b) has a mass comparable to
the air load, and c) has only resonances which are outside the working
frequency band. In order to meet these requirements, the radiator must be
subject to a mechanical force equal in amplitude and phase over its whole
surface. There are only two commercial systems which meet this requirement, viz, the constant-charge electrostatic and the ribbon electromagnetic
loudspeakers”.3
In practice, the ribbon is corrugated to give it more rigidity. In order
to avoid giving rise to resonances in its frequency band of operation it is
supported at each end but it is not stretched. The support of the ribbon
in the gaps is normally by means of elastomers and silicone rubber. As
a current flows through the diaphragm, the corresponding magnetic field
interacts with the static magnetic field from the magnets parallel to the
plane of the ribbon. This generates a force at right angles to the plane of
both the magnetic field and the ribbon, which moves the ribbon back and
forth, but parallel to the direction of the magnets. To maintain adequate
efficiency, the mass and electrical resistance must be kept as low as possible,
the latter being typically as low as 0.2 ohms and requiring an impedance
matching transformer in order to be useable with normal amplifiers. The
low impedances also imply high currents, so a conflict can arise between
the thickness of the diaphragm being low enough to keep the weight
down but high enough to keep the electrical resistance down, otherwise
the diaphragm might melt with the signal current. The classic Decca/Kelly
‘London’ ribbon loudspeaker had a horn attached to it, had a sensitivity of
92 dB SPL for 1 watt at 1 metre distance, and covered a frequency range
from 1 to 30 kHz with a power handling of 25 watts. Sonically, it was widely
appreciated.
Modern technical advances have led to printed circuit current sheets,
with the copper tracks on polyimide sheets of around 12 micrometres
thickness. The sheets can be made with overlapping copper tracks on
each surface, thus allowing the whole sheet area to be conductive. In conventional ribbons, however, the diaphragm material is usually aluminium,
because it has the best compromise between resistance and mass. In recent
years, the American company SLS Loudspeakers has made a big feature of
the use of ribbon loudspeakers beyond about 2 kHz. Ribbons, traditionally
have been delicate, and difficult to manufacture, but sonically they have
always had many friends.
2.5 Heil air-motion transformers
These devices often get mistaken for ribbon loudspeakers when people see
the folded diaphragms set in short horns, but they are definitely not ribbon
loudspeakers. A ribbon radiates sound by the whole diaphragm moving
backwards and forwards in a uniform manner, with the pleats never changing their angles. The air-motion transformer, quite differently, moves its
diaphragm in a concertina movement, drawing the air into the folds as
they expand, and expelling the air as they contract. The German company
A.D.A.M Audio have recently featured this technology rather in the way
that SLS have made big use of ribbons. The air motion transformer was
Diversity of design 51
designed by Dr Oskar Heil and its general outline is shown in Figure 2.24.
The current flows through a flat conducting track which is bonded to the
diaphragm, and which is folded such that the conductive strip lies parallel
to itself on the adjacent fold. When the current flows in one direction
through the entire circuit, it travels in different directions in the conductors on adjacent folds, and the magnetic field is either attracted to or
repelled from the nearby permanent magnets. When the current in the circuit reverses, the folds which were opened are then closed, and vice versa.
It is called an air motion transformer because there is a ratio of about four
to one between the air particle velocity in and out of the folds relative to
the velocity of movement of the pleated diaphragm. The magnet structures
need to be very large because the entire pleated diaphragm must fit in the
gap between the poles. The diaphragms are made from plastics such as
p.t.f.e. or polyethylene, which have good damping. Current units can work
from about 500 Hz to 20 kHz. Some models have been shown to produce
quite high levels of second harmonic distortion above about 5 kHz, but the
subjective audibility of this does not seem to be significant as the distortion products are all above 10 kHz and about 30 dB down relative to the
signal.
2.6 Distributed mode loudspeakers
These are the flat panels developed under licences from NXT and its
subsidiary New Transducers Ltd in the UK. The principal patent is held
by the British Ministry of Defence, on whose behalf Dr Ken Heron was
not actually trying to develop a loudspeaker at all – he was trying to build
lighter helicopters and stumbled upon an aluminium honeycomb panel that
radiated sound quite efficiently.
At first glance, the concept of a distributed mode loudspeaker (DML)
seems to be a total contradiction. It is a mess of resonances, when, in almost
all other aspects of loudspeaker design diaphragm, resonances are taboo.
The drive points where the electromagnetic exciters couple to the panel are
chosen so that they couple to as many of the vibrational modes as possible,
in order to excite the panel in the most uniform manner. The panels which
are currently used are typically made from resin impregnated glass-fibre
sheets bonded to a 3 mm honeycomb core of ‘Nomex’ - a polyamide which
is often used to make loudspeaker voice-coil formers. The panels are not
driven by a voice coil attached to the panel which is then connected to the
same frame/ chassis as the magnet, but rather the lightweight panel and coil
react against the mass of a much heavier, freely suspended magnet. Panels
are commonly excited by two or four coils, to more evenly distribute the
drive force. An example of a commercial panel is shown in Figure 2.25.
As the name ‘distributed mode loudspeaker’ suggests, they radiate all
frequencies from all parts of the panel, and so are naturally diffuse sources.
As such, they can work well in both studios and domestic circumstances
as the rear channels of a surround system, where they can create excellent
ambient diffusion effects. Their sonic colouration, though not unpleasant,
tends to render them inappropriate as main front channels where serious
listening is the goal, but their performance on the surround channels can
52 Loudspeakers
a)
b)
Magnetic flux
path
Current
flow
Vane
motion
S
S
N
N
Vanes (vertical
supports not shown)
c)
Figure 2.24 The Heil air-motion transformer. a) Perspective view of the basic concept.
b) Polarity changes in the conductors cause the opening and closing of alternating folds,
drawing in and expelling air on alternate half-cycles. c) A full-range loudspeaker system using
Heil air-motion transformers for the mid and high frequencies in a symmetrical, D’Appolito
layout – an A.D.A.M. S7
Diversity of design 53
Figure 2.25 A distributed-mode loudspeaker (DML)
be very involving, and numerous professional installations have used them
in this role. It is also interesting to note that the radiation from both sides
of the panel (if the rear is not enclosed) couples to the room neither in
an omnidirectional way nor as a figure-of-eight pattern (or dipole) like
electrostatic panel loudspeakers, but as something more akin to a bi-pole,
where the radiation from each side is only partially correlated. As such, and
if spaced away from a reflective wall, they can fill a room with reflexions
which have very little tendency towards showing typical summation and
cancellation effects (peaks and dips in the response) in different places
in the room. This characteristic can add still further to the beneficial way
that they can be used for ambience channels, where their inherent sonic
colouration appears to be little disadvantage.
A constant problem for DML loudspeakers has been the lack of low
frequency output, but designs are now emerging, such as the Fane Minipro,
which extend reasonably well down to 60 Hz. For surround use this is often
quite adequate, especially since many of these systems will be used with
bass management systems which will pass the low frequencies to a separate
(sub-) woofer. Panels with dimensions of about 40 cm × 60 cm are sufficient
for such purposes, but smaller panels suffer from much higher roll-off
frequencies. The low frequency response can be extended by mounting
the panels on a shallow, absorbent-lined box, of about 10 cm depth, but
care must be taken to avoid over-filling the box with absorbent material
or the damping on the rear of the panel can become too great. When the
open-backed panels are hung against walls they should be hung at an angle,
in order to prevent resonances in the parallel cavity formed between the
panels and the wall. As the general radiation directivity is very broad at all
frequencies, as shown in Figure 2.26(a), it is not necessary to point the panel
at a normal to the listening area. From almost whatever angle a panel is
54 Loudspeakers
90
100
120
60
90
80
30
50
70
60
180
0
50
330
210
240
300
220 Hz
1.2 kHz
6 kHz
17 kHz
270
4
2
relative pressure (dB)
0
–2
Fall-off of panel
–4
–6
Fall-off of 6″ cone
–8
–10
–12
0
0.5
1
1.5
2
2.5
3
3.5
distance from speaker (m)
Figure 2.26 Radiation characteristics from a typical DML. a) DML polar response at 220 Hz,
1.2 kHz, 6 kHz and 17 kHz. b) Computed comparison of loudness with distance – a distributed
mode panel versus a 6 inch (150 mm) piston. (From data published by NXT)
Diversity of design 55
radiating, and no matter where it is in a room, it will excite the whole room
with its full frequency range. Only from a position in line with the panel
edge is there a region of a few degrees where low frequency cancellation
takes place. The high frequencies radiate in an almost omnidirectional
manner, though from a spacially diffuse source.
As a result of the diffuse nature of the radiation, the fall-off of SPL with
distance is initially less than from a conventional loudspeaker, as shown in
Figure 2.26(b). It is more typical of larger, planar radiators, as discussed
in Sections 2.8 and 2.9. This can also be a benefit when filling a room with
ambient sounds, because the left and right signals, from positions more
or less laterally alongside the listeners, are more evenly distributed across
the room, even when the room acoustics are relatively dead. The coupling
to the room modes (see Chapter 7 if necessary) is also accomplished in a
different manner to the way in which conventional radiators couple with
modes. This again has been shown to give rise to fewer peaks and dips
in the room. When all the characteristics are taken together, the DMLs
do offer some interesting opportunities for surround applications. In fact,
the low frequency response can be noticeably better if panels larger than
those referred to above are used, but very large flat panels tend to become
unwieldy and can introduce resonance and reflexion problems into the
room when used in conjunction with other sources.
2.6.1 Panel/piston combinations
Since the mid 1990s, various efforts have been made to develop combinations of DMLs and conventional loudspeakers in such manners as to
take advantage of their uncorrelated and correlated radiation characteristics respectively. The thinking behind these ideas is that in live music
situations the direct propagation from the instruments to the ears tends
to be highly correlated, whilst the reflected energy from walls, ceilings,
floors and other hard surfaces tends towards being uncorrelated. In good
concert halls it has been found that the ones with low levels of inter-aural
cross-correlation tend to produce the generally most desirable sensations
of spaciousness. In domestic situations, the reflexions from walls do not
tend to be as diffuse and uncorrelated as in good concert halls, and their
frequency response is inevitably affected by the directivity characteristics
of the loudspeakers. To help to combat these deficiencies, the concept of
creating a sensation of diffuse reflexions has been pursued by the use of
relatively diffuse sources in combination with a conventional stereo pair
of loudspeakers. The relative level of the two types of sources can be
adjusted to taste.
The KEF company in the UK has patented a concept of using DMLs
behind conventional loudspeakers with the axes of the DMLs at right
angles to the axes of the conventional loudspeakers. The conventional
loudspeakers generally point towards the listeners, whilst the DMLs work
more omnidirectionally (although with their weak lateral nulls towards the
listening position) in an attempt to excite the rooms with diffuse reflexions
from the surround channel(s) of multichannel recordings.
Another system, marketed under the trade name of Layered Sound, was
patented by Dr Shelley Katz, a Canadian pianist, who initially researched
56 Loudspeakers
the concept as a means to make electric pianos sound less ‘stiff’ and
more acoustic. This technology was licensed for research purposes to the
Japanese company Korg. In the domestic reproduction or sound reinforcement formats, the panels are placed closely, above or behind the
conventional loudspeakers, but usually with the axes parallel to each other,
and not necessarily at 90 degrees as with KEF systems. The panels in this
system are fed with the same signal as the conventional loudspeakers, and
can also fed via a delay, with the delay time and the relative SPLs from
the different sources being used to control the overall effect.
By definition, such systems are not high-fidelity in the classical sense,
because they seek to introduce artefacts which are not in the original drive
signals. Nevertheless, that overall sense of realism which they can help to
generate may be considered in many cases to be highly faithful to the sensations of the performance spaces or the wishes of the recording personnel
or musicians. Proponents claim that as the current recording processes
via conventional microphones and the reproduction via conventional loudspeakers are still limited and compromised by the inherent short-falls of
their performance, then piston/panel combinations may be able to realistically add, globally, more than is lost in conventional reproduction, and so
can be considered to be more than making up for those short-falls. However, all assessments of these types of loudspeaker systems currently need
to be made subjectively, because there are still no measurement systems
which can reliably define the performances of such combined systems in
any meaningful manner.
Therefore, whilst technical accuracy in terms of conventional reproduction might be compromised, the developers of such combined systems can
reasonably claim that the perceptual fidelity, in terms of overall realism,
may be superior, at least on certain types of music, to reproduction on
systems with more measurable fidelity in the conventional sense. Whilst it
would seem to be unwise to use the combined systems for music recording
quality monitoring, the beneficial effects of Layered Sound for electric
piano amplification seems to be established. Of course, if recordings were
being specially made for reproduction on these composite systems or their
derivatives, then the monitoring of the recordings via such systems may
also be justified. Development of DMLs is still in progress, however, and
some new designs are already emerging with much less coloured responses
than have previously been achievable.
2.7 Beyond magnetics
All of the loudspeaker drive systems discussed in this chapter so far have
been electromagnetic transducers. One way or another, all of them have
employed the magnetic field generated by an alternating music signal current in a moveable conductor to react with a static magnetic field. The
force generated at right angles to the current and the static magnetic field
has then been applied to a diaphragm of some sort or other which has been
designed to move air and radiate sound. They are all, basically, variations
on the same theme. There are, however, various other means by which
loudspeakers can be made.
Diversity of design 57
2.7.1 Piezoelectric devices
There are certain materials which can be made to twist and bend when
electrical signals are applied to opposing surfaces, and, in general, there
is a useful proportional relationship between the applied voltage and the
degree of movement of the material. Such transducers have found use as
high frequency loudspeakers of very robust design, which have in turn
found use in guitar amplifiers and sound reinforcement systems where
conventional tweeters have been considered to be too fragile. Quartz,
Rochelle salt and some ceramics such as barium titanate have piezoelectric
properties, as do some high polymer plastics, such as polyvinylidene fluoride. Direct radiator and horn loaded piezoelectric radiators are available,
the horn-loaded Motorola device being quite widespread and has an axial
response within ±3 dB from 4 kHz to 20 kHz. Pioneer have also developed
a cylindrical piezo radiator. In these, a thin film of high polymer plastic
is made into a cylindrical shape which is then caused to pulsate with the
applied signal voltage. The response is respectably flat from 2 kHz to 20
kHz, with 360 horizontal radiation.
The piezoelectric units are rugged largely because they are selfprotecting. The impedance tends to rise as the frequency lowers, so driving
low frequency signals through them is difficult, even with no crossover.
They also, effectively, have nothing to burn out and nothing to go offcentre. Although they are very rarely encountered in loudspeakers used for
music monitoring, they can be found in domestic system as well as in music
amplification systems. The principles of their construction are shown in
Figure 2.27. Piezoelectric drivers tend to be mid-sensitivity devices, offering
the low 90s of decibels SPL for one watt (or at least its voltage equivalent –
2.83 volts – into their varying impedance) at one metre distance.
2.7.2 Ionic loudspeakers
It is unlikely that anybody will find these in use today because production ceased around 1968, but the concept is interesting. Radio frequency
interference and the production of irritating ozone were unwanted sideeffects that helped towards their demise, along with low output, but there
is widespread agreement that the sound of these devices was true high
fidelity. In ionic drivers a 27 MHz high voltage signal is fed to the electrodes of a quartz cell. A corona discharge results, giving off a blue light
as the air is ionised. When the radio frequency voltage is modulated by
an applied audio frequency signal the volume of ionised air will vary
and produce pressure fluctuations in the air. The frequency response was
given as 3 kHz to 50 kHz ± 2 dB, with only 0.5% distortion at 93 dB
SPL. Absolute peak output was around 98 dB SPL for the ‘Ionofane’ version. This was the cutting edge of high fidelity in the 1950s and ‘60s,
and is still good today, however, at higher SPLs, above about 96 dB at
1 metre, compression soon set in, seriously limiting the output. They
also cost 28 guineas each (just under 30 pounds, sterling) in the early
1960s, which was an entire month’s salary for many working people in
those days.
58 Loudspeakers
a)
Bending
element
Stiffness controlled
diaphragm
Applied
signal
voltage
Rigid
mounting
b)
Perspective view
Top view
Radiating foil outer layer
(metallised on both sides
for electrical connections)
Inner
damping
Polyurethane
damping foam
Signal
in
Perforated
support
Figure 2.27 Piezo-electric radiators. a) Section view of a typical piezo-electric HF radiator.
b) The Pioneer cylindrical piezo-electric driver – the High Polymer Radiator
2.8 Electrostatic loudspeakers
Just as dynamic microphones, such as ribbons and moving coils, have
their equivalent loudspeakers, and as piezoelectric loudspeakers relate to
crystal microphones, electrostatic loudspeakers are the counterparts to
condenser (capacitor) microphones. [Condenser is the old term, capacitor is the modern term, but the old terms often take root.] Within their
limitations, electrostatic loudspeakers can produce a sound quality which,
in microphone terms, we would only associated with the finest condenser
Diversity of design 59
a)
b)
Figure 2.28 Typical directivity pattern from a dipole radiator. a) Low to mid frequency
response. b) High frequency response
microphones. Sonically they can be astounding. The limitations are size,
(because they need large surface areas of diaphragm), relatively low maximum output SPL, and their figure-of-eight radiation pattern which does
not suit all room layouts. The typical radiation pattern from a full-range
electrostatic loudspeaker (ESL) is shown in Figure 2.28. The absorption
of the rear radiation is not a practicable solution unless the box is enormous because the air load would inhibit the movement of the extremely
light diaphragm, whose mass is critically chosen to match that of the free
air surrounding it. The loudspeakers therefore need to be placed away
from walls, and the nature of the walls close to the sides and behind them
need to be duly taken into account, acoustically, when the response in
front of the loudspeakers is being considered. Full-range electrostatic loudspeakers may therefore be less forgiving in terms of where they can be
placed.
These devices do not act as volume-velocity pumps like cone loudspeakers, but radiate as pressure gradient sources. This means that they do not
couple to the pressure anti-nodes of the room modes, but to the velocity anti-nodes, which are the pressure nodes (see Chapter 7). Other than
in anechoic chambers, this means that the optimal siting of electrostatic
loudspeakers will be different to that for moving coil loudspeakers. The
maximum SPL is limited (although 95 dB SPL should be no problem)
because at higher SPLs the polarising voltages would need to be so great
that highly specialised materials and techniques would need to be used in
the manufacture of the devices, and also because the air would reach its
own electrical breakdown limits. This is rather similar to the situation in
compression drivers, where the air itself begins to be the limiting factor at
higher SPLs. Air is not just something that you can do what you want with.
It has its own characteristic properties and it can impose its own limits on
what it can be made to do.
The basic concept of an ESL is shown in Figure 2.29. A polarising
voltage of around 3000 volts is applied to the diaphragm whilst the two,
outer, perforated electrodes, are grounded via resistances, and spaced away
by about 2 mm. The charge on the diaphragm keeps it centralised, in
60 Loudspeakers
a)
b)
Perforated
fixed electrodes
Moving diaphragm
Input signal
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
Polarizing
voltage
≈ kV
++++++++++++++++++++++++++++++++++++
Insulators
++++++++++++++++++++++++++++++++++++
Diaphragm
fixed
electrodes
Figure 2.29 The electrostatic radiator. a) The basic principle of operation of an electrostatic
loudspeaker. b) When the charge becomes opposite on the fixed electrodes the diaphragm
moves to take up a new equilibrium position. If the charge between the fixed electrodes
changes, the diaphragm position will change correspondingly
equilibrium, in the absence of signal. If, via an input transformer, a signal
voltage is applied across the electrodes, the equilibrium point will shift and
the diaphragm will move to chase it. The whole device operates on high
voltages and high impedances, so the signals have to be fed from the power
amplifiers via a step-up transformer, which itself requires careful design if
it is to pass all frequencies equally. Nevertheless, this type of loudspeaker
is largely a capacitor, so it still presents a predominantly capacitive load
to the amplifier, which therefore needs to be able to supply high currents
even when voltages are low, due to the phase angle difference between the
voltage and the current, (described previously in Section 1.6). The choice
of amplifier may therefore depend on its ability to supply current more
than its ability to supply power.
Diversity of design 61
Because of the inevitably small distances between the electrodes, necessary to maintain useful sensitivity with polarising voltages which will not
cause air breakdown, the distance that a low frequency diaphragm can
travel is severely limited. Therefore, the only way that the diaphragm can
move quantities of air sufficient to generate the required SPLs is to be
large. However, the diaphragm size of a single unit is limited by its ability
to maintain an even tension, and not to sag in places, so this also restricts
the SPL achievable by single units.
The large source area would, as with the DML, give a rather irregular
directivity at high frequencies, (but without the DMLs ability to produce
so many irregularities that they become almost regular again). Full range
ESLs therefore tend to be made as two or three-way devices, as with moving coil loudspeakers, using a much smaller radiating area for the higher
frequencies. The Quad ESL63 uses a series of concentric rings, as shown in
Figure 2.30, in order to mimic a point source situated some way behind the
diaphragm. These loudspeakers have also been made available with dipole
Figure 2.30 The Quad ESL 63 electrostatic loudspeaker with its concentric diaphragms. The
higher frequencies radiate only from the central sections
62 Loudspeakers
moving-coil sub-woofers mounted beneath them to extend their rather
limited low-frequency responses, or rather, their limited low-frequency
output capability due to the limited maximum excursion and size of the
diaphragms. Electrostatics are therefore not the ideal loudspeakers for
monitoring a solo bass drum in a large control room, but they do find use
in critical listening rooms and audiophile high fidelity applications, where
their natural sound and resolution of low-level detail are highly valued.
When heard in an anechoic room reproducing recordings of acoustic instruments recorded in the same room, and with the instruments alongside for
reference, their ability to mimic the original sound can be quite startling.
Granted, the anechoic response is not the be-all and end-all of loudspeaker
reproduction, but the general tendency is for anything which can work so
well in such circumstances to have a good start when transposed to other
circumstances. Figure 2.31 shows the step function response of a Quad
Electrostatic Loudspeaker: the attack of the signal is exemplary, and very
hard to beat with other loudspeakers. [The step function responses are
further discussed in Chapter 9.]
Although the electrostatic loudspeaker principle was experimented with
as early as the 1920s, it was not until 1957 that the first really viable
design was put into production. It took the advent of the concept of a
constant charge and the development of new plastic foils before it could
be fully realised. However, once all the pieces of the jig-saw were in place,
the progress was remarkable. A pair of ELSs from the 1950s can, even
50 years later, put many of the latest loudspeakers to shame in terms
of low colouration, low distortion, transient response, frequency response
flatness and, perhaps most of all, perceived sound quality. What Walker
and Williamson did when they developed the Quad ESL was to take a
step forwards to a degree that has rarely been equalled in the world of
sound reproduction, and this is especially so considering all the technical
difficulties which they had to overcome.
Whereas the moving coil loudspeaker exhibits non-linearities in its inner
suspension, outer suspension, magnetic flux disturbances, magnetic field
asymmetries and various other sources, the electrostatics more or less only
634
E– 03
V
INST
MGNY
– 32
E – 03
0
LOWER
CH2
TIME
25
(milliseconds)
Figure 2.31 Step function response of an electrostatic loudspeaker, showing the exemplary
attack (rise time)
Diversity of design 63
exhibit non-linearities due to very small asymmetries in construction, which
can be minimised by careful quality control. In general, the non-linear
distortion production by electrostatic loudspeakers is much lower than that
produced by most moving coil devices. The authors of this book have, for
decades, used full-range electrostatic loudspeakers as benchmarks against
which to judge other loudspeakers, both objectively and subjectively. This
is not to say that they cannot be surpassed on individual aspects of their
performance, but their global performance is hard to beat.
Occasionally, electrostatic mid-range drivers and/or high frequency
drivers can also be found in compound,electromagnetic/electrostatic
designs of domestic loudspeaker systems.
2.9 Electromagnetic planar loudspeakers
As if to rise to the electrostatic challenge, one of the electro-dynamic
(electromagnetic) responses was the planar loudspeaker. These use light,
thin, tensioned plastic film diaphragms which have voice coil circuits
printed on them, rather in the manner of a very thin printed circuit board.
The diaphragms are stretched over frames with many openings and a large
number of small magnets dispersed over their area. There is no attempt
to concentrate the flux in any area, but just to set up a field of fringe flux
in the vicinity of the magnets. In this way, a diaphragm is caused to move
by the reaction of the signal current in the printed tracks with the static
magnetic field, which results in the diaphragm being more or less uniformly
driven over its entire surface. As with large electrostatic diaphragms, they
must cross over at higher frequencies into drivers of smaller radiating area
if strange directivity problems are to be avoided. They do not have the
‘random’ distribution of high frequency sources as exhibited by the DMLs,
but neither do they tend to have as much colouration.
2.10 Summary
There are a considerable number of different ways to transform electrical
drive signals into sound waves, and no one system has all of the advantages
to itself. In fact, all the drive systems are electro-mechanico-acoustic transducers; that is, they must first convert the electrical signals into mechanical
forces which are then used to drive sound radiating diaphragms of some
sort or another. (The one exception perhaps, being the now defunct ionic
tweeter.) The necessary double conversion tends to involve a number of
non-linear processes, and it is largely the mechanical components which
are the main offenders. It is therefore unfortunate that we often refer
to loudspeakers as simply electro-acoustic transducers because it fails to
recognise the existence of the principal culprit for our problems.
At the limit, the air itself is non-linear, so when we try to reproduce loud
sounds from small sources that were originally produced by large sources,
local concentrations of high air pressures close to the small sources will
give rise to non-linearities, which our ears will recognise as not being the
real thing. The reason for describing this wide range of loudspeaker drive
64 Loudspeakers
unit concepts so early in the book (and there are other, less common ones)
is to establish the point that at the very heart of all loudspeaker systems
are imperfect components, and, as mentioned earlier, that the art of the
science of the designs is to find the best compromise for any individual
requirement.
References
1 Colloms, M., ‘High Performance Loudspeakers’, 5th Edition, John Wiley & Sons,
Chichester, UK (1997)
2 Briggs, G., ‘Loudspeakers, The Why and How of Good Reproduction’, Fourth
Edition, Wharfedale Wireless Works Ltd, Bradford, UK (1955)
3 Borwick, J., ‘Loudspeaker and Headphone Handbook’ Second Edition,
Chapter 2 (By Stanley Kelly), Focal Press, Oxford, UK (1994)
Bibliography
1 Chapter 3 of Reference 3, above, contains what is perhaps the definitive work
on electrostatic loudspeakers, written by the late Peter Baxandall. In the Third
Edition of the book, published in 2001, Peter Walker somewhat modified the
text. Either edition, in its entirety, is recommended reading for anybody wishing
to delve deeper into the world of loudspeakers and headphones.
2 The books mentioned in References 1 and 3 above
3 Eargle, J., ‘Loudspeaker Handbook’, Chapman and Hall, New York, USA and
London, UK (1997)
4 Borwick, J., ‘Loudspeaker and Headphone Handbook’, Third Edition, Focal
Press, Oxford, UK (2001)
Chapter 3
Loudspeaker cabinets
3.1 The concept of the infinite baffle
When the diaphragm of an open-framed driver moves forwards, the compression of the air at the face of the diaphragm is accompanied by a
rarefaction at the other side of the diaphragm, and the natural tendency is
for the pressure difference to equalise itself by a movement of air around
the sides of the driver. At frequencies whose wavelengths are large compared to the circumference of the diaphragm, the equalisation is almost
perfectly accomplished, and so almost no sound is radiated. It is therefore
necessary to discourage this pressure equalisation if low frequencies are
to be radiated. The simplest means of accomplishing this is to mount the
loudspeaker in a large, rigid board, or baffle, as shown in Figure 3.1. If
the board were to extend in all directions to infinity, it would be a true
infinite baffle. It would cause no change in the air loading on each side of
the diaphragm, it would exhibit no resonances, it could cause no diffraction, and, with a good quality driver (or drivers) would sound excellent.
Unfortunately, its great drawback is that it is a rather impractical concept.
The two practical realisations of this idea are the finite baffle, where a
baffle of perhaps a metre square is employed, or the so-called infinite baffle,
which is, in fact, a sealed box. The radiation pattern of the finite baffle is
shown in Figure 3.2(a). The cancellation around the sides of the extended
plane of the driver cause response nulls to the sides, in the direction of the
plane of the baffle, resulting in a three-dimensional figure-of-eight pattern
in free space. The low frequency cut-off is determined by the size of the
baffle. The final rate of low frequency roll-off is 18 dB per octave, but
some measures can affect the nature of the entry to the roll-off. Varying
the Q of the driver resonance, by mechanical and/or magnetic changes, can
yield response shapes such as those shown in Figure 3.2(b). By placing the
driver off-centre, the cut-off can be made more gradual due to the distance
from the driver to each edge of the baffle being different. Open baffles are
rarely used in recording studio control rooms because of the problems of
where to site them and how to control the rear radiation, but they find use
in listening rooms and domestic high-fidelity systems. In these instances the
baffles can be sited somewhat more flexibly than in an equipment-loaded
control room, and the loudspeaker and listener positions can usually be
found which give good results. Subjectively, open baffles tend to sound
very clean and, not surprisingly, open. They are largely free of resonances,
so their time-domain responses are limited only by the drivers and the
66 Loudspeakers
Figure 3.1 An open baffle of Wharfedale design from the 1950s. The front panel was a sandfilled plywood sandwich, to damp resonances. The upward-pointing tweeter was to generate
a more diffuse high-frequency response
a)
b)
10
Q=2
dB
0
–10
Q = 0.5
–20
–30
–40
10
100
1000
Frequency (Hz)
Figure 3.2 Directivity and roll-off of open baffles. a) Radiation pattern polar plot of an open,
finite baffle. b) Low frequency response roll-off of an open baffle, showing the effect of the
Q (degree of sharpness of resonance) of the driver. The final roll-off tends towards 18 dB per
octave below the driver resonance
rooms in which they are placed. The ways in which they couple to the
rooms will be discussed in Chapter 7.
When mounted on the floor, the solid surface below the open baffle
acts like an acoustic mirror, so a baffle of one square metre placed on the
floor behaves like a baffle of two square metres in free space. This enables
baffles of practical size to be useful down to frequencies of 40 Hz or below,
but the lack of anything other than atmospheric loading on the rear of the
diaphragms and poor efficiency of radiation may lead to over-excursion
problems with high sound pressure levels at low frequencies. The resonance
Loudspeaker cabinets 67
frequency of the driver on an open baffle will be that of its free-air resonance. Because the open baffle mounting does not push up the free air
resonance of the driver, and the back-pressures are not augmented by any
constraint of the air behind the diaphragm, lighter moving assemblies may
be used. Driver cooling is also something that poses no problem with open
baffles, so power compression problems are rarely encountered. The open
baffle, in the hi-fi world, still enjoys a devoted following of aficionados.
3.2 The sealed box
The practical realisation of an infinite baffle (the sealed box) is rarely
large enough to avoid significantly loading the rear of the loudspeaker,
so is best called what it really is, a sealed box. Just as open baffles tend
to sound ‘open’, sealed boxes often tend to sound ‘boxy’. However, this
need not be the case if the box and driver are of adequate size, wellmatched, and if sufficient attention is paid to the suppression of resonances
within the box. The constraint of the air within a sealed box causes it to
act like a spring, which reacts against the movement of the diaphragm in
either direction. This effectively stiffens the suspension of the drive unit,
and raises its resonant frequency. The smaller the box, the stiffer will be
the spring, so the higher will be the resonant frequency of the driver/box
system. As the system resonance defines the frequency at which the low
frequency roll-off will begin, then for any given driver the low frequency
response will become progressively more curtailed as the box size reduces.
The only way to counteract this tendency is to use drivers of lower free-air
resonance frequency, which means using a driver with a heavier moving
assembly or, to a lesser extent, a more compliant suspension, but both of
these characteristics have their drawbacks.
A heavier cone takes more energy to move it, so it will need more
amplifier power to drive it to produce the same SPL as a lighter cone.
A more compliant suspension will be much less rugged than a stiffer
suspension, and will tend to be much more easily damaged in the event
of an overload. What is more, a very loose, flexible suspension may not
be able to adequately resist the pressure changes inside the box at high
SPLs, and may physically deform, giving rise to non-linearities in its travel
and non-linear distortions in its radiation. This will all be discussed in
much more detail in Chapter 11, but suffice it to say here that a small
sealed box must suffer from either poor system sensitivity (due to its poor,
overall electro-acoustic conversion efficiency) or a low frequency roll-off
that begins well into the musical spectrum. The roll-off exhibits a rate
of 12 dB per octave below its frequency of resonance, but considerable
roll-off may begin well above this frequency, depending on the system
Q. Some typical roll-off curves are shown in Figure 3.3. Nevertheless, the
time responses (transient responses) of well-designed sealed boxes with
correctly matched drivers and adequate damping can be very accurate.
Largely for this reason, sealed boxes have a strong following, and large
sealed boxes can be the bases of excellent loudspeaker systems.
A sealed box system is said to be critically damped when its size and
the driver resonant frequency are matched such that the overall response
68 Loudspeakers
dB 120
118
116
114
112
110
108
106
104
102
100
98
96
94
92
90
F
10
E
D
20
C
B
30
A
50
70
100 Hz
200
300
500
(after
700
1k
Eargle1)
Figure 3.3 Typical low frequency roll-off behaviour of a sealed box loudspeaker, showing
the responses of the same driver in cabinets of six different volumes. All measurements in
free-field conditions
A, 7L. B, 14L. C, 28L. D, 56L. E, 112L. F, 224L
Loudspeaker free-air resonance 20 Hz
is already 6 dB down at the resonant frequency. With this alignment, the
transient response can be exemplary, with no perceptible ringing. The total
system QTC (or quality factor of resonance) is 0.5. The Butterworth ‘B2’
(maximally flat) alignment is very popular, with a QTC of 0.7. This exhibits
a system response which is 3 dB down at the resonant frequency, and
still has a transient response which is extremely well controlled. The low
frequency responses can be extended downwards with alignments where
the QTC is set at 1, or even up to 2, but as the Q increases, so does the
tendency for the transient response to become extended, and for audible
ringing or ‘boominess’ to become obtrusive. The outcome of these relationships is that if the low frequency −3 dB point is to be dropped to 30
Hz, and a fast, well-damped transient response is required at the same
time, then the box must be big. If high SPLs are required, then the only
solution to the compromise of a low resonance driver with an adequately
robust construction and a good sensitivity is that the driver must also
be big.
A 15 inch (380 mm) driver, of high quality, with a 20 Hz free air
resonance in a 500 litre enclosure can yield some very impressive bass.
However, ‘impressive’ in this context means full, flat, fast and low distortion – in other words, ‘accurate’. Unfortunately, many sealed boxes get
Loudspeaker cabinets 69
themselves a bad name by trying to use ‘boomy’ alignments in forlorn
efforts to keep the size down whilst seeking to extend the low frequency
response to frequencies that the box size cannot really support. The penalty
paid is in terms of low sensitivity and poor transient response. It must be
thoroughly understood that there is no clever computer program which
can solve this problem. The restrictions that we must accept are deeply
entrenched in the physical laws of the universe in which we live. They are
that fundamental!
Some manufacturers have tried to sacrifice system sensitivity by lowering the magnet flux in order to lower the system Q. There is a strong
‘amplifier power in cheap’ lobby, who believe that lower efficiency systems
can exhibit higher Qs, and hence can be extended in their low frequency
range. What they often seem to fail to realise is that a heavier current in the
voice coil and a lower power magnet will drastically alter the ratio of the
fixed magnetic field to the variable magnet field. The much higher variable
field due to the voice coil current can severely distort the position of the
flux lines of the weak, permanent magnet, and give rise to loss of low level
detail in the sound and increased levels of intermodulation distortion. This
highlights perhaps one of the worse aspects of the use of programmable
calculators or computers in the wrong hands – they can lead to good results
on paper, but they can give rise to unpleasant side-effects in practice.
Figure 3.4 gives a graphic illustration of the connection between system Q
(QTC ) and the transient response. The QTC is derived from the electrical,
magnetic, mechanical and acoustical properties of the total system – electro
1
1
Qtc = 0.50
Qtc = 1.3
0
pressure amplitude
pressure amplitude
0
1
Qtc = 0.71
0
1
1
Qtc = 1.6
0
1
Qtc = 01.0
Qtc = 2.0
0
0
0
1
2
t /2πT
time
3
4
0
1
2
3
4
t /2πT
time
(after small2)
Figure 3.4 Transient response of a sealed box enclosure as a function of the total system
Q (QTC ). As the QTC increases, the transient decay time also increases
70 Loudspeakers
magnetic damping, mechanical stiffness and air loading. Note that as the
QTC increases, the transient response becomes longer. This is perfectly
logical because the transient response becomes more resonant as the system QTC becomes more resonant. The amplitude response is boosted and
extended downwards by keeping the energy responding for a longer time,
and not by instantaneously boosting the level. As stated before, in order
to boost the level, and nothing else, a bigger box and driver are needed.
Small sealed boxes with relatively high rates of roll-off can be mounted
near to room boundaries, where the constraint of their radiation angle
can boost their low frequency output, acoustically, without suffering time
penalties (boundary effects are discussed in Chapter 7), but on pedestals in
the centre of a room, the low frequencies from small sealed boxes will be
found to be either weak, resonant or both. On the metre bridge of a solidlybuilt mixing console they can also receive some low frequency support, but
colouration problems due to the reflective surface being between the small
loudspeaker and the listening position can be a problem. This ‘acoustic
mirror’ concept was discussed in the previous section, but when applied
to floor standing open baffles, the mid and high frequency drive units
are usually mounted well clear of the floor. When a small sealed box is
placed on top of a mixing console, the sources of mid-range and high
frequencies are inevitably close to the reflecting surface, so comb-filtering
of the response is the likely result.
To put things into proportion with respect to size, a cabinet which is
3 dB down with a given low frequency driver at 80 Hz would need to be
4 times larger if it were to be 3 dB down at 40 Hz and 16 times larger to be
3 dB down at 20 Hz, so sealed box sizes do tend to get larger very quickly
if lower roll-of frequencies are required.
One advantage of sealed box systems is that they are relatively selfprotecting in terms of excessive cone excursions. Compared to the open
baffle, which offers almost no protection, an input signal below the resonant
frequency of a sealed box system will tend to drive the cone at a constant
excursion for any given input level, independent of frequency. (See Note 1
at end of chapter.) The thermal overload of the coil is therefore the biggest
risk factor in terms of driver integrity at input level extremes.
The lining materials in the boxes also have an effect on the low frequency response. Although they are primarily intended to prevent cabinet
resonances at mid frequencies, which may colour the sound by passing to
the outside via a relatively acoustically transparent cone, the lining materials can also affect the low frequency damping and total system Q. They
should not be too tightly packed, or effectively they will be more or less
solid and will reduce the enclosure volume. Neither should they be able
to move en masse, or they can introduce non-linear distortion due to their
somewhat erratic movement. Given just the right quantity, however, they
can not only reduce box resonances but can also make the boxes appear to
be up to around 20% acoustically bigger due to their ability to act as heat
sinks and slow down the speed of sound by absorbing heat on compression
half cycles and releasing it on rarefaction half cycles. The tortuosity of
the path through the pores or fibres also gives rise to sound absorption.
The density and quantity of the absorbent material inside a sealed box
Loudspeaker cabinets 71
are therefore chosen for the parts that they play in the air loading and
damping calculations for the whole system.
3.2.1 Acoustic suspensions
Developed in the 1950s by Edgar Villchur, in the USA. The principal is
to use a very low resonance loudspeaker in a small sealed box. The air in
the box may push up the resonance by an octave, or more, and is the predominant restoring force for centralising the diaphragm, because the low
resonance suspension is very weak. Generally, although an acoustic suspension system is a sealed box, the specialised term is normally only used when
the ratio of the cabinet (air) compliance to the driver’s compliance exceeds
a factor of about 4 to 11 . In the late ‘50s and early ‘60s, the company Acoustic Research enjoyed very great success with these designs by making huge
improvements in the low frequency fidelity of small loudspeaker systems.
3.3 Reflex enclosures
Also known as ported enclosures, vented boxes or phase inverters, reflex
enclosures use openings, or ports, to tune the cabinet resonance to a desired
frequency. Effectively, the air in the port, which may be a simple hole
or a tube, acts as a mass which resonates with the spring created by the
air inside the cabinet. In Figure 3.5, a mass is shown suspended below a
spring. Almost everybody will intuitively know what would happen if they
were to pull down on the weight and then let go – the weight would spring
back and the system would go into oscillation until the energy was finally
Figure 3.5 A mass/spring system. A mass suspended beneath a spring. It is easy to imagine
how pulling down on the weight and releasing it would set up an oscillation due to the
mass-spring interaction
72 Loudspeakers
dissipated. Adding more weight would cause the oscillation to slow down,
as would using a weaker spring. Therefore:
more weight
weaker spring
)
)
less weight
stronger spring
)
slower oscillation (lower frequency)
faster oscillation (higher frequency)
In the case of a reflex cabinet, a bigger box provides a weaker spring,
because the enclosed air is compressed or rarefied proportionately less
than in a small box for any given diaphragm displacement. For any given
diameter of hole (port), extending it with a tube will lower the resonant
frequency because a greater mass of air will be trapped within it. For
any given cabinet volume and mass of air in the port, changing the area
of the port will also change the resonant frequency. Increasing the area
will increase the resonant frequency. This is because there is more surface
area in contact with the air-spring, so more force acts upon the air mass,
effectively stiffening the spring. There are therefore three variables in the
equation, the cabinet volume, the length of the port, and the area of the
port – the latter two defining the volume of air in the port, and hence its
mass. Air weighs about 1.2 kg per cubic metre, and thus about 1.2 grams
per litre.
The cabinet tuning frequency can therefore be calculated approximately
from either of the two following equations, the first in imperial measure
and the second in metric units.
fv 2 =
2700A
√
VL + A
(3.1)
where:
fv = resonant frequency of box (Hz)
A = area of port in square inches
V = volume of box in cubic feet
L = length of port in inches
OR
1
f=
×
2
C2 A
V Le
where:
f = resonant frequency of box (Hz)
c = speed of sound in air − 340 m/s
A = area of port in square metres
V = volume of box in cubic metres
Le = effective length of port in metres
(3.2)
Loudspeaker cabinets 73
Note: Le allows for an end correction. The effective length of a port tube
is, in reality, somewhat longer than the physical length, but for many
calculations the actual, physical length can be used.
The formulae are not precise, because there are always variables such as
the quantity of air displaced by the drive units themselves, the air displaced
by the port tubes, the air displaced by internal bracing, and the effect of
the absorbent material inside the enclosure. Nevertheless, the formulae
give good working approximations or starting points for calculations. Of
course, the cabinet volume is calculated from the interior dimensions of
the cabinet, not the exterior dimensions.
In practice, when the frequency of resonance of the driver in the cabinet
is just above the resonant frequency of the box, the port resonance gives
rise to a high load on the diaphragm and greatly reduces the diaphragm
excursion. In this way, the ported cabinet can protect the driver from excessive travel while still maintaining a flat response. Below this frequency,
the driver output falls, but the port, itself, begins to radiate, thus extending downwards the frequency response. At still lower frequencies the port
and loudspeaker outputs occur in opposite polarity, so the response falls
off rapidly at 24 dB per octave. Moreover, below the port resonance, air
simply pumps in and out of the port under the influence of the driver. At
these frequencies, the cabinet is just a box with a big air leak, and it can
provide no loading on the driver diaphragm, which then behaves as if it
were in an open baffle with no air loading protection, so over-excursions
are easy to encounter in reflex enclosures unless the low frequency drive
signal is filtered, or has no natural content, below the resonant frequency
of the box.
A comparison of the performance of two different low frequency drivers
in an open baffle, a sealed box, and a reflex enclosure is shown in Figure 3.6.
In practice, a driver would be specifically designed for each type of loading,
because the different cabinets or baffles match more optimally with drivers
of specific QTC values. The QTS , which can be found in many formulae
and reference texts, is the sum of the QMS and the QES , which are the
mechanical and electrical system quality factors (sharpness of resonance),
respectively. The higher the Q, in each case, the more highly tuned is the
resonance, as shown in Figure 3.7. For reference, the Q terms commonly
found in loudspeaker texts are as follows2 :
QMS is the mechanical system Q. It is the ratio of the electrical equivalent
of the frictional resistance of the moving parts of the driver to the reflected
motional reactance at the free-air resonance frequency of the driver.
QES is the electrical system Q, which is given by the ratio of the voice coil
DC resistance to the reflected motional reactance at the free-air resonance
frequency of the driver.
QTS is the parallel combination of the QMS and QES , and the equation
takes the same form as that for two, parallel, electrical resistors:
QTS =
QMS × QES
QMS + QES
QTC is the total system Q of the driver and the cabinet.
(3.3)
a)
10
0
0
–10
–10
–20
20
Sealed
0
–20
–10
–30
–30
–20
–40
–40
–30
10
100
1000
Reflex
10
dB
Baffle
dB
dB
10
10
100
Frequency (Hz)
10
1000
100
1000
Frequency (Hz)
Frequency (Hz)
b)
10
Baffle
10
Sealed
0
0
–10
–10
–10
–20
–20
–30
–30
–40
–40
10
100
Frequency (Hz)
1000
dB
0
dB
dB
10
Reflex
–20
–30
–40
10
100
Frequency (Hz)
1000
10
100
1000
Frequency (Hz)
Figure 3.6 a) Response of one driver mounted in an open baffle, a 50L sealed box, and a 50L reflex enclosure with the driver Q optimised for the open baffle
response. b) As in a), but with the driver Q optimised for the reflex enclosure. Note how as the driver is optimised for one type of loading, the response may
suffer with other types of loading
Loudspeaker cabinets 75
1
C4
0
0
1
2
3
4
pressure amplitude
pressure amplitude
a)
1
B4
0
0
1
3
2
f 3t
f3t
time
time
C4 – Chebychev, fourth-order alignment
QTC = 0.518
4
(after Small2)
B4 – Butterworth, fourth-order alignment
QTC = 0.383
b)
0
(dB)
C4
–10
B4
10
20 30 40 50 100
200
500
1k
(Hz)
Figure 3.7 a) Transient response of a reflex enclosure as a function of the total system Q (QTC ).
Compare with Figure 3.4. b) Pressure amplitude response of the C4 and B4 alignments. Note
how the response extension of the C4 alignment corresponds with an increase in the decay
time, as shown in a). Transient response is traded for response extension
The free-air resonant frequency of the drivers for reflex enclosures may
also need to be different to the optimum resonant frequencies for sealed
enclosures of similar size or covering a similar frequency range. The modern tendency is to tailor complete driver designs to given box sizes and
system concepts, and the programs now available for computer analysis are
very powerful and very accurate. However, careful listening tests are still
a sine qua non because concentration on the optimisation of one aspect of
driver design may unexpectedly change for the worse some other aspect of
performance that was not under such close scrutiny. Unfortunately, listening rooms are expensive to build and listening panels can be an expensive
luxury. Computer time on the other hand is cheap, and quick, and there
has developed a strong tendency to design systems ever more by computer
and ever less by careful listening.
76 Loudspeakers
3.4 Acoustic labyrinths
These are sometimes referred to as transmission lines, but at low frequencies they are usually not transmission lines. A true transmission line needs
a rear cavity, straight or folded, at least a quarter of a wavelength long.
At 30 Hz, with a wavelength of about 11 metres, the line would need to
be around 3 metres long, and lines of this length are rare indeed. A true
transmission line works by presenting the correct acoustic impedance at
the rear of a driver so that all the backwards radiation propagates away
from the driver, never to return. This can be achieved by loading the rear
of the driver with an infinitely long pipe (which is rather impractical) or by
some other system that absorbs all the sound energy. A finite length pipe
can therefore be made to operate as a transmission line if it contains sound
absorbing material strategically placed to give the correct, purely resistive
acoustic impedance, such as an anechoic wedge. However, in order to work
at low frequencies this pipe still needs to be very long, so some form of
low frequency tuning is often employed.
If, instead of an infinite pipe we think of an organ pipe, it would exhibit a
series of resonant frequencies determined by its length. If we attach it to the
rear of the driver and fold it round to the front, there will be interference
between the sound from the front of the driver and that from the open end
of the pipe. When the pipe is one quarter wavelength long, there will be a
high acoustic pressure at the rear of the driver and a high acoustic velocity
at the open end, which combines with a phase difference of 90 degrees with
the acoustic velocity from the front of the driver, and this provides a useful
boost in output. As the frequency is lowered, the output from the pipe
increases in phase difference with respect to the direct output from the
driver, and so tends towards cancelling the combined output. This yields a
24 dB per octave roll-off below the tuning frequency, which leads to transient problems not unlike those of a conventional reflex cabinet. A finite
length open pipe, which is what the vast majority of so-called transmission lines certainly are, is clearly not a transmission line, as it works on a
completely different principle and yields a different acoustic performance.
A typical cross-section of such a design is shown in Figure 3.8(a).
In order to tame the strong resonant behaviour exhibited by the open
pipe, absorbent material is introduced into the pipe to add damping. As
the amount of absorbent material is increased, the acoustic performance
tends towards that of a transmission line except at very low frequencies,
where there is insufficient absorption. A carefully lined, or filled, openended pipe may thus exhibit some of the properties of a transmission line,
but may also rely on the quarter wavelength resonance to supplement the
total low frequency sound output. Most commercial ‘transmission lines’
are therefore really something between the two extremes of a transmission
line and an open pipe, depending on the amount of absorption present at
any given frequency.
Some versions of ‘transmission lines’ are closed. In these designs the line
is made to be as absorbent as possible. In reality it is a sealed box, but it
differs from the sealed box in that there is no added air-spring effect, and
therefore it does not raise the free-air resonance of the driver.
Loudspeaker cabinets 77
a)
b)
x
y
y
y
y
Vent
2x
4x
Vent
y/ 2
y/4
y/4
Figure 3.8 Acoustic labyrinths. a) A parallel labyrinth. b) A tapered labyrinth – each time
the section of the labyrinth changes, the length (x doubles and the width (y) halves. The
entire labyrinth would be lined with absorbent material in both a) and b)
In practice, the low frequency ‘pipe’, whether straight or folded, must
not only be a quarter wavelength long at the lowest frequencies, but must
also be wide enough so as not to obstruct the rear radiation from the
driver. In some cabinets, as shown in Figure 3.8(b), the line narrows along
its length, each section doubling the length of the previous section and
halving its cross-section. Inevitably, in order to maintain close to ideal
working, transmission line enclosures need to be large, therefore a small,
low frequency transmission line tends to be a contradiction in terms. The
smaller cabinets at low frequencies may act as either sealed boxes or reflex
enclosures, dependent upon the density and distribution of the absorbent
material. The labyrinth enclosures with open-end terminations tend to act
like reflex enclosures in that the cone excursions are much reduced at
the resonant frequency of the enclosure tuning, which may result in lower
distortion than might be expected from an approximately equivalent sealed
box at similar SPLs.
One other interesting aspect of acoustic labyrinths is that the highly
resistive rear loading can actually lower the driver’s free-air resonance due
to the mass of air which acts directly on the cone, effectively making it
heavier when in movement.
78 Loudspeakers
Labyrinths/transmission-lines have their following, but many designers
feel that they are a complex way of achieving rather little. In lines which
almost totally lose the rear radiation, there is no out of phase output at low
frequencies, so they exhibit 12 dB per octave roll-offs like sealed boxes.
3.4.1 Modern transmission lines
In the early 1990s, the British company PMC (Professional Monitor Company) began manufacturing a range of ‘transmission line’ loudspeakers
which have since achieved considerable acclaim and commercial success.
The subject of what is and what is not a transmission line has been rather
controversial in recent years, so Peter Thomas, the principal design engineer and managing director was asked by the authors of this book to try to
clarify the matter, and he subsequently supplied the following paragraphs
of this section.
The birth of the modern transmission line speaker design came about
in 1965 with the publication of A R Bailey’s article in Wireless World,
“A Non-resonant Loudspeaker Enclosure Design”3 , detailing a working
transmission line. Radford Audio took up this innovative design and briefly
manufactured the first commercial transmission line loudspeaker. Shortly
thereafter John Wright of IMF Electronics designed a range of transmission line designs and made them popular through his refinement and
development of Bailey’s theory. Although acknowledged as the father of
the transmission line, Bailey’s work drew on the work on labyrinth design,
dating back as early as the 1930s. His design, however, differed significantly
in the way in which he filled the cabinet with absorbent materials. Bailey
hit upon the idea of absorbing all the energy generated by the bass unit
inside the cabinet, providing an inert platform for the drive unit to work
from. Unchecked, this energy produces spurious resonances in the cabinet
and its structure, adding distortion to the original signal.
The transmission line (TL) is the theoretical ideal and most complex
construction with which to load a moving coil drive unit. The most practical implementation is to fit a drive unit to the end of a long duct that is
open ended. In practice, the duct is folded inside a conventional shaped
cabinet with the open end of the duct usually appearing as a vent on the
front of the cabinet. There are many ways in which the duct can be folded,
and Figure 3.8 illustrates two typical forms. The line is often tapered in
cross-section to avoid parallel internal surfaces that encourage standing
waves. Depending upon the drive unit and quantity – and various physical
properties – of absorbent material, the amount of taper will be adjusted
during the design process to tune the duct to remove irregularities in its
response. The internal partitioning provides substantial bracing for the
entire structure, reducing cabinet flexing and colouration. The inside faces
of the duct or line are treated with an absorbent material to provide the correct termination with frequency to load the drive unit as a TL. A theoretically perfect TL would absorb all frequencies entering the line from the rear
of the drive unit, but remains theoretical as it would have to be infinitely
long. The physical constraints of the real world demand that the length
of the line must often be less than 4 meters before the cabinet becomes
too large for any practical applications, so not all the rear energy can be
Loudspeaker cabinets 79
absorbed by the line. In a realised TL, only the upper bass is TL loaded in
the true sense of the term (i.e. fully absorbed); the low bass is allowed to
freely radiate from the vent in the cabinet. The line therefore effectively
works as a low pass filter, another crossover point in fact, achieved acoustically by the line and its absorbent filling. Below this ‘crossover point’ the
low bass is loaded by the column of air formed by the length of the line.
The length is specified to reverse the phase of the rear output of the drive
unit as it exits the vent. This energy combines with the output of the bass
unit, extending its response and effectively creating a second driver.
Phase inversion is achieved by selecting a length of line that is equal
to the quarter wavelength of the target lowest frequency. The effect is
illustrated in Figure 3.9(a), which shows a hard boundary at one end (the
speaker) and the open-ended line vent at the other. The phase relationship
between the bass driver and vent is in phase in the pass band until the frequency approaches the quarter wavelength, when the relationship reaches
90 degrees as shown. However by this time the vent is producing most of
the output – as shown in Figure 3.9(b). Because the line is operating over
several octaves with the drive unit, cone excursion is reduced, providing
higher SPL’s and lower distortion levels compared with reflex and sealed
box designs.
a)
M
L
S
S
A
b) 118.0
113.0
108.0
103.0
98.0
93.0
88.0
83.0
78.0
73.0
68.0
fixed
10.0
Vent Output (solid),
LF Drive unit (dotted)
c)
100.0
log Frequency – Hz
d)
Figure 3.9 PMC transmission lines. a) Phase relationship between the driver and the vent in
the quarter wave transmission line. b) The drive unit and vent contributions to the overall
output. c) Cut-away view of a PMC transmission line. d) A pair of large PMC cabinets, with
their designer
80 Loudspeakers
The calculation of the length of the line required for a certain bass
extension appears to be straightforward, based on a simple formula:
= 344/4 × f
(3.4)
where:
f is the quarter wavelength frequency
344 ms is the speed of sound in air at 20 degrees C
is the length of the transmission line
However the introduction of the absorption materials reduces the
velocity of sound through the line, as discovered by Bailey in his original
work. Bradbury published his extensive tests to determine this effect in
an AES Journal in 19764 and his results agreed that heavily damped lines
could reduce the velocity of sound by as much as 50%, although 35% is
typical in medium damped lines. Bradbury’s tests were carried out using
fibrous materials, typically longhaired wool and glass fibre. These kinds of
materials however produce highly variable effects that are not consistently
repeatable for production purposes. They are also liable to produce inconsistencies due to movement, climatic factors and effects over time. High
specification acoustic foams, developed by PMC with similar characteristics
to longhaired wool, provide repeatable results for consistent production.
The density of the polymer, the diameter of the pores and the sculptured
profiling are all specified to provide the correct absorption for each speaker
model. Quantity and position of the foam is critical to engineer a low pass
acoustic filter that provides adequate attenuation of the upper bass frequencies, whilst allowing an unimpeded path for the low bass frequencies.
There are therefore two distinct forms of bass loading employed in
a TL, which historically and confusingly have been amalgamated in the
TL description. Separating the upper and lower bass analysis reveals why
the TL has so many advantages over reflex and sealed box designs. The
upper bass is almost completely absorbed by the line allowing a clean and
neutral response. The lower bass is extended effortlessly and distortion is
lowered by the line’s control over the drive unit’s excursion. One great
advantage of the low frequency extension provided by transmission lines
is the perception of deep bass even at low listening levels, due to the
extended flatness of the response.
The complex loading of the bass drive unit demands specific ThieleSmall driver parameters to realise the full benefits of a TL design. Most
drive units in the marketplace are developed for the more common reflex
and sealed box designs and are usually not suitable for TL loading. To
design a high efficiency woofer with extended low frequency ability, one
tends to need cones which are often extremely light and flexible with very
compliant suspensions. Whilst performing well in a reflex design, these
characteristics do not match the demands of a TL design. The drive unit
is effectively coupled to a long column of air which has mass. This lowers
the resonant frequency of the drive unit, negating the need for a highly
compliant device. Furthermore, the control of this column of air requires
an extremely rigid cone, to avoid deformation and consequent distortion. The lack of available suitable drive units created the necessity for
PMC to design a series of drivers employing a flat, 6mm thick diaphragm,
Loudspeaker cabinets 81
manufactured from aerospace materials, that provide extraordinary stiffness whilst maintaining a relatively low mass.
The combination of extended frequency response, higher sound pressure
levels and lower distortion afforded by TLs, separates them from reflex
and sealed box models. In addition, phase accuracy is superior to many
other moving coil designs as a result of the absorption provided by the line
in the upper bass range. The low frequency roll off can be as low as 12 dB
per octave in highly damped lines, matching the sealed box arrangement
and avoiding the large phase changes inherent in reflex designs. A cutaway section of a PMC transmission line is shown in Figure 3.9(c), and a
pair of complete cabinets in Figure 3.9(d).
3.5 ABR systems
A variation on the use of reflex enclosures is to use an auxiliary bass
radiator (ABR) instead of a port. The ABR often takes the form of a
loudspeaker with no magnet assembly. They are often also referred to
as passive radiators or drone cones, and are normally of approximately
the same size as the cone of the driver. One of the primary advantages
of ABRs is that there is no air-flow associated with them, so there is no
turbulence or wind noise, which can be a problem when small diameter
ports are the only means of tuning a cabinet. On the negative side, the
compliance (springiness) of the suspension system of an ABR can be nonlinear at high excursions, and hence can be a source of distortion which
can be more subjectively noticeable than port distortion.
ABRs can be used in small boxes, giving them a reflex-type response
when the tuning frequency would require ports which would be too small
to be practical. In general, ABRs offer reflex-type advantages over sealed
boxes, such as 4–6 dB more output on typical programme material and a
lower −3 dB point at low frequencies, but the cut-off is more steep once
it begins, and, as with any resonant system, the transient response gets
smeared. The transient response of a resonant system depends upon the Q
of the resonance, as shown in Figure 3.7. There are some alignments (tunings) known as quasi-Butterworth third order (QB3) and sub-Chebychev
fourth order (SC4) which use lower Qs. They exhibit transient characteristics rather like sealed boxes of Q = 1 (see Figure 3.4) but maintain
the reduced diaphragm excursions of the reflex enclosures. However, the
choice of musical programme and room acoustics may well be the determining factor as to whether these alignments are beneficial or not. Electronic
music in a highly damped control room is much more revealing of tuning resonances than would be romantic music in a relatively live domestic
room. In many ways it is fortunate that we have at our disposal a range
of loudspeaker performances, because none are perfect, and we have a
similar range of musical and acoustical requirements.
ABR systems have not had a totally continuous development. They tend
to emerge from time to time as solutions to specific problems. When air is
used in a resonator, its density is fixed, so if not enough volume is available
in the cabinet for the necessary sized port, or if excessively long tubes are
called for (which suffer from viscous losses), then low tuning frequencies
82 Loudspeakers
a)
b)
SPL (dB)
90
80
70
60
10
100
log.Frequency (Hz)
1k
cone response
ABR response
total system response
Figure 3.10 The ABR. a) A passive radiator (ABR) loudspeaker system. b) Cone and ABR
contributions to the overall response
cannot be accomplished. An ABR offers the use of a number of different
materials of varying weights (masses, densities) and also offers the possibilities of lower box tuning when size is limited. Polystyrene diaphragms
of the correct weight, suspended in a loudspeaker-type surround (usually
a half-roll) are now often the choice of the designers who use ABRs, as
shown in Figure 3.10(a). The total acoustic output is the sum of the volume velocity of the front of the driver diaphragm and the out of phase
volume velocity of the ABR. The ABR is, of course, driven by the rear
of the driver via the air in the cabinet. The relative contributions of the
driver and the ABR to the combined output of the system is shown in
Figure 3.10(b). ABRs are also sometimes chosen for use in systems where
an air-tight cabinet is required, such as for outdoor use.
3.6 Bandpass cabinets
If the low frequency driver is enclosed with air volumes on each side of the
cone, and the only radiation to the outside air is via a port in one of the
air volumes, the result is a bandpass loudspeaker, as shown in Figure 3.11.
Bandpass cabinets are usually restricted to use as sub-woofers because the
pass-band is very limited – rarely more than one octave of flat response.
The roll-offs at either end of their spectrum of use tends to be 12 dB
per octave, because there is no direct radiation to give rise to the phase
differences that lead to the 24 dB per octave lower roll-off rate of reflex
enclosures, unterminated transmission lines or ABR systems. In the design
shown in Figure 3.11, the lower roll-off frequency is governed largely by
the inner, sealed chamber, and the upper roll-off frequency is governed by
the outer ported chamber.
However, there do exist some designs with both chambers vented, generally in an attempt to gain overall system efficiency in the pass band.
Loudspeaker cabinets 83
Figure 3.11 A typical bandpass enclosure
b)
Relative level (dB)
a)
f1
f2
24 dB/octave
12 dB/octave
Frequency (Hz)
Figure 3.12 a) A bandpass enclosure with the inner chamber ported to the outer chamber.
b) Roll-off responses of a)
Bandpass enclosures can normally be much physically smaller than other
configurations for any given output capability, but the responses, not surprisingly, tend to be resonant and thus exhibit poor transient responses.
Figure 3.12 shows the design of a bandpass enclosure in which both
chambers are ported, one to the outside and the other to the outer chamber.
This results in a 24 dB per octave roll-off at the lower frequency. A further
development is shown in Figure 3.13. In this instance, both chambers are
ported to the outside, resulting in a 30 dB per octave roll-off at the lower
frequencies and an 18 dB per octave roll-off at the higher frequencies. Both
of the latter two designs were developed by the Bose Corporation.1
Care must be taken in the acoustic treatment of the chambers which vent
to the outside because internal resonances at high frequencies can escape
through the ports if not dealt with internally. Care must also be taken when
siting bandpass enclosures, because their proximity to solid boundaries
may severely affect their response, and the high velocity ports must be free
from obstructions. Some designers claim better response linearities due to
reduced cone excursions for any given output SPL as compared to other
84 Loudspeakers
a)
Relative level (dB)
b)
f1
f2
30 dB/octave
18 dB/octave
Frequency (Hz)
Figure 3.13 a) A band pass enclosure with both chambers ported to the outside. b) Roll-off
response of a)
low frequency loudspeaker systems, but their use with true high-fidelity
systems is very limited due to transient response anomalies.
3.7 Series driver operation and isobaric loudspeakers
If the port in the outer chamber shown in Figure 3.11 were to be replaced
by another drive unit, a system would result as shown in Figure 3.14, with
the two drivers in acoustic series, (but with the drivers still connected in
Isobarik enclosure
Drivers electrically
linked in parallel
Main enclosure
Small linking
air volume
Figure 3.14 The Linn Isobarik enclosure concept. The loudspeaker drivers are connected in
acoustic series (cascade), but electrically in parallel
Loudspeaker cabinets 85
Figure 3.15 A variation on the theme of Figure 3.14
parallel, electrically). At low frequencies, the two drivers behave like a single driver with twice the moving mass. The result is a downward shift in resonant frequency to about 70% of that of just one of the drivers in the sealed
enclosure. The reduced back-pressure exerted by the enclosure on the
externally radiating driver will result in lower distortion because the inner
loudspeaker is tending to keep the pressure in the outer chamber constant.
However, in practice, the two drivers also tend to function as one due to
the strong coupling by the trapped air mass. Teifenbrun first used the term
isobaric for this type of operation – ‘isobaric’ meaning ‘same pressure’ (UK
patent 1,500,711). Another variation on the theme is shown in Figure 3.15.
3.8 General discussion
Although there are many esoteric designs of low frequency loudspeaker
systems on the market, the ones described so far in this chapter are the ones
which will cover 99.9% of the loudspeakers to be found in the mainstream
music recording and domestic reproduction environments. In general, high
levels of fast, flat responses are not available from small enclosures. This
subject is dealt with much more thoroughly in Chapter 11, but it seems obvious that nobody would choose to use large, expensive, unwieldy cabinets
if more compact solutions were available. Nevertheless, despite the barrage of marketing claims about revolutionary low frequency sources, and
a widespread tendency for many people to believe that computer control
and signal processing can resolve any problems, the fact remains that the
radiation of low frequencies is something that resides firmly in the domain
of the laws of acoustics, and they tend to be somewhat inflexible. It should
be noted that in nature, only large objects radiate low frequency sounds.
The tendency towards using compact, single, mono low-frequency
sources is something that can greatly improve the overall response, both
subjectively and objectively, in poor-to-quite-good circumstances of use.
However, as the room acoustics become better controlled and the signal path, including the loudspeakers, becomes higher in resolution, the
optimum choice for low frequency reproduction tends to return to favour
stereo sources in integrated loudspeaker systems – i.e. without physically
separated sub-woofers. What is optimum in the mid-to-reasonably-high
quality range of loudspeaker systems may not necessarily be extrapolated
as being best at the highest quality levels. One must be very careful not to
86 Loudspeakers
generalise about things which are for specific applications. For example, an
orchestral recording with phase differences in the left and right channels
at low frequencies would benefit, in a good room, from stereo bass. It has
now been determined that only by restricting the crossover frequency to
less than 50 Hz can the bass be summed into mono without loosing the spaciousness in the sound5 . However, in a poorly controlled room, a mono bass
may lead to less general confusion if crossed over and combined into mono
an octave higher. Such choices can be very circumstantially dependent.
3.9 Cabinet lining materials
Any hard-surfaced box will suffer from internal reflexions and resonances
when excited by a loudspeaker drive unit mounted in one of its surfaces.
The nature of cone loudspeakers is such that they are relatively transparent
to sound at mid frequencies, so any reflexions and resonances occurring
within the box are likely to pass to the outside via the cone, and combine
with the directly radiating sound in a way that will give rise to undesirable
colouration. One of the fundamental reasons for applying absorbent linings
of foams or fibrous materials to the inside of loudspeaker cabinets is to
reduce to inconsequentially low levels the colouration effects by rendering
the boxes as acoustically non-reflective as is reasonably possible. A further
advantage of the application of porous or fibrous materials is that they
can slow down the speed of sound, and thus make the cabinets appear
to be acoustically larger than they are physically. The practical limit to
this size increase appears to be around 20% (which is still a useful gain)
because the thermal transfer characteristics of the materials normally used
are not sufficient to achieve the theoretical 41% maximum. As briefly
mentioned in Section 3.2, air heats up when compressed and cools on
rarefaction. Both of these effects tend to augment the speed of sound on
the successive half-cycles because the air itself is a poor conductor of heat,
so the thermal changes are trapped within the waves. However, if the air is
in close contact with another material, distributed throughout its volume,
which can conduct the heat, the augmentation of the speed of sound due to
the heat of compression and the cold of rarefaction will not be apparent.
The ratio of the speed of sound with and without this augmentation is
about 1.41 to 1, hence the approximately 40% difference in apparent box
size if the heat conduction were total.
Partly for this reason, but also because fibrous materials are better
absorbers where the particle velocities of the air movement are at their
highest (they must be zero at rigid boundaries, so they are at their lowest close to the boundaries), the absorbent materials are best placed in
the volume of the box, lightly packed, and not only against the sides of
the box. Reticulated (open cell) foams, glass fibre, mineral wool, bonded
acetate fibres, polyester fibres and cotton-waste felt are all common lining
materials. The cut-away view of the ‘transmission-line’ cabinet shown in
Figure 3.9 illustrates the use of a synthetic foam lining which the manufactures specifically chose for its ability to maximally damp the line. Material
types and densities are normally chosen with care for specific applications.
Loudspeaker cabinets 87
The KEF loudspeaker company, in the 1980s, noticed some differences
in their loudspeaker frequency responses depending upon whether the
excitation signal was of a steady state or transient nature. The discrepancy
turned out to be due to non-uniform movement of some of the internal lining materials, which was somewhat uncontrolled after the shock excitation
of a transient signal. The lining materials should therefore not be in panels
which can vibrate en masse, or non-linear effects may be sufficient to be
noticeable in the sound from the loudspeakers. Vibrating lining materials
may settle into regular patterns on relatively steady signals, but can be
excited rather unpredictably by transient shocks. At high SPLs, the linings
can move in rather erratic manners, but the effects are usually swamped by
the higher SPLs of the radiation direct from the driver. Nevertheless the
ideal lining would be relatively inert. Colloms6 claims that unstable lining
materials can impair the sense of ‘rhythm’ from a loudspeaker system.
At low frequencies, the thicknesses of the lining materials are far too
little to provide much absorption, but the cabinets are normally also far
too small to support any resonant modes (100 Hz would require an internal
dimension of at least 1.6 metres) so the lack of absorption rarely becomes
a practical problem. However, at higher frequencies, the absorption is
important in order to reduce internal resonances which could powerfully
excite structural resonances in the cabinet walls, and which would then
radiate into the listening rooms.
3.10 Cabinet constructions
Above all, loudspeaker cabinets should be either rigid or heavy or both.
A non-rigid (and/or lightweight) cabinet will be excited into vibration
by the drive unit(s). In most cases, rigid materials tend to be heavy or
expensive, so light, cheap loudspeakers always tend to be sonically suspect
because they will probably suffer from cabinet vibration colouration. Any
part of a cabinet which vibrates in sympathy with the driver diaphragm will,
itself, act as a diaphragm and interfere with the driver output, leading to
colouration of the overall sound output. In order to prevent the structural
vibration of cabinets, sandwich constructions can be used, with lead sheet or
plasticised deadsheets between the layers. Internal bracing is also an option,
which pushes up the resonant frequencies into regions that tend to be more
easily damped. Phenolic materials are another common choice because
they can produce wood composites of very high density and rigidity. Lighter
weight, highly rigid materials are sometimes to be found, in the nature
of honeycombs or matrices, but they tend to be expensive and difficult
to manufacture. However, in all cases, the goals are similar – rigidity and
high vibration damping. It is important that the materials do not ring when
struck.
The panel radiation is proportional to the size of the cabinet, so the
problem of resonance avoidance becomes greater as cabinet size increases.
For this reason, a given thickness of material for the wall of a small cabinet
may need to be significantly increased as the cabinet size increases. The
weight therefore increases greatly, because not only are the panel sizes
larger, but they must also be thicker if the same vibrational insensitivity
88 Loudspeakers
is to be maintained. Large loudspeaker systems of high quality tend to be
very heavy indeed.
In many cases, a stiff, large panel, which is well-behaved at low frequencies may still ring at mid-frequencies, and a well-damped panel at mid
frequencies may flex at low frequencies. Finding solutions which are dead
at all frequencies is often difficult. In some of the more esoteric designs,
mineral-loaded acrylics and Melamine are used as panel materials, but they
can be very difficult to work with.
3.11 Cabinet shapes and diffraction effects
In many cases, modern loudspeakers, although basically of rectangular
shape, have rounded or chamfered edges. Figure 3.16 reproduces the classic work of Olson7 on the subject of the diffraction effects on the overall
loudspeaker response due to cabinet shape. The responses are for an identical drive unit in each cabinet. The sphere looks attractive, but difficulty
of manufacture and problems due to all the internal axial reflexion path
lengths being the same lead to practical problems in its implementation.
Figures 3.16 J and L are reminiscent of many modern designs, and their
validity is borne out by the response plots. Of course, with built-in/flushmounted loudspeakers, the diffraction problem is nullified, which is one
reason why so many professional monitors are so mounted.
At low frequencies, the sound from a loudspeaker cabinet is radiated
spherically if the loudspeaker is mounted in free space. At higher frequencies, where the wavelengths are small with respect to the front face
of the cabinet, the cabinet will tend to act like an infinite baffle, and the
radiation will be hemispherical. At still higher frequencies, where the wavelengths are small compared to the radiating diaphragm, the sound will be
beamed forwards, regardless of whether it is mounted on a baffle, or not.
The diffraction effects largely arise at the transition between the first two
zones of radiation, i.e. between the spherical and hemispherical radiation
zones.
As a sound wave in this transition zone radiates away from a source on
a finite-sized cabinet wall, it spreads out as it propagates in the manner of
half of a spherical wave. When the wave reaches the edge of the wall, it
suddenly has to expand more rapidly to fill the space where there is no wall
(see Figure 3.17). There are two consequences of this sudden expansion.
First, some of the sound effectively ‘turns’ the corner, around the edge,
and carries on propagating into the region behind the plane of the source.
Second, the sudden increase in expansion rate of the wave creates a lower
sound pressure in front of the wall, near the edge, than would exist if the
edge were not there. This drop in pressure then propagates away from
the edge into the region in front of the plane of the source. The sound
wave that propagates behind the plane of the source is in phase with the
wave that is incident on the edge, but the one that propagates to the front
is in phase opposition. These two ‘secondary’ sound waves are known as
diffracted waves and they ‘appear’ to emanate from the edge; the total
sound field may then be thought of as being the sum of the direct wave
from the source (as if it were on an infinite baffle) and the diffracted waves.
Loudspeaker cabinets 89
Figure 3.16 Olson’s classic work on the effects of cabinet shapes on driver responses5
The edges of the cabinets can be thought of as small loudspeaker radiating
in antiphase to the real driver. The direct wave exists only in front of the
baffle; the region behind is know as the ‘shadow’ region where only the
diffracted wave exists.
At low frequencies, the diffracted waves from all of the edges of the
finite-sized cabinet sum to yield a sound field with almost exactly one half
of the pressure radiated by the source of an infinite baffle. Thus behind the
cabinet there is pressure due to the diffracted wave only, and in front of the
cabinet there is the direct wave plus the negative-phased diffracted wave.
Assuming that the edge is infinitely sharp (has no radius of curvature),
90 Loudspeakers
Wavefronts
Diffracted
wavefronts
Source
Sharp
edge
Figure 3.17 Graphical representation of the sudden increase in the rate of expansion of a
wavefront at a sharp edge. The diffracted wave in the shadow region behind the source plane
has the same effect as the wave incident on the edge; the diffracted wave in front of the
source plane is phase reversed
there can be no difference between the strength of the diffracted wave
at low frequencies and that at high frequencies (the edge remains sharp
regardless of scale). The only difference, therefore, between the diffracted
waves at low frequencies and those at higher frequencies is the effect that
the path length differences between the source and different parts of the
edge has on the radiated field. The diffracted waves from those parts of the
edge further away from the source will be delayed relative to those from the
nearer parts, giving rise to significant phase differences at high frequencies
but not at low frequencies. The net result is a strong diffracted sound field
at low frequencies and a weak diffracted sound field at high frequencies.
Figure 3.18 shows the results of a computer simulation of the typical
effect that a finite-sized cabinet has on the frequency response of a loudspeaker. Figure 3.18(a) is the on-axis frequency response of an idealised
loudspeaker drive-unit mounted in a true infinite baffle. The response is
seen to be uniform over a wide range of frequencies. Figure 3.18(b) is
the frequency response of the same drive-unit mounted on the front of
a cabinet of dimensions 400 mm high by 300 mm wide by 250 mm deep.
The 6 dB decrease in response at low frequencies, due to the change in
radiation from baffled to unbaffled, is evident from a comparison between
Figures 3.18(a) and (b). Also evident is an unevenness in the response in
the mid-range of frequencies. These response irregularities are due to path
length differences from the diaphragm to the different parts of the diffracting edges and on to the on-axis observation point. Unlike the low-frequency
Loudspeaker cabinets 91
a)
10
0
dB –10
–20
–30
100
1000
Frequency (Hz)
b)
m
10
0m
30
0
m
0m
400 mm
150 mm
15
dB –10
–20
25
m
0m
m
–30
100
0m
15
1000
Frequency (Hz)
Figure 3.18 a) On-axis frequency response of an idealised loudspeaker diaphragm mounted
in an infinite baffle: the response is uniform over a wide range of frequencies. b) On-axis
frequency response of the same loudspeaker diaphragm mounted on the front face of a finitesized cabinet (the rear enclosure size is assumed to be the same in both cases). The response
has reduced by 6 dB at low frequencies and is uneven at higher frequencies. The differences
between this and Figure a), above, are due to the diffraction from the edges of the cabinet
behaviour, these are dependent upon the detailed geometry of the driver
and cabinet and the position of the observation point. Therefore, in order
to try to ameliorate these response irregularities, many loudspeakers have
contoured edges. Although this does not eliminate diffraction, it tends to
make the transitions from the baffled to the unbaffled conditions occur in
a less abrupt manner, and thus have a less disturbing effect on the axial
frequency response. The off-axis responses are also improved.
Although the combined effects of loudspeaker and rooms is the subject of Chapter 7, it is worth noting here the combined effect of cabinet
diffraction and nearby surfaces. Figure 3.19 shows the effect on the axial
response when the loudspeaker shown in Figure 3.18(b) is placed against,
and close to, a wall. The different distances to the wall, behind the loudspeaker cabinet, give rise to different reflected paths for the diffracted
waves, and hence different disturbance patterns in the on-axis, forward
response. The clear advantage of flush-mounting the loudspeakers into a
wall can be seen by comparison to Figure 3.18(a). Nevertheless, it should
be notes that loudspeakers designed for free-standing may have had their
low frequency responses engineered for a higher low frequency output, and
flush-mounting them may result in an excess of low frequencies. Active
loudspeakers often have filter controls which can compensate for this, and
reflex cabinets can sometimes have their ports reduced in size such that a
flat response can easily be restored. In other cases, a slight bass boost may
be deemed to be more acceptable than the irregular response resulting
92 Loudspeakers
b)
a)
10
10
0
0
dB –10
dB –10
–20
–20
–30
–30
100
1000
Frequency (Hz)
100
1000
Frequency (Hz)
Figure 3.19 a) On-axis frequency response of the same diaphragm and cabinet as in
Figure 3.18(b) but with the rear of the cabinet against a rigid wall. Interference between the
direct sound from the loudspeakers and that reflected from the wall produces a comb-filtered
response, but the response level at low frequencies is restored to that for the infinite baffle
case (Figure 3.18(a)). b) As in a), above, but with the rear of the cabinet 0.25 metres from
the rigid wall
from the diffraction. However, the bass rise due to the flush mounting is
much more easily equalised than the diffraction irregularities, which tend
not to be equalisable because of the complexity of the response delays
from the reflexions.
In Figure 3.16, most of the drive unit positions are symmetrically placed.
In practice, the diffraction effects can often be reduced by the nonsymmetrical positions of the drivers with respect to the cabinet boundaries,
but the necessity for this will depend upon the nature of the drive unit
and the size of the cabinet. Some modern loudspeakers have the mid and
high frequency drivers mounted in shallow horns, sometimes referred to
as waveguides, which can project the wave in a more forward direction,
and greatly reduce the effects of edge diffraction. In general, it is also
important to keep the front surface of the loudspeaker system as smooth
as possible by recessing the drivers and screw heads.
3.12 Front grilles
It is somewhat rare, these days, to see front grilles on loudspeakers for professional use. The fact is that there are no truly transparent grille materials,
but in domestic use their use is strongly justified, not only for aesthetic
reasons but also for protection against children and over-zealous cleaners. Fabric grilles usually require wooden frames, and these can become
diffraction sources as they provide a step at the edge of the baffle. Foam
grilles can avoid this problem, but self-supporting foams of sufficient thickness will exhibit different distances through which the sound must pass,
dependent upon the angle of radiation. They can also obstruct the air flow
in the ports of reflex enclosures (and open transmission lines) where the
exits are on the front face of the cabinets.
However, in some cases, the grille losses have been taken into account
in the design of the loudspeaker system, so the removal of grilles should
not be undertaken without careful listening to the effects. The diffusive
Loudspeaker cabinets 93
effects of some grilles have been reported to impair the stereo imaging of
some loudspeaker designs. In general, the best grille is no grille from a
purely sonic viewpoint.
3.13 Cabinet mounting
Figure 3.19 shows the effects of placing a loudspeaker near to reflective surfaces. Obviously, a floor standing loudspeaker should have been
designed for standing on the floor, but the intended mounting conditions
for small cabinets is not always so obvious. The well-known Yamaha NS10
was originally designed as a bookshelf loudspeaker for domestic use. Its
response was therefore tailored such that its bass/mid/treble response was
best balanced when the loudspeaker was placed with its back against a
wall. This fact was partly responsible for its success when mounted on top
of the meter bridges of mixing consoles, because the flat surface below the
loudspeaker tended to reinforce the low frequencies in the same way as
a wall behind the cabinet. Mounting this type of loudspeaker on a stand
in free space will lead to a reduction in the low frequency response, but
mounting the loudspeaker on a mixing console will cause time-smearing
and comb filtering, the causes of which are highlighted in Figure 3.20.
Mounting loudspeakers on table tops or work surfaces is something
that should be avoided, because the effects shown in Figure 3.20 will be
exaggerated and colouration of the sound will be inevitable. Far too many
people fail to realise that the mounting of a loudspeaker forms part of the
loudspeaker system itself, and no loudspeaker’s sound is independent of
its mounting conditions. A poor loudspeaker, well mounted, may sound
better than a good loudspeaker poorly mounted. The number of television
and video studios in which the loudspeakers are really appallingly mounted
indicates how little many of their users care about the sound, despite their
protestations to the contrary.
Wall mounting of loudspeakers will need to take into account the nature
of the wall, as not all walls can be considered to be rigid at low frequencies.
The nature of the wall – plasterboard, hollow bricks, solid bricks, stone,
concrete etc – will affect the loudspeaker response, so if the wall in the
showroom was not the same as the wall at home, the same low frequency
response will not be heard.
Placing loudspeakers on pieces of furniture is not recommended because
of the vibrational coupling which will lead to sound being radiated by the
furniture. Even so-called bookshelf loudspeakers should only be mounted
on substantial bookshelves, which should ideally also be rather full of
books, to add mass, damping, and reduce diffraction effects.
Heavy, narrow, floor stands are recommended, with wide bases for stability, and coupled to the floors (either wood, or carpeted) by spikes. Soft
rubber pads are not usually a good idea because they can give rise to
rocking; hard rubber is a better option. Broad, columnar stands can induce
floor reflexion problems by obstructing the free passage of the sound below
the cabinets. Under all circumstances, wobbly mounting systems should
be avoided, because the imaging can be severely impaired, even by small
movements of the cabinets.
94 Loudspeakers
a)
A
B
C
b)
Electrical input signal
[i]
LEVEL vs TIME
Response at 1 ft No reflexions apparent
[ii]
LEVEL vs TIME
Response at 2 ft Characteristic double trace
[iii]
LEVEL vs TIME
Response at 4 ft Even greater disturbances in tail
[iv]
LEVEL vs TIME
Figure 3.20 Effects of desk-top reflexions on transients. a) Positions A, B and C relate to the
1 foot (30 cm) 2 foot (60 cm) and 4 foot (120 cm)) responses, shown below. b) Transient
responses at the positions shown in a), above
Loudspeaker cabinets 95
In effect, all of these different mounting regimes can be thought of as
extensions to the loudspeaker cabinets, because they directly affect the
loading on the diaphragms and the radiated sound output. They are not
just simply different places to put a loudspeaker cabinet.
Note 1
In order to maintain a constant output SPL, a diaghragm needs to move
four times the distance each time the frequency falls by an octave. The fact
that the cone excursions are independent of frequency below the resonant
frequency of a sealed box loudspeaker system is what gives rise to the
12dB/octave roll-off below that frequency.
References
1 Eargle, J. M., ‘Loudspeaker Handbook’, Chapman and Hall, New York, USA,
(1997)
2 Small, R., ‘Direct Radiator Loudspeaker System Analysis and Synthesis – (Parts 1
and 2)’. Journal of the Audio Engineering Society, Vol 20, No 5, and Vol 21,
No 1, (1972 and 1973)
3 Bailey, A. R., ‘A Non-Resonant Loudspeaker Enclosure Design’, Wireless World
p 483–486, (October 1965)
4 Bradbury, L. J. S., ‘The Use of Fibrous Materials in Loudspeaker Enclosures’,
Journal of the Audio Engineering Society, Vol 24, pp 404–412, (April 1976)
5 Martens, W., Braasch, J., Woszczyk, W., ‘Identification and Discrimination of
Listener Envelopment Percepts Associated with Multiple Low-Frequency Signals in Multi-Channel Sound Reproduction’, AES 117th Convention, Pre-print
No 6229, (October 2004)
6 Colloms, M., ‘High Performance Loudspeakers’, 6th Edition John Wiley & Sons,
Chichester, UK (2005)
7 Olson, H. F., ‘Direct Radiator Loudspeaker Enclosures’, Journal of the Audio
Engineering Society, Vol 17, No 1, pp 22–29, (January 1969)
Chapter 4
Horns
No practical direct radiating loudspeaker can achieve high radiation
efficiency at low frequencies. For example, a diaphragm with a diameter of
250 mm has a radiation efficiency of just 0.7% at 50 Hz when mounted in an
infinite baffle, and half that when mounted in a cabinet. Sound power output is proportional to the product of the mean-squared diaphragm velocity
and the radiation efficiency, so a low radiation efficiency means that a high
diaphragm velocity is required to radiate a given sound power. The only
way in which the radiation efficiency can be increased is to increase the
size of the radiating area, but larger diaphragms have more mass (if rigidity
is to be maintained) which means that greater input forces are required
to generate the necessary diaphragm velocity. (This is discussed further in
Chapter 11.) The electroacoustic efficiency is defined as the sound power
output radiated by a loudspeaker per unit electrical power input. Because
of the relatively high mass and small radiating area, electroacoustic efficiencies for typical loudspeaker drive-units in baffles or cabinets are of the
order of only 1-5%. However, horn loudspeakers can combine the high
radiation efficiency of a large radiating area with the low mass of a small
diaphragm in a single unit. This is achieved by coupling a small diaphragm
to a large area via a gradually tapering flare. This arrangement can result
in electroacoustic efficiencies of 10-50%, or ten times the power output of
the direct-radiating loudspeaker for the same electrical input. Additionally, horns can be employed to control the directivity of a loudspeaker and
this, along with the high sound power output capability, is why they are
used extensively in public address and sound reinforcement loudspeaker
systems.
The following sections describe, in a conceptual rather than mathematical way, how horns increase the radiation efficiency of loudspeakers, how
they control directivity, and why there is often the need to compromise
one aspect of the performance of a horn to enhance another.
4.1 The horn as a transformer
Close to the diaphragm, in the hydrodynamic near-field, the change in area
of an acoustic wave as it propagates gives rise to a ‘stretching pressure’
which is additional to the pressure required for sound propagation. In other
words, imagine a balloon being inflated. As well as the outward movement
of the skin, radially, the surface is also expanding laterally. Dots painted
Horns 97
on the surface of the balloon would move apart as they moved away from
the centre. The dots moving apart represent the stretching pressure which
does not contribute to sound propagation as it is in phase quadrature (90
degrees) with the radial velocity, so the acoustic impedance in the nearfield is dominated by reactance (for readers unfamiliar with the concepts of
impedance, reactance and resistance see ‘Impedance’ in the glossary). As a
consequence, large particle velocities are required to generate small sound
pressures when the rate of change of area with distance of the acoustic
wave is significant. It is this stretching phenomenon that is responsible
for the low radiation efficiency of direct-radiating loudspeakers at low
frequencies. Physically, one can imagine the air moving sideways out of
the way, in response to the motion of the loudspeaker diaphragm, instead
of moving backwards and forwards. In the hydrodynamic far-field, the
stretching pressure is minimal, the acoustic impedance is dominated by
resistance, and efficient sound propagation takes place. The only difference
between the sound fields in the near- and far-fields is the rate of change
of area with distance of the acoustic wave; the flare of a horn is a device
for controlling this rate of change of area with distance, and hence the
efficiency of sound propagation.
Horns are waveguides that have a cross-sectional area which increases,
steadily or otherwise, from a small throat at one end to a large mouth at
the other. An acoustic wave within a horn therefore has to expand as it
propagates from throat to mouth. The manner in which acoustic waves
propagate along a horn is so dependent upon the exact nature of this
expansion that the acoustic performance of a horn can be radically changed
by quite small changes in flare-shape. It is usually assumed in acoustics
that changes in geometry that are small compared to the wavelength of
the sound of interest do not have a large effect on the behaviour of the
sound waves, so why should horns be any different? The answer lies in the
stretching pressure argument above. The concept of a stretching pressure
can be applied to horns by considering flare-rate. Flare-rate is defined as
the rate of change of area with distance, divided by the area, and usually
has the symbol m
mx =
1 dSx
Sx dx
(4.1)
Where Sxis the cross sectional area at axial position x. The simplest flare
shape is the conical horn, as shown in Figure 4.1, which has straight sides
in cross-section, and where S0 is the area of the throat at x = 0 and x0
is the distance from the apex of the horn to the throat. The sound field
within a conical horn can be thought of as part of a spherical wave field,
and has a flare-rate which is dependent on distance from the apex.
The flare rate in a conical horn (and in a spherical expanding wave) is
therefore highest close to the throat, decreasing with increasing distance
from the throat.
The radial dependence of the flare-rate in a conical horn (and a spherical wave) gives rise to a gradual transition from the reactive, near-field
dominated behaviour associated with the stretching pressure, to the resistive radiating, far-field dominated propagation as a wave propagates from
98 Loudspeakers
Horn walls
x = x0
Throat
x
Figure 4.1 Geometry of a conical horn
The origin for the axial coordinates is usually considered to be the imagined apex of the
cone
throat to mouth. The transition from near- to far-field dominance is gradual
with increasing frequency and/or distance from apex, so distinct ‘zones’ of
propagation are not clearly evident.
However, a more common flare shape for loudspeaker horns is the
exponential. The flare shape of the exponential horn is shown in Figure. 4.2.
The flare-rate of an exponential horn is constant along the length of the
horn, giving rise to a behaviour that is quite different from the conical
horn. At low frequencies, and throughout the entire length of the horn,
the reactive, near-field-type propagation dominates, and, if the horn is
sufficiently long, an almost totally reactive impedance exists everywhere.
Figure 4.2 The flare shape of an exponential horn
Horns 99
Above a given frequency, known as the cut-off frequency, throughout the
entire length of the horn, the far-field-type propagation dominates, leading
to an almost totally resistive impedance everywhere. The cut-off frequency
of an exponential horn marks a sudden transition from inefficient sound
propagation within the horn to efficient sound propagation. The cut-off
frequency for any given horn is dependent upon its rate of flare. As the flare
rate goes up (the horn expands more rapidly) the cut-off frequency also
goes up, therefore rapidly flaring horns cannot be used at low frequencies.
Physically, propagation within an exponential horn above cut-off is similar to a spherical wave of large radius, with minimal stretching pressure.
Below cut-off it is similar to a spherical wave of small radius, dominated
by the stretching pressure. The sharp cut-off phenomenon clearly occurs
because the transition from one type of propagation to the other occurs
simultaneously throughout the entire length of the horn as the frequency is
raised through cut-off. The acoustic impedance at the throat of an infinitelength exponential horn is shown in Figure 4.3, which clearly illustrates that,
at frequencies below cut-off, the resistive part of the acoustic impedance
is zero, which means that a source at the throat can generate no acoustic
power. At frequencies above the cut-off frequency, the resistive part of
the acoustic impedance is close to the characteristic impedance of air: a
source at the throat therefore generates acoustic power with a radiation
efficiency of 100% due to the perfect match.
In practice, horns have a finite length and so, unless the mouth of the
horn is large compared to a wavelength, an acoustic wave propagating
towards the mouth sees a sudden change in acoustic impedance from
that within the horn to that outside, and some of the wave is reflected
back down the horn. A standing-wave field is set up between the forward
propagating wave and its reflexion, which leads to comb-filtering in the
acoustic impedance. Figure 4.4 shows the radiation efficiency at the throat
of a typical finite-length exponential horn. Also shown are the radiation
efficiency of a conical horn having the same overall dimensions, and that of
a piston the size of the throat mounted on an infinite baffle. The frequency
Real
Z T /ρ c
1
Imag.
0.5
0
0.5
1
2
4
8
ƒ/ƒc
Figure 4.3 The acoustic impedance at the throat of an infinite length exponential horn f/fc is
the ratio of frequency to cut-off frequency, and c is the characteristic impedance of air. No
acoustic power can be radiated below the cut-off frequency as the real part of the acoustic
impedance is zero
Rad. Eff. (%)
100 Loudspeakers
100
50
0
0.25
0.5
1
2
4
8
ƒ/ƒc
Figure 4.4 The radiation efficiency of an exponential horn compared to that of a conical horn
(short-dashed line) of the same overall size. Relatively small changes in the flare shape of a
horn can have a large effect on the efficiency at low frequencies. The third curve (long-dashed
line) is the radiation efficiency of a baffled piston having the same size as the throats of the
horns
scale is normalised to the cut-off frequency of the exponential horn. The
comb-filtering, due to the standing wave field within the horn can be seen,
as can the improvement in radiation efficiency of the conical horn over
the baffled piston, and of the exponential horn over the conical horn at
frequencies above cut-off.
The exponential horn acts as an efficient impedance matching transformer at frequencies above cut-off by giving the small throat approximately the radiation efficiency of the large mouth. The power output of a
source mounted at the throat of a horn is proportional to the product of
its volume velocity and the radiation efficiency at the throat; thus, a small
loudspeaker diaphragm mounted at the throat of an exponential horn can
radiate low frequencies with high efficiency. Below cut-off, however, the
horn flare effectively does nothing, and the radiation efficiency is then similar to the diaphragm mounted on an infinite baffle. In practice, however,
this seemingly ideal situation is marred somewhat by the sheer physical
size of horn flare required for the efficient radiation of low frequencies.
The cut-off frequency is proportional to the flare rate of a horn, which
in turn is a function of the throat and mouth sizes and the length of the
horn. Therefore, for a given cut-off frequency and throat size, the length of
the horn is determined by the size of the mouth. To avoid gross reflexions
from the mouth, leading to a strong standing wave field within the horn,
and consequently an uneven frequency response, the mouth has to be
sufficiently large to act as an efficient radiator of the lowest frequency of
interest. In practice, this will be the case if the circumference of the mouth
is larger than a wavelength. For the efficient radiation of low frequencies,
the mouth is then very large. Also, a low cut-off frequency requires a low
flare-rate which, along with the large mouth, requires a long horn. By way
of example, a horn required to radiate sound efficiently down to 50 Hz
from a loudspeaker with a diaphragm diameter of 200 mm would need a
mouth diameter of over 2 metres, and would need to be over 3 metres long!
Compromises in the flare-rate raise the cut-off frequency, and compromises
Horns 101
in the mouth size gives rise to an uneven frequency response. Reference 1
is a classic paper on the optimum matching of mouth size and flare-rate.
A radiation efficiency of 100% is not usually sufficient to yield the very
high electroacoustic efficiencies of 10% to 50% quoted in the introduction
of this section. However, unlike ‘real’ efficiency figures, which compare
power output with power input, the radiation efficiency can be greater
than 100% because the figure is relative to the radiation of acoustic power
into the characteristic impedance of air . Arranging for a source to see
a radiation resistance greater than that of the characteristic impedance
results in radiation efficiencies greater than 100%. A technique known
as compression is used to increase the radiation efficiency of many horn
drivers; all that is required is for the horn to have a throat that is smaller
than the diaphragm of the driver, as shown in Figure 4.5
Assuming that the cavity between the diaphragm and the throat is small
compared to a wavelength, it can be shown that the acoustic impedance at
the diaphragm is approximately that at the throat multiplied by the ratio
of the diaphragm area to the throat area, known as the compression ratio.
A compression ratio of 4:1 thus gives a radiation efficiency of 400% at
the diaphragm. The ‘trick’ to achieving optimum electroacoustic efficiency
is to match the acoustic impedance to the mechanical impedance (mass,
damping, compliance, etc.) of the driver. If the compression ratio is too
high, the velocity of the diaphragm will be reduced by the additional acoustic load and the gain in efficiency is reduced. This can, however, have the
benefit of ‘smoothing’ the frequency response irregularities brought about
by insufficient mouth size. Some dedicated compression drivers operate
with compression ratios of 10:1 or more.
diaphragm
force from
motor system
horn
throat
Figure 4.5 Representation of the principle behind the compression driver. Radiation
efficiencies of greater than 100% can be achieved by making the horn throat smaller than
the diaphragm
102 Loudspeakers
4.2 Directivity control
Coverage angle (degrees)
In addition to their usefulness as acoustic transformers, horns can be used
to control the directivity of a loudspeaker. The directivity of a piston in a
baffle narrows as frequency is raised, as was shown in Figure 1.4. For many
loudspeaker applications, this frequency-dependent directivity is undesirable. In a public address system, for example, the sound radiated from a
loudspeaker may be required to ‘cover’ a region of an audience without
too much sound being radiated in other directions where it may increase
reverberation. What is required in these circumstances is a loudspeaker
with a directivity pattern that can be specified and that is independent of
frequency. By attaching a specifically designed horn flare to a loudspeaker
driver, this goal can be achieved over a wide range of frequencies.
Consider the simple, straight-sided horn shown in Figure 4.1. The directivity of this horn can be divided into three frequency regions as shown in
Figure 4.6. At low frequencies, the coverage angle reduces with increasing
frequency in a manner determined by the size of the horn mouth, similar
to a piston with the dimensions of the mouth. Above a certain frequency,
the coverage angle is essentially constant with frequency and is equal to
the angle of the horn walls. At high frequencies, the coverage angle again
decreases with increasing frequency in a manner determined by the size
of the throat, similar to a piston with dimensions of the throat. Thus the
frequency range over which the coverage angle is constant is determined
by the sizes of the mouth and of the throat of the horn. The coverage
angle within this frequency range is determined by the angle of the horn
walls. This behaviour is best understood by considering what happens as
frequency is reduced. At very high frequencies, the throat beams with a
coverage angle which is narrower than the horn walls, as if the horn were
not there. As frequency is lowered, the coverage angle (of the throat)
widens to that of the horn walls and can go no wider. As frequency is further lowered, the coverage angle remains essentially the same as the horn
walls until the mouth (as a source) begins to become ‘compact’ compared
180
Mouth
control
90
θwall
Horn wall control
Throat
control
Frequency
Figure 4.6 Simplified representation of the coverage angle of a straight-sided horn. At low
frequencies, the coverage angle is determined by the size of the mouth, and at high frequencies
by the size of the throat. The coverage angle in the frequency range between the two is fairly
even with frequency, and is roughly equal to the angle between the horn walls ( wall). The
dashed line shows a narrowing of the coverage angle at the lower end of the wall-control
frequency range, which is often encountered in real horn designs
Horns 103
to a wavelength and the coverage angle is further increased, eventually
becoming omni-directional at very low frequencies. The coverage angle
shown in Figure 4.6 is, of course, a simplification of the actual coverage
angle of a horn. In practice, the mouth does not behave as a piston and
there is almost always some narrowing of the directivity at the transition
frequency between mouth control and horn wall control. A typical example
of this is shown as a dashed line in Figure 4.6. Different coverage angles
in the vertical and horizontal planes can be achieved by setting the horn
walls to different angles in the two planes.
4.3 Horn design compromises
Sections 4.1 and 4.2 describe two different attributes of horn loudspeakers. Ideally, a horn would be designed to take advantage of both
attributes, resulting in a high-efficiency loudspeaker with a smooth frequency response and constant directivity over a wide frequency range.
However, very often a horn designed to optimise one aspect of performance must compromise other aspects. For example, the straight-sided
horn in Figure 4.1 may exhibit good directivity control but, being a conicaltype horn, will not have the radiation efficiency of an exponential horn of
the same size. The curved walls of an exponential horn, on the other hand,
do not control directivity as well as straight-sides horns. Early attempts
at achieving high efficiency and directivity control in one plane led to the
design of the so-called sectoral horn or radial horn shown in Figure 4.7. In
this design, the two side walls of the horn are straight, and set to the desired
horizontal coverage angle. The vertical dimensions of the horn are then
adjusted to yield an overall exponential flare. Whereas the goals of high
efficiency and good horizontal directivity control can be achieved with a
sectoral horn, the severely compromised vertical directivity can be a problem. Given that a minimum mouth dimension is required for directivity
control down to a low frequency, setting the horizontal and vertical walls to
Figure 4.7 The sectoral (or radial) horn
The walls controlling the horizontal directivity are set to the desired coverage angle. The
shape of the other two walls is adjusted to maintain an overall exponential flare, resulting in
less-than-ideal vertical directivity
104 Loudspeakers
Figure 4.8 The constant directivity horn
Different horn wall angles in the two planes can be achieved using compound flares. Sharp
discontinuities within the flare can set up strong standing-wave fields, leading to an uneven
frequency response
different angles, for example 90 degrees by 60 degrees, means that different
horn lengths are required in the two planes. To overcome this problem,
later designs used compound flares2 so that the exit angles of the horn walls
can be different in the two planes, but the mouth dimensions and overall
horn length remain the same. The so-called constant directivity horn (CD)
is shown in Figure 4.8. The sudden flare discontinuities introduced into
the horn with these designs result in strong standing wave fields within the
flare which can compromise frequency response smoothness. In fact, this
is true of almost any flare discontinuity in almost any horn. Modern public
address horn designs employ smooth transitions between the different flare
sections and exponential throat sections to achieve a good overall compromise, but constant directivity horns, because of the reflexion problems,
tend not to be used on the highest fidelity loudspeaker systems.
The control of directivity down to low frequencies requires a very large
horn. For example, in a horn designed to communicate speech, directivity control may be desirable down to 250 Hz at a coverage angle of
60 degrees.This can only be achieved with a horn mouth greater than 1.5m
across. The same horn may have an upper frequency limit of 8 kHz, which
needs a throat no greater than 35 mm across. Maintaining 60 degrees walls
between throat and mouth then requires a horn length of about 1.3 m.
Attempts to control directivity with smaller devices will almost always fail.
4.4 Non-linear acoustics
In the vast majority of studies in acoustics, and loudspeakers in particular,
the acoustic pressures and particle velocities encountered are sufficiently
small that the processes of sound radiation and propagation can be assumed
to be linear. If a system or process is linear, then there are several rules
that govern what happens to signals when they pass through the system
Horns 105
or process. These rules include the principal of superposition, which states
that the response to signal A + B is equal to the response to signal A +
the response to signal (B). Most of the analysis tools and methods, such as
Fourier analysis and the frequency response function, rely entirely on the
principal of superposition, and hence linearity. When a system or process is
non-linear, the principal of superposition no longer applies, and the usual
analysis methods cannot be used. In this section, the conditions under which
acoustic radiation and propagation may become non-linear are discussed,
along with some examples of the degree of non-linear acoustic behaviour
encountered in loudspeakers.
The speed of sound in air is dependent upon the thermodynamic properties of the air.
An acoustic wave consists of alternate positive and negative pressures
above and below the static pressure and, as this is an isentropic process,
the relationship between the instantaneous pressure and the density is
progressively more non-linear as SPLs rise.
In linear acoustic theory, the relationship between pressure and density
is assumed to be linear, which is a good approximation if the changes in
pressure are small compared to the static pressure. A linear relationship
between pressure and density means that the temperature does not change,
so neither does the speed of sound. However, when the changes in pressure
are significant compared to the static pressure, changes in instantaneous
temperature, and hence the speed of sound, cannot be ignored.
In addition, when an acoustic wave exists in flowing air, the speed of
propagation is increased in the direction of the flow, and decreased in
the direction against the flow; the acoustic wave is ‘convected’ along with
the flow. Although steady air flow is not usually encountered where loudspeakers are operated, the particle velocity associated with acoustic wave
propagation can be thought of as an alternating, unsteady flow. Again,
if the particle velocities are small compared to the speed of sound, the
effect can be neglected, but in situations where the particle velocities are
significant compared to the speed of sound, the dependence of the speed
of propagation on the particle velocity must be taken into account.
The result of all of this is that the speed of propagation increases within
increasing pressure and particle velocity, and decreases with decreases in
pressure and particle velocity. For a plane progressive wave, positive pressures are accompanied by positive particle velocities, and the speed of
propagation is therefore higher in the positive half-cycle of an acoustic
wave than it is in the negative half-cycle. The positive half-cycle then propagates faster than the negative half cycle and the waveform distorts as it
propagates. Figure 4.9 shows the distortion, known as waveform steepening, that occurs in the propagation of sound when the acoustic pressures
are significant compared to the static pressure and/or the acoustic particle
velocities are significant compared to the static speed of sound.
4.5 Examples of non-linear acoustics in loudspeakers
At the sound levels typically encountered when loudspeakers are operated,
the effect of pressure and particle velocity on the instantaneous speed of
106 Loudspeakers
Original waveform
p
Steepened waveform
higher C
C0
X
lower C
X=0
Figure 4.9 Waveform steepening due to acoustic pressures that are significant compared to
the static pressure and/or acoustic particle velocities that are significant compared to the
speed of sound, c0
The steepened waveform is no longer a sine wave, and therefore must contain harmonic
distortion
sound is so small as to be negligible, and the resultant linear approximation
is sufficiently accurate. However, there are some situations where this is
not the case. Two common examples are the high sound pressures in the
throats of horn loudspeakers, and the high diaphragm velocities of longthrow low-frequency drive-units.
When horn loudspeakers equipped with compression drivers are used
to generate high output levels, the pressure in the throat of the horn can
exceed 160 dB SPL, with even higher levels at the diaphragm. Sound propagation is non-linear at these levels and the acoustic waveform distorts
as it propagates along the horn. If the horn flares rapidly away from the
throat, then these levels are maintained only over a short distance and
the distortion is minimised. Horns having throat sections that flare slowly
suffer greater waveform distortion (it is interesting to note that the rich
harmonic content of a trombone at fortissimo is due to this phenomenon).
Nevertheless, investigations have shown that the distortion produced by
high-quality horn loudspeakers only exceeds that from high-quality conventional loudspeakers when the horn system is producing output levels
beyond the capability of most conventional loudspeakers.
The use of small, long-throw woofers in compact, high-power loudspeaker systems can also introduce non-linear distortion. The power output
of a loudspeaker diaphragm is proportional to the square of the volume velocity of the diaphragm, so for a given sound power output the
required diaphragm velocity is therefore proportional to the inverse of the
diaphragm area. Consider two loudspeakers, one with a diaphragm diameter of 260 mm, the other with a diameter of 65 mm. In order to radiate the
same amount of acoustic power at low frequencies, the smaller loudspeaker
requires a velocity of 16 times that of the large loudspeaker, as it has 1/16
of the area. The rms velocity of the large loudspeaker when radiating a
sound pressure level of 104 dB at 1 m at a frequency of 100 Hz is approximately 0.5 m/s. The same sound pressure level from the smaller loudspeaker
requires 8 m/s. Whereas 0.5 m/s may be considered insignificant compared
Horns 107
to the speed of sound (= 340 m/s), 8 m/s represents peak-to-peak changes
in the speed of sound of around 8%.
A secondary effect, which is a direct consequence of particle velocities that are significant compared to the speed of sound, is the so-called
Doppler distortion. If, at the same time as radiating the 100 Hz signal
above, the small loudspeaker were also radiating a 1 kHz signal, the cyclic
approach and recession of the diaphragm due to the low-frequency signal
would frequency modulate the radiation of the higher-frequency signal
by approximately 70 Hz. Hence long-throw woofers which are to be used
at high SPLs need to cross over to mid-range drivers at relatively lowfrequencies if Doppler distortions are to be avoided.
4.6 Practical horns in studios and homes
The previous sections have outlined in some depth the concept of the
way in which horn loudspeakers work. This has been necessary before
any meaningful discussions of horns can be undertaken because they are
so poorly understood by the vast majority of people who use them. The
normal state of affairs is that discussions about horns are based on hearsay,
bad experiences due to the abundance of bad designs, and a widespread
misapplication of good designs. In the worlds of public address and sound
reinforcement, the directivity pattern control of horns is a very useful tool.
The benefits of good pattern control normally greatly outweigh the more
subtle aspects of their sound quality. Unfortunately, in the past decades,
many horns which have been used in studio monitoring and domestic hi-fi
systems have been based on sound reinforcement technology, and there
has also existed a lack of understanding about how horn cross-sectional
shapes can have detrimental repercussions on sonic purity.
The non-linear acoustics discussed in Section 4.4 can be a problem
in horns. However, at the SPLs found in most music recording control
rooms and homes, the non-linear propagation region is only occasionally
reached on transient peaks at loud listening levels, and the audibility of
such distortion on transient signals is unlikely to be very great. In fact,
when other types of drive units are pushed to the same levels, they too
may well be suffering from their own forms of non-linearities. Misunderstanding and poor designs have, over the years, created a lot of bad
publicity for horns, yet some horns, such as the famous Tannoy 15 inch
Reds and Golds have been the very antithesis of all that has been said
against horns. As previously mentioned in Chapter 2, above about 1 kHz,
these loudspeakers are nothing more and nothing less than compression
drivers and axisymmetric horns. It has been quite remarkable how so
many people have been heard to say that they cannot work with horns
and yet have quoted the Tannoys amongst their favourite loudspeakers.
Figure 4.10 shows a studio monitoring horn of the highest quality. It bears
a remarkable similarity to the high frequency section of the Tannoy Dual
Concentric shown in Figure 5.10. The development work which led to
the horn in Figure 4.10 took four years to complete. The following summary is taken from Reference 3, which was based on the aforementioned
research.
108 Loudspeakers
Figure 4.10 Axisymmetric horn geometry
The AX2 (see also Figures 8.6(a) and 8.16)
4.7 Implications for practical horn design parameters
By the very careful choice of design parameters and construction, horns
can be produced for use above 1 kHz, or thereabouts, which approach
the performance of electrostatic loudspeakers with their very low levels
of deviation from their intended amplitude and phase (and hence time)
responses. It would appear, however, that there are finite practical limits
to the performance ranges over which horns can produce near optimum
results:
1) The cut-off frequency of a horn is a function of its rate of flare. A low
cut-off frequency demands a slow rate of flare.
2) If ‘horn-like’ sound characteristics are to be avoided in a practical horn,
the length should not exceed 12 inches (300 mm) or thereabouts.
3) Taking 1 and 2 together, if a horn has a low flare rate, and cannot exceed
12 inches in length, then given a 1 inch throat diameter, and, say a 250 Hz
cut-off frequency, the horn will inevitably have a small mouth area.
There will consequently be an abrupt change in cross-sectional area
when it meets the outside air. Samples 4 and 11 in Figure 4.11 highlight
this point, [both were short, low flare-rate horns with small mouths]
showing poor throat impedance linearity, or smoothness, especially near
cut-off. Subjectively, although almost always being grouped with the
direct radiators in the listening tests, as musical reproduction devices
they were not considered smooth, flat, or natural, despite not sounding
typically horn-like.
4) In order to achieve a smooth and trouble-free mouth termination, from
a 1 inch throat of a horn not exceeding 12 inches (300 mm) in length
(diaphragm to mouth), a mouth diameter of around 12 inches would
seem to be the smallest practical size. This dictates a flare rate which
results in a cut-off frequency in the order of 1 kHz, but can yield exceptionally smooth performance through cut-off if carefully designed; even
allowing use through cut-off, and utilising the acoustic roll-off as part
Horns 109
Sample No. : C
10
⏐Z⏐
Sample No. : 1
0
(dB re ρ c)
–10
(π)
∠Z
0
(rads)
0.5
1
2
3
4
5
–π
0.5
Frequency (kHz)
1
2
3
4
5
3
4
5
3
4
5
Frequency (kHz)
Sample No. : 4
10
⏐Z⏐
Sample No. : 5
0
(dB re ρ c)
–10
(π)
∠Z
0
(rads)
0.5
1
2
3
4
5
–π
0.5
Frequency (kHz)
1
2
Frequency (kHz)
Sample No. : 7
10
⏐Z⏐
Sample No. : 8
0
(dB re ρ c)
–10
(π)
∠Z
0
(rads)
0.5
1
2
Frequency (kHz)
3
4
5
–π
0.5
1
2
Frequency (kHz)
Figure 4.11 The logarithmic throat impedance plots of a selection of different mid-range
horns. (This figure is continued on the next page)
of the electroacoustic crossover (see Figure 4.12). [Sample 8 in Figure
4.11 shows the throat impedance plot of such a device.]
5) To minimise internal disturbances which can cause disruption to both
the on- and off-axis responses, all corners, angles and obstructions
should be removed, rendering axial symmetry and smoothly contouring
surfaces. Figure 4.11 shows the logarithmic throat impedance plots of all
110 Loudspeakers
Sample No. : 9
10
⏐z⏐
Sample No. : 10
0
(dB re ρ c)
–10
(π)
∠z
0
(rads)
0.5
1
2
3
4
5
–π
0.5
Frequency (kHz)
1
2
3
4
5
3
4
5
3
4
5
Frequency (kHz)
Sample No. : 12
Sample No. : 11
10
⏐z⏐
0
(dB re ρ c)
–10
(π)
∠z
0
(rads)
0.5
1
2
3
4
5
–π
0.5
Frequency (kHz)
1
2
Frequency (kHz)
Sample No. : 13
Sample No. : 15
10
⏐z⏐
0
(dB re ρ c)
–10
(π)
∠z
0
(rads)
0.5
1
2
Frequency (kHz)
3
4
5
–π
0.5
1
2
Frequency (kHz)
Figure 4.11 Continued
but one of the horns used in the tests. The vastly superior characteristics
of the AX2 (Sample 8) can be readily seen.
6) ‘Squashing’ the axisymmetric shape into an ellipse would perhaps allow
some change in directivity pattern without undue disturbance of the
time response.
Horns 111
a)
C0 = 346.6 m/s
Resistance
Reactance
Date: 21-7-88
Sample type: 1A
MIC. positions: 30 & 55 mm
3
Z/P0C0
2
1
0
1000
2000
3000
4000
5000
b)
3
Normalised throat impedance (Zt = pt/pcut)
Real
Imag.
Zt
2
1
0
0
5000
Frequency (Hz)
Figure 4.12 a) Throat impedance of a horn which has been widely used in studio monitor systems. The systems were generally considered to be typical of horn-loaded systems
b) Throat impedance of the AX2 horn, showing an absence of reflexion-induced irregularities
and a smooth impedance through cut-off. Systems using this horn have generally not been
considered to sound horn-like
Sample 8, mated with the TAD 2001 drive unit produced what would seem
to be a near optimum response in terms of both phase and amplitude (and
hence time), smooth directivity, a very smooth overall performance from
1 kHz to beyond 20 kHz, and was deemed to be very musical, natural,
transparent, and definitely not horn-like. It is interesting that in physical
dimensions, though not in its drive system, it strongly resembles the Tannoy
Dual Concentrics from around 40 years before. The fact that the shape
and size were so similar to the Tannoy 15 inch Dual Concentric HF horn
served to explain why the latter had enjoyed 40 years of use without being
112 Loudspeakers
considered to sound horn-like. It would appear that the Tannoy, all those
years ago, defined the physical limits for accurate performance, beyond
which horns will begin to run into trouble.
Whether the engineers at Tannoy knew all of this at the time when the
Dual Concentrics were first designed, or whether some of them merely
‘saw the logic’ of using a duly contoured bass cone for the horn of a co-axial
system, and recognised that it sounded good, maybe we shall never truly
know. In general, however, there is now no doubt that carefully designed
horns and drivers can produce both sonic and measured performances
as good if not better than the finest dynamic direct radiators, without
any hint of a ‘horn-like’ sound. Indeed, to run a truly seamless 1 kHz
to 20 kHz response within tight limits, whilst producing a very smoothly
controlled directivity pattern (courtesy of a horn emanating a section of
a spherical expanding wave, unlike a piston), a well designed horn and
driver combination can be superior to the vast majority of direct radiators.
If very high sound pressure levels are added to the list of requirements,
there are few alternatives to horns.
4.8 Summary of results
The tests leading to the above conclusions are fully documented, eminently
repeatable, and open to inspection. The initial findings suggest that short
horns can be produced having high efficiency, wide frequency range and
benign distortion levels, which are not sonically horn-like, and can be
grouped as audibly similar to typical direct radiators. Much of the audible
similarity of loudspeakers would appear to be in their time histories, and
where a mouth reflexion effect of a horn is in the same order as any
inherent reflexions in direct radiator units, then general audible grouping
can be expected. Long horns produce longer reflexion delays, and sonically
tend to group together, whilst electrostatics group together due to their
rapid and accurate transient responses. In fact, much of the general audible
similarity of all loudspeaker drive units of similar frequency range and
general overall quality, irrespective of generic type, lies not in the nonlinearities, nor solely in the pressure amplitude response, but in the time
domain response as specified by the linear distortions of the convolution
of the amplitude and phase responses.
The AX2 was developed for the listening tests which led to the
above conclusions at the Institute of Sound and Vibration Research
(Southampton, UK) in 198945 . It was designed to have the minimum number of characteristics which previous research had suggested would lead
to a horn-like ‘honky’ sound. The AX1 – Sample 4 in Figure 4.11 – was
designed to maximise the horn-like characteristics. Neither the AX1 nor
the AX2 were modelled on other loudspeakers, but were designed from
first principles. As it turned out, the AX1 was physically remarkably similar to a horn of widespread use and of well-known manufacture which was
often criticised for its harsh, nasal characteristics, and the AX2 resembled,
physically, the sweeter sounding Tannoys. As mentioned in the earlier sections of this chapter, when mouths are designed from the requirement of
Horns 113
associated components and directivity control only, the acoustic termination to the outside air is often very poor. This gives rise to strong reflexions
from the mouths, which in turn give rise to the roller-coaster impedance
plots typical of so many of the horns in Figure 4.11.
Conversely, the AX2 was designed to minimise the impedance irregularities, which was clearly successful (Sample 8 in Figure 4.11) but the size and
directivity were the natural result of the design, and could not be controlled.
Larger mouths could be smooth down to lower frequencies, but could
give rise to difficulties in closely locating the adjacent drivers at crossover
points. The practice of mounting high frequency horns and/or drivers on
the central axis of the larger horn may ruin the mouth termination of the
latter. The AX2 just about defines the practical limit for a MF/HF horn if
the highest audio quality is the sole aim.
The fact that such strong evidence exists which discourages the use of
horns below 1 kHz for the highest quality audio systems helps to explain
why so many horn-loaded systems have received bad reviews.
Figure 12.18 shows a low frequency horn in a discotheque. This horn is
flat down to 20 Hz. The floor mounting provides an acoustic mirror, so the
mouth is effectively 4 m × 2 m and the length is about 2 m. The loudspeaker
cabinets behind the 1 m2 throat are over a metre deep, and in the throat
are four 18 inch drivers. The sheer size of this horn precludes its use in
studios or homes, but its size cannot be reduced without compromising
its performance. In the discotheque it will produce 140 dB SPL, but the
power level also has nothing to do with its response. Even if it was only
required to produce 80 dB it would still need to be the same size. When a
large array of relatively small horn-loaded bass cabinets are seen at a rock
concert, the mouth areas combine to form one, composite mouth, equal to
the sum of the sizes of the individual mouths. It is no use buying just one
of the cabinets for a small venue and expecting the same response. So, the
large arrays are not just for more volume, but also serve to extend the low
frequency response by augmenting the overall mouth size and making a
better mouth termination to the outside air.
4.9 General horn characteristics
The resistive load which the air presents to a diaphragm when loaded by a
horn gives rise to rapid transient responses. Subjectively, good horns sound
‘fast’. The high sensitivity which is characteristic of most horn designs
leads to small voice coil currents in powerful static magnetic fields. This
tends to lead to less Bl profile distortion, because the integrity of the static
magnetic field against which the voice coil field must push is much less
disturbed as compared to a high voice coil current distorting the field of
a weaker magnet in a heavier diaphragm, low sensitivity design. Despite
many common beliefs, horn-loaded loudspeakers are capable of very low
distortion reproduction if only the appropriate rules are respected and they
are not pushed beyond the limits where the air, itself, is non-linear. In too
many cases horns have been used which are too small for the frequency
range in which they have been operated, and flare shapes have been used
114 Loudspeakers
Figure 4.13 The Meyer HD2, using an axisymmetric horn and a non-compression driver
Figure 4.14 A Genelec 1038A loudspeaker system which employs vestigal horns, or
‘waveguides’, to load the mid-range and high-frequency drivers
for their directivity performance with little consideration for the need for
low colouration through the use of smooth contours.
Figure 4.13 shows a loudspeaker system which effectively horn loads a
dome tweeter. In this case no compression driver is used. This is only one
step away from the design shown in Figure 4.14, where vestigial horns are
Horns 115
used as ‘waveguides’ (another name for horns) in a very popular studio
monitoring loudspeaker. In fact, a direct radiator on an infinite baffle is
mounted on a 180 degree horn of infinite flare rate. There is therefore no
dividing line between direct radiation and horn loading. They are part of
the same continuum which extends from the infinite 180 degree baffle to the
infinite parallel pipe. It therefore follows that if somebody says that they
do not like horns, one has to ask the question “Which horns?” The scope of
what constitutes a horn is enormous, and so is the scope of the compromise
points for any designs. Equally enormous, therefore, is the range of possibilities for making inappropriate compromises. Unfortunately, what we
generally consider to be horns are relatively complex, precise devices, and
hence are normally quite expensive when compared to direct radiators for
use at relatively low SPLs. So, when corners are cut in the production
process in attempts to reduce the costs, the sound quality usually suffers.
Again, horns in general cannot be criticised because of the failings of badly
engineered, cheap products.
The Tannoy Dual concentric concept has already been noted as not
sounding horn-like, however the principle does suffer from two drawbacks.
The high frequency horn is the cone of the bass driver, and it therefore
moves, axially, with the low frequency signal. At high SPLs, the movement,
peak to peak, can be a significant proportion of a wavelength at the highest
audible frequencies, so some modulation effects are only to be expected,
the degree of which are both level and frequency dependent. The Tannoys
therefore tend to sound sweeter at low levels than at high levels. The
second problem is that the voice coil gap, seen clearly in Figure 5.10, is a
discontinuity in the throat of the horn, which on the larger devices can be
a source of reflexions whose amplitude again depends upon the excursion
of the bass cone. Nevertheless, despite these drawbacks, the concentric
nature of the high and low frequency drivers facilitates the engineering of
a relatively seamless crossover and a radiation pattern uniformity which
many people consider to be sufficiently beneficial to offset the drawbacks
of the designs, especially when listening levels are relatively low.
Another characteristic of the Tannoy design is that it uses a lowcompression driver. As described in Section 4.1, high compression ratios
are often used in order to increase the sensitivity of the driver by increasing
the radiation resistance. However, if a high frequency horn loudspeaker is
only to be used with a relatively inefficient low frequency driver, and at
relatively low SPLs, there would seem to be no reason for compromising
its sonic purity by using unnecessarily high compression. The choice of
Tannoy has been to use low compression, low sensitivity, high frequency
horn systems in most of their Dual Concentric designs.
4.10 Phasing plugs
A horn loudspeaker is shown in Figure 4.13 in which the diaphragm is
mounted directly at the throat of the horn. No compression is used in this
design as the diaphragm and throat are of the same diameter. By contrast,
Figure 4.5 shows the concept of compression, where the diaphragm area
is much greater than the throat area. Unfortunately, except for use as
116 Loudspeakers
Section view
of compression driver
Magnet
Moving mass, MMS
(diaphragm plus
voice coil)
Magnetic gap
(flux density B)
b
End view
of phasing
plug
Projected area
of phasing plug, SD,
in square meters
Pole piece
Phasing
plug
Driver
exit
Compliance, C
Voice coil
Top
(length, l, in meters; plate
resistance, RE,
in ohms)
Area of
annular slits on
phasing plug, ST,
in square meters
ST
= 0.1
SD
Figure 4.15 A typical phasing plug (courtesy of JBL Professional)
an electric klaxon or evacuation alarm, the design of Figure 4.5 would
be of little use, because the pressure fluctuation from the perimeter of
the diaphragm would take longer to reach the throat of the horn than
the fluctuation from the centre of the diaphragm. The different distances
from the different parts of the diaphragm to the throat of the horn would
give rise to phase differences and severe losses at high frequencies. To
overcome this problem, compression drivers use phasing plugs as shown
in Figure 4.15.
There are various types of phasing plugs, using either a series of tubes
or axial slits to connect the various parts of the diaphragm to the horn
throat via equal length pathways. The geometry of these needs to be very
carefully controlled, because with a wavelength of only about 17 mm at
20 kHz, a path-length difference of only about 8 mm would reverse the
polarity of the wave at the exit, and cancellation would result.
Because of the extreme sound pressure levels that can exist in the tubes,
they represent one of the few situations in audio where actual air flow can
result, leading us into the domain of aerodynamics rather than acoustics.
Care must therefore be taken to avoid sources of turbulence, which can give
rise to modulation dependent noises and gross distortion. The small size
of the phasing plug tubes can also make visco-thermal losses significant.
Horns 117
4.11 Acoustics lenses
Figure 4.16 shows a selection of acoustic lenses, also known as a slant
plates, chip-cutters, crinkle plates and pepper-pots. These were in vogue
in the late 1960s and the 1970s and were developed as solutions to the
problem of how to better match a short, slow-flaring horn to the outside
air. They first came into use in the 1950s, in cinema loudspeaker systems,
but took some time to find their way into the music recording studios.
In all cases, the path through the centre of the lens is shorter than the
path through the outer sections, and thus the wavefront was bent into a
wider directivity pattern. Acoustic lenses worked well from a technical
point of view, but could give rise to audible colouration. The time during
which JBL used them for their studio monitor systems was quite short, but
the high respect for JBL and the high profile of their users led to other
companies copying them, and using them for many years after JBL had
already abandoned them for studio quality monitoring.
a)
b)
Top
view
Side
view
c)
Figure 4.16 A family of acoustic lenses (courtesy of JBL Professional)
118 Loudspeakers
4.12 Horn types
Already mentioned in Section 4.3, and illustrated in Figure 4.7 was the
radial horn, also known as the sectoral horn. The first name comes from
the fact that the straight side walls in one direction form the radial lines
of a circle, which meet at an imaginary apex behind the throat. They also
have the appearance in plan view of a sector of a ‘pie-chart’, hence the
name ‘sectoral’. For the highest quality subjective listening they have three
basic problems. First, the cross-sectional shape must somehow be made
to match the circular orifice of a compression driver. In some examples,
even expensive ones, this was rather abrupt, leading to uncontrolled waveexpansion in the sensitive throat area of the horn. Such practices are simply
begging for colouration due to reflexion problems. It has been shown that
any discontinuity in the flare, especially near the throat, will give rise to
reflexion-induced colouration 35 . Figure 4.17 shows a cepstrum plot of an
AX2 horn mated to an Emilar EK175 driver. The cepstrum plot is useful
for identifying echoes or reflexions in signals or responses. [See Chapter 9.]
The flare rate of the throat tube of the EK175 was not a precise match to
the flare rate at the throat of the horn, even though both were perfectly
circular, and the series of reflexion spikes before 2 ms was the result. When
the AX2 was mated to the TAD TD2001 compression driver, the flare
from throat tube to horn was continuous, and the reflexions disappeared.
The second problem with the radial horns is that the geometrical discontinuties at the junctions between the top, sides and bottom of the horns,
even though not affecting the flare rate, can lead to off-axis colourations
at normals to the discontinuities. In non-reflective environments this may
not be a problem, but it can lead to coloured reflexions in more lively
environments. The third problem involves the mouth termination, which
is often achieved by means of rounded lips which project from the front
Sample 6
2
1
0
0
2
4
6
time (ms)
Figure 4.17 Power cepstrum of the Emilar EK175/AX2 combination. The series of diminishing
echoes in the first 2 ms result from the flare-rate changes at the driver/horn junction
Horns 119
baffle. These can lead not only to diffraction problems from the horn itself,
but also from the obstructions which they may cause to the expanding
wavefronts from the other drivers of the loudspeaker system. Dividers,
which sectionalise some of these horns for improved directivity control also
can act as diffraction sources. The general rule for horns for the highest
fidelity is that nothing must disturb the flare rate, the flare should blend
smoothly into the baffle, and no geometrical changes should exist other
than the defined expansion rate. All of these things can detract from the
sonic purity of the horn.
Diffraction horns are another type of horn. They have mouths that are
wide in one direction and narrow in the other, the narrow dimensions
relying on diffraction from a relatively sharp edge to widen the directivity. Unfortunately, diffraction necessarily introduces reflexions, and, as has
just been stated in the last paragraph, for the highest fidelity, everything
should be done to avoid reflexions in the flare of a horn. The constant
directivity/uniform coverage horns also rely on the diffraction principle
for the wide directivity of the higher frequencies, so the same comments
apply. As discussed previously, attempts to take tight control of directivity
come at a cost in terms of other aspects of horn response. In this case,
the evenness of the throat impedance suffers from the reflexions given rise
to by the diffraction. In general, when listening in rooms with highly controlled acoustics, the reflexion-induced colouration resulting from diffraction horns is noticeable. The exception to this is on very high frequency
loudspeakers, say 7 kHz and above, where the reflexion delays are very
rapid and the sensitivity to this type of colouration at such high frequencies
is minimal.
Multicellular horns are rarely used nowadays, neither in studios nor
cinemas. A multicellular horn, as shown in Figure 4.18, is a grouping of
smaller horns which is designed to deliver an even frequency distribution
over a desired area by means of the use of many narrow horns of uniform
coverage angle. The mouth sizes sum, but unlike in the case of a radial
horn of the same sized mouth, the high frequencies are less likely to
loose contact with the walls because the individual horns are so narrow.
Nevertheless, similar to the situation with the radial horns, the question
arises as to how to match the throats of the compound horn to the throat
of the circular driver without any discontinuities. However, some modern
multicellular horns combine the horn cells with the phasing plug, thereby
eliminating problems caused by the manifolds used in earlier designs. For
a good compromise between sound quality and directivity control, a welldesigned multicellular horn is hard to beat.
4.13 Materials of construction
There should not really be sonic differences between horn construction
materials as long as they are sufficiently rigid and highly damped. However,
if these conditions are not met, the horns can be excited into resonance,
particularly noticeable on transient signals. Aluminium, solid wood, plywood, plastics and glass-fibre are all commonly used materials. The horn
120 Loudspeakers
Figure 4.18 A family of multicellular horns showing the throat adaptors which, after changing
section from round to square, must adapt the single driver to the multiple horn throats. This
is very difficult to achieve in any precise manner (photo by Altec)
shown in Figure 8.2 is made from a specially selected Japanese apitong plywood, which is dense and highly damped. The horn shown in Figure 8.6(a)
is made from glass-fibre which has been loaded with powdered slate. Some
metallic horns have exhibited characteristic rings, but these have rarely
found their way into studio monitoring or audiophile hi-fi loudspeakers.
Nevertheless, in musical instrument amplifier use they have been used with
no detrimental effect.
In many cases, the materials which have been used to make horns have
been chosen for reasons such as ease of manufacturing or conditions of
use. Massively heavy horns, for example, would be a poor choice for
mobile sound reinforcement equipment where the benefits of their subtleties would be totally lost, so lighter weight materials have been the
norm. Complex shapes have traditionally been easier to mould than to
machine, so they have tended to be made from mouldable materials for
manufacturing reasons, rather than for acoustic reasons. When material
choices have been made for purely acoustic reasons, the results, such as
the horns made from apitong plywood, have often been very expensive,
and are actually only found in limited quantities. One result of this situation is that relatively few people have experienced what horns can achieve
when the manufacture and marketing constraints are removed. Horns have
suffered from a terrible history of compromise.
4.14 Vestigial horns and ‘waveguides’
Shown in Figure 8.6(c) is the sculpted baffle of a large Genelec monitor system. The fact that Genelec refer to them as Directivity Control
Waveguides (DCWs) suggests that their prime design function is just that,
Horns 121
but nevertheless they are horns. In the Genelec case, they only slightly
increase the sensitivity of the drive unit. The principal difference between
the AX2 in Figure 4.10 and the DCWs is that the compromise points are
different. The AX2 aims at increasing sensitivity, and the waveguide role
is secondary, whereas the priorities are reversed for the DCW. It is also
true that the DCW does not use a compression horn, yet neither does the
high frequency horn shown in Figure 4.13, which places the diaphragm of a
tweeter somewhat similar to that which is used for the high frequencies in
Figure 8.6(b) at the throat of a horn similar to the AX2. In the latter case,
the extra sensitivity afforded by a compression driver was not necessary
for a system so small as the Meyer HD2. The system in Figure 8.6(b) uses
a titanium dome mid-range unit which is clearly mounted in a short horn
for reasons of improved sensitivity and directivity control.
To many people, the mid-range loudspeakers shown in Figure 8.6 a)
and d) are horn loaded, and the systems in Figure 8.6(b) and (c) are not
horn loaded, yet the truth is that they are all horn loaded at the mid and
high frequencies. In Morfey’s ‘Dictionary of Acoustics’ 6 the definition of
a horn is:
‘– a waveguide whose properties are arranged to vary monotonically
from one end to the other, in order to produce a resistance in the
lowest order waveguide mode . that is many times larger at the
driver end than at the opposite end’.
How many times larger is not specified. Therefore, by definition, a horn
is a waveguide, and the continuum shown through Figures 8.6(c), 8.6(b),
4.13, 8.7 (the low compression Tannoy), 8.6(a) and 8.6(d) demonstrates
a very wide range of increasing loading, but without any differences in
the operating principles of the waveguide/horn effects. Even a conventional loudspeaker cabinet placed on the floor in the corner of a room is
being loaded by a triangular cross-section low frequency horn, as shown
in Figure 7.9.
Sculpted baffles are therefore nothing magic, but are based on sound
acoustic principles. However, they were late arriving because until the
advent of computer modelling and CNC (computer numerically controlled)
machinery, their precise design and construction was difficult. Despite their
complex shape, the desired overall flare rate must be maintained up to the
point where they blend into the front panel.
4.15 Flare rates
Although the majority of horns are based upon exponential flares for the
reasons given in Section 4.1, other flare rates are also used. Hyperbolic
horns appear from time to time, but catenoidal and hypex horns have also
been used. In fact the horn shown in Figure 4.10 begins its flare on the
conical side of exponential, then passes through exponential. The design
aim was to maintain the optimum phase response in the expanding wave
122 Loudspeakers
a)
Conical
Exponential
Hyperbolic
Various horn shapes
1.2
HYP
ERBO
L IC
1.0
.8
EX
P
T
EN
ON
IAL
AL
.6
.4
IC
NORMALISED ACOUSTICAL RESISTANCE
b)
N
CO
ƒe = CUT OFF FREQUENCY
.2
0
ƒe
2ƒe
3ƒe
4ƒe
5ƒe
6ƒe
7ƒe
NORMALISED FREQUENCY
Throat impedance for
various flare shapes
Figure 4.19 Comparison of flare geometrics. a) An infinite variety of shapes is possible
between conical and hyperbolic. b) The drawing shows how the throat impedances for the
three main types of horn varies with frequency
leaving the mouth of the horn. The relationship between the three most
common shapes can be seen from Figure 4.19.
The throat cut-off frequency is determined by the rate of expansion of
the horn. Doubling the horn length for a given mouth and throat size will
halve the flare rate and lower the cut-off frequency by an octave. Halving
the horn length will double the cut-off frequency, (raise it by an octave) if
the throat and mouth sizes are kept constant.
As can be seen from Figure 4.19(b), exponential flares begin to loose
their efficiency well above the normal cut-off frequency, which means that
they are normally only used above about half an octave above cut-off.
The hyperbolic horns function almost all the way to the theoretical cutoff, but the abrupt nature of their response fall-off can give rise to phase
Horns 123
distortions which can lead to coloured responses. Nevertheless, for efficient
public address applications this may not be a problem, and their amplitude
benefits can be exploited.
At low frequencies, some loudspeaker cabinets use folded horns, but
it is very difficult to maintain a constant flare rate around all the folds,
so reflexions and resonances can be problems and response flatness can
be difficult to achieve. Some rather complex shapes have historically been
applied to such horns with varying degrees of success. Nowadays, however, with much more powerful low frequency drivers and amplifiers being
available, the use of low frequency horns has become a rarity, except for
sound reinforcement uses. Nonetheless, due to the resistive loading which
the horn provides on the face of the driver, horn loaded bass systems are
frequently liked for their characteristically fast and detailed subjective low
frequency response.
Richard Small, in his 1970 paper ‘Constant-Voltage Crossover Network Design7 ’ highlighted this difference between horn-loaded and directradiating devices, and considered its implication for crossover design when
used between horns and cones. He stated that whilst direct radiation
diaphragm motion is largely mass-controlled, horn diaphragms are resistance controlled, and that the result is a constant phase difference of 90
degrees between the transfer characteristics of the two types of drivers. As
previously stated in Section 4.1, the reactive loading (due to mass control)
and the resistive loading (due to horn loading) are the mechanisms primarily responsible for the sensitivity differences – more power being radiated
by the drivers which are resistively loaded, given the same electrical input.
References
1 Keele, D. B.Jnr., ‘Optimum Horn Mouth Sizes’, Presented at the 46th Convention
of the Audio Engineering Society, Preprint No 933 (1973)
2 Keele, D. B.Jnr., ‘What Is So Sacred About Exponential Horns?’ Presented at
the 51st Convention of the Audio Engineering Society, Preprint No 1038 (1975)
3 Newell, P., ‘Studio Monitoring Design’, Focal Press, Oxford, UK (1995)
4 Holland, K.R., Fahy, F. J, Newell, P. R., ‘Axi-symmetric Horns for Studio Monitoring Systems’, Proceedings of the Institute of Acoustics, Vol. 12, Part 8, pp
121–128, Reproduced Sound 6 Conference, Windermere, UK (1990)
5 Newell, P. R., Holland, K.R., ‘ Do All Mid-Range Horn Loudspeakers Have A
Recognisable Characteristic Sound?’ Proceedings of the Institute of Acoustics,
Vol. 12, Part 8, pp 249–258, Reproduced Sound 6 Conference, Windermere, UK
(1990)
6 Morfey, C. L., ‘Dictionary of Acoustics’, Academic Press, London, UK and
San Diego, USA (2001)
7 Small, R. H., ‘Constant-Voltage Crossover Network Design’, Journal of the
Audio Engineering Society, Vol. 18 pp 172–180 (1970)
Chapter 5
Crossovers
5.1 What is a crossover?
The term ‘crossover’ appears to have been originally used to describe the
relationship of the filter slopes – crossover filters – as shown in Figure 5.1.
In reality, and in many languages other than English, they are better
described as frequency dividing networks, or words to that effect, though
the name crossover has generally stuck. The fact that no loudspeaker drive
unit suitable for music monitoring or serious listening can provide a flat
response over the entire musical frequency range requires that the multiple
drivers in a system need to be fed by signals which are only appropriate
to their designed performance range. The two normal ways to apply these
filtered signals are via high level, passive crossovers – where the filter
components are placed between the power amplifier and the loudspeaker
drive units, or low level active crossovers – where the filters are placed
in the line level signal circuits, ahead of the amplifier inputs. In the latter
case, each filter output feeds a separate amplifier, which is then directly
connected to the corresponding drive unit(s). In some cases, mixtures of the
two concepts are applied to one system, such as an active crossover between
the bass and mid drivers, and a high level passive crossover between the
mid and high frequency drivers, as shown in Figure 5.2.
Other forms of crossover also exist, such as simple, low-level passive
crossovers, though they are rarely used because the filters can be more
precisely tailored when the components are part of the feedback path in an
electronic circuit. Mechanical crossovers are another type of filter. These
can take the form of aluminium domes in the centre of the cones, which
decouple from the main cone at higher frequencies and radiate separately,
extending the frequency response above that which could be achieved by
the main cone, alone. However, the response tends to be somewhat irregular, but this type of high frequency extension can find use in loudspeakers
for music production – as opposed to reproduction – and the technique
is extensively used in loudspeakers for musical instrument amplification,
such as guitar amplifiers. An example is shown in Figure 5.3. Figure 5.4
shows a ‘parasitic cone’ or ‘whizzer cone’. The concept is generally the
same in principle as that of the metal dome – the small cone decouples
from the main cone at high frequencies – although the response of the parasitic cone tends to be more controlled, and a flatter frequency response
can normally be achieved. Another concept, although not widely used, is
inductive coupling, where the high frequency cone is not electrically connected to the amplifier. In fact, the coil can be the single, shorted turn
Crossovers 125
Crossover
region
knee
LF
pass band
dB
HF
pass band
dBs down at
crossover point
crossover point
straight portion
of slope - described
in decibels per octave
Hz
crossover frequency
Figure 5.1 The basic concept of a pair of crossover filters
4 kHz passive, high level
crossover between mid and
high frequency drivers
Level control
Low level
crossover
Full-range
line level
input
Active
two-way
filter
800 Hz
crossover
Power
amplifier
Mid and
high
frequency
output
High
frequency
driver
Mid
frequency
driver
Low
frequency
output
Level control
Power
amplifier
Low
frequency
driver
Figure 5.2 Example of a crossover system employing both active, low-level and passive,
high-level filters
formed by the metal dome itself. The dome and a former are simply placed
over the centre pole of the magnet assembly, sharing the same gap as the
LF/MF cone assembly. Such inductively coupled transducers, or ICTs, are
operated by the modulated magnetic coupling between the ‘coil’ and the
magnetic circuit. This type of ‘crossover’ is neither electrical, electronic
nor mechanical, but is simply a magnetic-inductive effect.
5.2 Reconstruction problems
Unfortunately, the division of the frequencies is not all that a crossover
must achieve. They must divide the frequencies in a way that the individual
drive units can re-construct in the acoustic far-field of the loudspeaker
126 Loudspeakers
10
Frequency Response
0
–10
10000
5000
2000
1000
500
200
100
50
–20
Closed Box
Figure 5.3 The Gauss model 4281, 12 inch (300 mm) drive unit for musical instrument use,
which used an aluminium dome to extend the high-frequency response to over 5 kHz
a representation of the waveform which was electrically applied to the
electronic amplification system, and it is not an easy task to do so. Figure 5.5
shows a representation of a typical, two-way loudspeaker system. Note
how, due to the physical requirement of the radiation of the different
frequency bands, the sizes of the drive units give rise to a displacement
of the voice coils if the front faces of the drives share a plane, common
baffle. If the displacement were to be 10 cm, then a frequency with a
wavelength of 20 cm would be received on the axis between the two drivers
with its polarity reversed from either driver with respect to the other. The
wavelength () can be calculated by dividing the speed of sound (c), in
metres per second, by the frequency (f ) in Hz, so we arrive at the formula:
=
c
f
(5.1)
To find the frequency with a wavelength of 20 cm, we can re-arrange the
formula as:
c
f=
Therefore: f =
340
= 1700 Hz
02
Crossovers 127
Surround
Free-edged
parasitic cone
Main cone
Coil former
Dust dome
Figure 5.4 Parasitic, free-edged cone for high-frequency extension
HF driver
LF driver
= displacement of alignment
of the voice coils
Figure 5.5 Elevation of a two-way loudspeaker system showing the typical offset of the voice
coils in the axial plane
128 Loudspeakers
dB
1.7 kHz
100
1000
Hz
10 k
Figure 5.6 Composite response of the loudspeaker shown in Figure 5.5 on its central axis if
the distance x were to be set at 10 cm
At 1700 Hz we would have cancellation on axis, producing a response as
shown in Figure 5.6
However, this is not the only complication which arises in the reconstruction. All conventional filters exhibit the property of ‘group delay’. There
is a finite time necessary for the information in a signal waveform to pass
through a filter, which is a function of the slope of the filter and its cut-off
frequency. As the frequency drops, the delay increases. As the steepness of
the filter slope increases, so does the group delay. A filter of 24 dB/octave
at 300 Hz would exhibit a group delay of around one millisecond. With a
speed of sound of 340 m/s, one millisecond would represent 340/1000 m/s, or
a 34 cm equivalent physical displacement. If the loudspeaker represented
in Figure 5.5 were to be fed via such a crossover, the real radiation from the
low frequency driver would be delayed by the equivalent of being mounted
44 cm behind the HF driver, (34 cm due to the filter and 10 cm due to the
physical misalignment). Figure 5.7 shows the step-function responses of
four loudspeaker systems with different degrees of arrival synchronisation
from the drive units. Figure 5.7(d) shows the step response of a commercial
3-way loudspeaker which clearly exhibits delays between the arrival times
of the individual drive units.
In effect, if not compensated for, the flat-response-axis of the loudspeaker shown in Figure 5.5 would be tilted, as shown in Figure 5.8, for
moderate low frequency signal delays. Conversely, though, if we engineer
a flat response on axis by compensating for the delays, it follows that the
frequency responses off-axis must be incorrect, as shown in Figure 5.9. So,
it can be appreciated that once the drive units have been physically separated, the problem of reconstructing the waveform of the original signal can
become very difficult indeed. The problem can be partially solved by the
use of concentric loudspeakers, but these concepts bring their own problems with them. For example, with the Tannoy, Dual Concentric approach,
or the KEF Uni Q for that matter, the low frequency cone serves as a
horn/waveguide for the high frequency driver. Modulating the LF cone
with high levels of low frequencies can hardly be expected not to affect the
high frequencies. In the case of the Tannoys, the LF coil gap also serves as
an unwanted discontinuity in the HF horn. The general concepts of these
drivers are shown in Figure 5.10, along with the Altec/UREI approach. In
Crossovers 129
a)
b)
1
Amplitude
Amplitude
1
0
–1
0
–1
0
5
10
15
0
20
5
Time (ms)
c)
15
20
15
20
d)
1
Amplitude
1
Amplitude
10
Time (ms)
0
–1
0
–1
0
5
10
15
Time (ms)
20
0
5
10
Time (ms)
Figure 5.7 Step function responses with one, two and three drivers. a) Integrated attack of
a relatively wideband, single driver. b) Integrated attack of two-way system with excellent
time alignment. c) Separate rise times visible from the two drivers of a system with slightly
delayed low frequency driver response. d) 3-way system with a clearly delayed response from
the bass driver
In the latter case, the delay was a consequence of designing the system so that the main
lobe of irregular response was forced upwards into a generally inoffensive direction. The
trade-off was considered to be beneficial to the overall performance in typical situations in
which is was expected to be used
the latter case, the separate, concentrically mounted horn is left hanging in
free air, but this method of mounting is really, too abrupt for proper mouth
termination at the 1 kHz crossover frequency. The termination problem
was discussed in detail in the previous chapter. Therefore, as so very often
is the case with loudspeaker design, the tendency is to be trading one problem for another, rather than solving them – finding the best compromise
for each situation – but that is often the reality of loudspeakers, which is
something that will form the basis of discussion in Chapter 8.
5.3 Orders, slopes and shapes
Despite the different solutions on offer, electrical filters are overwhelmingly the most common manner of dividing the frequency bands. Whether
this is done at high level, low level, actively or passively, the same basic filter
concepts apply. Figure 5.11 shows a simple high pass filter, (a) to (d) showing first, second, third and fourth order roll-offs, respectively. Each inductor
or capacitor adds 6 dB per octave of roll-off, and each 6 dB is known as an
130 Loudspeakers
Point equidistant
between driver
axes
Geometrical axis
°
°
Acoustical axis
at crossover
frequency
Point equidistant from the driver
voice-coil centres - hence time
of arrival from each driver will
be simultaneous, and therefore
in phase alignment
Figure 5.8 Tilting of the acoustic axis at the crossover frequency due to voice-coil physical
displacement. On this axis, the response dip shown in Figure 5.6 would not be observed – the
response would be flat
Z
Common geometrical
and acoustical axis
Cabinet with two
identical drivers
radiating equally
Z
Figure 5.9 Lobing of the response when physically displaced drivers radiate a common
frequency whose wavelength is close to, or smaller than, the distance between the drivers
Z = axis of phase cancellation – varies with frequency – cancellation occurs whenever the
distance to the two drive units varies by half a wavelength. The pattern shown therefore
represents the situation at one frequency, only
Crossovers 131
a)
Phasing plug, to extend
and smooth HF response
Roll surround for stability
in low bass response
Acoustic balance
cavity for reduced
distortion
Ribbing, to greatly reduce
cone break-up at high
excursions
HF diaphragm
High-temperature voice-coil
Acoustically transparent
dust dome
Aluminium voice-coil
Concentric HF horn, the
extension of which is
provided by the LF cone
Magnet shunt for
increased LF flux
b)
c)
LF cone
HF diaphragm
HF horn
HF magnet LF magnet
assembly
assembly
HF dome
Figure 5.10 Some concentric drive units. a) Tannoy Dual Concentric – with Alnico magnet
structure (courtesy of Tannoy Ltd) b) The KEF Uni-Q. c) The Altec 604
order of roll-off, a term which comes from the mathematical application
of filter theory. An alternative approach to the inductor/capacitor (LC)
design is a resistor/capacitor (RC) method shown in Figure 5.12. The LC
approach is preferred for high level crossover in the loudspeaker/amplifier
interface because the power losses are much less, but the RC approach is
preferred in low level circuitry because of its simplicity (perfect inductors
are not easy to make) and its relative insensitivity to drift and interference
pick-up. In the active circuits, where gain is plentifully available, the higher
losses of the RC circuits are of little consequence.
First order crossovers are rarely used, because the low rate of roll-off
requires the individual drivers to have respectably flat responses for at least
132 Loudspeakers
pass band
C
1st order
IN
OUT
dB
slope - 6 dB/octave
Hz
C
2nd order
L
IN
OUT
dB
slope - 12 dB/octave
Hz
C
C
3rd order
L
IN
OUT
dB
slope - 18 dB/octave
Hz
C
C
IN
L
L
4th order
OUT
dB
slope - 24 dB/octave
Hz
Figure 5.11 Capacitor/inductor filters – circuits and slopes. Values C and L depend upon the
turnover frequency and the load impedance
two, if not three, octaves each side of the crossover point, which is usually
not practicable. Nonetheless, when they are able to be used, they have the
advantage that they are the only conventional crossovers whose combined
outputs reconstruct the input waveform. This is shown in Figure 5.13, and
results from the fact that although each side of the filter is only 3 dB down
at the crossover frequency (voltage summing would normally require that
they should be 6 dB down to sum back to a flat response) the +45 degrees
phase shift through one half of the crossover and the −45 degrees phase
shift through the other half give rise to a 90 degrees combined shift
which leads to another 3 dB of attenuation. The combination of amplitude
roll-off and phase shifts leads to the perfect reconstruction shown in
Figure 5.13.
Crossovers 133
C
1st order
R
IN
OUT
C
C
C
C
R
R
R
C
C
IN
OUT
C
R
IN
2nd order
R
R
IN
3rd order
OUT
C
R
C
R
4th order
R
OUT
Figure 5.12 Resistor/capacitor equivalents of the filters shown in Figure 5.11
Except for the first-order filter, and where the R is supplied by the loudspeaker load
impedance, these filters are not suitable for use as high-level filters because of the excessive
power dissipated in the resistors. Values of C and R depend on the turnover frequency and
the load impedance
+
(i)
VOLTAGE
0
OR
PRESSURE
–
DC INPUT
STEP
(ii)
(iii)
LOW FREQUENCY
OUTPUT
+
HIGH FREQUENCY
OUPUT
(iv)
=
SUMMED
OUTPUT
TIME
Figure 5.13 6 dB/octave crossover waveform reconstruction
Second order crossovers, with their 12 dB/octave roll-offs, are very popular with the manufacturers of small, two-way cabinet loudspeakers. They
are relatively cheap to construct and the power losses through the filters are
quite small, but, as can be seen from Figure 5.14, they will not reconstruct
134 Loudspeakers
a)
+
(ii)
(i)
VOLTAGE
OR
PRESSURE
(iv)
0
D C INPUT
STEP
LOW FREQUENCY
OUTPUT
HIGH FREQUENCY
OUPUT
TIME
–
SUMMED
OUTPUT
IN PHASE
c)
b)
+
+
(v)
VOLTAGE
OR
PRESSURE
(iii)
0
0
D C INPUT
STEP
–
(vii)
(vi)
CROSSOVER
POINT
SUMMED
OUTPUT
OUT OF PHASE
TIME
–
SUMMED ELECTRICAL OUTPUT
FREQUENCY (AMPLITUDE) RESPONSE
STRAIGHT LINE = OUT OF PHASE CONNECTION
DOTTED LINE = IN PHASE CONNECTION
FREQUENCY
Figure 5.14 12 dB/octave crossover waveform reconstruction. a) In-phase. b) Reversed
polarity. c) Amplitude responses
Note that whichever polarity is applied, the output waveform is not a true representation
of the input waveform. (The waveform in Figure 5.13 reconstructed perfectly)
the original waveform. The group delays associated with the phase shifts
cause a temporal offset between the two halves, so the reconstruction is
not summing the two outputs at the same instant. This ‘latency’ in one half
of the filter, relative to the other, creates a phase shift at the crossover
frequency which does not compensate for the amplitude summation; hence
the time and amplitude summations shown in Figure 5.14(a). Despite the
fact that the reversing of the polarity of one of the outputs yields a flat
amplitude response, the time response (waveform) becomes even more
distorted. This is shown in Figure 5.14(b). There are ways of ‘juggling’ this
arrangement by offsetting the 3 dB down points so that the filter sections
overlap, but this can introduce other irregularities unless it is very carefully implemented. However, in general, a standard second order crossover
yields either a flat frequency response or a synchronous time response, but
cannot exhibit both properties at the same time.
Third order crossovers, with slopes of 18 dB/octave are popular in more
expensive passive loudspeaker systems, and are not infrequently used in
active crossovers. They are more expensive in the passive form than the
second order types, not only because they use more components, but also
because the components may need to be less lossy. Otherwise, with so many
components between the amplifier and the drive units, they would begin
to sap considerable power from the signal. Typical circuit diagrams are
shown in Figure 5.15, and a response summation is shown in Figure 5.16.
The 18 dB/octave roll-off is useful in reducing the disturbance from out
of band irregularity of the driver responses, because the driver responses
can be almost 20 dB down an octave beyond the crossover frequency. This
allows drivers to be used over almost all of their flat response region,
but with third-order crossovers there is no ‘correct’ polarity relationship
between the outputs. The phase responses for normal and reversed polarity are shown in Figure 5.17, and the reverse polarity connection actually
Crossovers 135
a) Parallel circuit
L1
L3
1.7 mH
0.6 mH
C2
Input
C1
33 µF
Low
frequency
output
C3
14 µF
43 µF
L2
0.9 mH
High
frequency
output
C3
10 µF
Low
frequency
output
2.4 mH
High
frequency
output
b) Series circuit
L1
1.6 mH
C2
33 µF
Input
L2
0.8 mH
L3
C1
16 µF
Figure 5.15 Typical, 2-way, 18 dB/octave, 3rd order passive crossover circuits
Approximate values shown for 1 kHz crossover frequency and a uniform loading of 8 ohms
Input
voltage
–10E– 03
time (ms)
49.52E– 03
Output
voltage
time (ms)
Figure 5.16 Summed output of a 3-way, 18 dB/octave crossover
The signal path delays through the individual filter sections are clearly evident
136 Loudspeakers
Phase angle (degrees)
0
Inverted
–180
–360
Normal
f0
Log frequency
Figure 5.17 Phase relationships through the crossover region for the normal and inverted
polarity connection of a third-order Butterworth crossover – f0 is the nominal crossover
frequency
exhibits less phase shift through the crossover region after the summation
of the outputs. However, this is the effect of simply summing the electrical
outputs. Once those outputs are connected to physically displaced loudspeakers the story can be rather different.
One of the most popular types of crossover filter for use in active designs
is the fourth order Linkwitz-Riley. The 24 dB/octave slope is achieved by
cascading a pair of Butterworth (see next section) 12 dB/octave crossovers.
The 24 dB/octave slopes are beneficial in high-power loudspeaker systems,
where out-of-band energy is rapidly cut off, and for use with drivers whose
out-of-band response is also irregular. The power response exhibits a dip
at the crossover frequency, but the width of the dip is so narrow as to be, in
many cases, almost inconsequential. The on-axis amplitude response is flat,
because each section is normally designed to be 6 dB down at the crossover
frequency. The two outputs sum to unity (−6 dB = half voltage [or half
pressure], therefore 1/2 + 1/2 = 1) because each section of the crossover is
rotated 180 degrees, and the overall response therefore remains in phase.
However, due to the shape of the polar response, there are dips off axis
at the crossover frequency, hence the dip in the total power response.
The degree of audibility of this effect depends on how much reflected
energy is returned to the listening position. In typical highly damped control rooms, the effect is usually imperceptible close to the axis and around
the typical principal listening positions. With these crossovers, the narrowness of the band of frequencies over which the drivers on either side
of the crossover frequency are simultaneously radiating ensures that the
interference effects are kept small.
Filter orders higher than fourth are not normally used in crossover
pairs, but they can sometimes be found in asymmetrical designs, such
as a sixth order with a second order, to help to compensate for group
delays or physical alignment delays. These individual filters sometimes
also have their 3 dB or 6 dB- down points offset in frequency, in order to
achieve a flat on-axis response or flat power response, depending upon
the circumstances. In practice, filters above sixth order are rarely used
because they tend to serve no useful purpose, and due to their tendency
Crossovers 137
to introduce time response anomalies may actually create more problems
than they can solve.
5.4 Filter shapes
Until now we have been looking at standard filters, where, for generating
higher orders, the filters are simply repeating the characteristics of the
first order sections. However, different entry slopes and different response
shapes can be contoured by adjusting the components which are used to
derive the higher orders. Therefore, by adjusting the Q of the filter, the
‘knee’ of the curve – between the flat response and the uniform slope –
can be adjusted in shape to produce either a more abrupt or more gradual
entry to the final roll-off. The modified shapes can be used to help to
achieve the desired, overall electro-acoustic response when the individual
responses of the drivers are taken into account, or when system summation
is affected by physical displacement problems. Many different Q factors –
or quality factors – are in use. Butterworth filters are ‘maximally flat’ until
the roll-off begins. Bessel filters are more abrupt in their transition from
flat to sloping response, but exhibit alternating up and down responses
before the main roll-off begins. Figure 5.18(a) shows a typical 6 dB/octave
roll-off produced by a simple capacitor-resistor filter, but Figure 5.18(b)
a)
C
dB
R
IN
slope - 6 dB/octave
OUT
Hz
b)
RS
C1
IN
C2
R
dB
OUT
slope reduced by addition
of Rs /C2 combination
Hz
Figure 5.18 Response contouring. a) A simple high-pass filter of first order characteristic rolloff. The response will be 3 dB down at the frequency where the reactance of the crossover
equals the resistance (R). Note, a resistor having the same value as R, substituted for C,
would give rise to a 6 dB reduction of level at the output. The 90 degree phase shift through
the capacitor is the reason for the 3 dB difference. b) Added components for reducing the
slope
138 Loudspeakers
shows how the addition of an extra resistor can limit the rate of roll-off.
There are therefore means at our disposal to modify the slopes of the
curves of the filters, which is extremely useful when we have to tailor
curves to mirror the responses of real drivers, which never behave like
pure resistors, and so can never ideally terminate the standard filters which
were discussed in Section 5.3.
Figure 5.19 shows an example of a conjugate network. These are used to
flatten the impedance curves of drive units by compensating for the reactive
properties of their electro-mechanico-acoustic characteristics. However,
the resistors in these networks do dissipate power, so the overall efficiency
of the system may reduce when conjugate networks are applied. Sonically,
they can be questionable, and some complicated passive crossovers applying such technology for electrical and response flattening purposes have
been considered to sound worse than simpler networks, but the overall
effect may also depend on whether the power amplifiers with which they
are used are capable of driving complex loads, or not. If they are not, then
the conjugate networks may be helpful, but in professional situations, the
choice of a more load-tolerant amplifier is often the preferred solution.
Complex passive crossovers are not entirely distortion free, because the
inductors, in particular, can produce non-linear distortion. Cases tend to
need to be judged individually, partly because, as will be discussed in the
next chapter, amplifier outputs stages and power supplies vary so widely
in design concept.
Clearly, where complex circuitry is involved, it is essential to use components whose values remain stable if the performance of the overall
system is not to change as time passes. Unfortunately, the large electrolytic
capacitors which tend to be required by high-power, low frequency passive crossovers are notoriously prone to changing their capacitance as they
age. Likewise, changes in mechanical compliances of the drive units with
R1
R2
Input
L1
C2
C1
Figure 5.19 A conjugate network
Figure 1.5 shows the impedance curve of a typical low frequency driver. In the circuit above,
R1 , C1 , and L1 , provide compensation for the impedance rise at the resonant frequency of
the driver, whilst R2 and C2 compensate for the rising impedance at higher frequencies due
to the voice-coil inductance. Opinions vary about the sonic effects of this type of impedance
equalisation, but such circuits are undoubtedly useful to flatten the response of systems using
hi-order, passive crossovers
Crossovers 139
age can also cause a drift in the circuit parameters. These factors tend
to put high-level, passive crossovers at a disadvantage when compared to
low level active circuitry, especially when precise tailoring of the response
is required. The higher impedance, active circuitry of the latter case can
avoid the use of large value capacitors, and can therefore employ smaller
value components of much greater long-term stability. This is an important
concern when we need to produce very precise response curves. Active
circuitry can also eliminate the need for lossy, and potentially non-linear
inductors.
5.5 Target functions
Until as late as the 1970s it was commonplace to treat a moving coil
loudspeaker as if it were a resistor when designing crossover circuitry, but,
as we saw in Chapter 1, this is usually a long way from reality. In fairness,
before the 1970s, and the seminal work of Thiele and Small123456 , it was
not always very easy to find the necessary electro-mechanical information
about drive unit characteristics, so design and development were often
two separate processes – design it ideally, and then select components
during tests, to modify the response. Since the 1980s, with much more
data available, it has been customary to look at a drive unit as a complex
impedance, and to view its response for what it actually is, and not as an
ideal response. There has subsequently emerged the concept of the ‘target
function’.
Whereas in Figure 5.1 the plots represent the responses of the filter
circuits which presume that the driver is of constant impedance and has
a flat acoustic response, we can also view the same plots as the target
response for our combined electro-mechanico-acoustic system. In order
to achieve this, the desired filter response becomes whatever is required
to combine with the actual driver response to realise the target response.
Figure 5.20(a) shows a target response; (b) shows the response of an actual
driver, and (c) shows the response of a filter which, when used with (b)
will yield the response shown in (a). This ‘new’ approach obviously calls
into question the value of purchasing ready-made crossovers as standalone devices, be they active or passive. They may be of value for sound
reinforcement systems, where each loudspeaker box has been engineered
to be more or less flat, and multi-band system equalisation is de rigueur, but
their use may be over-simplistic when applied to many other loudspeaker
systems. Also, many modern drive units are not necessarily engineered for
flat responses if other benefits can be gained by sacrificing the flatness.
Computer-aided filter design can then be applied in order to design a
crossover which will achieve the required target function from the complete
system. In fact, in the current cost-conscious world, it is often less expensive
to use electronic means to flatten a response rather than electro-mechanical
means. Nonetheless, despite having said that, there is still in the experience
of many listeners a certain je ne sais quoi about the purity of sound of
an inherently flat driver. It should also be acknowledged that the more
complex filter shapes such as that shown in Figure 5.20(c) are much more
easily implemented with active crossover designs.
140 Loudspeakers
a)
b)
dB
dB
Hz
Hz
c)
d)
dB
dB
Hz
Hz
Figure 5.20 Target functions –practical realisation. a) Desired target function. b) Measured
driver response. c) Electrical filter response – allows for a non-flat driver response. d) System
response as measured – equal to a), i.e. it achieves its target
5.5.1 Minimum and non-minimum phase effects
The selection of the target function is somewhat more complicated than it
may initially appear, because the phase shifts and group delays associated
with the filters, and the physically induced delays due to the different
drive units occupying different points in space, lead to non-minimumphase responses. A minimum-phase response is one where the correction
of the amplitude towards a flat response also leads to a corresponding
flattening of the phase response, or vice versa. In the case of a nonminimum phase response, the correction of either the amplitude or the
phase response does not automatically correct the other. Non-minimumphase responses give rise to situations where a flat amplitude response
cannot be accompanied by an accurate transient (time) response. The
amplitude and phase responses are defined by the time response, and vice
versa, which is why the Fourier Transform and Inverse Fourier Transform
can be used to derive the frequency response from the impulse response
or the impulse response from the frequency response. [For more on this
subject, see Chapter 9.] The frequency response, in this case, is referring
to the complete frequency response, i.e. the amplitude and the phase. Nonminimum-phase effects are typically associated with the recombination of
non time-synchronous signals, such as a recombination of a reflexion with
a direct signal, or the summation of signals where different group delays
or digital latency have been incurred.
Unfortunately, for loudspeaker designers and users, the non-minimumphase effects often prevent the perfect reconstruction of a waveform from
a multi-drive unit loudspeaker system. When this fact is coupled with the
fact that no single drive unit can cover the whole frequency range in a
manner which is flat in frequency response and adequate in its directivity
pattern (at least not at useful sound pressure levels) we are condemned
to compromise. The time-shifted sections of the overall response cannot be equalised flat in a minimum-phase manner, and so the transient
Crossovers 141
responses and directivity patterns will be altered. Even when using concentric drivers, where the vertical and lateral displacements can be avoided,
the problem of the crossover group delays still dogs the design process,
although, if crossover frequencies are carefully matched to distances on
the front/back plane, they can sometimes almost be eliminated. The effects
of trying to equalise non-minimum phase responses are clearly shown in
Figures 11.17 and 11.18, in which the time response aberrations are very
evident.
5.5.2 Corrective measures and side-effects
In some cases, the electrical crossover filters can be overlapped to some
degree, in order to take into account certain physical aspects of the relative
driver positions and in order to vary the polar pattern of the complete
system. Lobes in certain directions may or may not be problematical dependent upon the intended position in which the loudspeaker is expected to be
used, for example, see Figure 5.21. If a loudspeaker system does exhibit a
lobed radiation pattern with an aberration in the frequency response, then
that lobe is best directed towards places where there is least likelihood of
returning a reflexion to the listening position which would be detrimental
Axis of
synchronous arrival of sound
wave from both drive units.
HF
LF
Figure 5.21 This type of lobing could be problematical if an irregular frequency response
returns towards the listener from a reflective floor. Some designers choose to invert the
cabinet in order to direct the irregular response above the listeners’ heads, especially if the
ceiling is high, or more absorbent than the floor
142 Loudspeakers
to the overall perception of the music. Decisions must also be made about
whether the most likely movements of the listener to the loudspeaker will
be in the horizontal or vertical direction when the loudspeakers are in
critical use. For example, either sitting in a chair whilst moving left or
right along a mixing console, or working predominantly in one place but
at various times either sitting down or standing up.
In Section 5.3 it was described how a first-order crossover could reconstruct a perfect waveform. However, if the crossover is used with physically
non-coincident drivers, then even a first order crossover will suffer from
the above problems except on its acoustic axis, which may not always correspond with its physical axis. This means that off-axis reflexions would
not have time-coincident origins, and there would be a lobe which was
tilted, either upwards or downwards. One reason for the great popularity
of the fourth order Linkwitz-Riley filters for high quality monitoring is
that the in-phase relationship between the two drivers on either side of the
crossover gives rise to the main lobe being symmetrical about the central
axis between the drivers.
A very important point to emphasise here is that the design of crossover
filters is not by any means the easy task which many people believe it to be.
Many things must be taken into consideration before the filter functions
can be decided upon, and the design of suitable filters can be work of a
very specialised nature. Computer aided design of filters has been a great
boon to loudspeaker engineers.
5.6 Active versus passive crossovers
For high quality loudspeaker applications, the consensus is almost universally in favour of active crossovers. By virtue of their feedback loops they
can remain remarkably stable over very many years, and complex filter
shapes can be devised without any loss of power efficiency. Conversely,
passive crossovers rely entirely on the long term stability of each component part for their overall stability, which is not easy to achieve when the
low impedances of loudspeaker circuits call for high value capacitors – both
in terms of capacitance and working voltage – which in turn call for capacitors of types which may not be able to provide good, long-term stability.
Complex filter shapes may need to use many components, which when
placed in the power circuitry will probably lead to lower system efficiency,
wasting many watts of amplifier output. If large electrolytic capacitors are
needed, their stability can be questionable, but, if the much larger, solid
dielectric capacitors are used, their physical construction and large size can
lead to them having considerable unwanted inductance, which can upset
the crossover operation.
Active filters are free from these problems, and in fact require no inductors at all. What is more, if state-variable filters are used, any drift which
does occur can reflect equally in both halves of the crossover response,
thus only slightly varying the crossover frequency as opposed to opening
a gap or causing an overlap. The overall frequency response of the system
is therefore unlikely to be affected. There can be no equivalent to this
type of stability or self-correction with passive crossovers, and neither can
Crossovers 143
0.6 mH
4.
7µ
H
F
4.7 µF
55
m
0.
8 ohm
loudspeaker
Input
0.
55
7
4.
µF
4.7 µF
m
H
0.6 mH
Figure 5.22 An all-pass delay circuit
Tannoy developed a delay circuit similar to the one shown, but unwanted phase-shifts,
response ripples and mistermination problems tend to prevent the theoretical benefits of
its approximately 150 microsecond delay from being fully realised. One hundred and fifty
microseconds of delay would ideally compensate for the distance of about 5 cm between the
voice coil planes
passive crossovers easily compensate for group delays. Figure 5.22 shows
a passive all-pass circuit (an analogue delay circuit) of a type which has
been applied commercially to loudspeaker systems, but there are people
who feel that this type of circuitry between an amplifier and a loudspeaker
can again cause as many problems as it solves; if not more!
Conversely, active filters can easily incorporate delay compensation for
driver mounting offsets, such as when a horn driver is set behind the
woofers. Response tailoring is independent of the loudspeaker impedance
complexities. The list of advantages in favour of active crossovers and
multi-amplification is impressive:
1) Loudspeaker drive units of different sensitivities may be used in one
system without the need for lossy resistive networks or transformers.
This can be advantageous because drive units of sonic compatibility
may be electronically incompatible in passive systems.
2) Distortions due to overload in any one band are captive within that
band, and cannot affect any of the other drivers.
3) Occasional low frequency overloads do not pass distortion products
into the high-frequency drivers, and instead of being objectionable
may, if slight, be inaudible.
4) Amplifier power and distortion characteristics can be optimally
matched to the drive unit sensitivities and frequency ranges.
5) Driver protection, if required, can be precisely tailored to the needs
of each driver.
6) Complex frequency response curves can easily be realised in the electronics to deliver flat (or as required) acoustic responses in front of the
loudspeakers. Driver irregularities can, except if too sharp, be easily
regularised.
144 Loudspeakers
7) There are no complex load impedances as found in passive crossovers,
making amplifier performance (and the whole system performance)
more dynamically predictable.
8) System intermodulation distortion can be significantly reduced.
9) Cable problems can be dramatically reduced.
10) If mild low frequency clipping or limiting can be tolerated, much higher
SPLs can be generated from the same drive units (vis-à-vis their use
in passive systems) without subjective quality impairment. (See 2) and
3) above.)
11) Modelling of thermal time constants can be incorporated into the drive
amplifiers, helping to compensate for thermal compression in the drive
units, although they cannot totally eliminate its effects.
12) Low source impedances at the amplifier outputs can damp out-ofband resonances in drive units, which otherwise may be uncontrolled
due to the passive crossover effectively buffering them away from the
amplifier.
13) Drive units are essentially voltage-controlled, which means that when
coupled directly to a power amplifier, (most of which act like voltage
sources) they can be more optimally driven than when impedances
are placed between the source and load, such as by passive crossover
components. When ‘seen’ from the point of view of a voice coil, the
crossover components represent an irregularity in the amplifier output
impedance.
14) Direct connection of the amplifier and loudspeaker is a useful distortion reducing system. It can eliminate the strange currents which can
often flow in complex passive crossovers.
15) Higher order filter slopes can easily be achieved without loss of system
efficiency.
16) Low frequency cabinet/driver alignments can be made possible which,
by passive means, would be more or less out of the question.
17) Drive unit production tolerances can easily be trimmed out.
18) Driver ageing drift can easily be trimmed out.
19) Subjectively, clarity and dynamic range are generally considered to be
better on an active system compared to the passive equivalent (i.e.
same box, same drive units). [See also Figure 5.23.]
20) Out of band filters can easily be accommodated, if required.
21) Amplifier design may be able to be simplified, sometimes to sonic
benefit.
22) In passive loudspeakers used at high levels, voice-coil heating will
change the impedance of the drive units, which in turn will affect the
crossover termination. Crossover frequencies, as well as levels, may
dynamically shift. Actively crossed-over loudspeakers are immune to
such crossover frequency changes.
23) Problems of inductor siting (to minimise interaction with drive unit
voice coils at high current levels) do not occur.
24) Active systems have the potential for the relatively simple application of motional feedback, which may come more into vogue as time
passes.
Crossovers 145
Comparison
8
6
4
2
0
fullness
brightness
softness
pleasantness
fidelity
spaciousness
clarity
–2
Passive crossover
Active crossover
10
Category
Figure 5.23 Active versus passive crossovers – subjective data (after Campbell)7
The results show a clear overall favour for the active crossover. The assessment of the
extra brightness from the passive crossover could well be due to greater levels of non-linear
distortion, which may in fact not be a result in its favour
Conversely, the list of benefits for the use of passive, high level crossovers
for studio monitors would typically consist of:
1) Reduced cost? Not necessarily, because several limited bandwidth
amplifiers may be cheaper to produce than one large amplifier capable
of driving complex loads. What is more, the passive crossovers for the
1000 watt Kinoshita studio monitors shown in Figure 8.2(a) cost over
3000 euros each.
2) Passive crossovers are less prone to being misadjusted by misinformed
users, who think that crossovers are some sort of ‘adjust to taste’ tone
controls. On the other hand, passive systems have a tendency to misadjust themselves with age.
3) Simplicity? Not really, because very high quality, passive, high level
crossovers can be hellishly complicated to implement, not to mention
the amplifiers which are needed to drive them.
4) Ruggedness? No, because the electrolytic capacitors (necessary for the
large values) are notorious for ageing, and gradually changing their
values.
However, it must be stated that in less demanding circumstances than studio monitor loudspeakers passive crossovers obviously have their appropriate applications, but the above lists highlight the benefits of active designs
where the highest system performance levels are required.
Clearly, the advantages of active, low level crossovers completely eclipse
those of passive, high level crossovers, yet it was only around the late 1980s
that dedicated active crossovers began to be seriously used on large scale
monitor systems. Prior art used stock electronic crossovers, and perhaps
146 Loudspeakers
these caused some delay in the acceptance of totally active designs because
they were usually made with fixed slopes on all the filter bands. This tended
to necessitate the use of multi-band equalisers, many of which were of
dubious sonic quality. It took some time before people generally began
to accept the need to buy a specific crossover with a monitor system,
which was relatively useless in any other application. There was still a
mix-and-match mentality towards components parts, each of which was
expected to function as a ‘stand alone’ device. Once attitudes like this
become established it can be very difficult to introduce new concepts. In
fact, it took a long time before self-powered, actively crossed-over small
monitors could establish their place in studio use, but domestic resistance
to their acceptance has been even more pronounced. Established practices
die hard, and they can be remarkably difficult to change, even in the face
of clearly superior technology.
In 2003 and 2004, Alex Campbell worked on a performance comparison
between active and passively crossed-over domestic loudspeaker systems at
the Institute of Sound and Vibration Research, in the UK. He had an identical amount of money to spend on each design. His findings were presented
to an international conference of the UK’s Institute of Acoustics.7 Even at
this modest level of engineering, aimed at the retail price range of £400 –
£500 (E600 – E750) per pair, the subjective assessment, made under ISVR
control and using a panel of 30 subjects, came out heavily in favour of the
active design. The results are reproduced in Figure 5.23, with the ‘clarity’ and ‘fidelity’ ratings being strongly in favour of the active designs,
[probably also as a result of greatly reduced intermodulation distortion].
In fact, the only tendency for the passive design to show a more positive
result than the active design was in ‘brightness’, which could perhaps be a
result of higher non-linear distortion levels. Perhaps the only real block to
the general acceptance of the superiority of active crossovers and multiamplification in the world of domestic hi-fi is the fact that so many hi-fi
enthusiasts want to select their own favourite amplifiers and loudspeakers
as separate items, but this perhaps has more to do with human psychology
rather than audio engineering. Also, of course, choosing your own system
with future up-grades in mind, as extra money becomes available, is a fun
part of building up a hi-fi system, and perhaps a necessity in some smaller
studios.
5.7 Physical derivation of crossover delay
Crossovers are more than simple filters. As we have seen, due to the group
delays which exist in filter circuits, the outputs of the various filter sections
are time-shifted by virtue of the phase shifts which are inextricably linked
to the roll-offs. The result is that when the outputs are re-combined, either
electrically or acoustically, there are often non-minimum-phase response
irregularities in either the amplitude or phase responses. Essentially, they
cannot be corrected by analogue, electrical means. Digital crossovers can
be made to provide summing outputs, but the sonic benefits are not necessarily worth the efforts. For example, digital crossovers, unless they
employ high sampling rates, (96 kHz or more) may introduce limitations
Crossovers 147
in such a way that would make it difficult to accurately monitor analogue
or high sampling rate digital recordings. What is more, a three-way stereo
crossover would require six D to A converters on the outputs, and two
A to D converters if they were being fed from analogue sources. If these
were to be of the highest quality (and in a high quality monitoring system
they should be expected to be nothing less) the cost of the unit could be
exorbitant. Using anything less than the finest converters would make a
mockery of trying to monitor recordings made through the best converters.
This subject is discussed further in the following section.
There is, however, an analogue means of deriving delays. The loudspeaker cabinets, themselves, can be stepped, or the different drivers can
be mounted in separate enclosures which are then mounted at different
distances from the listeners. These two systems are depicted in Figure 5.24,
but care needs to be taken to ensure that diffraction effects do not become
problematical due to the increased number of cabinet edges. Figure 5.25
shows how a composite system using direct radiating bass drivers and a
horn-loaded mid/high frequency driver can compensate for the delayed
output from the bass units. In this case, the ‘natural’ position of the high
frequency voice coil is behind the coil of the bass driver. All of these means
achieve the same result by delaying the high frequency signals with respect
to the low frequency signals. The distances between the voice-coils of the
different drivers can be further physically off-set to whatever degree necessary to compensate for the electrically derived group delays. Given the
speed of sound at 20 degrees C, each centimetre that a driver is mounted
behind another (relative to their voice-coils) would give rise to a delay of
29.4 microseconds. Ten centimetres would therefore give rise to a delay of
294 microseconds, which would be sufficient to reverse the polarity of a
wave at 1.7 kHz. (Look again at Figure 5.6.) Incidentally, the voice coils are
used as an approximate reference for the source of the sound propogation
because even though the diaphragms are ahead of the voice coils there is a
finite time of propogation from the coil to the diaphragm face which, with
most loudspeaker constructions, is roughly of the same order as the speed
of sound in air.
5.8 Digital crossovers
As time passes, digital crossovers have become more commonplace in
professional loudspeaker systems, although their use in domestic circumstances is still largely restricted to home recording facilities. They are
particularly attractive because of the easy implementation of almost any
amplitude response, phase response, signal delay, driver compensation and
even room compensation. However, all this flexibility comes at a considerable cost.
Sonically, in terms of ‘hi-end’ hi-fi or high resolution studio monitoring, the highest fidelity can only be achieved if the sample rate and bit
rate used in the crossovers at least equal those of the recording medium,
or exceed the resolution of the ear and produce no audible artefacts. It
may be difficult to hear the difference between a 20 bit/96 kHz recording
and a 24 bit/192 kHz recording when listening to a crossover based on
148 Loudspeakers
a)
Common
axis
b)
Conventional voice coil
alignment, intended to
produce phase coherent
wavefronts. This
obviously ignores the
effects of mechanical
propagation delays or
electrical group delays
in the crossover filters.
Figure 5.24 Methods for the physical compensation of propagation delays
a) The stepped baffle. b) Separate boxes
Crossovers 149
Voice
coils
In this case the voice coil of the high frequency
driver is behind the low frequency coil, which is
rarely the case for direct radiating high frequency
drivers sharing a common baffle with a low
frequency driver - see, for example, Figure 5.8.
Figure 5.25 Flat baffle with a horn-loaded high frequency driver
In many cases it is possible for horn mounted compression drivers to align themselves very
closely to the ideal whilst sharing a common, flat fronted baffle with a low frequency driver
when the electrical group delays of the crossover filters are also taken into account, especially
when steep-slope crossovers are used
16 bit/48 kHz processing. Even if a crossover has internal processing which
seems higher than necessary, the resultant output after signal manipulation
has taken place may not be as great as the marketing figures would suggest.
The main problem, however, is concerned with the converters. As the
finest amplifiers are still of the analogue variety, D to A (digital to analogue) conversion must take place in each output of the crossover, and, for
either professional monitoring or ‘high-end’ high fidelity, these crossover
D to As must be of higher resolution than any other part of the signal
chain. If they are not, then they will limit the quality and the resolution
of the chain. As with the power amplifiers and loudspeaker cables (which
will be discussed in the next chapter) the splitting of the frequency bands
does offer some respite from the demands of handling the full audio bandwidth. Nonetheless, to achieve the highest levels of sonic quality, D to A
converters are expensive, and a stereo, three-way digital crossover would
require six of them. At the time of writing, and whilst analogue power
amplifiers are the general order of the day, it would be reasonable to
expect to pay 3000 to 5000 euros for those six converters. If analogue inputs
were required, then the A to D (analogue to digital) converters may add
another 1000 euros or so to the price of the crossover if the equivalent
quality was to be expected.
150 Loudspeakers
Under less critical circumstances, digital crossovers can be very useful
tools, but when they are user-programmable, they run the risk of being
inappropriately applied. One must be very careful when trying to ‘solve’
amplitude/phase problems that the solutions do not go against the laws of
nature. Straightening out the phase associated with an amplitude roll-off
may be very tempting, especially where the application is at the extremes
of the frequency bands, but the results can sound unnatural because they
are unnatural. On the other hand, in concert sound applications, where
subtleties are by no means as important as solving the normal problems
faced by such events, digital crossovers have been an enormous step forwards. Their real drawback is their cost when they must operate at the highest levels of sonic transparency. In many such cases, analogue crossovers
may simultaneously be simpler, cheaper, more robust, and better.
References
1 Theile, A. N., ‘Loudspeakers in Vented Boxes’, Part 1, Journal of the Audio
Engineering Society, Vol 19, No 5, pp 382–392 (1971)
2 Theile, A. N., ‘Loudspeakers in Vented Boxes’, Part 2, Journal of the Audio
Engineering Society, Vol 19, No 6, pp 471–483 (1971)
3 Small, R. H., ‘Vented Box Loudspeaker System’, Journal of the Audio Engineering Society,
Part I, ‘Small signal analysis’, Vol 21, No 5, pp 363–372 (1973)
Part II, ‘Large signal analysis’, Vol 21, No 6, pp 438–444 (1973)
Part III, ‘Synthesis’, Vol 21, No 7, pp 549–554 (1973)
4 Small, R. H., ‘Closed Box Loudspeaker Systems’, Journal of the Audio Engineering Society,
Part I, ‘Analysis’, Vol 20, No 10 (1972)
Part II, ‘Synthesis’, Vol 21, No 1 (1973)
5 Small, R. H., ‘Passive Radiator Loudspeaker Systems’, Journal of the Audio
Engineering Society,
Part I, ‘Analysis’, Vol 22, No 8 (1974)
Part II, ‘Synthesis’, Vol 22, No 9 (1974)
6 Small, R. H., ‘Direct Radiator Loudspeaker System Analysis and Synthesis’,
Journal of the Audio Engineering Society, Vol 20, No 5 (1972)
7 Campbell, A. M., Holland, K. R., ‘Active vs Passive Crossovers for Mid-Priced
Hi Fi Loudspeakers’, Proceedings of the Institute of Acoustics, Vol 26, Part 8,
pp 116–123, Reproduced Sound 20 conference, Oxford, UK (Oct 2004)
Bibliography
1 Colloms, M., ‘High Performance Loudspeakers’, 6th Edition [Chapter 6],
John Wiley & Sons, Chichester, UK (2005)
2 Borwick, J., ‘Loudspeaker and Headphone Handbook’, Third Edition [Chapters 5 and 6], Focal Press, Oxford, UK (2001)
Chapter 6
Effects of amplifiers and cables
Clearly, no loudspeaker can do its job unless it is connected to a suitable
power amplifier, and to make that connection, an appropriate cable is
required. As no cable can improve any signal which it is passing (unless it
is filtering out some other problem that should not be there) it must be
concluded that the best cable is no cable. Moreover, as no amplifier can
improve the accuracy of the signal which it is passing, the only conclusion
which can be drawn is that the combination of amplifier and cable can
only degrade the signal. However, as we must use an amplifier and a cable,
art and science are both employed in order to minimise the inevitable
degradation.
Well, at least that is the situation as far as accurate monitoring is concerned. In the case of amplifiers which are used for musical instrument
amplification, the amplifier is actually a part of the instrument, so whatever sounds right is right. The gross distortion produced by an old, valve,
Leslie tone-cabinet, when amplifying a Hammond organ beyond the point
of overload, was one of the most emotive sounds in the history of rock
music, but we will come to that in Chapter 8. Similarly, the popularity of
valve amplifiers in many domestic hi-fi systems is widely attributed to the
pleasing ‘musical’ sounding even harmonics which they tend to produce.
Again, this will be discussed further in Chapter 8, but as these effects are
totally subjective in terms of their desirability, it is very difficult to deal
with the subject in any definitive way. Therefore, what we will attempt to
do in this chapter is look at the problems of amplifiers and loudspeaker
cables when accuracy of reproduction is the goal, and which we can deal
with in an objective manner.
6.1 Amplifiers – an over-view
The purpose of a power amplifier is to take a voltage signal, usually in the
order of up to one or two volts peak, and deliver the waveform of that signal
in a way that a proportionally larger voltage can be supplied to drive current
through a loudspeaker motor system. This, in turn, is used to generate a
radiated acoustic output which is also the best replica possible, in terms of
pressure fluctuations, of the input signal to the amplifier. Driving power
into a resistor is a reasonably simple exercise, but driving the signal into a
load similar to that shown in Figure 1.7 is a different matter. Driving power
into a load such as that shown in Figure 6.1, an electrostatic loudspeaker,
152 Loudspeakers
Mechanical compliance due
to electrical effects - force
on diaphragm proportional
to its displacement
(negative capacitance)
Motional
current
diaphragm
constants
Voltage
source
principal diaphragm
capacitance, plus
spurious wiring
capacitance
air
load
Figure 6.1 Load impedance presented by an electrostatic loudspeaker
can be an even more difficult problem to overcome, because the first thing
that an amplifier ‘sees’ is a large capacitor across its output terminals. As
explained in the previous chapter, the current and voltage are not in phase
when passing through loads which are predominantly either inductive or
capacitive.
Traditionally, power amplifiers have been rated into resistive loads. This
makes sense, even though it is unrealistic, because there is no standard
loudspeaker load – the range of variability is just too great – but driving a
loudspeaker nevertheless tends to be very different from driving a resistor.
There was, and perhaps still is to some extent, an objectivist lobby who
claim that all well-engineered amplifiers exhibiting adequate output power
and minimal distortion will sound identical. In the opinions of the authors
of this book, this is absolutely not the case. Amplifiers do sound different,
at least once they can be heard through high resolution loudspeakers in
well controlled rooms. Undoubtedly, part of the reason why they sound
different is due to their performance when driving loads which are typically
represented by Figures 1.7 and 6.1, although numerous other factors also
play their parts.
An interesting incident occurred at the Tannoy factory in Scotland1 , in
the early 1990s, where a group of people of some repute in terms of their
auditory acuity were assembled to select an amplifier to offer as standard
with a new range of loudspeakers. There were four loudspeakers in the
range, and four different amplifiers had been short-listed for audition. The
intention was to select one amplifier from the four. However, in the blind
tests, one amplifier was selected as sounding most accurate on one of the
loudspeakers, another amplifier was chosen for another loudspeaker, and
a third amplifier was deemed to sound most accurate on the remaining
two loudspeakers of the range. The loudspeakers in question were all of
similar design concept, but varying in size. The participants in the tests
were all highly experienced and respected engineers, and all had been
Effects of amplifiers and cables 153
expecting that they would choose one amplifier for the whole range of the
loudspeakers.
It could have been the case that certain characteristics of the individual amplifiers counterbalanced opposing characteristics in the different
loudspeakers, and this could also have been due to the different load characteristics presented by each loudspeaker. The component values in terms
of the circuit shown in Figure 1.8 could all have been different. However,
we do not have anything like a perfect loudspeaker to use as a reference,
so it is difficult to say which of two amplifiers is definitely better or worse
when the differences are subtle and there is no ‘audible quality meter’ that
we can connect to their outputs. In fact, we listen to amplifier/loudspeaker
combinations, rather than just to amplifiers, and we can add listening rooms
to those combinations in most circumstances. Given the fact that the rooms
constrain the air which loads the loudspeaker diaphragms, it can be seen
from Figure 1.8 that the rooms will also reflect back their presence into
the loading of the amplifiers.
Ultimately, the ear is the only judge, and as it listens to the systems,
it often cannot differentiate the sources of some audible effects from the
sources of others. We also all have different ears, with different perception
of sound, and as no microphone is perfect, we have no perfect sources of
sound to compare anything with. To further compound all of this, unlike
the optic nerve, which carries a measurable and recognisable signal from
the eye to the brain, the auditory nerves disappear into about six different
parts of the brain, and our understanding of how the mind puts the whole
sound together is still not well advanced.
So just what can we say about amplifiers if they have to perform in such a
murky world of variable loading and variable perception? This is a question
that we must address in a very careful way if we are not to descend into
the realms of misguided subjectivism, which may be appropriate in some
circumstances, but which cannot lead to a robust consensus in professional
circumstances.
6.2 Basic requirements for current and voltage output
Contrary to much popular thinking, amplifier power should not be matched
to the power rating of the loudspeakers or individual drivers to which
they are connected. The amplifiers should have a margin of at least 6 dB
(four times the power) above the peaks of the highest level that they will
be likely to be called upon to deliver. If it is to be presumed (somewhat
sarcastically but nonetheless realistically) that most loudspeakers will at
some times be used to their limits, then some common sense needs to be
applied to their use because this means using amplifiers which can maintain
an undistorted output beyond the peak level rating of the loudspeaker.
However, the last requirement is not always easy to assess from any simple
Ohm’s law calculation. The reactive components in the impedance of a
loudspeaker can give rise to significant phase shifts between the current
and the voltage. If the phase shifts become significant, currents can be
drawn which are totally beyond any expectations which would be calculated
from the treatment of the load impedance as being largely resistive. Many
154 Loudspeakers
amplifiers of seemingly adequate power rating have been shown to fail to
be able to supply adequate current with difficult loads, even though their
voltage headroom has been easily sufficient for their proposed use.
Such amplifiers may be found to be seriously lacking in the quality of
sound that they can achieve with a loudspeaker which presents a highly
non-uniform impedance to its output terminals, yet many of these amplifiers may be considered to give excellent reproduction when driving a
more benign load. In general, it is loudspeakers with passive crossovers
which present the greatest problems, at least when we are considering
moving coil loudspeakers, but attempts to flatten the impedance curves by
the addition of compensation networks in the crossovers has often been
found to detrimentally affect the overall sonic performance of the system.
In the previous chapter a strong case was made against the use of passive
crossovers for very high quality loudspeaker systems, but many popular
monitor loudspeakers still use this approach, so the problems which they
give rise to still need to be considered.
6.3 Transient response
In the perception of music, the leading edge of a waveform is highly significant for the recognition of instruments. With the leading edges removed
it can be difficult to tell the sound of a guitar from the sound of a violin,
for example. It follows that the subtle differences between different guitars
and different violins – and most other instruments for that matter – can be
very dependent upon the accuracy of the transient waveform of the onset
of the note. Apart from the need to supply adequate current when a bass
drum is played loudly through the loudspeakers, slew rate and frequency
response are also important factors. The former is measured in volts per
microsecond, and is a measure of the speed with which the output of an
amplifier can respond to the input signal. Forty volts per microsecond
would be the typical slew rate capability of a good monitoring amplifier,
but this same rate needs to be maintained at high levels, and not just at
low levels, or slew limiting will occur, which can produce some very odd
waveform distortion.
The transient response is also greatly affected by the frequency response
of the amplifier. An electrical step function is shown in Figure 6.2. This
waveform is also known as a Heaviside function, named after Oliver Heaviside. (Discoverer of the Heaviside layer which surrounds the Earth.) The
generalised function is defined by
Hx = 0
for x < 0
Hx = 1
for x > 0
Its value at x = 0 is not defined
It is an all or nothing function, also known as a step function, and it
contains all frequencies. A battery switched on and off, with a few seconds
between switching, is a form of step function generation. If connected
to the input of a spectrum analyser, a 11/2 volt battery will demonstrate
Effects of amplifiers and cables 155
Amplitude
1
0
–1
0
5
10
15
20
Time (ms)
Figure 6.2 Waveform of a step-function (Heaviside function)
the wide frequency distribution. When connected or disconnected, all the
columns of the analyser will be seen to be excited, giving rise to a straight
line response with a roll-off of 3 dB per octave relative to the flat response
of pink noise.
If an amplifier has high and low frequency roll-offs which begin too
close to the audible frequency extremes, it will exhibit phase shifts as
shown in Figure 6.3. The instantaneous onset of the step function requires
that all the frequencies begin at time zero. Any phase shifts present in
the system will give rise to signal delays, which will smear the waveform.
Figure 6.4 shows a step function after passing through an amplifier whose
response is 3 dB down at 15 Hz and 30 kHz in (a), then 3 dB down at 30 Hz
and 15 kHz in (b), with 12 dB/octave roll-offs in each instance. Rates of
change of phase beyond about 5 degrees per octave in the audible range
are noticeable to most people, at least when demonstrated on monitoring
systems which are themselves relatively phase-accurate. However, many
monitor loudspeaker systems have phase responses that are so appalling
Phase (deg.)
180
30 Hz – 15 kHz
15 Hz – 30 kHz
90
0
–90
–180
10
100
1000
10000
100000
Frequency (Hz)
Figure 6.3 Roll-offs and their corresponding phase shifts
Changing phase-shifts associated with different bandwidths. In the case shown, the roll-offs
are second order – 12 dB/octave. When the rate of change of phase exceeds about 5 degrees
per octave in the audio band, noticeable changes in the timbre of musical instruments become
noticeable in high quality monitoring conditions (especially with loudspeakers exhibiting fast
transient responses in well-damped rooms)
156 Loudspeakers
a)
b)
1
LF
0.5
Amplitude
Amplitude
1
0
–0.5
–1
LF
0.5
0
–0.5
–1
0
10
20
30
40
0
50
10
c)
30
40
50
d)
1
1
HF
HF
0.5
Amplitude
Amplitude
20
Time (ms)
Time (ms)
0
–0.5
–1
0.5
0
–0.5
–1
–0.1
0
Time (ms)
0.1
–0.1
0
0.1
Time (ms)
Figure 6.4 Effects of bandwidth on transient responses. Note different time scales
The result of passing the waveform shown in Figure 6.2 through the filtered bandwidths
shown in Figure 6.3. The plots (a) and (b) show the decay of the waveform when subjected
to second-order roll-offs (12 dB/octave) at 15 Hz and 30 Hz respectively. Note the tendency
for the 30 Hz roll-off (b) to overshoot the zero axis as it decays. The effect manifests itself
as ‘ringing’, or resonance. The time (transient) response takes longer to return to a flat, zero
line than is the case with the 15 Hz response shown in (a)
The plots (c) and (d) show the effect of filtering the response at 30 kHz and 15 kHz
respectively. It can clearly be seen how the response filtered at 15 kHz (d) takes longer to
rise to its maximum value than in the case of the 30 kHz roll-off shown in (c)
The higher frequency of roll-off at the low frequencies therefore can be seen to extend
the decay of a signal, whilst the lower frequencies of roll-off at high frequencies can be seen
to extend the attack time of a signal. In either case, as the bandwidth is restricted, the time
(transient) response is lengthened
that they can swamp the audible effects of phase shifts elsewhere in the
system, rendering them inaudible, but this can hardly be considered to be
‘monitoring’. In general, it is desirable for a good monitor amplifier to have
a flat amplitude/frequency response between around 5 Hz and 80 kHz –
two octaves either side of the audible frequency range – if good transient
responses are to be expected.
It should be noted that phase shift, however, is something which exists
only in the frequency domain, because it is the rate of change of phase with
frequency. In the time domain we should speak of the phase slope, which
gives rise to the phase distortion that changes the waveform shown in
Figure 6.2 to those shown in Figure 6.4. Under good monitoring conditions
the transient response of a step function can be heard to change as the
bandwidth is reduced. The bandwidth can clearly be demonstrated to have
an effect on the attack of a tight sounding bass drum or tom-tom, although,
as mentioned above, it takes a good loudspeaker system to show the effects
clearly.
Effects of amplifiers and cables 157
This brings us to another ‘chicken and egg’ situation, because when
using loudspeakers with poor transient responses the benefits of using a
fast responding amplifier may not be appreciated. This can lead to people
drawing the conclusion that a wideband response of an amplifier is unnecessary, and reasons may then be found to curtail the bandwidth, applying
the philosophy that “the wider the window is opened, the more dirt blows
in”. Given the ever-increasing amount of electromagnetic radiation in the
atmosphere, there can be a great temptation to filter it out, stage by stage,
but the phase shifts through the filters of a recording chain are cumulative.
Closing the window unnecessarily in the monitor system is unwise if the
monitor system is to be capable of revealing transient problems elsewhere
in the system. Maintaining wideband frequency responses throughout the
electronic system is very important for maintaining the transient accuracy
of the chain.
6.4 Non-linear distortions
Until now we have been speaking about the linear distortions of the
amplifiers. A linear distortion involves a change in the waveshape, or the
frequency response, but where no new frequencies are introduced that
are not present in the input signal. If either the amplitude or phase of
the frequency response are distorted, they are linear distortions, and will
affect the waveform. Academically speaking, the full frequency response
includes both the amplitude and the phase responses, although in more
general conversation the term ‘frequency response’ usually simply relates
to the amplitude portion, variously known as the magnitude or modulus
of the frequency response.
Unlike the linear distortions, a non-linear distortion is one where new
frequencies are introduced into the output of a system. In the case of
harmonic distortion, these extra frequencies are multiples of the input frequencies. Intermodulation distortion occurs when the various frequencies
in the input signal interact to produce sum and difference frequencies
which may have no harmonic relationship whatsoever to the input frequencies. Noises and rattles also constitute forms of non-linear distortion in
mechanical systems. In general, the non-linear distortion in well-designed
electronic systems is way below the levels produced in loudspeakers. This
situation has given rise to suggestions that the non-linear distortion in
amplifiers will be insignificant when heard below the much higher levels of
loudspeaker non-linearities. However, electronic and electro-mechanical
distortions are produced by very different mechanisms. Loudspeaker distortion tends to be benign compared to electronically-produced non-linear
distortion, which tends to be much more subjectively disagreeable.
Intermodulation distortion has always been an elusive property to
measure. It depends on:
1)
2)
3)
4)
the
the
the
the
signal level
bandwidth of the signal
complexity of the signal
peak to mean ratio of the signal
158 Loudspeakers
5) the signal waveform
6) the interaction between any of the above, and a number of other factors
Historically, and currently, harmonic distortion is still the measured quantity, but harmonic distortion, alone, is not necessarily either unmusical or
unpleasant. Referred to the above list, harmonic distortion for any given
frequency is only dependent upon level, because a sine wave:
1)
2)
3)
4)
5)
has no bandwidth
has no complexity
has a fixed peak to mean ratio
has a defined waveform
cannot interact with itself
Chapter 9 will deal with the deeper aspects of the relevance of distortion
more closely, but these points need to be made now because the ways
in which amplifiers produce non-linear distortions is much more varied
than would be expected simply from reading the brochures, where all good
quality transistor amplifiers tend to produce approximately similar levels
of harmonic distortion in the range of 0.01%. As such low levels of purely
harmonic distortion are almost certainly not detectable by the human ear,
it implies that other forms of non-linear distortion are the culprits where
there is harshness, lack of clarity, lack of transparency, lack of ‘air’, or
where other similar descriptions are used to qualify the less than desirable
sound of any amplifier, or the difference between amplifiers. The situation
is that from published distortion figures alone, there is little that can be
implied about the musical accuracy of an amplifier. Conclusions can only
be drawn about the sound of an amplifier by listening to it in the specific
system with which it is intended to be used. However, the ‘biasing class’
can give some guide to possible performance under specific circumstances.
6.5 Amplifier classes and modes of operation
There are many different designs of amplifier output stages, but they are
all usually grouped into a system of classification relating to their output
biasing or switching. Classes A, B and C are unswitched stages, whilst
Classes D, E, G and H are switched stages. As with so many things, there
are pros and cons to each design, and amplifier designers must use their
experience to decide which class seems to be most appropriate for the
intended use of the amplifier. Although this is an enormous subject in
its own right, we need to at least outline the concepts here, because the
choice of the type of amplifier can significantly affect the characteristics
of a loudspeaker system in ways which may not be apparent from simple,
traditional measurement techniques.
As discussed in the last sections, things such as intermodulation
distortion and instantaneous current capacity into reactive loads can give
rise to distinct sonic differences between amplifiers of different design
implementations. As the above two problems are unlikely to be shown
up by any normal static tests of amplifiers performance, they may well
Effects of amplifiers and cables 159
not appear on any specification sheets. Until now, there has not arisen
any standardised test for intermodulation distortion with any close correlation to subjective listening assessments. Although proposals have been
discussed12 , the number of variables listed in Section 6.4 may still mean
that, in many cases, only certain types of music at certain levels and with
certain combinations of instruments will lead to problems. The question
then arises as to how to cover all eventualities. Clearly, amplifiers should
be free of problems to the greatest degree possible, but at what cost? One
approach may be to build an amplifier with big reserves of performance,
but if its construction is too big and heavy to fit in a small, self-powered
monitor system, it is no option at all. However, in this discussion we will try
to stick to performance, and only mention practical considerations when
they can be seen to affect the overall thinking.
6.5.1 Class A amplifiers
Class A biasing has always been highly regarded. In high quality line output
stages, such as in microphone pre-amplifiers, equalisers or compressors,
it is popular, but as these devices are rarely capable of supplying more
than about one watt, the problems of the inefficiency of Class A do not
usually arise. Class A refers to continuous conduction through the output
device(s), none of which are ever cut off. To allow for symmetrical clipping,
and to maximise the output voltage for a normal musical signal, the nosignal current passing through the devices is set to 50% of the maximum
output current. However, by using this means, twice the rated output power
of the amplifier will be dissipated whether any signal is present or not. As
discussed in Section 6.1, many loudspeakers require large, transient voltage
and current swings due to the reactive components of their impedance.
This may require an output capability in watts that is rarely, if ever, used,
just to have the individual swings available when necessary. Nevertheless,
in Class A, double that output power would always be being dissipated by
the amplifier during all the time when it was switched on, except when it
was supplying a portion of it into the loudspeaker load. For this reason,
beyond about 50 or 100 watts, Class A power amplifiers usually become
impractical.
In a recording studio, for example, where perhaps a 500 watt amplifier
would be needed for each loudspeaker, a pair of Class A amplifiers would
be dissipating 2000 watts all the time that they were switched on. If the
amplifiers were in the control room, additional air-conditioning capacity
would be needed to remove that heat. More probably, such hot devices
would be mounted outside the control room, because they would be likely
to need cooling fans, the noise of which would not be desirable in any
listening room. Unfortunately, this would perhaps be in conflict with the
need for short loudspeaker cables, as will be discussed later in this chapter.
Therefore, with the amplifiers being asked to supply a maximum of about
100 watts, average, of music signal, during maybe 10% of the working day,
perhaps 3 kW of electricity would be needed to both supply the amplifiers
and keep them cool. Convection (fan-free) cooling is possible on 500 watt
Class A devices, but the heat sinks would need to be huge and the amplifiers
would need to be mounted in an open, well-ventilated place. The power
160 Loudspeakers
supply components would also need to be larger than for an amplifier of
similar output power but of one of the other classes of output stage. Large
Class A amplifiers therefore tend to be expensive to build, expensive to
run, difficult to site conveniently and generally very wasteful of electricity.
Despite these drawbacks, it must still be appreciated that Class A designs
do have advantages over many other amplifier classes.
1) There is no crossover distortion where signal is transferred from one
output device to another because no such transfer occurs. This type
of distortion can occur in some power amplifiers at very low levels,
but is almost non-existent at the high levels at which most amplifier
distortion measurements are taken. For this reason, the authors have
applied Class A amplifiers to the highly sensitive compression drivers in
some studio monitoring loudspeakers, where, at a level of 70 dB at the
listening position, only around 1 milliwatt of power is being taken from
the amplifier. In such instances, with sensitivities reaching 110 dB SPL
for 1 watt input at one metre, any low-level distortion in the amplifier
could be highly detrimental to the sonic transparency of a monitor
system.
2) Given the constant total current draw of the amplifier, irrespective of
signal levels, the power supplies, both AC and DC, are not subjected to
the current surges which can inject distortion into the low level stages
of the amplifiers, or other surrounding equipment.
3) There is no doubt that Class A circuits are simpler to realise, and there
is a general tendency for simple circuits to do less sonic damage to the
signal. However, simpler circuits may take longer to stabilise, and for
this reason there has been a tendency to switch-on Class A amplifiers
well in advance of their expected time of use.
4) The harmonic structure of any distortion products which do arise tends
to be more benign, sonically, than those produced by many other classes
of amplifiers.
5) Being inherently of lower distortion than many other amplifier designs,
the Class A amplifiers can often exhibit greater tolerance of complex
loudspeaker and cable loads, because the lesser degree, or nonexistence, of global negative feedback may render the amplifiers less
prone to disturbance by the complex back EMFs generated in the
complex loads.
6.5.2 Class A derivatives
A number of ways have been devised to try to maintain as many of the
advantages of Class A whilst reducing the total power consumption, and
hence the weight, heat, cost and inconvenience of pure Class A designs.
Class A sliding bias is one such means, where small signals experience
Class A conditions, but where, as the signal increases, the larger signals
experience Class A/B conditions. Super Class A is perhaps not what it at
first appears to be, but is in fact a low level Class A amplifier in series with
a Class B amplifier for the higher level signals. It is, in fact, a Class A + B
design. In reality, although the maximum dissipation is lowered, some of
Effects of amplifiers and cables 161
the beneficial aspects of pure Class A operation are lost. The name smacks
more of marketing than engineering.
On the other hand, Dynamic Class A maintains most of the benefits,
if not all, of pure Class A. With these circuits, even in the late 1970s,
distortion levels of as low as 0.03% were being achieved from transistor
amplifiers without global negative feedback, which is in the order of only
1% of the open-loop distortion of many Class AB designs. Intuitively, such
a low distortion basic design always seems to be a good starting point.
6.5.3 Class AB
Pure Class B was originally developed to save battery life in portable
amplifiers, such as in battery powered radios of either valves or transistors.
In this mode, only one transistor of a push-pull pair is ever conducting,
depending on whether the signal waveform is positive or negative. Class B
amplifier produce only around 10% of the waste heat of Class A amplifiers,
but, as each half of the output stage is baised almost to cut-off on no
signal conditions, there can be audible unpleasantness arising from the
discontinuities in the signal waveform as the handling of the signal passes
from one transistor to another. Pure Class B amplifiers are therefore not
used in high fidelity audio applications. Nonetheless, by adjusting the bias
on the transistors in the direction of Class A biasing, Class AB working
can be achieved. Unlike in the cases of Dynamic Class A or Sliding Bias
Class A, Class AB amplifiers are not operating in true Class A conditions
when operating at low levels. Particularly after loud passages of music, the
thermal delays in the output devices can give rise to bias changes, which
can lead to a form of crossover distortion in some designs when one side of
the output devices does not perfectly mirror the other side. The potential
unpleasantness of this type of distortion relates to the production of high
order harmonic and inharmonic spectral products.
On the other hand, Class AB amplifiers can be very practical devices, and
advancing technology has continually sought ways to overcome the limitations of Class AB. In many cases, these limitations have been overcome to
a very great degree, and Class AB amplifiers are, at the time of writing, by
far the most numerous in use in professional audio. Output stage biasing
can be critical, and after heavy use and many thermal shocks, the transistor
parameters tend to change as time passes. Class A circuits are relatively
immune to this process, partly because of less sensitivity to precise biasing,
and partly due to their more constant temperature of operation, albeit
high for much of the time. (Constant high temperatures tending to be less
damaging in the long term than temperatures which are always changing.)
6.5.4 Class D
Class C amplifiers have no place in audio, but do find use in radio transmitters. Class D, on the other hand, is an emerging technology. Class D
amplifiers are frequently referred to as digital amplifiers, but some designs
are better described as switching amplifiers. They essentially consist of a
switch-mode power supply, supplying current into the load (loudspeaker)
162 Loudspeakers
under the control of the audio input waveform, with the output being
low-pass filtered in a similar manner to digital-to-analogue converters.
Class D amplifiers are light in weight and can be relatively cheap to build.
However, when extreme high fidelity is required, things can become more
difficult to achieve. They are also very energy efficient, beginning from
about 75% at 5% power to beyond 95% at full power. Sonic performance
improves year by year. In self-powered loudspeakers they can find willing
partners because of their small size, low cost, and low heat generation.
However, they still can be prone to the emission of troublesome electromagnetic interference (EMI) because of the high switching frequency
used, (and the whole concept of switching, itself). Of course, they all must
meet current electromagnetic compatibility (EMC) regulations, just like
the office fax machine and digital radio/alarm clock, but, as this is being
written, those devices must often be switched off in order to clearly hear
the BBC World Service on a small, portable radio. Fast switching always
generates harmonics into the megahertz regions, and such emissions have
a great potential to interfere with nearby electronic equipment.
In other words, compliance with EMC regulations is one thing, but being
a good neighbour with the rest of the sensitive equipment in a recording studio is another thing. This is especially so when ‘vintage’ equipment is in use,
designed before there was a need to even think about digital switching transients. Nevertheless, as time goes on, improvements will be made, and Class
D amplifiers are steadily progressing. The promise of an efficient, cheap,
lightweight and high quality amplifier is a strong spur to commercial development. At the time of writing, some questions still exist about the sonic
performance of the top two octaves of the audio frequency range in Class D
circuitry. The very low level switching artefacts which many designs exhibit
can prove to be problematical when using high sensitivity loudspeakers,
such as mid-range and high frequency horns. Achieving low noise and
distortion at both low and high power still presents many design difficulties.
In effect, there are two types of Class D amplifiers. Early designs used
analogue inputs, which were compared to a triangle wave running at the
switching frequency. This type of switching, when the audio signal crossing the triangle wave causes the output to switch, gives rise to a PWM
(pulse width modulation) output. Some later designs, however, accept a
linear PCM (pulse code modulation) digital input, and use more sophisticated modulation techniques. As such, these designs are effectively digital
until the output filtering which removes the unwanted switching artefacts.
The output transistors are switched on and off typically at a rate from
100 kHz to 1 MHz, so switching noise is only to be expected. It also leads
to quantisation noise, because the output switching rate is finite.
However, factors such as the need for very low-jitter clocking and the
use of air-cored output filter inductors are complications which are not
always easy to solve. Clocking errors and ferrite inductor cores can lead to
non-linear distortion. The filtering is necessary because the direct output
waveform is a high frequency square wave, which, if left unfiltered, could
radiate large amounts of radio frequency (RF) interference from the loudspeaker cables, which can act as transmitter aerials. Output inductors that
behave well at these frequencies but which do not exhibit much loss at
Effects of amplifiers and cables 163
audio frequencies can be difficult to make. The required clocking accuracy
of less than 100 picoseconds may also be hard to achieve.
In order to reduce the potential for clashing clocks, it can be necessary
to synchronise the clock of the switch-mode power supply with the clock of
the amplifier, which can also be beneficial in ensuring that the maximum
current is available exactly when needed. The demands made of the power
supplies are quite exacting. Any changes in power supply voltage causes a
proportional change in the output signal, whereas in Class A, the current
drawn is relatively constant, and in Class AB designs the audio feedback
circuitry tends to compensate for the moderate fluctuations. The power
supplies for Class D amplifiers may also have to deal with absorbing the
power which can be reflected back from the output filter inductors.
6.5.5 Class G and H
There seems to exist some geographical confusion about the application of
the terms G and H. However, in both cases, they involve multiple or variable supply rails, the higher voltages only being brought into play via fast
switching circuitry when high output is called for. Thus, a Class AG or AH
amplifier can operate in Class A at low signal levels, without excessively
wasting heat, but higher-voltage power supplies are brought into service
when the required output level of the signal exceeds the capabilities of the
first rail. The high voltage supplies are therefore only used when needed,
greatly improving the overall efficiency of the amplifier. Overall performance can be excellent, with the waste heat, weight and component costs
being almost as low as Class D, but with the distortion products being
almost as low as pure, simple Class A.
6.6 MOSFET or BJT?
The bipolar junction transistor (BJT) has long been generally preferred
to the MOSFET for high quality, professional power amplifiers, but some
excellent MOSFET designs do exist. [MOSFET, according to the “Power
Mos Fet Data Handbook, Page 7, published by Hitachi in August 1985,
standing for Metal, Oxide and Silicon, Field Effect Transistor – although
other meanings of S are sometimes to be seen in print.] Hitachi was the
first company in the world to produce 100 watt, complimentary power
MOSFETs, in 1977. Somewhat like valves (tubes) MOSFETs are voltage
controlled devices. BJTs, on the other hand, are relatively low impedance
current controlled devices, so the driver stages which feed them need,
themselves, to be small power amplifiers. The concept of operation is
therefore very different, as can be the circuitry which surrounds them,
so it is hardly surprising that there can be sonic differences between the
amplifiers which employ the different devices. Another difference exists in
the minimum resistance through the devices when they are turned full on.
The BJT tends to have lower resistance than the lateral MOSFETs used
in audio. There are vertical MOSFETS, which do have lower resistance,
but they are not suitable for high power audio use. The MOSFETs also
exhibit higher input capacitance than BJTs, and this must be taken into
164 Loudspeakers
account when designing the driver stage which comes before the power
output devices. All of these factors conspire to change the circuit concepts
in ways which may have audible repercussions.
When MOSFETs fail, they tend to do so in ways which are less disastrous
to loudspeakers and driver stages than do BJTs. The MOSFETs themselves
are generally also more tolerant to abuse than BJTs. They tend to thermally
protect themselves, and are not prone to the ‘thermal runaway’ that can
let BJTs get totally out of control. Theoretically, power MOSFETs also
exhibit a higher bandwidth than BJTs, though to some peoples’ ears, the
BJTs sound sweeter. However, none of these apparent advantages and
disadvantages are clear-cut situations. There are simply so many circuit
possibilities for each type of device that many other factors contribute
more to the sound of an amplifier than the simple choice of MOSFETs or
BJTs. Furthermore, both types of device are still being developed, and the
pendulum can swing with the arrival of new devices or circuit concepts.
6.7 Choosing an amplifier
In many ways it is advantageous that so many design options are available, because different types of loudspeaker drivers, different types of
enclosures, differing requirements in terms of power levels, different loudspeaker sensitivities, different musical styles, and a host of other variables
means that there is no, single amplifier to fit all needs. There is much
casual talk about the pros and cons of different amplifier components or
characteristics, but often it is of little value because it is applying specific
circumstances to the general cases – ‘Cats have tails, my dog has a tail,
therefore my dog is a cat. Fact!’ Or so go many of the arguments!
In general, well-designed, well-engineered amplifiers, specifically tailored for their purposes, can give excellent results despite employing many
different technological approaches. Difficult load impedances may be handled more easily by some designs than by other designs; transients with
heavy low frequency content may favour one amplifier whilst smooth string
sections may favour another. Clearly, what we all would like is the perfect
amplifier to suit all applications, but such is not the nature of compromise,
and in the commercial world, the marketing and business people now hold
more sway over the designers and engineers than ever before. Even in
the case of small, powered monitor loudspeakers which unashamedly market themselves as fully-professional monitors, there is usually nothing in
those amplifiers which could be considered to be ‘over the top’. They are
almost always engineered to a price and performance which is no more
than necessary to satisfy the majority of their customers. One perceived
problem with powered monitors, therefore, is the lack of ability to upgrade
the system. Indeed, a 12,000 dollar Krell amplifier can ‘improve’ the sound
of a pair of Yamaha NS10s (600 dollars) compared with their use with a
more modest amplifier, but the two could hardly be marketed together as
a viable package.
Inevitably, therefore, a question of balance tends to pervade the subject
of design selection. Questions such as whether mass sales are envisaged, or
whether the designs are to be tailored to a very specific use, all need to be
Effects of amplifiers and cables 165
taken into account, but the chosen points of balance may also be influenced
by the personal philosophies and the order of the priorities of the individual designers. We have already discussed how high sensitivity compression
drivers can expose any low-level distortion in the amplifier, such as crossover
distortion, whereas an HF driver 20 dB less sensitive, needing 100 times the
power for the same acoustical output, may highlight other aspects of an amplifier’s failings. The choice of which amplifier to use for the high frequencies
of a system can therefore depend very much on the choice of tweeter, even if
the desired maximum output SPL is the same in each case.
Undoubtedly, the most difficult task to ask an amplifier to perform
is to deliver the highest quality when delivering a high power, full frequency range, ultra low distortion signal into a loudspeaker with a passive
crossover having a ‘difficult’, widely varying input impedance. An amplifier
to suit this purpose is probably going to be big, heavy and expensive. On the
other hand, equal sonic quality may be achieved from amplifiers of much
greater simplicity by splitting the frequency range with an active crossover,
then driving each loudspeaker motor separately. In this case, the amplifiers
would probably need to be of lower power, and as they would each be
driving a much more limited frequency range, and hence a less complex
waveform, the ultra low distortion would be easier to achieve from smaller,
lighter, less expensive amplifiers. The concept of the system therefore has
to be defined before the most appropriate amplifiers can be chosen.
What is most appropriate in each case is very much governed by what
an amplifier is being called upon to do. In general, at low frequencies, a
high current capacity is beneficial, and an amplifier which can handle large
current surges with ease will tend to produce a tight and effortless-sounding
bass. At higher frequencies, low levels of intermodulation distortion are
essential for maintaining an open, sweet, transparent sound. Wide, flat
frequency response bandwidth is also essential if the transient response of
the entire system is not to be compromised, though it should be obvious
that extending the -3 dB bandwidth from 30 Hz down to 10 Hz would hardly
be relevant for an amplifier which was only being used on mid and high
frequencies. Neither would the response above 20 kHz be too meaningful
for an amplifier which was only being asked to drive bass frequencies. In
general, the job of any amplifier is greatly simplified when its range of use
can be restricted to four or five octaves, rather than ten or eleven. In itself,
the band-splitting results in greatly lowered intermodulation distortion.
The same is somewhat more obviously true for loudspeaker drive motors,
where the high power, low distortion, wide directivity, high sensitivity,
wide bandwidth loudspeaker driver does not exist. Many of the advantages
of band-splitting were discussed in the previous chapter, and more will
be said about it in the final sections of this chapter, but it is now wellrecognised that for any part of an audio system which either delivers power,
or has mechanico-acoustic properties, eleven octaves is a very wide range
of frequencies to handle together. Amplifiers which are best suited to
very low frequency reproduction may not be the best for reproducing high
frequency subtleties. Or, perhaps one amplifier could do both jobs equally
well, but perhaps not both at the same time. In fact, the same concepts of
band-splitting and the subsequent selection of appropriate characteristics
for each band can also be applied to the choice of loudspeaker cables.
166 Loudspeakers
Whilst this book is primarily about loudspeakers, and not amplifiers, the
problems given rise to by the complex impedance which many loudspeakers
present to the amplifiers has inevitably required at least a brief look at amplifier technology, or the repercussions of the impedance problem would not
be fully understood. Likewise, perhaps now we need to consider a little more
about the component part which connects the amplifier to the loudspeaker –
the loudspeaker cable – because the subject is not quite so simple as some
people would have us believe. (Although neither is it quite as shrouded in
Voodoo as others may have us believe!)
6.8 Loudspeaker cables and their effect on system performance
Few subjects in the world of audio systems excite so much controversy
and heated debate as the subject of loudspeaker cables. A truly enormous
amount of pseudo-science has been written about this subject, and, once
again, so many cases have been reported which have tried to extrapolate
from the specific to the general case, which is clearly nonsense. In the world
of high fidelity, there are many esoteric designs of amplifiers and loudspeakers which do not show the robustness of more typically professional
equipment, and they tend to be used in domestic circumstances where electrical installations will not have been made with the type of attention to
detail that would be found in a top professional recording studio. In some
of these cases, a certain cable may clean up a sound, but the same cable
in different circumstances, such as when used with professional equipment
with clean electrical supplies, may not lead to any sonic improvement whatsoever. Granted, an inadequate cable can certainly degrade a system, but
there is no justification for using inadequate cables if serious listening is
contemplated. So, perhaps we should look at what we mean by adequate.
6.8.1 The bare minimum
A loudspeaker cable, like an electrical power cable, needs to have a current
carrying capacity such that it will not overheat, and a voltage insulation such
that it will not arc, but the current carrying capacity of a loudspeaker cable
cannot be calculated from the simple W = I2 R formula that would apply
to the wiring of an electric heater. What is more, loudspeaker cables may
be carrying 11 octaves of frequency range and not just the single frequency
of an electrical supply, so what happens over the whole range of operation
is of interest, and all frequencies must be passed as uniformly as possible.
In the case of the vast majority of transistor amplifiers we are dealing
with what amounts to a constant voltage source. This means that from
the minimum rated load impedance up to infinity, the output voltage of
the amplifier, for any given input voltage and at any frequency within its
range, will be independent of the load to which it is connected. However,
this is not the case with valve (tube) amplifiers, whose output loads must
be critically matched to the output impedance of the valves, usually via
a relatively complex output transformer, but for now we will restrict our
discussion to the more typical transistor amplifiers.
Effects of amplifiers and cables 167
In order to behave as a voltage source, and remain independent of load,
the output impedance of the amplifier needs to be very low indeed – typically hundredths of an ohm. The ratio of the load impedance to the output
impedance gives us the damping factor, which is an indication of the ability
of the amplifier to suppress the natural resonances within a loudspeaker.
This electrical damping effect can be easily tested by lightly tapping the
cone of a low frequency loudspeaker with the amplifier connected but
turned off, then comparing the sound by tapping again with the amplifier
switched on. A significantly deader sound should be heard in the latter
case, when the near zero output impedance of the amplifier short circuits
the voice coil. A similar effect can be demonstrated without an amplifier, simply by connecting a wire between the loudspeaker terminals, thus
short-circuiting the coil.
When a loudspeaker diaphragm is struck, it behaves like a microphone.
In fact, when a loudspeaker is connected to a microphone pre-amplifier
input it makes quite a good microphone. The movement of the diaphragm
in response to vibrations in the air moves the coil within the field of the
magnet, which generates a voltage across the terminals. If the terminals
are short-circuited, a current flows which tends to drive the voice coil in
a direction which opposes the resonant movement of the diaphragm. The
shorted coil acts as a dynamic brake. The damping effect of an amplifier can
greatly ‘tighten up’ the sound of the bass, because it allows the amplifier
to better control the resonant movement of the low frequency drivers. In
other words, the transient response is improved. The need for a very good
short circuit is important, so if the resistance/impedance of a loudspeaker
cable is not close to zero, the damping will not be as close to perfect
as possible, and therefore the effect of the amplifier on the loudspeaker
resonance will be reduced.
When dealing with such low impedances as are found in typical loudspeaker circuits, such as 4 ohms or less, we are dealing with impedances
much lower than would normally be encountered in general electrical
wiring. In order to achieve a moderately good damping factor of 40 on a 4
ohm load, the total of the series impedance exhibited by both the amplifier
output impedance and the cable impedance could not exceed one tenth of
an ohm.
The principal concern of an electrical engineer, when choosing a gauge
of cable, is that it will pass the required current without either overheating
and producing a fire risk, or causing a voltage drop due to its predominantly
resistive impedance (at 50 or 60 Hz) which would reduce the effectiveness
of the device to which it is connected. So, if the motor is running at its
correct speed and the cable is stone cold, then that is more or less the end
of the story from an electrician’s point of view.
Conversely, far from dealing with a fixed voltage at a single frequency,
a loudspeaker cable has an impedance which may be dominated by its
resistance only at low frequencies. At high frequencies the inductance
can be contributing more to the impedance than the resistance, and a
loudspeaker working on the end of a 10 metre cable producing the same
SPL as when connected to the output of the amplifier with 50 cm of cable
is no indication that the cable is lossless. If a cable has a resistance of
1 ohm and is connected to an 8 ohm loudspeaker, the voltage drop across
168 Loudspeakers
the cable would be one part in 9 (i.e. across 1 ohm out of 9 ohms total). This
represents about 11%, or about 1 dB, which would be barely audible. For a
voice announcement installation, such a cable may be entirely acceptable,
but for a high quality music system it would impose a serious limit on
the damping factor, and hence on the accuracy of the transient response
at low frequencies. The subsequent resonance due to the loss of damping
may even restore the 1 dB loss of perceived volume, but the nature of the
sound would have changed.
From the point of view of the loudspeaker, the cable is a part of the
output impedance of the amplifier, and the damping factor is defined by:
Z load
Z source
In other words, the load impedance divided by the output impedance.
Therefore, if an 8 ohm load was connected directly to an amplifier having
an output impedance (source impedance) of 0.1 ohm, the damping factor
would be 8/0.1 or 80. If the two were now connected by a cable having
a resistance of 1 ohm, the damping factor would be dependent on the
combined resistance of the source and the cable: 1+01 ohms. The resulting
damping factor would be:
8
= 72
11
which in audio engineering terms is poor, and likely to lead to subjectively
woolly bass.
At higher frequencies, the drive units which are used do not generally have the mass or compliance to freely resonate, and are additionally
resistively damped by the air load. However, at these frequencies the cable
inductance can behave like a frequency dependent resistor, and act as a
filter. When used with loudspeakers which present variable impedance
loads with relation to frequency, both the resistance and the reactive components of the impedance can act as potential dividers, giving rise to a
frequency response that varies according to the relative values of cable
impedance and loudspeaker input impedance. The loudspeaker response
will then vary in different ways as cable length is varied.
Cables also have capacitance between the conductors, but this is not
usually problematical because the capacitive reactance is so low compared
to the impedances of loudspeaker circuits that its effect would not normally become apparent until hundreds of kilohertz. However, it has been
known to affect some marginally stable amplifiers, although it could be
said that these problems should be solved at source. Some cables are intentionally capacitive, up to 0.2 microfarads, to maintain the high frequency
response at the loudspeaker terminals, but they may unpredictably alter
the performance and stability of amplifiers.
6.8.2 The status quo
In terms of professional use, a marginally stable amplifier has little to
justify its use. In fact, a marginally stable professional amplifier is almost
Effects of amplifiers and cables 169
an oxymoron – a contradiction in itself. However, in the world of hi-fi,
some designs exist which are so esoteric that practicality and justifiable
engineering are not high on the list of design priorities. Some of these
are more works of art than works of science, and they are designed to
be pampered and appreciated rather than to be bolted into a rack and
forgotten about. Nevertheless, without doubt, some of these specialised
hi-fi amplifiers do perform extremely well under the limited circumstances
of their intended use, but some are so minimalistic in their design, (even
if not in their price) that they can sometimes be only marginally stable
(although very few), and often their unbalanced input circuits and high
sensitivity (100 mV as opposed to 1 volt) make them more prone to disturbance than the less sensitive and often more robust professional designs. It
is therefore not surprising that such amplifiers may show a higher degree
of sensitivity to both the input and output cables with which they are
connected than do the more robustly designed amplifiers for professional
use, which must work even in relatively hostile environments. However,
the term ‘professional’ does not ensure sonic transparency, and some supposedly professional amplifiers which are more robust than transparent
would not be very sensitive to cable differences due to their own limited
performance.
In all fairness, it must be stated that domestic high fidelity and professional recording are two different worlds. Despite the fact that they have a
lot in common, they also have many differences. Whilst professionals tend
to work with standardised, known, and objectively designed equipment,
domestic equipment tends to be individualistic, and marked by diversity
more than commonality. Often, in the home of a hi-fi enthusiast, the equipment has pride of place, where aesthetic design can be almost as important
as sonic design, and where minimalism and purity at domestic listening
levels take precedence over the tolerance of hard-driving and abuse which
may be needed by professional equipment. An idiosyncratic, 8 watts per
channel valve amplifier has rarely found a home in a professional recording studio, and especially not if it cost 5000 euros or more. It is therefore
worth re-emphasising that the innumerable stories about either input or
output cables magically changing the sound of domestic equipment (whilst
a giant and highly respected organisation such as the BBC has ‘no policy’
on esoteric cables) are more a testament to the sensitivity of much domestic
equipment to minor changes in termination than to the general importance
of esoteric cable design or materials of construction. However, that is not
to say that cables are cables, and that any cable will suffice for connecting
a loudspeaker as long as it manages not to catch fire at full volume. So,
perhaps we can now look at some of the more important aspects of professional loudspeaker cable design. [Although we should perhaps note, here,
that professional recording engineers do tend to be rather more conscious
of microphone cable design].
6.8.3 Cable designs for loudspeaker use
The first way to combat the resistance problem is to shorten the cable;
halving the length of the cable will halve all the impedance components.
Another way to halve the resistance would be to double the cross-section
170 Loudspeakers
of the cable, but whilst this may be effective on the resistive part of the
impedance, the increased spacing between the centres of the conductors
will increase the inductance. The effect may therefore be beneficial at low
frequencies but detrimental at high frequencies. A way to overcome this
problem is to use a co-axial cable, where the two conductors share the
same axis. This can minimise the inductance by effectively cancelling the
opposing magnetic fields in the two conductors, but as a result of this construction there is more opposing surface area between the conductors, so
the capacitance can increase moderately, although this will usually not be
a problem. What is important is to always keep the pairs of loudspeaker
wires as close and parallel as possible. This enables the magnetic fields
around each core to cancel as much as possible of the inductance. Twisting
the wires is another way to achieve this, but twisted wires are inevitably
slightly longer than straight wires for any given overall length of cable.
Well designed twisted cables have proved to be successful in high quality
applications. What should be avoided is the use of single wires, each following its own route to the loudspeaker. Such configurations can act as
effective aerials, and can introduce RF interference into amplifier circuitry.
Figure 6.5 sums up the general philosophy.
There is also a phenomenon known as skin effect. It is a controversial
subject as to what effect it has at audio frequencies, but, as was shown in
Figure 6.3, if high frequency roll-offs give rise to significant phase shifts
below 20 kHz, then their effects may be audible. Skin effect is the tendency
for high frequencies to travel through the outer skin of a conductor, and not
through the centre of the core. The whole cross-section of the conductor
is therefore not used, so the resistance rises as the conducting section of
the cable reduces, introducing a high-frequency roll-off. Once again, the
shorter the cable, the less the problem.
Some manufactures have opted to address the problem by plating the
outside of the conductors with a lower resistance metal. Another approach
is to use Litz-wire, where multiple, individually insulated, hair-like wires
are twisted together. They thus have a much greater ratio of surface area
to volume. The evidence seems to suggest that on lengths of 10 metres
or more, this type of cable can exhibit improved results when compared
with ‘ordinary’ loudspeaker cables, but in professional situations, placing
the amplifiers 10 metres from the loudspeakers would not normally be
considered to be good engineering practice, for other reasons which will
hopefully become apparent from the latter sections of this chapter. But
first let us look at some detailed measurements which were made on
loudspeaker cables
6.9 The amplifier/loudspeaker interface
It must be clearly understood that when a loudspeaker is used with an
amplifier employing negative feedback from the output stage, either globally or locally, (and at least 99.9% of amplifiers in professional use are so
designed) the loudspeaker cable passes signal in both directions. The amplifier sends drive voltages to the loudspeaker, which cause currents to flow
through the complex impedances which the loudspeakers present as a load.
Effects of amplifiers and cables 171
a)
b)
c)
Figure 6.5 Magnetic fields surrounding cables. Better cancellation lowers the inductance.
a) parallel conductors. Partial cancellation as parallel conductors exhibit only weak external
magnetic fields – the resulting inductance is low. b) Coaxial pair. Almost total cancellation
of the magnetic field due to the concentric conductors – the resulting inductance is very low.
c) Unrelated pair. Due to the relatively wide and random spacing of the conductors there is
little cancellation of their magnetic fields, so the inductance tends to be higher than for the
cables shown in (a) and (b)
The reactive components of the impedance, and in particular the moving
mass component of the diaphragm/coil assembly, give rise to back-EMFs as
the whole assembly resonates in the magnetic field. These EMFs (electro
motive forces, or voltages) produced by the resonating loudspeaker acting
as an electrical generator rather than as a motor, arrive at the amplifier
output terminals via the loudspeaker cables. The circuit of the system is
shown in Figure 6.6. The low output impedance of the amplifier cannot
effectively damp the back EMFs (reverse voltages) generated by the natural movements of the loudspeaker if an excessive impedance, in the form
of a cable, is separating the coil from the output terminals of the amplifier.
Cable impedance (or lack of it) is therefore critical in terms of optimising
the performance of the amplifier/loudspeaker combinations. It can thus be
seen how the cable can control what passes from the amplifier to the loudspeaker, by virtue of the frequency dependent nature of its impedance,
172 Loudspeakers
CABLE
a)
Z cable
AMPLIFIER
Z
out
Z
L.S.
load
b)
effective Z out
From the loudspeaker,
the very low output
Z
impedance of the
L.S.
load
amplifier is not seen
because of the cable
impedance.
Z
CABLE
cable
very
low
Z
Z
AMPLIFIER
out
c)
Z Cable
cable impedance.
L.S.
Back-EMF
voltage source
Potential
divider
Amplifier
Z
output
out
impedance.
Back-EMF signal voltage
to feedback circuitry
reduced in level by the
potential divider circuit
formed by the cable and
amplifier impedances
Figure 6.6 Circuit diagram of the amplifier, cable and the loudspeaker impedances. a) Basic
circuit. b) Effect on damping. c) Effect on back-emf
and it can also control what passes to the amplifier from the loudspeaker,
and hence affect the damping of the transducer system. The effect of any
loudspeaker cable therefore must be considered in both directions.
One great problem about generalising about many, or most, of the effects
of the performance of loudspeaker cables (once the basic properties of
resistance and inductance have been adequately specified) is that their
Effects of amplifiers and cables 173
effects can be so system-specific. In other words, what occurs with one
combination of amplifier, loudspeaker and location may have very little in
common with what occurs with a different combination. The only universal
solution for minimising the effect of loudspeaker cables is to minimise their
length, by mounting the power amplifiers as close as practically possible
to the loudspeakers. A total length of about 2 metres from the amplifier
terminals to the motor/driver terminals is a reasonable maximum to aim
for. And of course, suitable cable must be used. In the experience of
the authors, the differences between cables of appropriate resistance and
inductance at lengths below 2 metres are too small to be of any real
significance, but exactly what section should be used for what power rating
of loudspeaker is something that needs to be worked out case by case. For
example, as previously mentioned, an excessively large format cable may
be detrimental to the response of a tweeter because the increased cable
inductance, due to the cable spacing, may be more of a problem than the
increased resistance of a thinner cable.
There exist some large, high powered, passively crossed over, professional monitor systems that are very difficult to drive. When the drive
voltages going forward meet the back-EMFs coming in the other direction,
all in the highly reactive circuitry of a low impedance, passive, high order
crossover, peak currents of up to 100 amps have been measured during
some complex musical passages at high studio monitoring levels. It would
seem obvious that a cable specified for such a system, using amplifiers
capable of driving continuously 3000 watts into half an ohm, would need a
higher specification than the cables used in a system of similar power rating
and acoustic output but using an active crossover, multiple amplifiers, and
where the low frequency drivers presented an almost uniform impedance
to the amplifier, (at least in the frequency range over which they were
being driven).
When calculating the cross-section of loudspeaker cables, we cannot
simply take the approach:
1000 watts into 4 ohms
W = I2 R
I2 =
W
R
I2 =
1000
4
I2 = 250
√
I = − 250
I = 16 amps
As 1 mm2 of cable will safely carry 5 amps, we will therefore use 4 mm2
cable to give a little margin of security.
In terms of electrical engineering, the above concept is a perfectly safe
and viable approach, there is no possibility of the cable overheating, but
174 Loudspeakers
it in no way takes into account the effect on the sonic perception of
musical signals when amplifiers are driving difficult loads. In the case of
loudspeaker cables, the emphasis is on the cable impedance rather than
thermal/current capacity.
6.10 Some provable characteristics of cable performance
In the autumn of 2002, the authors, together with other collaborators,
made a presentation to the Reproduced Sound conference of the Institute
of Acoustics2 . Figures 6.7, 6.8 and 6.9 were taken from that paper. They
were from an experiment made at Czerwinski Laboratories in California,
by two Russian engineers, Alexander Voishvillo and Alexander Terekhov,
accompanied by Eugene Czerwinski, (the founder of Cerwin Vega). [In
the 1950s Czerwinski had designed the first of its kind 10,000 watt amplifier using germanium transistors for sonar systems for the US Navy.] They
carried out tests on three, 6 metre lengths of different cables, firstly into a
resistive 8 ohm load (Figure 6.7), then into a full-range loudspeaker system (Figure 6.8), and finally into a cabinet-mounted low frequency driver
(Figure 6.9). The amplifier driving the cables was fed with a multitone test
signal34 , designed to show up non-linear distortions; in particular intermodulation distortion. In Figure 6.7 it can be seen that all six plots are
more or less the same. The left hand plots were measured at the amplifier
output terminals, whilst the right hand plots were measured at the other
end of the 6 metre cables – at the resistive load. The three very different
cables all appeared to perform equally. This was what the experimenters
were expecting to occur, independently of the load. They were all very
much sceptics with regard to significant loudspeaker cable differences –
at least between adequately rated cables. However, when they replaced
the 8 ohm resistive load with a passively crossed-over loudspeaker system,
they were surprised to see the results as shown in Figure 6.8. With the
more complex load, all the plots had changed. After changing the load
to the low frequency loudspeaker, all the plots changed again, as shown
in Figure 6.9. The distortion patterns were noticeably different, not only
between the cables, but also between the input and output ends of each
cable. The implication here is that the cables change the way that the complex load is seen by the amplifier. Voishvillo reported that upon seeing
this, Czerwinski exclaimed “But they’re only short cables!”
Figure 6.10, taken from the same IOA paper2 , shows six twin plots.
In each case the upper trace was the measurement at the amplifier end
of the cable, and the lower trace was made at the loudspeaker end. The
measurements were taken in a city-centre office with typical city EMI
(electromagnetic interference). The input signal was a 1.6 kHz square wave,
and the load was a TAD 2001 compression driver, mounted on an axisymmetric horn and producing 70 dB SPL at a distance of one metre. This
was intended to represent conditions of realistic use. Plots a) and b) are of
5 metres and 50 metres of RG59 coaxial RF cable, respectively. Plots c) and
d) are of a typical, transparent insulation, oxygen-free copper loudspeaker
cable, again 5 metres and 50 metres respectively; and plots e) and f) are as
a) and b), but with the conductors reversed (i.e. screen to hot and core to
Effects of amplifiers and cables 175
Test 7 (input)
20 V RMS, 8 Ohm resistive load
SPL (dB)
100
SPL (dB)
100
90
90
80
80
70
70
60
60
50
20
50
100 200 500 1k 2k
Frequency (Hz)
5k 10k 20kHz
50
20 50 100 200 500 1k 2k 5k 10k 20kHz
Frequency (Hz)
Object: Input signal (cable Phoenix Gold)
User:
Location: Cerwinski Laboratories Inc.
SPL (dB)
100
Test 8 (input)
20 V RMS, 8 Ohm resistive load
Object: Signal after (cable Phoenix Gold)
User:
Location: Cerwinski Laboratories Inc.
SPL (dB)
100
90
90
80
80
70
70
60
60
50
20
50 100 200
5k 10k 20kHz
500 1k 2k
Frequency (Hz)
Test 9 (input)
20 V RMS, 8 Ohm resistive load
Object: Signal after (cable Isoteric Audio USA)
User:
Location: Cerwinski Laboratories Inc.
SPL (dB)
100
90
90
80
80
70
70
60
60
50
20
50 100 200 500 1k 2k
Frequency (Hz)
5k 10k
Object: Input signal (cable Romex)
User:
Location: Cerwinski Laboratories Inc.
20kHz
Test 8 (output)
20 V RMS, 8 Ohm resistive load
50
20 50 100 200 500 1k 2k 5k 10k 20kHz
Frequency (Hz)
Object: Input signal (cable Isoteric Audio USA)
User:
Location: Cerwinski Laboratories Inc.
SPL (dB)
100
Test 7 (output)
20 V RMS, 8 Ohm resistive load
Test 9 (output)
20 V RMS, 8 Ohm resistive load
50
20 50 100 200 500 1k 2k 5k 10k 20kHz
Frequency (Hz)
Object: Signal after (cable Romex)
User:
Location: Cerwinski Laboratories Inc.
Figure 6.7 Three 6 m cables feeding on 8 ohm resistive load. The left-hand plots are from
amplifier output terminals. The right-hand plots were taken from the load
176 Loudspeakers
Test 1 (input)
SPL (dB) 20 V RMS, Cerwin-Vega AIG loudspeaker
100
Test 1 (output)
SPL (dB) 20 V RMS, Cerwin-Vega AIG loudspeaker
100
90
90
80
80
70
70
60
60
50
20
50
100 200
500 1k
2k
5k 10k 20kHz
50
20 50 100 200 500 1k 2k 5k 10k 20kHz
Frequency (Hz)
Frequency (Hz)
Object: Input signal (cable Phoenix Gold)
User:
Location: Cerwinski Laboratories Inc.
Object: Signal after cable Phoenix Gold
User:
Location: Cerwinski Laboratories Inc.
Test 2 (input)
SPL (dB) 20 V RMS, Cerwin-Vega AIG loudspeaker
100
Test 2 (output)
SPL (dB) 20 V RMS, Cerwin-Vega AIG loudspeaker
100
90
90
80
80
70
70
60
60
50
20
50 100 200
500 1k 2k
5k 10k 20kHz
50
20 50 100 200 500 1k 2k 5k 10k 20kHz
Frequency (Hz)
Frequency (Hz)
Object: Signal after cable Isoteric Audio USA
User:
Location: Cerwinski Laboratories Inc.
Object: Input signal (cable Isoteric Audio USA)
User:
Location: Cerwinski Laboratories Inc.
Test 3 (input)
SPL (dB) 20 V RMS, Cerwin-Vega AIG loudspeaker
100
Test 3 (output)
SPL (dB) 20 V RMS, Cerwin-Vega AIG loudspeaker
100
90
90
80
80
70
70
60
60
50
20 50 100 200 500 1k 2k 5k 10k
Frequency (Hz)
Object: Input signal (cable Romex)
User:
Location: Cerwinski Laboratories Inc.
20kHz
50
20 50 100 200 500 1k 2k 5k 10k 20kHz
Frequency (Hz)
Object: Signal after cable Romex
User:
Location: Cerwinski Laboratories Inc.
Figure 6.8 Three 6 m cables feeding a full-range loudspeaker with a passive crossover. The
left-hand plots are from the amplifier output terminals. The right-hand plots were measurements from the loudspeaker cabinet input terminals
Effects of amplifiers and cables 177
Test 4 (input)
20 V RMS, Cerwin-Vega SW box
SPL (dB)
100
SPL (dB)
100
90
90
80
80
70
70
60
60
50
20
50
100 200 500 1k 2k
Frequency (Hz)
5k 10k 20kHz
50
20 50 100 200 500 1k 2k 5k 10k 20kHz
Frequency (Hz)
Object: Input signal (cable Phoenix Gold)
User:
Location: Cerwinski Laboratories Inc.
SPL (dB)
100
Test 5 (input)
20 V RMS, Cerwin-Vega SW box
Object: Signal after cable Phoenix Gold
User:
Location: Cerwinski Laboratories Inc.
SPL (dB)
100
90
90
80
80
70
70
60
60
50
20
50 100 200
5k 10k
500 1k 2k
Frequency (Hz)
20kHz
Test 6 (input)
20 V RMS, Cerwin-Vega SW box
Object: Signal after (cable Isoteric Audio USA)
User:
Location: Cerwinski Laboratories Inc.
SPL (dB)
100
90
90
80
80
70
70
60
60
50
20
50
100
200
500 1k
2k
5k 10k 20kHz
Frequency (Hz)
Object: Input signal (cable Romex)
User:
Location: Cerwinski Laboratories Inc.
Test 5 (output)
20 V RMS, Cerwin-Vega SW box
50
20 50 100 200 500 1k 2k 5k 10k 20kHz
Frequency (Hz)
Object: Input signal (cable Isoteric Audio USA)
User:
Location: Cerwinski Laboratories Inc.
SPL (dB)
100
Test 4 (output)
20 V RMS, Cerwin-Vega SW box
Test 6 (output)
20 V RMS, Cerwin-Vega SW box
50
20 50 100 200 500 1k 2k 5k 10k 20kHz
Frequency (Hz)
Object: Signal after cable Romex
User:
Location: Cerwinski Laboratories Inc.
Figure 6.9 Three 6 m cables feeding a sub-woofer box. The left-hand plots are from the
amplifier output terminals. The right-hand plots were measurements from the loudspeaker
cabinet input terminals
178 Loudspeakers
a) 5 m coaxial cable
b) 50 m coaxial cable
c) 5 m parallel cable
Figure 6.10 Effects of cable on 1.6 kHz square wave. All upper traces are from the amplifier
output terminals; all lower traces are from the loudspeaker input terminals
Effects of amplifiers and cables 179
d) 50 m parallel cable
e) 5 m coaxial cable with screen as live
f) 50 m coaxial cable with screen as live
Figure 6.10 Continued
180 Loudspeakers
ground). Whilst listening only to the background noise from the amplifier,
at very low level, no change could be heard between any of the cables,
but the potential for such changes in interference patterns, especially on
the longer lengths of cable, does not bode well for the inaudibility of these
effects on complex musical signals. It was suspected that some amplifier
designs could be more susceptible than others to this type of interference
entering their feedback circuits via the output terminals. The gross differences in the interference patterns between b) and f), using the selfsame
cable but reversing its polarity [hot down the screen in f)] is suggestive of
something untoward occurring.
Twelve months later, a further paper was presented, this time to the
Reproduced Sound 19 conference, in Oxford5 , largely intended to answer
questions raised during the previous year’s presentation. A series of five
tests were undertaken, interchanging the amplifier, cable, and loudspeaker
within the same basic tests set up, to see if any changes were noticed in
the interference levels. As had been seen the year before, a considerable
amount of hash was being received from the air, including a 13 kHz signal
which seemed to disappear around 9 pm each evening, even though nothing
in the office or workshop was switched off at that time. In the first set up,
a high sensitivity compression driver was used as a load, mounted on a
horn and producing a 1 kHz tone at 80 dB SPL at one metre. It was driven
by a Class A amplifier, designed for professional use and connected via 28
metres of 4mm2 OFC (oxygen-free copper), parallel conductor loudspeaker
cable. The results are shown in Figure 6.11. The test was then repeated, but
with a dome tweeter of similar frequency response but 20 dB less sensitivity.
The amplifier was duly increased in gain to once more produce 80 dB SPL
at 1 metre, and the resultant plots are shown in Figure 6.12. Inspection of
Figures 6.11 and 6.12 clearly shows how, whilst the absolute interference
level has remained almost constant, the extra 20 dB of signal has swamped
the noise in the second test. The plots were normalised to the level of the
1 kHz signal level, towards the left hand side of each graph. The frequency
scales are linear, not logarithmic. The implication from this is that if the
interference pick up could affect the performance of the amplifier, even
if it was not directly audible from the loudspeakers, then the effect would
be more noticeable on higher sensitivity drivers than on lower sensitivity
drivers.
This was an interesting finding, even though it was not definitive, because
the motivation to do the investigations leading to the 2002 paper4 came after
the usual OFC loudspeaker cables were changed to RG59 coaxial cables
between the amplifier and compression drivers in a large studio monitoring system. Many people noticed the difference, even though no difference
could be measured in the acoustic output. People (professionals) reported
the sound as being smoother with the coaxial cable. The studio in question
was sited close to emergency service aerials (fire and police) yet nobody had
commented about similar problems in similar monitor systems in other locations. The original complaints of an unusual slight harshness in the sound only
applied to the high sensitivity loudspeakers, and not to any other loudspeakers in the studio. The change to the RG59 solved the problem.
The next test in the series was a repeat of the test whose results were
shown in Figure 6.11, except that the parallel conductor, 4 mm2 OFC cable
Effects of amplifiers and cables 181
a) Input A voltage at loudspeaker terminals
Input B voltage at amplifier output terminals
b) Noise spectrum at loudspeaker terminals
c) Noise spectrum at amplifier output terminals
Figure 6.11 Class A amplifier/parallel cable/compression driver
182 Loudspeakers
Figure 6.12 Class A amplifier/parallel cable/dome tweeter
Effects of amplifiers and cables 183
was replaced by a 25 mm2 coaxial loudspeaker cable (not a co-axial RF
cable, as used in Figure 6.10). The results are shown in Figure 6.13, which,
when compared with Figure 6.11 show much less interference at the loudspeaker end (which may, or may not, be consequential) but a greater level
of the 13 kHz interference at the amplifier end of the cable. The voltage
sensitivity of the measurement scales is approximately equal in each case.
The fourth measurement in the series used the same loudspeaker and
cable as in the previous measurement, but the Class A amplifier was substituted for a Class AB amplifier. The amplifiers differed considerably in
their quantity and application of negative feedback. The results of this
test, shown in Figure 6.14, differ greatly from those shown in Figure 6.13.
Repeating the last test with parallel cable in place of coaxial cable gave
the results as shown in Figure 6.15. In the paper it was stated “Comparison
[of the plots in the figures] shows that the interference signal measured at
the loudspeaker driver terminals is affected differently by each amplifier,
and that the difference in the interference patterns from cable to cable
is also influenced by the amplifiers to which they are connected. Given
the obvious interdependence of all the parts of the circuit, the findings
help to explain why such a lack of consistency exists between reports of
the beneficial effects of using certain loudspeaker cables. It would appear
to be the case that certain cable benefits can only be claimed for certain amplifier/loudspeaker combinations, and that any perceived audible
improvement heard on any one combination may not necessarily be able
to be expected when the cable is used on any other combination”.
Perhaps it is also worth looking at some other findings from the same
paper, which attempted to measure the losses actually occurring within different cables of different construction and with different loads. Figure 6.16
shows the results of some measurements made by connecting the two
inputs of a differential amplifier across the amplifier and loudspeaker ends
of some two-metre sections of cable5 . The rise in the plots above 2 kHz is
a result of the less effective rejection at higher frequencies, so the graphs
are comparative rather than absolute: the decibel (vertical) scale is not
calibrated. Nevertheless, the differences are real enough. Figure 6.16(a)
shows the plot resulting from the measurement of a 25 mm2 , screened, twin
twisted-conductor loudspeaker cable. Figure 6.16(b) shows the results for a
cat-5 data cable, and Figure 6.16(c) shows the plot for a 6 mm2 twin, parallel conductor loudspeaker cable. All were driving an 8 ohm woofer, but in
the latter case, (c), the cone was blocked to prevent any movement. With
the cone blocked there is no mechanical resonance, so the dip at around
80 Hz in the first two cases is absent in the case of Figure 6.16(c). The plots
clearly show how the losses within different cables are quite different, and
how the changes in impedance at the loudspeaker end can further affect
the losses in the cables. All the measurements of Figure 6.16 were on
lengths of only two metres of cable. Despite the fact that the scaling of the
amplitude is only relative, it can still be seen that differences in the losses
do exist, not only in terms of overall level but also in frequency balance.
As the evidence presented in this chapter has shown, loudspeaker cables
seem to be sensitive to the equipment to which they are connected, and
vice versa. What is more, the entire systems seem to be sensitive to their
environment, at least in electromagnetic terms. Nevertheless, the concept
184 Loudspeakers
Figure 6.13 Class A amplifier/coaxial cable/compression driver
Effects of amplifiers and cables 185
Figure 6.14 Class AB amplifier/coaxial cable/compression driver
186 Loudspeakers
Figure 6.15 Class AB amplifier/parallel cable/compression driver
Effects of amplifiers and cables 187
a)
dB
31.5
63
125
250
500
1k
2k
4k
8k
2k
4k
8k
2k
4k
8k
Frequency (Hz)
b)
dB
31.5
63
125
250
500
1k
Frequency (Hz)
c)
dB
31.5
63
125
250
500
1k
Frequency (Hz)
Figure 6.16 a) Spectrum of the difference between the voltage signals at either end of a
25 mm2 screened cable. b) Spectrum of the difference between the voltage at either end of
a CAT5 data cable. c) Spectrum of the difference between the voltage at either end of a
figure-of-eight cable with the cone of the low frequency loudspeaker blocked (i.e. prevented
from moving). Vertical scale not calibrated
188 Loudspeakers
of minimising loudspeaker cable lengths seems to be well founded, but the
practice of separating the frequency range into narrower bandwidths also
seems to reduce the demands made of the amplifiers and cables, alike.
This is a concept which it is now worth looking at in a little more detail,
before expanding the concept to polyamplification and multiamplificaiton.
6.11 Some passing comments
Unfortunately for people who have not had a very great degree of experience of the subject, sorting out what is solid from what is nebulous in terms
of so much that has been published in the hi-fi press about loudspeaker
cables is not an easy task. Nevertheless, despite some critics claiming that
it is all a load of nonsense, it is the opinion of the authors that far too
many people of good repute have claimed that sonic differences do exist
to be able to dismiss the subject of loudspeaker cables out of hand. One
of the main obstacles to verification has been the cost of double-blind,
controlled tests, with sufficiently large groups of subjects, coupled with the
extraordinarily large number of possible equipment combinations and test
locations, and the fact that a cable which shows benefits in one of those
combinations may show no benefit in another. One component in isolation
may not exhibit any noticeable difference over another component. However, when they are used in some combinations with other components,
the differences may be readily apparent.
Whilst writing this book, a short, written note was received from Martin
Colloms, an eminent authority on the subject of high fidelity loudspeakers.
There is nothing to suggest, from either his professional conference papers
or his well-respected text books, that he is either cloth-eared or a charlatan,
and neither can the authors of this book refute his opinions. An extract
from his communication will serve as a good summary.
A fair percentage of my reviewing life has been spent listening to
and dealing with cables. Most evaluations I still do blind. I think that
I have correlated with reasonable precision the key aspects of cable
design from some 400 examples.
Metallurgy: the actual metal or alloy and its state/annealed/
crystalline composition/extrusion direction and subsequent build
orientation.
Dielectrics alter the sound, as do different plastics in film capacitors, the issues including dielectric factors, DF with frequency, piezo
effects, self-damping including semiconducting insulation, and dielectric constant.
Geometry: spacing, stranding, Litz or bunched.
Mechanico-acoustic: physical strength, rigidity, self-damping,
microphony issues.
RFI: can be very important; if you spectrum analyse (I work up to
1.5 GHz) the dominant RFI (radio frequency interference) is about
1 MHz for many loudspeaker cables.
Many amplifiers are no longer anything you would recognise by
100 kHz, never mind the 1 MHz, and the RF gets in the output
Effects of amplifiers and cables 189
terminals and intermodulates around the feedback loop. A speaker
cable is often a good medium-wave aerial.
Cables vary greatly in how they dump RF interference into the
amplifier output port. The Zobel filter has little effect as it is generally
buffered by 10 ohms. If the RFI doesn’t get in the positive line, it
common modes into the ground line.
At 1 MHz or more, the RFI hardly cares what kind of amplifier it is.
Contacts and connectors also matter, as do their tightness and
vibration resistance. Acoustic energy ends up being mechanical watts
and everything shakes about.
It is amazing how mild that vibration can be and still affect the
sound of an electrical component, including a cable. Simple tests
on vibration isolation and suppression show this clearly. Acoustic/
mechanical coupling remains one of the most insidious modes of
sound quality loss.
In a recent conversation, Paul Frindle, one of the designers of the Sony
Oxford R3 digital mixing console and many of the Sony professional plugins, recalled an occurrence during his time as a designer at Solid State
Logic. There had been complaints from many studios around the world that
mixes done on the small faders, which were simple potentiometers, sounded
better than mixes done on the large faders, which operated VCAs (voltagecontrolled amplifiers). They proceeded to make countless measurements at
the factory but could find no apparent cause for the described difference in
the sound. Some of Paul’s comments were very reminiscent of loudspeaker
cable anomalies.
P.F. “You could end up in a situation where a single signal sounded
fine, but its relationship with everything else was ill-defined. You
could set up a mix on the pots (the small faders), with no VCAs,
and it would sound great; but going through the main faders, with
the VCAs, it would sound oddly wrong. Yet, if you soloed any single
VCA channel you could hear no difference compared to the small
fader. It was fascinating! I found that this was caused by very small
amounts of signal dependent delay variance through the VCAs, which
was a complex kind of distortion that was unfamiliar within the design
context. In my opinion this was one reason that led to the perception
that the VCAs sounded bad, and many people went in the direction
of consoles with motor driven faders instead.
This problem has some similarity to issues resulting from analogue
to digital converters. For instance, if you have different clock-jitter,
between channels – this is a lovely one! If your system has timing errors, when you use an ADC and a DAC back to back in a
monitoring capacity, the clock is common and simultaneous to both
the encoding and decoding stages. Since the timing errors are synchronous they partially null out. However, if you delay the signal – or
store it then play it back later – even though the system is the same,
the jitter is no longer synchronous, and the resulting sound quality is
compromised. In fact, the sound is reminiscent of the mixes done via
the VCAs on the old SSL consoles. Of course, this is one of many
190 Loudspeakers
good illustrations of how the sound can change through a system,
even though the recorded bits are unaffected and no numerical errors
have actually occurred.
Another similar problem can exist when you dither signals, because
of relative correlation. When you dither a number of channels, the
dither noise of any one channel should be unrelated and uncorrelated
to any other, or you risk the relative correlation of the dither noise
starting to become evident. You can end up with statistically partially
‘mono’ dither-noise, which can close in the stereo effect, especially
on fade-outs. Again, a single channel works fine, a stereo channel
apparently sounds fine whilst the music is playing, but as channels
build up with the same dither, the stereo begins to close in. We spent
a fortune on the R3 finding 256 independent noise sources, because
it was a strange problem to solve. It is hard to measure, and the
sound problems are something which you often need to be working
on day after day before they become clearly apparent. You feel a
sort of unease, that something is wrong, but you can’t quite explain
what it is. At one time, before we found an easier solution, 30% of
the processor of the R3 was dealing with this problem. [And the R3
had about 3000 times the processing power of a current (2005) Pro
Tools system. P.N.]
The illusiveness of these types of problems are not dissimilar to the illusiveness of definitive, irrefutable evidence about the differences between
loudspeaker cables, but whereas Sony and Solid Stage Logic have been
able to throw vast amounts of money at the problems, low volume producers of special loudspeaker cables have not enjoyed such luxury. Two of
Paul Frindle’s sentences in the previous paragraph are very relevant to the
issue. “It is hard to measure, and the sound problems are something which
you often need to be working on day after day before they become clearly
apparent. You feel a sort of unease, that something is wrong, but you
can’t quite explain what it is”. There are the hardnosed objectivists who
would say that if you cannot measure it, then it cannot be important, but,
once Solid State Logic solved their VCA problem, the complaints stopped
from the users around the world. Surely this is evidence that the problem
had been real enough. There is no logic in claiming that if Paul and his
colleagues had not found the problem, then that would have proved that
the problem was imaginary. Similarly, if people cannot prove the reasons
why cables should sound different, the implication is that not enough effort
has been put into finding the problem, and not that the problem does not
exist. And, of course, a subtle difference in the sound, given rise to by two
loudspeaker cables, will almost certainly not be audible if the resolution of
the loudspeakers being used to audition them is not, in itself, high enough
to show up the difference.
Nevertheless, the evidence is now overwhelming that cables can give
rise to sonic differences. The situation is somewhat paralleled by the relationship between stress and the functioning of the human immune system.
Believe it or not, despite the fact that most people ‘know’ that when people are stressed they seem to be more prone to illness and infection, no
clinically proven, scientific evidence currently exists to make a definite
Effects of amplifiers and cables 191
link between stress and susceptibility to illness. However, in 2002, Ronald
Glaser, et al, at Ohio State University, published in the Journal of Consulting and Clinical Psychology a paper stating that whilst no proof existed,
the circumstantial evidence was too overwhelming to be ignored. The conclusion was that stress did lead to more illness and infection, and that the
fact that they could not prove how it could do so did not mean that it could
not be said that it did do so.
6.12 Multi-cabling
It is widely accepted that bi-wiring with conventional loudspeaker cable
will almost universally impart a greater sonic improvement to any multiway loudspeaker system than a change from a single conventional cable
to a single esoteric cable. Bi-wiring takes separate cables from the output
terminals of the amplifier to the separated inputs of the high and low
frequency sections of the passive crossover filters. Figure 6.17 shows the
principles of bi-wiring. Tri-wiring simply extends the concept to three filter
sections and three cables. Although each cable still receives the same
voltage drive from the amplifier, the current passed by each cable is only
that which relates to the frequency band that it is handling. As it is the
current which gives rise to the linear and non-linear processes which are
a)
Crossover
input
Amplifier
output
HF
LF
b)
Original crossover
input now for one
filter section only
Amplifier
output
terminals
HF
Internal links broken
between inputs to
filter section
New terminals for
separate access to
other filter section
Separate cables run
from amplifier to each
individual filter section input
Figure 6.17 a) Conventional amplifier-to-crossover wiring. b) Bi-wiring
LF
192 Loudspeakers
attributed to magnetic effects, the separation of the currents into two or
more frequency bands can be beneficial. The high frequency signals are
therefore unaffected by the heavy low frequency currents.
The materials used for the conductors can influence the sound quality
performance of loudspeaker cables, as can the materials used for the insulators. The physical construction of a cable is also considered by many to
be a significant factor in terms of sound quality, with some complex plaiting
arrangements of the conductors being highly regarded by many specialists.
Given these differences, appropriate cable designs and dimensions can be
more ideally matched to the frequency and current requirements of the
individual drivers in a system if multi-cabling is employed.
6.13 Polyamplification and multiamplification
What has just been discussed is the way in which the separation of the audio
spectrum into different frequency bands can make much fewer demands
on the loudspeaker cables, and that in separating the bands, intermodulation distortion can be reduced. This idea can be extended one step further
by using separate amplifiers, as well as separate cables, a practice known
as polyamplification as shown in Figure 6.18. However, once one has progressed to this stage, there can be little justification in using high level,
passive filters when low level, active filters could do the job in a more precise and less lossy way, although the design of audiophile-standard active
filters is not an easy task. Nonetheless, the polyamplification system has
seen use, and the amplifiers, like the cables in the previous case, are driven
HF
amp.
Input to HF filter
(original single
input)
Separate amplifiers and cables to high
and low frequency filter sections
Amplifier
inputs
paralleled
LF
amp.
HF
Internal
filter input
links broken
New separated
input to LF filter
LF
Extra
LF amp.
Optional extension of principle for use with
twin bass driver systems, but here the LF
filter component values must be changed
as load impedances will be doubled as the
two originally parallelled drive units are
separated.
Figure 6.18 Extension of bi-wiring to bi-amplification whilst still using passive, high-level
filters
Effects of amplifiers and cables 193
by the full, composite signal voltage, although they only need to supply
current over their specific frequency bands, reducing intermodulation distortion to a greater degree than bi-wiring or tri-wiring alone.
When the filters are placed ahead of the amplifiers, and the amplifier
outputs are connected directly to the loudspeaker drive units, with no
components other than the cable between them, the practice is known as
multi-amplification. Multi-wiring (bi-wiring, tri-wiring etc), polyamplification and multiamplification are three distinct steps forward, respectively,
in terms of sonic quality, and it usually does not require trained ears to
notice the benefits.
There is no doubt that it is asking a lot of any amplifier, or loudspeaker
cable, to faithfully pass up to 11 octaves of musical signal with a dynamic
range of 90 dB or more. Considering the fact that no loudspeaker driver can
do this, it seems perfectly reasonable to split the frequency bands ahead of
the amplifiers and drive each frequency range independently. The benefits
of doing this were amply described in Chapter 5, but further repercussions
of this practice on amplifiers and cables can be expanded on, here.
It does not take too much imagination to realise how a 20 or 30 amp low
frequency current can modulate high frequency signals passing along the
same cable at levels of 40 dB below. The bass currents cause the conductors
to flex, mechanically, under the mutual magnetic field. Piezo and structural
modulation then carries interference into the low level high frequency
system. In terms of power ratios, say between tympani and triangles, or
bass guitar and mandolin, that 40 dB represents 10,000:1, or a current ratio
of 100:1. The more that the frequency bands are separated, the easier they
are to handle, as with the drive units themselves. It has been the experience
of the authors that as the frequency bands become narrower, the need for
specially selected cables reduces considerably. The Litz wire referred to in
Section 6.8 may be beneficial when used in 10 metre lengths and handling
the full audio frequency range, but those benefits when used in 2 metre
lengths when handling only frequencies below 1 kHz would be minimal.
In a similar way, the separation of the different frequency bands can
allow the selection of amplifiers which are less heavy, expensive, heat
producing or physically large, without significantly compromising performance. What is more, if any non-linearity exists in the circuitry, which it
must to some degree, the potential for the production of intermodulation
distortion will be greatly reduced. The potential for the low frequencies
to modulate the more delicate high frequencies will not occur, and, as discussed in Chapter 5, the generally prevailing opinion is that multi-amplified
systems sound ‘cleaner’ than equivalent systems using single, full-range
amplifiers. And of course, with multiamplification, multi-cabling is an automatic result.
6.14 System design
Before selecting amplifiers or cables for any loudspeaker system, it is
necessary to have a clear view of the purposes for which the entire system
194 Loudspeakers
will be used. There simply does not exist any ideal amplifier or ideal cable
to serve for all purposes. One cable which improves the sonic quality
of given combinations of amplifier and loudspeaker may show absolutely
no benefit whatsoever with a different combination. One amplifier which
sounds stressed at high levels when driving a loudspeaker exhibiting a
‘difficult’ input impedance may perform excellently in combination with a
loudspeaker with a more uniform impedance curve.
Perhaps nothing highlights the concept of component matching quite
so easily as carefully listening to the performance of digital-to-analogue
converters (DACs). The subtle, or even not-so-subtle, differences between
better quality DACs will be revealed by a high resolution monitor system
in a good listening room. However, it is possible to substitute loudspeakers
of progressively lesser quality of reproduction, and to continue to repeat
the tests until no difference can be heard between the different DACs. To
a lesser degree, the same effect may be noticed when changing amplifiers
or loudspeaker cables. When considering the components for a system it
is not usually considered to be commercially viable to over-specify any
component part. For this reason, in general, an amplifier will be used
in a powered loudspeaker which is ‘only’ of a quality up to which it is
deemed that no further improvements in amplifier performance would
give rise to any significantly noticeable improvement in the sound of the
complete system. Even in professional systems, it is rare in the 21st century
for manufacturers to over specify anything. However, in terms of professional engineering, as opposed to engineering for the market, it can still
be beneficial to design systems with an extra margin of quality to allow
for minor deterioration over time, or to allow for minor degradations elsewhere in the chain. A 1000 euro, star quad, polarised, screened cable may
possibly make a difference in geographical areas of high electromagnetic
interference, and when used with amplifiers which are sensitive to having
long ‘aerials’ hung on to their outputs, but there would be no justification
using the same cable in interference-free areas with amplifiers which were
immune to the problem.
What equipment is truly professional and what is not can be difficult
for many inexperienced people to decide in days when marketing is so
aggressive, and when ‘professional’ is a word often used more as a sales
device than an accurate representation. In fact, as so much recording
is carried out in places which could hardly be described as professional
in the traditional sense, and yet which do much work commercially, the
whole line between professional and domestic equipment has become very
ill-defined.
References
1 Newell, P. R., ‘Studio Monitoring Design’, Chapter 6, Focal Press, Oxford, UK
(1995)
2 Newell. P., Castro, C., Ruiz, M., Holland, K., Newell. J., ‘The Effect of Various Types of Cables on the Performance of High Frequency Loudspeakers’,
Proceedings of the Institute of Acoustics, Vol 24, Part 8, Reproduced Sound 18
conference, Stratford-upon-Avon, UK (Nov 2002)
Effects of amplifiers and cables 195
3 Czerwinski, E., Voishvillo, A., Alexandrov, A., Terekhov, A., ‘Multitone Testing
of Sound System Components – Some Results and Conclusions, Part 1: History
and Theory’, Journal of the Audio Engineering Society, Vol 49, No 11, pp
1011 – 1048 (Nov 2001)
4 Czerwinski, E., Voishvillo, A., Alexandrov, A., Terekhov, A., ‘Multitone Testing of Sound System Components – Some Results and Conclusions, Part 2:
Modeling and Application, Journal of the Audio Engineering Society, Vol 49,
No 12, pp 1181 – 1192 (Dec 2001)
5 Castro. S.V., Newell, J. P., Ruiz, M., Holland, K. R., Newell, P. R., ‘Loudspeaker
Cables for High Frequency Transducers – A Further Assessment’, Proceedings
of the Institute of Acoustics, Vol 24, Part 8, Reproduced Sound 19 conference,
Oxford, UK (Nov 2003)
Bibliography
1 Duncan, B., ‘High Performance Audio Power Amplifiers’, Newnes, Oxford, UK
(1996 – Reprinted with revisions 1997)
2 Newell, P. R., ‘Studio Monitoring Design’, Focal Press, Oxford, UK (1995)
3 Newell, P. R., ‘Recording Studio Design’, Focal Press, Oxford, UK (2003)
4 Harris, S., ‘Class D Audio Power Amplifiers’ Audio Engineering Society, 18th
UK Conference Proceedings, London (2003)
5 Colloms, M., ‘High Performance Loudspeakers’, 6th Edition, John Wiley &
Sons, Chichester, UK (2005)
Chapter 7
Loudspeaker behaviour in rooms
7.1 The anechoic and reverberation chambers
It is customary to measure loudspeakers in anechoic chambers, which
represent as closely as possible a free acoustic field with no boundaries.
The wedges which line the surfaces of most chambers serve to avoid abrupt
changes in acoustic impedance and absorb from all angles to a uniform
degree. The very high degree of absorption achievable with such systems
functions down to a frequency where the length of the wedges exceeds
one quarter of the wavelength. Below this frequency the absorption begins
to reduce, and reflexions begin to occur. A room with one metre wedges
would therefore be anechoic down to a frequency which has a four metre
wavelength, which corresponds with a frequency of around 85 Hz. What
happens below this frequency depends on the mounting conditions, the
shell structure, and the size of the chamber – the larger the chamber, the
weaker will be the reflexions at the measuring positions.
Loudspeaker measurements are made in such rooms because they provide an invariable reference which enables like to be compared with like.
Real rooms tend to be like human fingerprints, with no two being exactly
alike, so measurements made in real rooms would not be representative of
the loudspeaker, alone. Although gating techniques exist which can allow
computer-based measurement systems to eliminate the room effects, the
gating systems themselves tend to introduce anomalies of their own. Large
anechoic chambers, although very expensive to build (upwards of 1000
euros per square metre of total surface area for a 70 Hz chamber), really
have no equal for measurement accuracy and repeatability.
Where absorption is very high, but incomplete, a room can be considered
to be semi-anechoic. In such circumstances, and for given positions in
the room, a response equalisation curve can be generated which allows
compensation of the measurements for the small, smooth irregularities of
the room, allowing an anechoic response plot to be realised in less than
true anechoic conditions. A hemi-anechoic chamber, on the other hand,
has one of its surfaces highly reflective and very rigid. If either the source
of sound or the measuring microphone is set into the rigid boundary,
no reflexions will be evident, although at higher frequencies, where the
equipment in the room (either loudspeaker or microphone support) is
comparable in size to the wavelength, a weak reflexion may return after
travelling between the equipment, the hard-wall surface, and back again;
or vice versa. The measured response in such chambers will show a rise
at low frequencies due to the mounting in the boundary, the effect of
Loudspeaker behaviour in rooms 197
which will be discussed later in the chapter. Fortunately, this can easily be
compensated for by electrical means to yield a similar response to a fully
anechoic measurement. The hemi-anechoic chamber represents radiation
into a hemisphere, whereas in a fully anechoic chamber the waves are free
to radiate spherically. The formula for the surface area of a sphere is 4r2
(4× the square of the radius), and for a hemisphere 2r2 . Consequently,
the spaces are commonly referred to as 4 and 2 spaces. An anechoic
chamber is shown in Figure 7.1.
At the other extreme, we have the reverberation chambers. These are
built with massive, rigid, non-resonant walls and a non-parallel construction. The rooms are typically made from concrete, with the inner surfaces
plastered and painted to provide a very smooth surface which is highly
reflective up to the limits of audibility. The aim is to provide a uniformly
diffuse sound field at all points in the chamber, although when the dimensions become small by comparison to the wavelength some modal, spacially
dependent responses begin to appear. By means of the diffuse mixing of
the sound, the total energy radiated by the source can be measured at
any point within the volume of the chamber that is not too close to a
boundary or the direct field of the source itself. Figure 7.2 shows a reverberation chamber with a decay time of around 8 seconds. It is useful in
a chapter about room effects to begin with the two extremes of anechoic
and diffusely reverberant spaces because all practical rooms lie somewhere
in-between, and to a greater or lesser degree exhibit the properties of both
of the above extremes.
The response of a loudspeaker measured on-axis and at various angles
off-axis in an anechoic chamber is shown in Figure 7.3. The response of
the same loudspeaker measured in a reverberation chamber is shown in
Figure 7.4. If one can imagine measuring the loudspeaker in an anechoic
chamber at all angles and in all planes, and then integrating the results, the
Figure 7.1 The large anechoic chamber at the ISVR, Southampton University, UK. A section
of the removable floor grids can be seen at the left-hand side. The wedges are made of
glass-fibre, covered in muslin, and are one metre long. Above 70 Hz, the surfaces are almost
totally absorbent
198 Loudspeakers
Figure 7.2 The reverberation chamber, adjacent to the anechoic chamber shown in Figure 7.1.
The reverberation time at low frequencies is around 8 seconds. At the left of the photograph,
the flash from the camera can be seen reflecting from the shiney wall surface
mean response of all of the plots such as the ones shown in Figure 7.3 would
look like the response shown in Figure 7.4. The reverberation chambers
therefore act as acoustic power integrators, and provide a much quicker
means of determining the total power response than the thousands of individual measurements that would need to be taken in an anechoic chamber.
Most cabinet loudspeakers are omnidirectional at low frequencies and
rather directional at high frequencies, therefore the extra low frequency
power radiating in all directions is the reason for the bass rise in Figure 7.4.
To maintain a flat response on axis, more total power must be radiated by
the loudspeaker at the frequencies which spread out over a greater volume
of the room. There are two common means of describing the directivity,
the directivity index (DI) and the directivity factor. The DI is given by
10 log10 Q, where Q is the directivity factor. In plain English, the DI is
the ratio in decibels of the on-axis sound pressure compared to what it
would be if the same radiated energy was distributed omnidirectionally.
The directivity factor is the ratio of the actual directivity to the omnidirectional directivity, and has no units. For example, a source radiating into
a hemisphere would have twice the directivity factor of a source radiating
into a free field. Radiating into quarter space from a floor/wall junction
would yield a directivity factor of 4. Q is perhaps the most commonly used
symbol for directivity factor, but one also sees DF , and even R with
a subscript Greek letter theta ().
7.2 Boundary loading and room gain
When a loudspeaker radiates in unrestricted space, the radiated waves are
free to expand in all directions. Below about 250 or 300 Hz, the radiation
pattern from a ‘monopole’ source (such as a loudspeaker cabinet) tends
Loudspeaker behaviour in rooms 199
10
0
–10
Axial Response
15 degrees
30 degrees
dB
–20
45 degrees
60 degrees
–30
–40
20
100
10000
1000
Frequency (Hz)
Horizontal off-axis frequency response
10
0
–10
Axial Response
15 deg. up
30 deg. up
15 deg. dn
dB
–20
30 deg. dn
–30
–40
20
100
1000
10000
Frequency (Hz)
Vertical off-axis frequency response
Figure 7.3 Axial and off-axis pressure amplitude responses as measured in an anechoic
chamber
10
0
dB –10
–20
20 k
10 k
5k
2k
1k
500
200
100
50
20
–30
Frequency (Hz)
Figure 7.4 Total power response of the loudspeaker whose anechoic responses are shown in
Figure 7.3. The reverberation chamber sums the responses from all directions
200 Loudspeakers
High frequency
Mid frequency
Closed back radiation
pattern
Low frequency
Figure 7.5 Typical radiation pattern from a closed back loudspeaker cabinet
On the axis (arrowed) all frequencies arrive with equal pressure, but the frequencies which
radiate over a wider area also radiate more total power in the room, giving rise to the type
of power response shown in Figure 7.4
to be omnidirectional, but at higher frequencies, for conventional loudspeakers with the drivers mounted on a single front baffle, the radiation
becomes more directional, as shown diagrammatically in Figure 7.5. For
dipole sources, which radiate from both sides of their diaphragms, a figureof-eight radiation pattern is more typical, as shown in Figure 7.6. Most
cabinet loudspeakers, whether sealed boxes, reflex cabinets or transmission
lines, act as monopole sources at low frequencies. Examples of common
dipole sources are flat panel loudspeakers, such as some electrostatics, and
open-backed guitar amplifier loudspeakers.
When a wave expands spherically, the sound intensity (which is measured
not in sound pressure level but in watts per square metre) is distributed over
Open back radiation
pattern
High frquencies propagate in a
forward direction, but low and
mid frquencies largely radiate
in a figure of eight pattern
High frequency
Mid frequency
Low frequency
Loudspeaker radiates in
opposite phase on each
side of the diaphragm
Figure 7.6 Typical radiation pattern from an open-backed loudspeaker cabinet
It is typical for less mid and high frequencies to radiate behind the loudspeaker cabinet
due to mechanical obstructions
Loudspeaker behaviour in rooms 201
the surface of the expanding wavefront. Given a sphere of one metre radius,
the area of its surface calculated from the formula given in Section 7.1
(4r2 would be:
4 × 12 = 4 × 1 = 4 m2
126 m2
A sphere of two metres radius would have a surface area of:
4 × 22 = 4 × 4 = 16 m2
503 m2
which is four times the area of a sphere of one metre radius
A sphere of four metres radius would have surface area of:
4 × 42 = 4 × 16 = 64 m2
201 m2
, of course, being approximately 3.142
Sixty-four square metres is four times 16 m2 which is four times
4 m2 . Therefore, each time that we have doubled the radius we have
increased the surface area by four times:
1 m radius = 4 m2 surface area
2 m radius = 16 m2 surface area
4 m radius = 64 m2 surface area
The sound intensity is a measurement of power distribution, so for any
point on the surface of the expanding wave the intensity is reduced by a
quarter each time that the distance from the source is doubled, because the
same radiated power is spread over four times the surface area. Each time
that intensity (or power) is halved, the level reduces by 3 dB. Each time
that it is doubled, it is increased by 3 dB, so when the intensity is reduced
to one quarter (one half of one half) it reduces by 6 dB (3 dB + 3 dB).
Therefore, as the radius of a sphere doubles, and its surface area increases
by a factor of four, the intensity at each point on the surface of the sphere
is also reduced by a factor of four, and thus falls by 6 dB. This is the
principle behind the well-known ‘double distance rule’, which states that
each time the distance from the source is doubled, the sound pressure level
(SPL) drops by 6 dB. The reduction is nothing to do with absorption in the
air, but is purely a result of spreading the power over a greater area. Air
absorption losses at short distances are negligible.
If the wave propagation were to be restricted to travelling along a tube, as
shown in Figure 1.1, no expansion would take place, and therefore the only
losses would be those incurred due to the non-perfectly smooth-and-rigid
walls of the tube acting as absorbers. This is why it was possible in old ships
to provide speaking tubes from the bridge to the engine room, and to speak
and to be heard clearly over great distances and in noisy environments. In
the 19th century, experiments were conducted with speaking tubes which
were usable over distances of three kilometers, and conversations (by Biot,
in Paris) in a low voice were possible at 1 km1 .
202 Loudspeakers
Note, however, that although the sound power reduces by 3 dB when
it is halved, the halving of sound pressure requires a 6 dB reduction. This
is because the sound power is proportional to the square of the sound
pressure. In electrical terms, voltage can be considered to be the electrical
pressure, or electro-motive force. In Spanish and Portuguese, for example,
the word ‘voltage’ translates as ‘tension’, just as in English we can refer
to the very high voltages on a cathode ray tube as EHT, or extra high
tension. In Spanish and Portuguese, blood pressure also translates as ‘blood
tension’, so this concept of using the same word ‘tension’ highlights the link
between voltage and pressure. The well-known equation for calculating
the output power of an amplifier from the signal voltage and the load
resistance is
W=
V2
R
(7.1)
Where W is the power, V the voltage and R the resistance.
This clearly shows the voltage (pressure) squared relationship to the
power. Power, on the other hand, is power, whether mechanical, electrical, or heat, and a decibel is always a power ratio. A decibel is also
always a decibel: there are no separate decibels for power, voltage, pressure or intensity. The relations are fixed and the decibel never changes.
If a reduction
of 3 dB takes place, the power is halved and the pressure
√
falls by 2. If a reduction of 6 dB takes place, the power is quartered and
the pressure halves. This relationship needs to be well established here,
because when dealing with rooms, we need to deal with radiated power
from the sources but we measure sound pressures within the rooms. This is
principally because human ears are pressure detectors, so hearing relates
better to pressure changes than to power changes, but loudspeakers radiate
acoustic power and heat. Loudspeakers do not radiate pressure, because
when all of the positive and negative pressure half-cycles are summed, no
net pressure change takes place. A bomb-blast, on the other hand, radiates
a unidirectional pressure wave.
7.2.1 Restriction of radiating space
If we mount a loudspeaker cabinet in an infinite, plane boundary, such
as is simulated by the hard wall in a hemi-anechoic chamber, two things
occur relating to the radiation of the low frequencies which are different
to what happens when the loudspeaker is mounted in free space. Firstly,
as no sound can radiate behind the source, the radiation can only radiate
in a forward direction. As all of the power is radiated forwards, the
pressure on-axis will rise by 3 dB, as the half of the radiated power which
would have travelled behind the loudspeaker is driven forwards. Secondly,
the increased pressure on the face of the diaphragm, resulting from this
restriction of the expansion of the wave, tends to resist the movement
of the diaphragm. In effect, the radiation impedance has been increased,
which in turn gives the diaphragm something more substantial to act upon.
The mounting surface can be thought of as a special case of a 180 degree
horn of infinite flare rate (see Chapter 4), so it provides a more resistive
Loudspeaker behaviour in rooms 203
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
Figure 7.7 Radiation into quarter space ( space)
A loudspeaker bounded by two infinite planes at right angles to each other could only
radiate into one quarter of the space compared to that of a free-field. The space restrictions
would both constrain the expansion of a propagating wave and give rise to a greater acoustic
loading on the diaphragm
termination. This extra loading gives rise to approximately another
3 dB of increased axial sound pressure, resulting from the increase in
radiated power, although the precise increase is related to the loudspeaker
sensitivity.
If another boundary is introduced, just below the loudspeaker, as shown
in Figure 7.7, the same effects occur. This is known as ‘quarter space’
loading, or space, because the free-field (4 space) has been halved by
the introduction of the first plane (2 space) then halved again by the
introduction of the surface immediately below the loudspeaker ( space).
If a further plane, rigid boundary surface is introduced at 90 degrees to
each of the other surfaces, as shown in Figure 7.8, these effects will be
repeated once more. This is akin to mounting a loudspeaker on the floor
(or ceiling) in the corner of a room. The potential 6 dB increase which is
added to the axial response as each boundary surface is added means that
when placed in a three surface corner of a room, the axial radiation at low
frequencies can be up to 18 dB (6 dB + 6 dB + 6 dB) higher than when the
loudspeaker is receiving the same electrical input power and is radiating at
the same distance from the measuring point in free space. This boost is a
minimum phase effect, and incurs no penalty in the time or phase responses
of the loudspeaker. There is no resonance associated with this effect, and
no reflexions exist so long as the radiated wavelengths are substantially
larger than the largest physical distances between the radiating surface and
the walls enclosing it. This will be discussed further in Section 7.8. The
loading can be thought of as mounting the radiating surface at the throat
of a horn of triangular cross-section, as shown in Figure 7.9.
A clear significance of this boundary loading effect is that a domestic
loudspeaker which is considered to be light on bass may have its LF
response reinforced by placing it close to a corner. Conversely, if a corner
204 Loudspeakers
∞
∞
∞
∞
∞
∞
∞
∞
∞
Figure 7.8 Radiation into eighth-space (1/2 space)
Radiating from the corner of three infinite, rigid boundaries, the loudspeaker would be
constrained to radiating into one-eighth of the space of a free-field. In ideal conditions, the
low frequency axial sensitivity of the loudspeaker could be up to 18 dB higher than for the
same power input into free space
Figure 7.9 A triangular horn
In this representation, Figure 7.8 has been re-drawn to show how, in effect, the loudspeaker
constrained by three mutually perpendicular planes is mounted in a triangular horn
Loudspeaker behaviour in rooms 205
is the only position suitable for the placement of a loudspeaker in a room,
then a loudspeaker should be chosen which is somewhat bass light in its
free-field response if a flat response in the room is the goal. In fact, one of
the principal uses of tone controls on hi-fi systems is to compensate for such
changes of overall responses due to loudspeaker positioning. The additional
radiating efficiency also means that a loudspeaker which is placed in a
position where its output is augmented 6 dB with respect to its input will
need only one quarter of the power in order to achieve the same SPL
in the room. Reliability will be increased and distortion will be reduced.
However, in real rooms, other complications may arise such as the driving
of extra room modes, and colouration due to the response boost not exactly
matching the inverse of the natural roll-off of the loudspeaker.
7.2.2 The mirrored room and mutual coupling
Another way of looking at the above concept is to imagine that the
surfaces constraining the loudspeaker were all mirrored, and that in
every place where one saw a reflexion of the loudspeaker a real loudspeaker existed which was radiating exactly the same signal. This idea
is shown in Figure 7.10, and indeed, if one removed all of the reflective surfaces and put real loudspeakers in place of the reflexions, then
the response at low frequencies would be exactly the same as that with
one loudspeaker and the boundaries in place. In the case of a single
boundary, the low frequency response rose by 6 dB. If two loudspeakers were placed back to back, with no boundary between them and fed
with the same signal at the same power level, the result at low frequencies, radiating omnidirectionally, would also be a 6 dB increase. Now, if
we drove each loudspeaker with one watt, the total input power would
be double that of one loudspeaker, which would be a 3 dB increase.
The additional 3 dB needed to yield the 6 dB output increase experienced in real situations is a result of a phenomenon known as mutual
coupling.
When one loudspeaker radiates into free air, the local pressure on the
diaphragm is that due to its own motion. When an identical second loudspeaker is added, placed very close to the first loudspeaker and driven with
the same signal and with the same phase relationships, the local pressure
into which each diaphragm radiates is its own pressure plus the pressure
radiated by the other, adjacent diaphragm. This additional pressure exhibits
itself as an increased radiation impedance, which gives rise to more sound
being radiated.
Large diaphragms, in general, radiate low frequencies more efficiently
than smaller diaphragms because there is a mutual coupling effect between
all the individual sections of the one diaphragm. One can think of a large
diaphragm as being made up of many small, individual surface areas. The
bigger the diaphragm, the more difficult it is for the air in contact with
it to move out of the way of the diaphragm motion. The ‘congestion’ of
the air particles presents a more resistive load to the vibrating surface of
the driver.
So far, we have only been discussing mutual coupling at low frequencies,
but it is not just a low frequency phenomenon. In fact, it occurs at all
206 Loudspeakers
Figure 7.10 The mirrored room
If we imagine a loudspeaker radiating low frequencies from the corner of a room with
mirrors on all surfaces, what we would see would be cluster of eight loudspeakers. The power
radiated by the single loudspeaker constrained by the walls and the floor is exactly the same
as would be radiated in that space if the walls and floor were removed and the cluster of eight
loudspeakers, each receiving the same power input as the one loudspeaker in the constrained
space, were radiating into a free-field. Within the frequency range of mutual coupling, each
doubling of the quantity of loudspeakers, all receiving the same input power, will raise the
radiated output by 6 dB. Therefore, compared to one loudspeaker, two will radiate 6 dB more
power, four 12 dB more, and eight 18 dB more power, hence the acoustic power increase
referred to in Figure 7.8. However, this theoretical maximum is difficult to achieve, and may
reduce with increasing loudspeaker sensitivities.
frequencies, but it is only at low frequencies where it is entirely constructive. It can be considered to be 100% constructive up to frequencies where
the distance between the radiating surfaces is no more than one eight of a
wavelength, which means that the radiation from one loudspeaker reaches
the other substantially in-phase with its own radiation. As the distance (or
frequency) increases, the mutual coupling boost diminishes and actually
becomes slightly negative at some wavelengths as the phase relationship of
the two pressure components drift further apart. At still higher frequencies
the mutual coupling effect becomes negligible. The zones of coupling are
shown diagrammatically in Figure 7.11.
7.3 Room reflexions
When a vibration in the air reaches any boundary, three things will occur.
Part of the energy will be absorbed, and converted into heat. Another
Loudspeaker behaviour in rooms 207
a) Pressure amplitude response in an anecholic room
C
SPL
(dB)
6 dB
B
A
20 Hz
100 Hz
200 Hz
Frequency
A: Response of single loudspeaker, anywhere in the room.
B: Response of a stereo pair of loudspeakers, each receiving
the same input as “A”, anywhere in the room, except on the
central plane: precise response may be position dependent.
C: As in “B”, but measured on the central plane only.
b) Frequency response of a pair of loudspeakers at any position
in a reverberant room – combined power output
10
dB
0
–10
10 Hz
100 Hz
1 kHz
10 kHz
Frequency
Figure 7.11 Mutual coupling effects – omnidirectional sources (continued on next page)
part of the energy will pass through the boundary, and will be transmitted
beyond it. The remaining energy will be reflected back into the room. As
nothing on this planet is either perfectly absorbent, or perfectly reflective,
all the above things must occur on each and every contact of a sound wave
with a surface. Reflexions from room boundaries will combine at any given
point with the direct radiation from the loudspeaker, and the pressure
at that point will be the sum of the direct sound and all the individual
reflexions which pass through it at the same time. Note, however, that the
direct sound will still fall off at a rate of 6 dB per doubling of distance
from the source, even though the overall direct/reflected sound level may
fall off at a much lower rate.
It is also important to understand that when pressures cancel to zero,
the waves do not disappear. They merely pass through each other. Sound
208 Loudspeakers
c) Zones of loading/coupling – general response as in b)
3 dB
A
B
C
D
Zone A: Region where the separation distance between the loudspeakers is
less than the quarter wavelength distance, and where wholly constructive mutual
coupling is effective.
Zone B : Region where the separation distance between the loudspeakers is
less than half a wavelength, but where the mutual coupling is becoming less
effective as the frequency rises.
Zone C : Region where the separation distance is greater than half a wavelength,
and where the mutual coupling alternates, as the frequency rises, between being
constructive or destructive.
Zone D : Region where the mutual coupling has ceased.
Figure 7.11 Continued
waves have a pressure and a velocity component, and when either one
is at a maximum, the other is at a minimum. The concept is similar to
that of a swinging pendulum – when the height is at a maximum, the
pendulum stops, before falling back, so the velocity is at a minimum. As it
swings through the bottom of its trajectory, the height is at its lowest point
(minimum height), but the velocity is at a maximum. Likewise, when a
sound wave hits a wall, the particle velocity must be zero, because the wave
motion must stop and change direction. The energy, which can neither
be created nor destroyed, must therefore all reside in the pressure. In
the pendulum, the energy constantly cycles through potential (height) and
kinetic (velocity), and in an acoustic wave it constantly cycles between
pressure (potential energy) and velocity of particle motion (kinetic energy).
These motions are 90 degrees out of phase. If one considers a sine wave, the
energy cannot be at zero when the pressure passes through zero, because
it if had disappeared, where would the energy come from to produce the
next half cycle? It comes, of course from the velocity component, which
was actually at a maximum (it had all the shared energy) when the pressure
wave passed through zero.
The pressure components of reflected waves can also load loudspeaker
diaphragms, but the fact that they may have travelled considerable distances means that their sound pressures will have fallen significantly by
the time that they return to the diaphragm of their origin, so the effect
is small. When two identical signals (either electrical or pressure waves)
are added together, if either one is more than around 6 dB lower than
the other, the total signal will not be significantly greater than the larger
Loudspeaker behaviour in rooms 209
of the two, alone. Therefore, reflected energy in the far-field of a loudspeaker will have more effect in terms of the way in which it combines by
superposition with the direct signal rather than any effect that it has by
directly impinging on the diaphragm.
7.3.1 Resonant modes
A special case arises when a reflexion can, through multiple reflexions,
retrace its own path, and arrive at a boundary with the same phase
relationship and in the same direction as when it left, as shown in
Figure 7.12. In this case, known as a resonant mode, each subsequent reflexion superimposes itself on the previous one, or the sum of the previous
ones, and the energy in the mode builds up. Once the source of the energy
is switched off, the energy stored in the mode will take some time to
decay, dependent upon the reflectivity of the surfaces between which it is
resonating. There is much more energy trapped in resonant modes than is
normally encountered in single reflexions, and it is the modes which are
largely responsible for the colouration which untreated rooms impart to
the responses of nominally clear sounding loudspeakers. The energy in a
modal resonance can be higher than the direct energy received from the
source, whereas simple, reflected energy is always lower.
One sometimes hears the term ‘standing wave’ being used for resonant
mode. Whilst it is true that all resonant modes are standing waves, all
standing waves are not resonant modes, so the term ‘room modes’ is
preferable to ‘standing waves’. Likewise, whilst all cows are mammals, all
mammals are not cows. One can therefore call a cow a mammal, but one
cannot call a lion a cow! [And whilst both Scots and English are British,
it is wisest not to call a Scotsman ‘English’ or serious violence is likely to
ensue!]
Low frequency source positioned
on a pressure anti-node
High pressure
Static pressure
Low pressure
Pressure component of a sound wave in a room
Figure 7.12 The driving of a resonant mode
At resonance, where an exact number of half-cycles can fit between the walls, the direct
and reflected waves will superimpose constructively to create a resonant build-up, shown
dashed. When the source driving the mode is switched off, the energy trapped in the mode
will continue to resonate until it is dissipated by absorption
210 Loudspeakers
In Figure 7.13, modal pressure and velocity distribution are shown superimposed. If a conventional monopole loudspeaker, which radiates omnidirectionally at low frequencies, is placed on the node of the pressure wave,
where the pressure is at a minimum, it will be unable to radiate a steady
tone at that frequency which coincides with the mode, because the modal
energy will constantly cancel the direct energy. Conversely, if the loudspeaker is placed at an anti-node, where the pressure is maximum, it will
strongly reinforce the mode, just like a correctly timed push of a child on
a swing, at the peak of the travel, will add impetus to the motion. On the
other hand, a dipole loudspeaker, which radiates reverse polarity pressures
equally from each face of its diaphragm, acts as a pressure source, and not
a volume/velocity source like a monopole, and couples best at the pressure
node of a mode, which is, of course, a velocity anti-node because of the
90 degree phase shift between the pressure and velocity peaks, as shown
in Figure 7.13.
Therefore, if one were to compare a figure-of-eight radiating, electrostatic loudspeaker and a normal cabinet loudspeaker with an almost identical on-axis frequency response when measured in an anechoic chamber,
the responses could be expected to vary widely when placed in the same
place in a room with reflective boundaries. Part of the difference would be
due to the difference in radiation patterns, and hence the different ways in
which each one drove the reverberant field. The other great source of variation, particularly at low frequencies, would be due to the different ways
that each loudspeaker coupled to the room modes. Consequently, when
comparing the sound of open-backed and closed-backed guitar amplifiers
it is useless to do so without finding room positions for each of them individually which support their tone. Similarly when assessing domestic high
fidelity loudspeakers of monopole or dipole nature, it is essential to consider how each one will couple to the room modes. Clearly, one position
will be unlikely to suit both, and it should also be remembered that because
of the way that a dipole radiates in a figure-of-eight pattern, it will only
drive the modes which occur between the parallel room surfaces which
face the front and rear of the loudspeaker, whereas the omnidirectional
Max pressure
Max positive
velocity
Zero pressure
Zero velocity
Min pressure
Max negative
velocity
Velocity component of a sound wave in a room
(Pressure component shown dotted for easy comparison)
Figure 7.13 The relationship between pressure and particle velocity in a resonant mode
The particle velocity component of the wave must always be at a maximum when the
pressure component is at zero, in order to conserve the energy contained in the wave. The
energy cannot simply disappear when the pressure is zero, or there would be no energy left
to continue the cycle
Loudspeaker behaviour in rooms 211
low frequency radiation from a monopole source will drive modes in all
three dimensions.
7.4 Flush-mounting
The response of a loudspeaker, except in a free acoustic field (i.e. without
boundaries) is absolutely inseparable from the modifications which will
be imposed by the room within which it is placed. Rooms form part of a
loudspeaker system because they provide loading on the diaphragms which
actually affect the sound radiation directly from the source. Rooms are
not simply environments in which loudspeakers with fixed responses are
used. If every position in every room will give rise to its own characteristic
response for any loudspeaker placed there, it introduces a great variable
in music monitoring conditions if the loudspeaker placement is not very
carefully chosen. In many music recording studios, and in almost all film
dubbing (mixing) theatres, the principal loudspeakers are flush mounted
in the front wall.
By this means, questions of room positioning are eliminated, and as all
rigid walls are pressure anti-nodes for all the modes which they support,
these modes will all be driven equally. Conversely, no position within the
room can drive all of those modes, because the node and anti-node positions vary with frequency. Flush-mounting loudspeakers in a boundary also
means that no rear radiation can take place, so none can bounce off the
wall behind the loudspeaker and return to the listening position with varying phase relationships to create peaks and dips in the pressure amplitude.
What is more, flush mounted loudspeakers will effectively experience 2
radiation, as explained in Section 7.1, and will benefit from the greater
sensitivity afforded by the increase in the radiation resistance and the constrained angle of radiation. In a room, which already constrains the wave
expansion to some degree, as opposed to in a free-field, the sensitivity
increase due to flush-mounting may be around 3 dB to 6 dB. This can be
useful at high power levels because the halving of the heat in the voice
coil even due to the 3 dB power reduction can be important in reducing
thermal compression and increasing long-term reliability. Distortion can
also be reduced due to the smaller cone excursions necessary to generate the same SPL. Frequency dependent cabinet edge diffraction effects
are also eliminated. When all is considered, flush-mounting enjoys many
advantages over free-standing, and no obvious disadvantages; at least in
mono and stereo rooms. For these, flush-mounting is the choice of the
great majority of large, professional studios. Of course, there also exists
a further, non-electro-acoustic advantage for flush-mounting – it leaves
the room much less obstructed, especially when very large loudspeaker
cabinets are used.
One problem which can arise from flush-mounting if it is not well executed is that the front wall can vibrate, thus radiating an unwanted extra,
resonant sound energy into the room. Some designers favour the resilient
mounting of the cabinets, to avoid transmitting the cabinet vibrations into
the structure. Other designers favour the rigid mounting of the cabinets
into a heavy, rigid structure, too heavy to significantly vibrate with the
212 Loudspeakers
available energy. Resilient mounting in a heavy structure is another option,
but the advantage of rigid mounting in a heavy wall is that the cabinets
are kept absolutely stable under all drive conditions. Cabinets that are
intended for mounting in this way usually have no decorative finish except
on the front face, because they will be fixed into the frame of the structure
during construction.
7.5 Multichannel considerations and phantom imaging
When loudspeakers act in multiples, the response is not necessarily merely
the sum of the individual components. When two loudspeaker cabinets are
brought close together when reproducing different, uncorrelated signals,
at the same sound pressure level, the overall pressure at the same distance
from the loudspeakers will rise by 3 dB, which is the simple sum of the two
radiated power levels. On the other hand, if the loudspeakers are radiating the same signal, the on-axis pressure will increase by 6 dB, due to the
in-phase pressure superposition, although elsewhere in the room, at places
where the phases cancel, lower levels will be evident. Figure 7.14 shows the
a)
15
10
{ }
10 log10
W4
(dB)
W1
5
0
–5
10
1000
100
Frequency (Hz)
b)
{ }
x = 1 m, y = 1.5 m
p4
20 log10 p (dB)
1
Loudspeaker B
Loudspeaker A
x = 1.2 m, y = 2.25 m
10
3m
0
4m
Microphone
–10
x
y
Loudspeaker C
Loudspeaker D
10
100
1000
Frequency (Hz)
Figure 7.14 Frequency responses for four ‘perfect’ loudspeakers radiating the same signal.
a) Total power response in a highly reverberant room. b) Combined frequency response of
four omnidirectional loudspeakers at two different positions in an anechoic chamber
Loudspeaker behaviour in rooms 213
pressure amplitude of the frequency response of four loudspeakers radiating the same signal, measured in free space at two different positions. The
only point where a flat response could be received would be at the single
point equidistant from the four sources. The loudspeakers represented in
the figure are theoretically perfectly flat sources. The significance of this
figure is that it shows that no matter how perfect the loudspeakers, or
how flat the room, a single signal fed into four loudspeakers will not be
able to deliver a flat response except in one spot, due to the phase cancellations given rise to by the different path lengths from the sources. For
each frequency, and hence each wavelength, the spacial distribution will
be different.
A wavelength is simply the distance in metres which it takes for a wave,
travelling at the local speed of sound, to pass through a full cycle. The
frequency, in turn, can be defined as the rate of change of phase with time,
so the number of cycles per second is also the number of wavelengths
that a sound wave will travel through in one second. The equation that
relates frequency to wavelength, normally represented by the Greek letter
(lambda), is:
=
c
f
(7.2)
where
= wavelength in metres
c = speed of sound in metres per second
f = frequency in hertz
For example, for 20 Hz and a sound speed of 340 metres per second:
=
340
20
17 metres
For 100 Hz:
=
340
100
34 metres
For 500 Hz:
=
340
500
068 metres = 68 centimetres
For 1 kHz:
=
340
1000
034 metres = 34 centimetres
For 5 kHz:
=
340
5000
0068 metres = 68 centimetres
214 Loudspeakers
For 20 kHz:
=
340
20000
0017 metres = 17 centimetres
This relationship ensures that the phase relationship between the acoustic
pressures radiated from each loudspeaker will vary in all parts of the area
between them. In fact, in free space, each quadrant shown in Figure 7.15
will be a mirror image of the adjacent quadrants, but when we take these
loudspeakers into a room, the situation changes dramatically. The reflected
energy from the room boundaries will complicate the sound field greatly.
Unless all the wall surfaces and structures were absolutely identical, the
symmetry of the quadrants would also be lost, because the absorption and
reflexion properties would be asymmetrical. As the power radiated by the
ideal loudspeakers that we are discussing is considered to be flat with frequency, (and let us presume that they are omnidirectional radiators) then
the resulting sound field in a room with perfectly rigid walls would be uniform, with a flat response at all places, because the reflexion density would
be so great as to ensure that all places receive all frequencies with all phase
relationships. This is the integration process that was referred to at the
beginning of this chapter when discussing reverberation chambers. Unfortunately, as neither anechoic chambers nor reverberation chambers make
good control rooms, it means that all practical rooms exhibit frequency
responses that are frequency and position dependent. The difference
A
B
w
x
y
y
R
S
x
l
l
x
C
T
U
y
y
w
x
D
Figure 7.15 Symmetry of radiation patterns of multiple drivers
If loudspeakers at positions A, B, C and D are all radiating the same signal, the microphones
at the symmetrical positions R, S, T and U would all receive the same signal. The response
at each position would be identical
Loudspeaker behaviour in rooms 215
between the response of one loudspeaker in two different places in one
room can often be greater than between two rather different loudspeakers
in the same place in the same room. Room positioning is therefore a very
critical subject, and sound control room designers go to great lengths to
try to ensure consistent responses over the critical listening areas.
If we now go back to our four loudspeaker array, and consider its performance in a normal room, the effect on the low frequency performance
can be very dependent on the musical signal. With a different instrument
in each loudspeaker, the outputs are not correlated, so each loudspeaker
will act as an individual source. If the loudspeakers are not symmetrically
placed in relation to all three axes of the room, and if the room, itself, is not
perfectly symmetrical in shape and construction, then each loudspeaker
will drive the room in a different way, and some listening positions in the
room may be better for some loudspeakers than for others. Conversely,
from the listening position, some loudspeaker positions may be better than
others in terms of the received flatness of response.
In the case where the loudspeakers are all receiving the same input signal,
such as a centrally panned instrument, the situation changes. The correlated
signal now means that there are four physically displaced sources, with
a very fixed phase relationship between them. As previously stated, the
central position would be the only one where the flat response could be
received, even without the room reflexion complications. Furthermore,
mutual coupling between the sources would also take place at frequencies
where the distance between the loudspeakers was less than about a quarter
of a wavelength, or where a boundary was within about an eighth of
a wavelength of a source. The overall frequency response would thus
change as the distance between the loudspeaker was changed, or as the
loudspeakers were moved in relation to the walls, floor, or ceiling of a
room. Not even one loudspeaker can produce a flat frequency response in
a non-anechoic room, but when four loudspeakers radiate the same signal,
the situation can become much more complicated. This is a subject that
will be discussed further in Chapter 12.
The abovementioned effects have implications for signal panning, also.
If a signal in one loudspeaker is panned into the centre of a pair of
loudspeakers, the central image, when emanating from two loudspeakers,
cannot have the same, in-room response as when only emanating from
one loudspeaker. In a totally dead room, when each loudspeaker in a pair
is radiating the same signal, the central phantom signal, on the central
plane, will be 6 dB higher than the signal radiations from either the left
or right loudspeakers alone. It will be 3 dB higher than the sum of the
outputs of the left and right loudspeakers radiating individually. This is
due to pressure summation on-axis, because when the pressure doubles,
the response is 6 dB higher. In a reverberant room, no extra level will be
detected at the listening position between a single, central source and the
phantom sum of a stereo, two sided source, (except at low frequencies
where mutual coupling occurs), because the room reflexions will tend to
integrate the overall power response.
Most mixing console manufacturers use pan-pots which are about 41/2 dB
down in the centre position, not only because most rooms lie somewhere
in-between the anechoic and reverberation chamber responses, but also
216 Loudspeakers
because mono electrical summing also needs pots which are 6 dB down
in the centre (doubling the voltage gives a 6 dB increase). As was made
plain in Chapter 1, even single loudspeakers are not simple devices. When
we use them in multiples, the way that they behave is complex, and is
anything but obvious to the majority of users. The acoustic summation of
two loudspeakers, except on an extremely thin plane which divides them
in an anechoic environment, does not sum like an electrical mix of the
two signals. Few people using loudspeakers, even professionally, seem to
realise that pan-pot laws are related to room acoustics.
To recapitulate, loudspeakers in normal rooms tend to sum power
(double power = +3 dB), whereas pressures sum like voltages (double
voltage = +6 dB),but the true pressure sum only exists on the central plane
in an anechoic room. As 20 kHz has a wavelength of only 1.7 centimetres,
and because only within a quarter of a wavelength can true summing be
expected, then the full frequency range of the +6 dB summation plane is
only around 4 millimetres wide.
7.6 Stereo perception in rooms
The man who conceived and patented the two channel stereo concept
was Alan Dower Blumlein, working for the EMI company in England
in the mid 1930s. In his patent he referred to a listener in a stereo seat.
That seat was to form an equilateral triangle with two loudspeakers, which
therefore subtended an angle of 60 degrees at the listening position. There
is nothing about a pair of loudspeakers that creates stereo. The image
that we perceive of a sound stage laid out before us is an illusion created
within our brains. This is why we refer to phantom images, because there
is no sound actually emanating from the directions from which we hear
the images arriving unless they are coming from the extreme sides of the
sound stage, i.e. out of one loudspeaker only.
Many loudspeakers are said to have good stereo imaging, but in reality it is not the loudspeakers themselves which have good stereo imaging. Good stereo imaging is perceived from loudspeakers that can supply
the appropriate information to the ears which the brain can process as
a phantom sound stage, but between the loudspeakers and the ears the
signal has to cross the room, and rooms can do a good job of scrambling the information. The positioning of the loudspeakers in many studios
in confined spaces, or where horizontal reflexions are likely, is guaranteed to diminish the stereo imaging perception from any pair of loudspeakers. Loudspeakers of only moderate imaging can easily out-perform
potentially better loudspeakers if they are better located. There is nothing inherent in a loudspeaker’s performance which give it the ability to
create precise stereo imaging sensations independently of its mounting
conditions.
In the open space of a domestic lounge, with large expanses of reflective
walls, a loudspeaker with a wide, relatively flat off-axis response may tend
to give the best stereo imaging. On the other hand, in the clutter of a
cramped control room, a narrower directivity with a rolled-off bass power
response, but still reasonably flat on-axis, may give the best stereo. It is
Loudspeaker behaviour in rooms 217
just simply impossible to say which loudspeaker responses give which best
results without knowing the acoustic conditions in which they will be used.
Many commercial loudspeakers are designed to give the best results in the
majority of the rooms in which their designers have expected that they will
be used. Nonetheless, no matter how successful the design may be in the
majority of cases, it still does not mean that that design is generally better
than a design which takes a different approach. The positions of nearby
reflective surfaces may strongly influence the choice of loudspeakers for a
specific purpose.
Any fast reflexions of less than about 1 millisecond delay with respect
to the direct sound (less than about 30 cm path length difference) will pull
the image in the direction of the reflexion. Reflexions with more than one
millisecond of delay will not do this, as the ear will lock the direction
to the first arriving wavefront (known as the Haas effect, the precedence
effect, or the law of the first wavefront) but colouration will result from
the way in which the signals re-combine with different phase relationships,
and transient signals will be smeared. If these things occur asymmetrically,
say with a reflecting surface close to one loudspeaker of the stereo pair
and not to the other, then the stereo imaging will surely suffer.
Floor reflexions are almost an inevitability, but as these will always
arrive at the ear from the same horizontal angle as the direct sound,
their effect on the stereo imaging is less noticeable. What is more, the
ear is much less sensitive in the vertical plane than it is in the horizontal
plane, presumably because humans and their ancestors have not had to
worry about either predators or prey from either under ground or in the
air. Ceiling reflexions tend to behave similarly if the loudspeakers are
mounted high up. Wall reflexions can contribute to the spacial stability of
stereo imaging, especially if the loudspeakers have a wide and flat off-axis
response. It seems that the ear can detect reflexion patterns which are
uniquely related to certain source positions, but it must be remembered
that a phantom image has more than one source. The tendency is for stereo
images to be more precise in highly absorbent rooms, but more spacially
stable in rooms with some lateral reflexions. That is to say, the image in
the stereo ‘hot seat’ will be better in absorbent rooms, but the images will
tend to collapse towards one loudspeaker or the other as one moves off
centre. Conversely, in more reflective environments, a wider area of stereo
perception may be available, but nowhere will it be perceived with the
precision afforded by the absorbent rooms. This situation has led to some
varied approaches to the design of critical listening rooms, with different
designers having different priorities.
7.7 Rooms for critical listening
The rooms in which musical instruments and their amplifiers will be used
are usually designed to have some acoustic life which will enrich the sounds
and help to inspire good performances. Stereo imaging is not a relevant
concept in the design or use of such spaces because the images are almost
invariably real, and not phantom. In the control rooms and listening rooms,
on the other hand, stereo imaging is a great priority. There is a generally
218 Loudspeakers
accepted philosophy in the design of such rooms that no reflexions should
return to the listening area within 15 milliseconds of the direct sound or
with a level above 15 dB below the level of the direct sound. This has led to
the development of room geometries which deflect early reflexions away
from the listeners, and only allow reflected energy to return via diffusely
reflected surfaces. Philosophies such as the Live-End, Dead-End rooms use
such principles2 . Other approaches, such as the Non-Environment rooms,
seek to maximally absorb all but the floor reflexions (although in some
rooms, these too are absorbed), and provide life for the speech and actions
of people working within the room by means of a highly reflective front
wall3 . As in the case with the hemi-anechoic chambers, if the source is
set into the hard surface, it can only radiate away from it. If there are
no reflective surfaces in the room to return the sound waves to the front
wall, then no reflexions can bounce off the front wall in any way that
could create either tonal colouration or image smearing. Readers wishing
to study more about control room designs should refer to the Bibliography
at the end of this chapter. Figure 12.19 also shows some design concepts
for stereo listening rooms.
Room acoustics is a big and complex subject, but even when the room is
‘right’, and even when the loudspeakers exhibit exemplary performances, it
only requires the introduction of furniture and equipment into the listening
room, arranged in inappropriate places, to severely affect the perceived,
overall response. In recording studio control rooms, the equipment needs
to be readily accessible for practical reasons, but the positioning of the
equipment needs careful thought. In domestic circumstances it almost goes
without saying that no reasonable hi-fi enthusiast would put the dining
room table and a few cupboards between themselves and the loudspeakers before listening, yet people, many times out of necessity, do very
similar things in control rooms with the mixing consoles and equipment
racks. In general, loudspeakers should be mounted in positions which are
as unobstructed as possible, and careful thought should be given to the
siting of nearby video monitors if sound-colouring reflexions are to be
avoided.
Mounting loudspeakers high up is also not a recommended procedure,
and Figure 7.16 shows how the tendency is then to listen from above one’s
head, which will not produce the same audible sensations as listening with
the sound in front of one’s nose. The high mounting in studio control
rooms also tends to produce strong reflexions from the upper surface of the
mixing console, which introduces time-smearing of transient sounds and
colouration of more steady sounds. And whilst on the subject of mounting,
Figure 7.17 shows how multi-driver, non-coaxial loudspeakers should be
mounted. Many loudspeaker manufacturers now show such drawings in
their instruction leaflets. The drivers should be kept in the same vertical
line so that lateral movement of the listeners will not give rise to arrival
time differences from the separate drivers in a cabinet; hence the stereo
imaging and timbral colouration do not suffer so much. This point is easily
demonstrated by feeding a pink noise signal to a loudspeaker and moving
one’s head laterally from side to side. The tonal change with the loudspeaker drivers displaced horizontally will be much more noticeable than
with the drivers mounted vertically. Conversely, the listener could remain
wind o w
Loudspeaker behaviour in rooms 219
Figure 7.16 When monitor loudspeakers are mounted at a steep angle, the high frequencies,
in particular, arrive at the ears from an angle totally inappropriate for the perception of an
accurate frequency balance. High frequencies will tend to be under-perceived when a listener
is looking at the equalisation controls of the mixing console. What is more, unless the ceiling
is highly absorbent, the low frequencies will suffer augmentation due to the proximity of
multiple room boundaries. The off-axis radiation, shown by the continues lines, will also tend
to reflect from the top surface of the console and smear the transient response
Figure 7.17 Orientation of loudspeakers.
It is preferable to mount loudspeakers with the drive units aligned vertically. When the
listener moves to the left or right, the relative distances to the drive units will not change.
If the loudspeakers are mounted horizontally, sideways movements will change the relative
distance to the high and low frequency drivers, and give rise to phase shifts which will affect
the perceived response, especially in the region of the crossover frequency
in the same place whilst an associate swivelled the loudspeaker; the effect
would be substantially the same. Mounting reflective surfaces behind the
listener as shown in Figure 7.18 should also be avoided if colouration is to
be minimised.
220 Loudspeakers
strong reflected
sound returning
to ears
Figure 7.18 In many cases, an effects rack placed behind the engineer for easy access also
performs the function of an acoustic mirror, returning strong reflexions to the primary
listening positions. This is especially problematical when the main monitor loudspeakers are
mounted high up
7.8 Electronic, digitally adaptive response correction
Electrical response-equalisation has long been a feature of loudspeaker
design. The earliest forms were just simple potentiometers to adjust the
tweeter levels to better subjectively suit their surroundings. Modern monitor loudspeakers with built-in amplifiers offer much more flexibility.
Figure 7.19 shows the block diagram and the response flexibility of a
Genelec 1030A monitor loudspeaker, designed to provide limited compensation for mounting conditions and boundary proximity. If the loudspeaker
were to be placed close to a wall, the radiating space would be reduced, as
described in Section 7.2, so the ensuing bass boost would be compensated
for by suitable adjustment of the bass tilt and roll-off controls. As previously stated, such loading changes give rise to response changes which are
of a largely minimum phase nature (which we shall look at in more detail
in the following section), but many response variations which involve signal delays, such as reflexions, resonances and group delays due to filters
and loudspeaker driver physical displacements, give rise to non-minimum
phase responses. Such responses can often only be corrected by the use of
acausal filters. ‘Acausal’ means effect before cause, and so these problems
can only be dealt with by the insertion of signal delays which allow a filter
to act on the signal before being incorporated into the output. There are
no analogue solutions to such problems, so inevitably these methods reside
in the world of digital signal processing.
The combined response of a loudspeaker and a conventional room is
extremely complex. In fact it is absolutely, absurdly complex; far beyond
what common sense would suggest. In the 1980s there was great excitement
in some circles about the future of digital response correction, and it being
the end of the line for room acousticians, but these expectations have not
come to pass. It was widely believed that, despite the size of the problem,
signal processing technology would develop apace, which indeed it has
Loudspeaker behaviour in rooms 221
a)
Balanced
Audio Input
CROSSOVER FILTER
2 INPUT AMPLIFIER
1
TREBLE TILT
POWER AMPLIFIERS
Treble
3
Main Level
Treble and Bass
driver protection
circuit
T-CAL
Bass
B-CAL
Start/stop
Mute
BASS ROLL-OFF BASS TILT
Power Supply
circuits
Mains Input
b)
AUDIO PRECISION 1030anec LEVEL (dBr)
100
VS FREQ (Hz)
14 JAN 94
12:09:56
AP
95
TREBLE TILT
90
BASS TILT
85
80
75
BASS ROLL-OFF
70
65
60
55
50
20
100
1k
10 k
20 k
Figure 7.19 Controls and response flexibility of a Genelec 1030A loudspeaker. a) Block
diagram showing active crossover filters, power amplifiers and drive units. b) The curves show
the effect of the ‘bass tilt’, ‘treble tilt’ and ‘bass roll-off’ controls on the free-field response
done, but complication after complication have arisen to confound many of
the hopes. In fact, some excellent room/loudspeaker correction can indeed
be achieved with modern technology, but there are prices to be paid for
many of the improvements. As will be described further in Chapter 12,
if one considers responses below about 100 Hz, and restricts oneself to
dealing with largely minimum-phase problems, then signal processing can
be put to some very good use. Loudspeaker manufacturers such as JBL
222 Loudspeakers
and Genelec have adopted the philosophy that whilst a great many people
will make decisions about professional sound recordings in less than ideal
surroundings, largely due to the ever greater financial pressures, then active
signal processing can make beneficial contributions to such environments.
Using relatively inexpensive technology they can make improvements to
conditions where neither space nor money allows for acoustic treatment.
However, such responsible manufacturers also acknowledge that there is
no real substitute for good room acoustics if the very highest levels of
reproduction quality are required. In very good rooms, it can actually be
the case that signal processing can introduce more problems than it solves,
so one should always be aware of this.
It has also been shown that many systems of loudspeaker/room correction are only significantly beneficial at short distances4 . Figure 7.20 shows
the modulation transfer function (MTF) plots of three loudspeakers in a
relatively neutral room at distances of one metre and four metres. The
MTF scale (vertical) is really a measure of response accuracy in terms
of information content; ‘1’ being perfect reproduction and ‘0’ being total
inaccuracy. As can be seen from the one metre and four metre plots, the
response accuracy generally tends to fall off with distance. (In an anechoic chamber the plots would be identical at both distances). Figure 7.21
shows the same loudspeaker responses after digital response equalisation.
It is clear to see that the responses at one metre have been significantly
improved, but no such improvement is evident at the four metre distance.
d=4 m
MTF
Monitor #1
MTF
d=1 m
1
0.8
0.6
0.4
0.2
0
1
0.8
0.6
0.4
0.2
0
31 40 50 63 80 100 125
31 40 50 63 80 100 125
1
0.8
0.6
0.4
0.2
0
Frequency Band (Hz)
MTF
Monitor #2
MTF
Frequency Band (Hz)
1
0.8
0.6
0.4
0.2
0
31 40 50 63 80 100 125
31 40 50 63 80 100 125
1
0.8
0.6
0.4
0.2
0
Frequency Band (Hz)
MTF
L-C Domestic
MTF
Frequency Band (Hz)
31 40 50 63 80 100 125
Frequency Band (Hz)
1
0.8
0.6
0.4
0.2
0
31 40 50 63 80 100 125
Frequency Band (Hz)
Figure 7.20 MTFs of three loudspeakers in a reasonably well-damped studio recording room
at different distances (d) from the loudspeakers
Loudspeaker behaviour in rooms 223
d=1 m
Monitor #1
1
0.8
0.6
0.4
0.2
0
d=4 m
1
0.8
0.6
0.4
0.2
0
31 40 50 63 80 100 125
31 40 50 63 80 100 125
Frequency Band (Hz)
Frequency Band (Hz)
Monitor #2
1
0.8
0.6
0.4
0.2
0
1
0.8
0.6
0.4
0.2
0
31 40 50 63 80 100 125
31 40 50 63 80 100 125
Frequency Band (Hz)
Frequency Band (Hz)
1
0.8
0.6
0.4
0.2
0
1
0.8
0.6
L-C Domestic
0.4
0.2
0
31 40 50 63 80 100 125
Frequency Band (Hz)
31 40 50 63 80 100 125
Frequency Band (Hz)
Figure 7.21 MTFs of the loudspeakers in a reasonably well-damped studio recording room at
different distances (d) from the loudspeakers after equalisation
The implication is that where the loudspeaker response dominates the
overall response, in the close-field, the digital correction can be greatly
beneficial, but in the far-field, where the complex room responses tend to
dominate the overall response, the correction processes lose control over
the response. It thus becomes evident that whilst such equalisation may
be effective in the close-field monitoring situations of a poorly treated
post-production room, it is no answer when a spacially uniform response
is required in a large sound control room, where the non-minimum-phase
room responses dominate, unless the room is well acoustically controlled.
The MTFs are discussed in further detail in Chapter 9.
In 2004, Norcross, et al, published an overview of the situation in an
Audio Engineering Society paper5 . In the abstract to the paper, they
stated “When the [response] is non-minimum phase, the artefacts [of
the correction process] tend to become more severe and become distinctly audible. The artefacts produced by the inverse-filtering process can
actually degrade the overall signal quality rather than improve it.” They
recognised that without doubt, in many cases, the inverse filtering of a
room/loudspeaker combination could improve perceived responses, but
they were warning of the necessity to carry out very careful subjective
listening tests before committing to the use of any signal processing system
for professional purposes. Also, as discussed in Chapter 5, whenever digital
signal processing is used in a way that needs immediate re-conversion to
224 Loudspeakers
analogue, the converter quality is also critical if it is not to limit the resolution of a system. Digital processing is better employed within a digital signal
chain and then passing the whole chain through only one re-conversion
process. Once again though, when we are faced with a chain of processors,
converters, loudspeakers and rooms, if only one link limits the resolution
then other deficiencies in the chain may well not be noticed. Low resolution loudspeakers may not show the differences between good and very
good processors or converters, and the decisions which are made on low
resolution monitoring loudspeakers during the recording/mixing process
may negatively affect the quality of a recording by not making evident the
benefits of superior equipment.
The responses of most loudspeakers in rooms have a mix of minimum
and non-minimum phase components, and the mathematically most correct inverse response may not always yield the most subjectively improved
response. One loudspeaker may also prove to be more subjectively correctable than another, even where no obvious evidence for this can be seen
from their uncorrected responses. Another factor which must be taken into
consideration when applying complex inverse filtering is that the correction may be evident only in one small region of a room, and that in most
other places the response may be significantly worse than before correction. A further related problem is where correction is used to flatten the
axial response of a loudspeaker with an irregular off-axis response. As it
is the same driver radiating the signal and its correction, it obviously cannot change the axial response by itself without also affecting the off-axis
response. The reflexions returning from nearby surfaces with the modified
off-axis response may be subjectively undesirable. It is thus very easy to
publish the improved axial results, perfectly legitimately, but which do not
reflect the true sonic situation in normal use. The significance of the offaxis response could also be very room dependent, in which case so could
be the overall effects of the correction.
Furthermore, inverse filtering can produce pre-echoes, which can give
rise to audible artefacts. These are inevitable by-products of certain types
of inverse, acausal filtering that cannot be entirely eliminated. Sometimes,
the processing artefacts can be as low as 60 dB below the signal, yet listening
tests have shown them to be audible5 . Every year, progress is made in the
domain of digital signal processing. In live sound technology, the adoption
of digital processing has been widespread, rapid and deep. Great strides
forward have been made in terms of intelligibility and subjective sound
quality. Obviously though, in live performance venues, audience noise,
ventilation noise, and even the unavoidable air-related distortions resulting
from the very high sound pressure levels close to the loudspeakers tend to
mask any low level processing artefacts, so the benefits can clearly outweigh
the penalties. Conversely, in recording studios, where the perception of
small details is much greater than during live concerts, and where no visual
performance is distracting the brain from concentrating on the sound,
there have only been limited applications for the digital signal processing
of monitor systems because of the great sensitivity to low level artefacts
resulting from the correction algorithms. However, when people work on
music recordings in rooms where computer discs and ventilation fans are
whirring away, producing up to 40 or even 50 dBA at the principal listening
Loudspeaker behaviour in rooms 225
positions, many subtleties of the recorded sound will also inevitably not be
heard. It is imperative if high quality audio monitoring is to be achieved
that such mechanical noises be banished from control rooms. There are
no technical reasons why the noisy equipment cannot be located outside
of rooms where high resolution loudspeaker monitoring is required. The
introduction of so much noisy equipment into the lower level of studios
has been a very retrograde step.
7.9 Minimum and non-minimum phase responses
In the previous section we mentioned non-minimum phase responses and
acausal filters. A minimum phase system is one in which the phase shift
associated with the amplitude response is the minimum that can be allowed
whilst still exhibiting the properties of a causal system. A causal system
is one in which the output never arrives before the input. In minimum
phase systems there is a very strict relationship between amplitude and
phase, and correcting either one will always tend to correct the other.
The response boost at low frequencies given rise to by flush mounting a
loudspeaker in a wall is an example of a minimum phase response change,
which can be equalised with normal analogue filters to restore the freefield axial response in terms of both frequency response (amplitude and
phase) and time response. The essential factor in a minimum phase system
is that there is no appreciable delay between the generation of the signal
and the effect of whatever is influencing it. If there is no appreciable delay,
then there can be no appreciable phase shift, hence only minimal phase
shifts will be evident. This is the origin of the term ‘minimum phase’.
In the case of non-minimum phase responses, amplitude correction,
alone, cannot correct the phase responses. The Fourier transform is a
mathematical means of linking the time domain representation of a signal to its frequency domain representations of amplitude and phase. The
application of the Fourier transform to a signal waveform (time response)
reveals the frequency components in terms of their magnitude and relative phase (i.e., the ‘spectrum’). The application of the inverse Fourier
transform to the spectrum yields the original waveform. This unbreakable
connection between the amplitude and phase on one hand, and the time
response on the other, means that if the correction of a response in terms
of its amplitude, alone, cannot correct the phase response, then the time
response will not be correct. Transient sounds can be very dependent upon
their waveforms in terms of their sonic characteristics, so non-minimum
phase systems tend to have distorted time responses.
The far-field response of a loudspeaker system in a reflective room (but
not in an anechoic chamber) is an example of a non-minimum phase effect.
Here, there is a delay between the signal generation by the loudspeaker
and the addition of the boundary reflexions to the composite signal at the
listening position. The arrival time differences of the reflected waves give
rise to phase irregularities which are frequency and distance dependent,
so no simple manipulation of the amplitude response of the source can
adequately compensate for the complex disturbances. This is why one-third
octave-band equalisation of loudspeaker systems in rooms is only, at best,
226 Loudspeakers
a very rough approximation of the application of the true inverse of the
response, and also why many equalised systems sound no better, or even
worse, than the unequalised responses. The equalisers may only, in effect,
be moving the response bumps and dips around, and may actually be
worsening the transient responses as they try to correct the non-minimum
phase amplitude responses.
Another example of a non-minimum phase response is in the combination of the various outputs from crossovers, as discussed in Chapter 5.
In any filter circuit, either mechanical or electrical, there are inherent
group delays for any signals passing through them. The amount of group
delay increases as the filter slope increases and as the frequency lowers.
A crossover will consequently have a different group delay associated
with each section. When the outputs are recombined they will therefore
not produce an exact replica of the input signal. For this reason, conventional equalisation cannot be used to correct response errors at crossover
points, and physical differences in the driver mounting positions may give
rise to further non-minimum phase responses of the same general nature.
Amplitude correction of the response irregularities given rise to by either
the mechanical or electrical misalignments will lead to further phase distortions and hence further time response errors which may be noticeable on
transient signals. The degree of deviation of a response from the minimumphase response is known as the excess phase. Whenever time-shifted signals
are mixed, the tendency is for the excess phase to build up.
Adaptive digital signal processing can deal with these problems, but it
can realistically only be achieved to a very high degree at one point in
space, or to a lesser degree over a wider area. In all cases, for every part of
a room that benefits, another part of the room will suffer a deterioration in
the response. In effect, the correction systems are redirecting the acoustic
waves. It is a little like having a room with some finite layers of sugar cubes
on the floor. The more that one builds up a pile in one place, the level
must go down elsewhere. Very high quality control rooms and monitor
systems tend to be expensive because there is really no substitute for high
quality drive units in big boxes working in heavily acoustically treated
rooms if flat, low distortion, high level, wide frequency band, spacially
uniform monitoring is required. The problems must be eliminated at their
sources, because electronic correction systems all have their compromises
and drawbacks. However as mentioned in the previous section, if people
will persist in trying to do professional recording in poorly controlled
rooms on inexpensive loudspeaker systems, then digital correction may
offer some overall performance benefits at affordable prices. Its application
to sub-woofer processing will be discussed in Chapter 12.
In general, non-minimum phase response irregularities are difficult to
deal with, and so are best avoided by the use of mechanical and acoustical
means. The irony is that digital correction is best applied to rooms and
components that are so good that they barely need correcting. For example,
a related technology is the motional feedback of loudspeakers, where a
sensor is placed on the woofer cone and is used to detect the actual cone
movement. In Chapter 1, Section 1.5, it was noted how the entire surface
of a diaphragm does not always move in unison. Consequently, a sensor
on a cone only senses the movement at that part of the cone where it is
Loudspeaker behaviour in rooms 227
placed. On transient signals, delayed, non-minimum phase responses can
occur which risk wild instability in the system loop, which can be controlled
by careful filtering, but the amplifiers tend to need to be much bigger than
would normally be necessary in order to handle the superimposed audio
signals and correction signals. The costs soon spiral upwards to a point
where in many cases it would perhaps be better all-round just to build
a better quality loudspeaker system in the first place.
No matter whether digital correction is being applied to the loudspeaker
alone, or the loudspeaker/room combination, the need for this extra headroom always needs to be taken into account. This is one reason why large
loudspeaker systems are rarely processed, because the amplifiers may need
to be unreasonably large; and anyhow, large systems can be made with
good transient responses and flat, low distortion frequency responses without the aid of signal processing. Given that the idea of motional feedback
has been around since the 1930s 6 , the fact that it is still such a rarity
suggests that it is not an easily realisable solution for electro-mechanicoacoustic transducer inadequacies. One of the greatest successes in active
control has been in extending the lower frequency responses in relatively
small boxes. Nevertheless, by whatever means that it is achieved, a given
SPL requires a given volume of air to be moved at a given rate, so small
drivers, no matter how they are processed, can still only achieve low SPLs
at low frequencies.
References
1 Tyndall, J., ‘On Sound’, Sixth Edition, p 13, Longmans Green and Co., London,
UK (1895)
2 Davis, Don and Davis, Chips., ‘The LEDE Concept for the Control of Acoustic
and Psychoacoustic Parameters in Recording Control Rooms’, Journal of the
Audio Engineering Society, Vol 28, No 9, pp 585–595, (September 1980)
3 Newell, P. R., Holland, K. R., ‘A Proposal for a More Perceptually Uniform Control Room for Stereophonic Music Recording Studios’, 103rd AES Convention,
Preprint No 4580, New York, USA (1997)
4 Holland, K. R., Newell, P. R., Castro, S. V., Fazenda, B., ‘Excess Phase Effects
and Modulation Transfer Function Degradation in Relation to Loudspeakers
and Rooms Intended for the Quality Control Monitoring of Music’, Proceedings
of the Institute of Acoustics, Vol 27, Part 8, Reproduced Sound 21 conference,
Oxford, UK (2005)
5 Norcross, S. G., Soulodre, G. A., and Lavoie, M. C., ‘Subjective Investigations
of Inverse Filtering’, Journal of the Audio Engineering Society, Vol 52, No 10,
pp 1003–1028, (October 2004)
6 Colloms, M., ‘High Performance Loudspeakers’, 6th Edition, John Wiley & Sons,
Chichester, UK (2005)
Bibliography
1 Newell, Philip., ‘Recording Studio Design’, Focal Press, Oxford, UK (2003)
2 Cooper, Jeff., ‘Building a Recording Studio’, Fourth Edition, Synergy Group Inc,
Los Angeles, USA, (1984)
228 Loudspeakers
3 Davis, Don; Davis, Carolyn, ‘Sound System Engineering’, Second Edition, Focal
Press, Oxford, UK (1997). NB: originally published by Howard W. Sams, USA
(1987)
4 Walker, Robert., ‘A New Approach to the Design of Control Room Acoustics
for Stereophony’, 94th AES convention, Berlin (1993)
5 Walker, Robert, ‘The Control of Early Reflections in Studio Control Rooms’,
Proceedings of the Institute of Acoustics, Vol 16, Part 4, pp 299–311, UK (1994)
6 Walker, Robert, ‘A Controlled-Reflection Listening Room for Multichannel
Sound’, Acoustics Bulletin (Journal of the UK Institute of Acoustics), Vol 24,
No 2, pp 13–19, St Albans, UK (March-April 1999)
7 Newell, Philip, ‘Project Studios’, Focal Press, Oxford, UK (2000)
Chapter 8
Form follows function
8.1 The chain
The recording chain under discussion here begins with the musicians and
ends in the rooms in which the people who buy the recordings choose to
place their music systems. Domestically, we must really limit this discussion to reasonably high fidelity systems, because once we introduce in-car
listening and ghetto-blasters on the kitchen table, or portable radios in the
bathroom, we begin to enter a realm of variability which, firstly, become
unable to be qualified and secondly, in the majority of cases, cannot really
be considered capable of truly representing the music producers’ wishes.
Manufacturers of such equipment may go to great lengths to produce
pleasant-sounding equipment, and record producers may go to equally
great lengths to ensure the compatibility of their mixes with such systems
because they represent the majority of the market for recorded music,
but this book is essentially dealing with the concept of high fidelity reproduction. This is not to say that many in-car systems are not capable of
remarkably high fidelity in many aspects of their performance, but their
reproduction quality is still idiosyncratic in a way that generally sets it
apart from what we expect to hear from a ‘high-end’ system in the home.
The loudspeakers used in the recording chain can be separated into five
basic groups:
1)
2)
3)
4)
5)
loudspeakers for musical instrument amplification
recording monitors
mixing monitors
mastering monitors
domestic high fidelity loudspeakers
There are many people who will argue against this concept, citing that
a good, professional, well conceived, well-engineered loudspeaker should
be suitable for all of the above purposes. However, the recording chain
is a very varied chain, and what will be discussed in this chapter are
the specific requirements at each stage of the process which tilt certain
designs or concepts towards being advantageous for the different needs of
those specific requirements. In fact, the reality of the current situation is
that different loudspeakers do tend to be used in different stages of the
recording/mixing/ mastering process where financial restraints do not limit
the choice of equipment, and there are many good reasons why this state
of affairs exists.
230 Loudspeakers
In their own ways, the last four of the loudspeakers on the above list
all try to achieve the closest approach to the original sound. They are
all reproducers, trying to emulate as accurately as possible within their
design criteria a faithful acoustical output of the electrical waveform being
fed to them. All of them will generally be required to show a wide, flat
frequency response, a well-damped time response, low levels of non-linear
distortion and a directivity pattern appropriate to the rooms in which they
are each expected to be used. The balance of priorities will vary with the
intended applications, as we will discuss later, but the above characteristics
are common to all of them.
Conversely, loudspeakers for use with musical instruments are part of
the instruments which they are amplifying. They are sound producers,
not reproducers, and what they produce is, in itself, definitive. They are
unlikely to have flat frequency responses, and the range of those responses
may well be defined by the harmonic range of the instruments with which
they will be used. Colouration of the sound is usually a desirable asset –
something which is anathema to hi-fi or monitoring – and ‘musical’ forms
of distortion may also be considered to be beneficial. Time responses which
contain resonances can impart warmth and character to the musical timbre,
and directivity control may be something which is given very little consideration whatsoever. In fact, the design of loudspeakers for the production
or reproduction of music have very little in common. Music reproduced
via musical instrument loudspeakers may be very far from what the record
producers intended, and electric instruments played via high fidelity loudspeakers may tend to sound lifeless and uninspiring.
It may be more appropriate to begin this chapter by looking at the
reproducers before discussing the producers, because the idiosyncrasies of
the latter will be better understood after the rigours of the reproduction of
music have been better appreciated. Nevertheless, there is no hierarchy of
superiority in the concepts, because unless an interesting sound is there to
be recorded, there cannot be much enjoyment from reproducing it. Indeed,
the factories which produce the better musical instrument loudspeakers
spend just as much time and attention on the design, manufacture and
quality control of the instrument loudspeakers as they do on the best
monitoring loudspeakers. In some ways, designing for flatness and low
distortion can be easier than trying to design something to make that
elusive, ‘magic’ sound.
8.2 Recording monitors
Until the early 1970s, recording monitors, mixing monitors and mastering
monitors – in those days, mastering being essentially disc cutting – were
largely one and the same thing. It was not uncommon for the same type
of loudspeakers to be used throughout the principal rooms of a recording
studio complex, although in the disc cutting rooms, which were usually
smaller in size than the recording control rooms, the sound was rarely the
same as in the usually better acoustics of the control rooms and mixing
rooms. In those days, also, the musicians tended to stay in the recording
Form follows function 231
rooms, and only ventured into the control rooms when invited to hear a
‘playback’.
As time progressed, and the musicians began to become more involved
in the whole process, they began to spend much more time in the control rooms, and they began to expect to feel the same sensations as they
ventured from the performing studios to the control rooms, in order not
to lose the ‘vibe’. Volume levels in the control rooms began to rise in
order to avoid the deflationary sensation of playing in the studio at 100 dB
SPL then listening to the ‘take’ in the control room at 85 dB SPL. If the
levels changed, the perception changed, and with it the ‘buzz’ of excitement could change, leaving the musicians in doubt about whether they
had achieved their aims, or not. Within a very few years, and especially
after the advent of synthesisers and other portable keyboard instruments,
it began to become commonplace to actually perform in the control room.
It can be argued that if what is perceived at 100 dB will not translate to
85 dB or less, then there is an inconsistency that suggests that the recording
may disappoint when reproduced domestically. However, it should be well
understood that, at least for multitrack recordings, the recording phase is
about capturing a performance. The experience of the recording staff will
be important in deciding if the sounds can be optimised at lower levels,
but the achievement of the maximum impact of the performance can only
effectively be captured during the recordings.
Around 100 dB SPL, music begins to affect perception and emotions in
a different way to what we perceive at lower levels. Chemical changes take
place in the brain, which are not unlike those caused by sex and certain
drugs. This explains why music at discothèques needs to be loud, or the
sensation to dance will not be stimulated and the tendency towards exhibitionism will not be aroused. The exhibitionist tendency is also important
in the recording process, because musicians are performers, and a performance is an exhibition. Therefore, if musicians are to perform at their best,
they may well need a stimulus, very similar to the disco dancers needing
a stimulus. Obviously, the type of stimulus depends on musical style, but
under almost all circumstances, the correct stimulus will not be achieved
unless the musicians are performing in a control room at reasonably similar
levels of sound pressure to those which they would normally be receiving
during a concert performance.
Perhaps coincidentally, the tendency to perform in control rooms began
around the same time that some ‘mini-PA systems’ were beginning to
appear as studio monitors, which could easily produce over 120 dB SPL at
the mixing console. In all fairness, much more is known about psychoacoustics in 2005 than was known in 1975. However, in those early days, the
mini-PA system with a pair of high power 15 inch drivers, a compression
driver straight from sound reinforcement technology on a barely modified
horn, and a high power compression tweeter seemed to be a reasonable
means to achieve the sort of high SPL, wide bandwidth, relatively low
distortion sound that was being called for. Two such systems are shown
in Figure 8.1, and even at low SPLs the performance of these systems
was better than many of the previously used monitors, at least for many
types of music, but they did have many design faults by modern standards.
Time has refined these concepts, and room acoustics have taken great steps
232 Loudspeakers
a)
b)
Figure 8.1 Large studio systems from the mid-1980s. a) Giant Eastlake Audio systems at
Marcus Music, London, UK. b) Urei 815s at Jacobs ‘Court’ studio, Farnham, UK
forward, guided by a much greater understanding of psychoacoustics, but
in the conditions of the mid 1970s the failings of the loudspeaker/room
combinations in many cases led to problems when using these main monitors for mixing, which in turn led to the use of small reference loudspeakers
such as the Auratones, and later the Yamaha NS10s, to name two popular
examples. The concept of separate recording and mixing monitors had thus
begun to establish itself, and it began to become clear that each had their
place in the music recording process. Nonetheless, whilst it is by no means
obligatory to use different monitors at the recording and mixing stages,
it tends to be rather expensive to achieve conditions with a single system
which are optimal for both purposes. Cost-cutting has had a big impact
on the limitation of monitoring acoustics to something which is often well
below what is achievable.
Form follows function 233
8.2.1 Basic requirements
Recording monitors need to do two jobs at the same time. The musicians
may be considering them to be stage monitors – performance monitors –
whilst the recording engineers will also be using them to assess recording
quality and instrumental timbre. They therefore need to simultaneously
achieve high SPLs and great subtlety. The musicians will also be expecting
them to go as deep as their lowest bass instrument would achieve in a
live performance, or their sense of the performance may be diminished.
The musicians may also be distributed around the room, and each of them
will be expecting to receive their fair share of the sound. The latter fact
tends to mean that the loudspeakers need to insonify the entire room to
a reasonably equal degree. If this is to be achieved in a way in which
the recording engineer can still hear all the necessary detail in the sound,
the room will need to be extremely well controlled acoustically, and the
loudspeakers would need to be flush-mounted in the wall. Not surprisingly,
these are precisely the conditions which are to be found in most of the
control rooms of the world’s most famous studios. Some rooms complying
with these requirements are shown in Figure 8.2.
A typical frequency response requirement is shown in Figure 8.3. The
low frequency response needs to go to around an octave below the lowest
note on a conventional bass guitar, at 41 Hz. The extra octave is needed
both to minimise colouration due to phase shifts associated with the roll-off,
which can extend well above the roll-off turnover frequency, and also to
accommodate instruments such as the less common five-string bass guitars,
and the sub-bass from synthesisers. The perceived colouration due to the
roll-off at around 20 Hz is considerably less in this lowest octave of the
audio frequency range.
The roll-off at the high frequency end of the spectrum is something which
has developed over time. In the early to mid 1970s, when the recording
monitors were also the mixing monitors, it was customary to use multi-band
equalisers to achieve a flat response up to 20 kHz. However, it soon became
apparent that this was leading to dull mixes in the homes of the record buyers. There were several schools of though about why this should be so. One
idea was that the higher monitoring levels in the studios meant that the
mixes were being done at levels where the ear was more sensitive to high
treble than would be perceived at the levels of typical domestic reproduction. Consequently, what would seem to be a balanced frequency response
in the studio would seem top-light in the home. Another reason frequently
discussed was that the ‘bass trapping’ which was employed in many control
rooms, to flatten the low frequency response of the rooms, was not a part
of most domestic constructions. Therefore, the increased bass build-up in
many domestic living rooms required a corresponding treble boost if a balanced low/high frequency relationship was to be achieved. Nevertheless,
whatever the reasons actually were, the treble roll-off became a normal
alignment for the large monitors, and it seemed to lead to better results.
Nowadays, even if the large monitors are not used so frequently for mixing,
the generally higher SPLs at which they are used seems to be less fatiguing
with the roll-off of the high frequencies, and a more natural, representative
balance is perceived. A rather similar process occurred in the film industry,
234 Loudspeakers
a)
b)
c)
Figure 8.2 a) Kinoshita monitor system at Capri Digital, Capri, Italy. b) Blackwing, London,
UK, with its unusual Yamaha NS40 close-field monitors and a pair of 4-way amplified Reflexion
Arts 235 monitors, mounted above the soffit. c) Eurosonic, Madrid, Spain
Form follows function 235
10 dB
180 deg.
20
100
1k
10k
Frequency
Figure 8.3 Two-way monitor measured on-axis at 2 metres distance in a control room at LMH
where an empirically derived ‘X-curve’, with a significant high frequency
roll-off, became the industry standard, because it works!
By the same token, it would be reasonable to expect that the low frequencies should also be rolled-off. The curves of equal loudness are shown
in Figure 8.4, and from them it can be seen that the ear becomes much
more sensitive to the low frequency as the level increases. Nevertheless,
as we have just discussed, in many domestic rooms the bass is much less
controlled than in the most recording studio control rooms, so it would
seem to be reasonable that the low frequency increase due to the listening
Figure 8.4 The Robinson-Dadson curves of equal loudness
236 Loudspeakers
level in the control rooms will very often be matched by the bass build-up
in domestic rooms when listening at 10 to 20 dB less SPL. But whatever the
reason, at the recording stage of the process, the performance is paramount.
Who wants to hear a great recording of a poor performance? The frequency response target of Figure 8.3 certainly seems to work for recording
monitors, and experience has shown that it also works well for mixing in
the far-field.
Another important aspect of recording monitors is a fast decay time
across the entire frequency band. A typical decay plot is shown in
Figure 8.5. A fast decay is important because any resonant overhang will
tend to lift the response at the resonant frequencies, just as a resonant mode
in a room will cause a lump in the room response close to its antinode(s).
The resonances can also mask detail in the sound, as will be discussed
in more detail in Chapter 11. Unfortunately, many small monitor systems
purposely employ resonances to extend their low frequency responses (see
‘Reflex enclosures’ in Chapter 3), but this technique is bound to blur detail
and create the potential for misjudgements about the musical balance
between instruments containing mixtures of low frequencies of both transient and steady-state nature, such as the combination of bass drums and
10
0
–10
dB
–20
–30
20
40
60 ms
80
100
20
100
1000
10000
Frequency (Hz)
Amplitude
1
0
–1
0
5
10
15
20
Time (ms)
Figure 8.5 In-room decay response of a large monitor system in a well-controlled control
room. The resonance evident in the waterfall plot at 120 Hz was the resonance of an empty
cable tube in the floor
Form follows function 237
bass guitars. Their timbral balance will, to different degrees, be coloured
by the resonance, so the recording personnel will be left unsure about
which part of the sound is contributed by the recording, and which part
is contributed by the loudspeakers and the room. It is therefore important to use physically large monitor loudspeakers because at peak levels
of 110 dB SPL at reasonable listening distances, it is simply impossible to
achieve fast decaying, low distortion, low frequency responses from small
loudspeakers. There is no technology or trickery to overcome this problem
because it is deeply rooted in the laws of physics.
Mixing is made much easier if the recording stage has been well monitored and controlled. There are far too many cases of problems being
heard at the mastering stages due to the mixes having been done on small
monitors of recordings which were also done via small loudspeakers, and
thus which were not adequately monitored in the first instance. Commercial pressures, and the general decline and de-professionalisation of the
recording industry in the late 20th , century has given rise to so many studios
which use small monitors for the entire recording process. Many excellent
recordings have been made in such studios, partly due to the adaptation
of musical styles, such as by using instruments with pre-programmed, wellbalanced sounds, and also by the degree of familiarity with the systems
which has been developed by the recording personnel. Nevertheless, a
whole industry of mastering has since grown to unforeseen levels, partly
fed by the uncertainly which many people feel when working in conditions
of inadequate monitoring when only small loudspeakers are available.
8.2.2 Proportional costs
Since the 1980s, the cost of multi-track recording systems has plummeted.
When inflation is taken into account, the degree to which the prices have
fallen is enormous. On the other hand, the price of good recording monitors
and excellent acoustics has remained at similar, real, proportionate levels
to what they were in the 1980s. That is to say, if a large, stereo monitor
system and acoustic treatment cost the same as a new Mercedes car in 1985,
then the cost of the same, top-line monitor system and acoustic treatment
in 2005 would still cost the same as a new Mercedes car, whereas the
price of a recording system has fallen from the price of three entire cars
to the price of a replacement engine. Monitor loudspeakers and acoustic
control systems are works of engineering, which require skilled labour and
careful planning. They do not follow the trend in electronic development at
the signal processing level, and micro-miniaturisation and mass production
techniques cannot be applied. Even the power amplifiers which are used
are physically large devices, which take considerable labour to construct.
They also require expensive chassis and bulky components to handle the
power levels involved and to dissipate the waste heat. In fact, as time
progresses, skilled labour has tended to increase in proportional costs,
but mechanisation does not easily lend itself to specialised, low quantity
production processes, so high quality amplifier prices also remain high.
This disproportionality in the cost of the recording systems to the monitor systems has strongly militated against the purchase of large recording
monitors. In cases where they have been bought, but used in rooms which
238 Loudspeakers
were not suitably treated for financial reasons, they have often unjustly
been criticised for being difficult to use. This however, is down to their
inappropriate circumstances of use rather than the failings of the monitor
systems, themselves, because such systems cannot be expected to work well
in rooms which are not appropriately designed. Much of the criticism which
modern, large monitors receive are based on this type of misapplication,
although it must be said that some manufacturers have clouded the issue
by attempting, for marketing reasons, to make their large monitors mimic
the rounder sound of the wider-range smaller monitors. The real job of
the large monitors is to do well some things that the small monitors cannot
do. Their job is not simply to be a louder version of the small monitors.
8.2.3 Different approaches
Designing a large loudspeaker system to respond in a delicate and subtle
manner whilst producing high SPLs is not an easy task. Unfortunately, as the
solutions to some problems become easier as size goes up, the solutions to
other problems become more difficult to achieve. The diversity in the design
of many of the large systems which will now be discussed reflect the different orders of priority which their designers have given to the points where
compromises must be made. A loudspeaker system cannot recreate the threedimensional sound-field produced by an acoustic instrument, but ears are
very sensitive to changes in sound-fields. Room acoustics also become more
relevant as the loudspeaker to listener distance becomes greater, so the
design of the loudspeakers and rooms becomes inextricably linked. The
combined sound-field is what the listeners perceive, so if some compromises in loudspeaker system design can be mitigated in their effect by corresponding room acoustic changes, better overall results can be achieved.
The above statement also implies that a loudspeaker system which is
designed for one room-acoustic concept may not be appropriate when
used in acoustically different rooms, and vice versa. Therefore, to put any
large monitor system into a relatively untreated room will be asking for
problems – small systems at close distances tend to be a better solution.
Nevertheless, a good large system in an appropriate room may be able
to achieve a level of overall response accuracy which would simply be
unattainable by any monitor system in a poorly treated room, or any small
loudspeaker system in any room. However, as previously stated, the option
of a large monitor system in an appropriate room is not likely to be a
cheap solution to realise.
Figure 8.6 shows four large monitor systems of very high quality, but
none of them can achieve their potential without a considerable amount
of acoustic design in the control room. And by ‘acoustic design’ we are
not referring to sticking some foam panels on the wall. Acoustic control
systems which work at 20 or 30 Hz are necessarily large, and their size is
dependent upon wavelength, and wavelength alone. They will not scale
with room size or budget. This means that rooms with well controlled low
frequencies need to be considerably larger than the working space which
will be required after the room is finished. Two hundred cubic metres
would be a good volume to begin with – a room of around 7 m × 7 m × 4 m
high (the fact that it is square may be of no account when the necessary
Form follows function 239
degree of treatment is installed1 – but such spaces are often considered
to be uneconomical in the post 2000 recording world. Nonetheless, economics has nothing to do with physics, so the fact remains that in the top
professional studios, where things are built to a quality, rather than to a
cost, the control rooms tend to be of over 200 m3 in their basic shell sizes.
All the systems shown in Figure 8.6 use multiple bass drivers. The production of low frequencies essentially involves moving a quantity of air
which is the product of the moving area and the velocity. In other words, a
small radiating area can be moved with a high velocity, or a large radiating
area can be moved with a low velocity to achieve the same high SPL.
However, the low-velocity, high radiating area approach produces significantly less non-linear distortion. The larger surface area also increases
the radiation efficiency, as the large area better matches the characteristic
impedance of the air in contact with it. Quite obviously, this cannot be
achieved in a small box. The use of multiple low-frequency drivers also
mean multiple voice coils, and this tends to lead to better dissipation of
the waste heat, so problems of thermal compression are reduced.
Another reason for using multiple drivers as opposed to simply using
larger, single drivers is because it tends to become difficult to maintain
the rigidity of the piston (the cone) much beyond diameters of 15 inches
(380 mm). Beyond 18 inches (460 mm) adequate cone rigidity only tends
to be possible by employing means that significantly increase the weight
of the moving assembly, which leads to reduced efficiency. Conversely,
as the resonant frequency is related to both the weight of the moving
system and the stiffness of the suspension, a small, light cone can only
achieve low resonance with a very loose, low stiffness suspension. That
is, as the weight reduces, the stiffness must also reduce if the resonant
frequency is to remain the same. This can lead to excessive fragility for
professional use, so cones of less than 12 inches (300 mm) tend not be
used in large monitor systems, because they tend to be either inefficient
or fragile. Where responses are desired down to 20 or 25 Hz, 15 or 16 inch
(380 – 400 mm) drivers seem to be an optimum choice.
The choice of whether to put multiple drivers in the same enclosure
or to provide them with individual enclosures is another option. Each of
two similar drivers in a 500L enclosure behave theoretically exactly as one
loudspeaker in a 250L enclosure. Therefore, whether a cabinet with two
drivers has a single 500L volume or is divided into two separate volumes
of 250L will in no way affect the theoretical performance of the system. If
the loudspeakers are reflex loaded, then obviously the two sections would
need their individual tuning ports in a divided enclosure, and the sizes
of those ports would be different from the ports needed for the larger,
single enclosure. However, if the two enclosures were tuned to the same
frequency as the single enclosure, the loading on the drivers would be
identical to the case of both drivers being situated in one, larger enclosure.
Well, at least that is the case in theory, but in practice the drivers are
rarely, if ever, identical in their performance or resonant frequency. Some
designers feel that drivers sharing a single cabinet run the risk of detuning the systems by one driver dominating the port response, but this
problem appears to be negligible with large enclosures tuned to very low
frequencies. It is a characteristic of more consequence in small, domestic
240 Loudspeakers
loudspeakers. What is more, as the resonant frequency goes down, the
tuning of big boxes tends to become much broader, much less precisely
tuned than smaller boxes with higher resonant frequencies. The only real
advantage of using separate enclosures for the double woofers in large
cabinets is the ability to modify the overall response by using different
tuning frequencies for each cabinet, which can be useful in adjusting the
response contour to a desired target function.
a)
b)
Figure 8.6 a) Garate Studios, Andoain, in the Basque region of Spain, with a Reflexion Arts
234 monitor system. b) Strongroom studios, London, UK, with a Quested Q215 loudspeaker
system. c) Genelec 1035A monitor system in JVC Aydama Studios, Japan. d) Olympic Studios,
London, UK, with 4-way Westlake Audio HR1 monitors
Form follows function 241
c)
d)
Figure 8.6 Continued
8.2.4 Crossover points
As described in Chapter 1, the maximum frequency to which a cone driver
can operate with reasonable directivity control is when the wavelength is
equal to the diameter of the cone. When four drivers are used in a square
pattern, the group behaves at low frequencies as one large driver. When
two drivers are used side-by-side, the horizontal directivity becomes that
of a driver with the same width as the pair; that is, it would be narrower at
higher frequencies than that of a single driver. With a vertical arrangement,
the horizontal directivity may remain as it would be for one driver, whilst
242 Loudspeakers
the vertical directivity would narrow. Depending upon the nature of the
room acoustics, and whether the surfaces are absorbent or diffusive, designers must decide upon the physical distribution of the drivers, how many
crossover points to use, and at which frequencies to make the transitions.
The off-axis radiation will need to be as flat as possible if any significant
reflected energy is likely to be returned to the listener. Wideband diffusers
will return the frequency balance which impinges upon them, so a tonally
coloured, non-flat off-axis response reflecting back to the listening position
will tend to colour the overall perception in the room.
The general tendency is for manufacturers who sell large monitor systems
for incorporation into a wide range of room designs to make multi-way systems. By splitting the frequency range into three or four bands, directivity
control can be well maintained and off-axis energy can be kept relatively
smooth in frequency balance. Designers who know that their loudspeakers
are going to be installed in relatively absorbent rooms can concentrate
on the axial response and a region of around 60 degrees in the horizontal and 30 degrees in the vertical, taking the advantage of using two-way
systems which minimise the problems normally associated with crossover
alignment and acoustic reconstruction. Essentially, in absorbent rooms, the
off-axis energy which may be directed outside of the designated working
area, and which may not have a flat frequency response due to directivity
problems, is of little concern because nobody will be there to hear it and it
will be absorbed at the boundaries. It therefore cannot return to the room
or colour the axial response.
These concepts tend to be very poorly understood by the majority of
people now working in the recording industry, and who, in ignorance,
may make entirely inappropriate changes to, or of, studio systems. In so
many cases, people choose their supposedly favourite loudspeakers and
try to use them without any understanding of what they are really doing.
It is imperative to understand that a loudspeaker system drives vibrations
across a room, and that it is the combined response that is perceived.
Nobody would buy a Formula One racing engine and expect it to work
optimally when mounted in a tractor chassis, yet this is a close analogy
of what many people do with their loudspeakers. If an axial response
perception is desired, the room must be relatively absorbent. If a more
lively sound is required, then the loudspeaker must be engineered to give
good off-axis performance. This, as stated earlier, can have a great bearing
on the choice of the number of crossover points. Fewer points tend, in
general, to lead to better axial responses, whilst more crossover points
tend, in general, to facilitate the engineering of a wider, more even off-axis
response. However, nothing is absolute here, so designers work to find the
most practical compromises for different circumstances of use.
Once that the number of ways has been decided upon, the crossover
points need to be chosen. The decisions about where to cross over can be
determined either by the usable frequency range of the chosen drivers, or
the need to maintain a smooth off-axis response. Clearly though, where
two-way systems are concerned, the chosen drivers must deal with greater
frequency ranges than the drivers in systems with more crossover points.
In the case of the monitor system shown in Figure 8.6(a), the crossover
is placed at 1 kHz. It is unusual to operate 15 inch drivers up to such a
Form follows function 243
high frequency, but the d’Appolito layout (in this case both vertically and
horizontally symmetrical) and fourth order Linkwitz-Riley filters help to
form a line source around the crossover frequency which is well-behaved
both on-axis and over the working area. However, the low frequency
drivers used in these systems are more expensive to produce than most
low frequency drivers of similar size. They need to work smoothly from
1 kHz all the way down to 20 Hz – five and a half octaves. Due to the
gradual decoupling of the outer regions of the cones as the frequency rises,
the radiating area is progressively reduced, allowing response flatness and
directivity to be maintained up to the crossover frequency. Nevertheless,
the directivity change will inevitably lead to a non-flat response off-axis,
so such loudspeaker designs tend to be used in rooms with absorbent
side-walls.
Low frequency alignment and box size will dictate the sensitivity of
the low frequency drivers. Some alignments cannot be achieved with high
sensitivity drivers, but a reduction in driver sensitivity would require more
power from the amplifier in order to achieve the same SPL. This fact has
repercussions on amplifier choice, total power consumption, and thermal
compression considerations, but, at least with large, in-built monitors, box
size – and hence alignment – is not of such a critical nature as when
designing smaller monitor systems.
The choice of mid-range radiators for high level monitor systems is
largely dictated by function. In the low frequency part of a two-way system
it is almost impossible to go from 20 Hz to beyond 1 kHz. Even to achieve
1 kHz is only possible with difficulty in physically large systems. This means
that the upper frequency range from 1 kHz, or less, up to 20 kHz, or more,
must be handled by one driver. If levels of 100 dB-plus are to be heard
at a mixing console, 3 metres from the source, then levels of 110 dB-plus
must be produced at one metre from the loudspeaker, with peaks perhaps
up to 120 dB SPL. Only compression driver/horn combinations can be
expected to work reliably over this frequency range as single drivers at
such high sound pressure levels. The radiation pattern from horns is unlike
that from pistonic radiators. Horns radiate a pattern much more like a
section of a spherical expanding wave. For this reason, they can cover
many octaves without the lobing which occurs when a piston begins to
radiate at wavelengths which are less than its diameter. For a piston to
work at 1 kHz and at levels of 110 dB SPL, it would need to be at least
about 4 inches (100 mm) in diameter, if only for reasons of having a voice
coil large enough to dissipate the waste heat. Given that at 20 kHz, the
wavelength is only about 17 mm, a 100 mm diaphragm would be much
too large for controlled radiation over a wide angle. Conversely, a 20 mm
diaphragm would have no possibility of being able to dissipate 200 watts
of heat from its small coil, so the requirements for radiation at such high
SPLs at 1 kHz and 20 kHz are not compatible in a direct radiator.
Horns, on the other hand, exhibit much higher sensitivity. With a sensitivity of 108 dB for 1 watt at one metre, a horn loudspeaker could radiate
120 dB SPL with a total power input of only 16 watts. Given that perhaps
25 per cent of that power would actually be radiated as acoustic power,
the dissipation of 12 watts of heat from a 2 inch (50 mm) coil is quite reasonable, especially given the large amount of metal in the magnet system
244 Loudspeakers
surrounding it. Once the output from this diaphragm is squeezed through
a one inch (25 mm) throat and matched to a horn of suitable size, the
frequency range of 1 kHz to 20 kHz can be achieved with comfort, even at
such high SPLs. A monitor system designer is therefore not totally free to
choose whatever type of driver for a given system. Physical and engineering
restraints limit the freedom of choice in many cases.
Although much is said about the unpopularity of horn loaded monitors
in Europe, despite their wide use in the Americas, as previously mentioned
in Chapter 4 many people seem to forget that the very widely used Tannoy
15 inch Dual Concentric monitors were exactly compression driver/horn
loudspeakers from 1 kHz upwards. A cross-section of such a driver is
shown in Figure 8.7. The monitor system shown in Figure 8.6(a) uses a horn
which is relatively similar in geometry, but uses a fixed axisymmetric horn
and a much more advanced compression driver with a vapour deposited
beryllium diaphragm, the TAD TD 2001. Much of the criticism levelled
against horn monitors was due to the misapplication of the technology
and the legacy that was left from the ‘mini PA system’ monitors of the
1970s. Unfortunately it must also be added that both ignorance of what
is possible, and unscrupulous comments from people marketing non-horn
systems, have led many people to incorrectly believe that horn loaded
upper sections in monitors cannot achieve the highest fidelity, but this
is simply not true. The colouration and distortion levels of the monitor
system shown in Figure 8.6(a) are extremely low, and their directivity in
the type of room in which they are intended to be used is not an issue.
The system shown in Figure 8.6(b) is a three-way system, using a
3 inch (75 mm) soft-dome mid-range driver and a 11/4 inch (34 mm) dome
tweeter. The crossover frequencies are set at 450 Hz and 4.5 kHz. The lower
crossover point is necessary with this cone driver arrangement because the
horizontally wide distribution of the total radiating area of the bass drivers
would be too large to radiate wavelengths of much less than one metre,
equivalent to 340 Hz, without severe directivity problems. The interference patterns would be exhibiting an excessive number of lobes, so an
Figure 8.7 A Tannoy Dual concentric with single ferrite magnet serving for both the high and
low frequency coils (see also Figure 5.10)
Form follows function 245
even directivity could not be maintained. As direct radiators can rarely be
expected to span more than a decade of frequencies (or 3 octaves) the midrange driver would begin to suffer from the same problems above 5 kHz,
so the 11/4 inch tweeter takes over the response for the top two octaves.
Figure 8.6(c) shows another three-way design, but this model can be
mounted with the bass drivers either side-by-side or vertically. The sculpted
panel containing the mid and high frequency drivers can be re-oriented
through 90 degrees. The panel takes the form of three shallow horns, or
waveguides, which serve to control the directivity of the radiation at mid
and high frequencies and reduce the effect of cabinet diffraction. The midrange drivers are a pair of vertically mounted 5 inch (125 mm) cones, whilst
the high frequency driver is a 1 inch (25 mm) compression driver. In this
system, the crossover frequencies are 400 Hz and 3.5 kHz.
A four-way system with side-by-side bass drivers is shown in
Figure 8.6(d). In this design the bass drivers only operate up to 250 Hz,
from where a 10 inch (250 mm) cone driver takes over until 1000 Hz. From
here on, a 2 inch (50 mm) throat, 4 inch (100 mm) diaphragm, compression
driver, connected to the large wooden horn, takes the response to 4 kHz,
from where a small wooden horn, fitted with a 1 inch (25 mm) throat compression driver with a 2 inch (50 mm) diaphragm continues the response to
beyond 20 kHz.
From time to time, 5-way systems are also to be found, and all of these
concepts from 2-way to 5-way have their applications. It should also be
added that they are the results of different design philosophies which may
not only reflect their intended application, but which may also reflect the
order of priorities which the different designers gave to various aspects of
their overall responses.
8.2.5 Power consideration
All the loudspeakers shown in Figure 8.6 are very fine systems, capable of flat responses from 30 Hz to over 20 kHz within ±25 dB when
flush-mounted, although in many installations a high-frequency roll-off is
employed for the reasons described earlier. In each case the designers
have opted for different approaches to achieve what is essentially the same
goal – a clean, undistorted, full-range sound, with a dynamic capability
of supplying sound pressure levels at 3 or 4 metres distance far beyond
what the ear can itself perceive in an undistorted manner. This excess of
dynamic capability serves to allow transient headroom, damage tolerance,
and reliability in long-term daily use.
However, there are big differences in system efficiency. The amplifiers
normally supplied with the system in Figure 8.6(a) are specially made twochannel amplifiers, supplying 300 watts Class AG to the bass drivers and
50 watts, Dynamic Class A, to the horn. The extreme sensitivity of the
horn means that at levels of 80 dB at 3 metres it would be receiving an
input level of only around 10 milliwatts, so the low-level performance of
the amplifier is extremely important. The Class A design was chosen to
ensure the absence of low-level crossover distortion. Even at 100 dB at
3 metres, only about 1 watt is consumed by the mid/high driver, with the
low frequency driver taking around 20 watts. This is a very high efficiency
246 Loudspeakers
system, in which thermal compression is almost non-existent due to the low
power levels and the high thermal capacity of the large magnet systems.
A stereo pair, without signal, draws about 0.4 amps from a 230 volt supply
(92 watts) and at full power 4 amps (920 watts).
Some designers feel that by using drivers of lower sensitivity they can
better achieve their design goals. The systems shown in Figures 8.6(b)
and 8.6(c) use amplifiers with output capabilities of over 2.5 kilowatts per
side, a stereo pair requiring at least a 30 amp supply from 230 volts mains.
The four-way system shown in Figure 8.6(d) uses medium and high sensitivity drive units, and a pair can operate comfortably from a 10 amp
supply.
In all cases, though, oversized power cables should be used in order
to keep the supply impedance down. Some amplifiers can draw current
in surges, which can instantaneously drop the voltage of supplies without
an adequately low impedance. Not only can this rob the bass of transient
punch, but the harmonics created by the change in waveform as the voltage
sags can cause problems in associated equipment, and can even crash
computers. It is best to supply the amplifiers with their own, dedicated
supply cable or cables, fed straight from the incoming mains supply at the
main circuit breaker board. The breakers feeding the amplifiers may need
to be of the delayed action type, because some amplifiers draw high surge
currents on switch-on.
The question of total power consumption can be important. In hot countries, such as in southern Europe, it can be difficult to dissipate heat when it
is 40 C in the shade. In many places, high current supplies to buildings are
hard to organise, and when an extra 2 kVA of air conditioning is needed,
just to cool the amplifiers, it can put a great strain on the whole studio
electrical installation. Many people have said that it can be cheaper to
make low efficiency systems because magnets are expensive and amplifier
power is cheap. Well, it is cheap to buy the amplifiers, but the running
costs over years can be very expensive indeed when system efficiency is
low. Depending upon circumstances, things such as this may or may not be
important to the users, but they nonetheless need to be considered because
the electricity bills and the heat production cannot be ignored.
There is also a tendency for higher sensitivity systems to exhibit faster
transient responses due to the more stable static magnetic fields which
are a part of their general character. Computer-aided loudspeaker design
programs can often call for lower sensitivity drivers in order to achieve
certain design aims, but ears can sometimes ask for something different.
One has to be very careful when balancing design parameters if one is
not to gain in one department but lose in another. This all tends to be
a question of there being too many design parameters which may affect
audible responses but which are not available for incorporation into the
computer-aided design processes. So, if the whole story does not go in,
then it is unlikely that the whole story will come out.
The monitors shown in Figure 8.2(a) are interesting in that they are twoway but use high level passive crossovers. The pair of 16 inch (400 mm) bass
drivers operate up to about 300 Hz, with the compression driver handling
the upper six octaves. The dynamic impedance can dip to as low as 0.8 ohms
at some frequencies and under some drive conditions, and can demand
Form follows function 247
as much as 100 amps (peak) from the amplifiers. Very few amplifiers
can deliver this amount of output current, and those that can tend to
be very expensive indeed. These monitors are frequently used with FM
Acoustics, or JDF amplifiers, which can deliver 3000 watts into half an ohm.
In 2000, the price was around 100,000 dollars per pair for the loudspeakers,
amplifiers and cables, the latter of which cost around 2500 dollars per side.
The demands on the cables are obviously great, and bi-wiring is standards.
With the cable to the horn carrying six octaves and the low frequency cable
up to 100 amps, the prospects for intermodulation in a single cable would
be considerable. The crossover components are also large and expensive,
with oxygen-free copper inductor coils.
The engineering of such systems is not a simple task. In fact, despite initially appearing to be the simpler solution, the high-level passive crossover
option can be extremely difficult to implement if the highest achievable
sound quality is the goal. Multi-amplification actually simplifies many
things, even though it perhaps initially seems to be a more complicated
approach. However, in the above case, the designer Shozo Kinoshita, in
his experienced view, chose the passive crossover option.
One of the largest commercial monitor systems is shown in Figure 8.8.
The Quested HM 415 loudspeaker weighs about a quarter of a ton, and the
maximum output is claimed to be 130 dB SPL at one metre. The bass units
are four 15 inch drivers with external chassis, which help to improve the
Figure 8.8 The enormous Quested HM415, 1 m 26 in height, 1 m 06 in width, and weighing
over 260 kg, using a combination of rigid-dome and soft-dome radiators in the mid-range.
Each 15 inch (380 mm) low frequency driver is in its own triple-ported chamber. The external
chassis of the LF drivers aid the cooling of the voice coils. The systems are rated to deliver
130 dB SPL at one metre distance
248 Loudspeakers
cooling of the voice coils. The low mid-range driver is a 7 inch (175 mm),
rigid, polyurethane foam dome. The high mids are radiated via a 2 inch
(50 mm) soft dome, and the high frequencies radiate from a 28 mm dome.
The amplifier system uses 5 channels, the bass being split into two parallel
channels, and the full power consumption is 3.5 kVA per channel from the
electrical supply for 2400 watts of output power.
8.2.6 Interfacing with the rooms
The ‘high-end’ recording monitor systems such as the ones described above
are the ‘Formula One’ of monitoring. However, just as the thoroughbred
racing cars need a good track to race on, the high-end monitor systems need
to be mounted in well designed rooms. Formula One racing cars cannot
perform on rough roads, and neither can the top monitor systems perform
in poor rooms. As we get further into the discussion of loudspeakers for
different applications we will begin to deal with loudspeaker designs which
are intended to be more room-tolerant, but the larger systems, partly due
to their physical size and widely spaced distributions of the drivers, cannot
be considered to be particularly room tolerant. It is therefore entirely
unreasonable to make judgements about the sound quality of such systems
in rooms which cannot do them justice. It is sad to say that many comments
which are heard in the recording industry, relating to large monitors, are
based on pure ignorance, or bad experiences of misapplication.
Unfortunately, the requirement for the necessary degree of room control
in order to be able to mix on the large monitors means that the total cost
of providing such a facility is not something that everybody can afford.
Large monitor systems in small rooms can be overpowering, because it
can be impossible to get them far enough away from the listening position to avoid geometrical near-field effects, where the sound is heard from
individual drivers, and not an integrated source. Figure 8.9 shows a scaled
down system in a small control room, albeit still in large, 200L cabinets
(6 cubic feet). To use any of the systems shown in Figure 8.6 in such a
small room would be absurd. The use of such large systems only begins
to become viable in rooms of 40 to 50 m2 , which would perhaps leave 30
to 35 m2 of useable space after treatment. When the cost of the monitor system and acoustic control for such a room would perhaps begin at
around 40,000 euros, many studio owners decide that it is difficult to get
a return on the investment. Nevertheless, the larger studios understand
the importance of the recording monitors where engineering excellence is
concerned. Marketing only really seeks to achieve the maximum profit for
a given investment, whereas professionals and artistes seek to earn a living
from doing what they do to the best of their ability, and the maximisation
of the financial returns are not their sole concern. The pressures to find
less expensive solutions are nowadays very great, but it still needs to be
understood that just because something cannot be afforded does not mean
that it is not necessary!
The tendency to use near-field, or, more properly close-field monitors is
often simply an attempt to take the room out of the monitoring equation.
One problem with this approach is that there is not much room for more
than one or two people to hear the optimum sound, and what is more, the
Form follows function 249
Figure 8.9 A small control room, under construction in Ubeda, Spain, with a miniaturised
Reflexion Arts 240c system. The cabinets are large, to allow a generous and fast low frequency response, but the drivers form a compact group to minimise the geometrical near-field
problems at short listening distances. The rear wall, side walls and ceiling are highly absorbent
behind their fabric coverings
frequency range of the small loudspeakers is necessarily curtailed at the
lower end of the frequency spectrum. (Sub-woofers rarely yield accurate
bass, as will be discussed in later chapters.) The close-field is the space
within the critical distance – the critical distance being that at which the
energy which is contributed to the overall sound is equally supplied by the
direct and reflected sound fields. It thus follows that as the room decay time
is reduced, the close-field increases in size. The high degrees of absorption in some control room designs thus seeks to extend the close-field of
the large monitors all the way to the listening position. This effectively
yields a close-field response but with a greater optimum listening area.
[The acoustic near fields, strictly speaking, both geometric and hydrodynamic, are regions very close to the loudspeakers where a highly complex,
unintegrated sound-field exists, and where the composite sound that we
hear in the far-field has not had time or space to jel into an integrated
wavefront. Listening to the monitors shown in Figure 8.6(d) at a distance
of one metre would be a typical example – the physical distribution of the
individual sources would audibly be very evident.]
There is also a lot of nonsense spoken about control rooms, especially
by people who are just repeating hearsay; and it has to be said that the
marketing pressures lead to some very partisan passing of opinions which
are little more than attempts to gain a commercial advantage. Clearly, the
majority of studio owners who cannot afford good control room acoustics
and large monitors are rarely going to admit that their studios would be
much better if they could afford them, so the received wisdom about these
things often has little to do with fact. Comments that well-controlled rooms
are not necessary should be treated with suspicion. If such things were not
necessary, then why would almost all the top studios have them?
250 Loudspeakers
8.2.7 A word about listening levels
Some people may be shocked reading about listening levels of 100 dB, or
more, when so much safety information now restricts industrial levels to
95 dBA or less. However, as the levels within symphony orchestras can
easily exceed 95 dBA or 100 dBC (the C-weighting measuring more of the
bass) it would seem to suggest that all orchestral musicians should be deaf
after a few years of work. This is patently not in accordance with the reality,
as most experienced classical musicians exhibit excellent hearing acuity. It
also follows that if the performance levels do not damage the ears, (except
in some cases where musicians play directly in front of the trumpets), then
the loudspeaker reproduction of such ‘natural’ levels should also lead to
similar results.
Hammer blows, on the other hand, despite only reading 95 dBA on a
sound level meter can produce rapid peaks of 135 dBA or more, but they
are too short for the meters to read. It is these peaks which damage the
hair cells in the ears, but the more rounded waveforms of music rarely
contain any peaks so far above the measured levels. Therefore, whilst
mixing is not recommended to be carried out at such high levels, for many
perceptual reasons, it is still not unreasonable to work during the recordings
at the realistic acoustic levels experienced by the musicians. Drum kits
would have already been banned in many countries, for health and safety
reasons, if a short career as a drummer automatically led to deafness.
Classical soprano singers can also produce over 120 dBA one metre from
their mouths, and this is why many good recording engineers never place
a recording microphone closer than one metre from a soprano – to save
the microphones from overload – yet there are few reports of people
being deafened by sopranos. Nevertheless, it is still wise to only monitor
loudly when deemed necessary, and not to make a habit of doing so if
not required. Perceptually, also, mixing is better carried out at levels more
close to end user reproduction levels, but that will be dealt with in the next
section.
8.3 Mixing monitors
Once we arrive at the stage of mixing the multitrack recording down to
stereo, or surround-sound, we are no longer in an environment where we
can affect the performance of a piece of music. Stimulating the musical
performance is no longer either necessary or possible, although ‘vibing’ the
mixing personnel, who are still very much a part of the creative process, is
still a possibility. A quick blast at 105 dB can, at times, be very satisfying,
but mixing at such levels is rarely a good idea. The equal loudness contours
shown in Figure 8.4 demonstrate clearly how at different listening levels
we perceive different frequency balances. In general, when people are
listening to music at home, they tend to listen between 75 and 85 dB
SPL. The dBC weighting curve which is used on many sound level meters
represents something very similar to the inverse of the 80 phon curve of
Figure 8.4. (The more common dBA curve being similar to the inverse of
the 40 phon curve – used for the assessment of background noise nuisance.)
Form follows function 251
Figure 8.10 The 70 and 100 phon curves overlayed to coincide at 1 kHz. Note that they
coincide elsewhere only at around 200 Hz and 6 kHz. At the frequency extremes they differ
by as much as 10 dB, with the ear being more sensitive low frequencies at the higher SPL
but less sensitive to the 15 kHz region. The way that the curve intertwine does not make the
prospects of automatic correction a very practicable proposition
In Figure 8.10, the 100 phon curve has been superimposed on the 70 phon
curve. If we mix at 100 dB SPL, then listen at 70 dB SPL, the perception of
the low and high frequencies relative to the mid-frequencies will change
by the difference between the curves. A mix which seems balanced in
frequency at 100 dB SPL will sound at 70 dB SPL like the bass should have
been mixed 3 or 4 decibels higher, and it may sound somewhat dull due to
the ear’s lower sensitivity to the treble frequencies. Mixing at high levels
is therefore unlikely to lead to well-balanced mixes at normal listening
levels. Furthermore, mixing at 100 dB SPL plus for day after day will
almost surely lead to serious hearing fatigue. It will also lead to temporary
shifts in the hearing threshold as the ear’s protection mechanisms come
into play, and normal perception will not be possible. In fact, from the
hearing sensitivity contours shown in Figure 8.4, it can be seen that the
contours tend close up at low levels of low frequencies. Despite the fact
that 10 dB is generally considered to double loudness, it can be seen that
at 70 dB SPL and at 40 Hz there is only about 4 dB between the adjacent
loudness doubling/halving contour lines. This implies that a 4 dB difference
in overall level at 70 dB SPL may subjectively double or halve the relative
loudness of low frequencies, whilst the mid frequency loudness would
change by a much lesser amount. This is another reason to avoid mixing
at much higher levels than the expected reproduction levels, because the
low-frequency/mid-frequency relative balance will be difficult to judge in
relation to how it will generally be perceived domestically.
Mixing also tends to be a much more continuous process than recording, so sustained high level mixing can lead to more problems than high
level monitoring during recording. Even if recording engineers do animate
musicians or look for noises at 105 dB SPL, they probably would not be
exposed to such levels for more than about an hour a day, and in short
bursts at that. And, despite ‘common knowledge’ about recording engineers being deaf, there is no evidence to support that idea. Most of them
have very acute hearing, which they probably take care of more than most
other people do. [DJs, – well, that is another matter!]
252 Loudspeakers
In the world of mixing cinema soundtracks, the monitor volume level is
fixed, to guarantee that the audiences in the cinemas hear the same level,
and hence frequency balance, as the mixing personnel in the studio dubbing
theatres. This is a luxury which cannot be enjoyed by music mixers, but,
as few people will listen seriously in their homes at either 60 dB SPL or
100 dB SPL, an 80 to 90 dB SPL mixing level seems quite reasonable, or a
little lower or higher if desired.
Mixing monitors therefore do not need to be capable of the same output
levels as the recording monitors, and this fact can be significant. Ten decibels less in peak output capability means ten times less power handling
capacity if the same sensitivity of drive units are used. This could make
the engineering much simpler and the area occupied by the drivers more
compact. However, the tendency is to use physically smaller loudspeaker
cabinets at closer listening ranges. Essentially, what the mixing personnel are trying to do, subconsciously or otherwise, is to remove the room
response from the listening chain. To move the loudspeaker close is a much
cheaper alternative to treating the room. However, the smaller cabinets
require less sensitive drive units if the bass response is to be maintained,
(as was described in Chapter 3) so the amplifier power still needs to be
quite considerable in many cases, even to work at a maximum average
level of 100 dB SPL at 1.5 metres distance. It also means that some of
the potential advantages of using much lower powers are not realised, so
thermal problems arising from needing to lose the same amount of heat
from smaller drive units can have its repercussions on design priorities. In
some cases, sensitivities as low as 81 or 82 dB for one watt at one metre are
encountered, whereas it is rare indeed to find recording monitors with sensitivities below the 90 dB sensitivity level. The widely used UREI 815s of
the 1980s had sensitivities of 103 dB for one watt at one metre. Figure 8.11
shows the two extremes. Obviously, when the smaller loudspeaker needs
almost 200 times the power (22 dB) that the large ones need to produce
Figure 8.11 The Urei 815 and ATC SCM10 loudspeaker systems. The smaller loudspeaker
needs an input of almost 200 watts to develop 103 dB SPL at one metre distance. The UREI
815 will achieve the same SPL with an input of only 1 watt
Form follows function 253
the same SPL, the engineering considerations can be very different in the
two cases. Such are the problems that face loudspeaker designers.
For many people, mixing is an insecure process. Some of the reasons why
will be discussed in Chapter 10, but some of the insecurity is reduced by
following fashions in the choice of mixing loudspeakers. In the rock music
world, the Yamaha NS10M served as an unofficial reference standard for
twenty years or more. Of course, to become an international standard,
even if unofficially, the loudspeakers need to be internationally available,
so the offerings of large companies tend to be favoured rather than the use
of locally manufactured brands – even if their performances are similar.
Nevertheless, it is not all down to fashion and marketing. There is usually
some reason why so many people in so many places gravitate towards
certain monitor loudspeakers out of the plethora available to them. Some
manufacturers have made studies of hundreds of loudspeaker responses,
both professional and domestic, and concluded that a loudspeaker which
exhibits something close to the mean response will be likely to succeed
as a mixing monitor. However, that work applies only to the frequency
response amplitude, but there are many more qualities which people look
for during music mixing.
Domestic loudspeakers are usually inadequate for music mixing because
they lack the robustness to withstand such operations as the soloing of bass
drums, which are essential during the mixing process. Characteristics such
as absolute sound quality and the ability to give a realistic response under
the conditions of use found in mixing rooms are aspects of mixing monitor
performance which may differ very significantly from the requirements of
use found in most domestic environments. It is rare, for example, for people
to listen seriously to music with the loudspeakers placed on top of the far
side of the dining-room table, but this would not be too unlike the placing
of loudspeakers on top of a mixing console. Therefore, for professional
mixing purposes, the desired anechoic response must take into account the
mounting conditions under which the loudspeakers will actually be used if
reasonably accurate mixes are to be created.
The aforementioned dominance of the NS10M as a mixing monitor for
pop/rock/electronic music, over so many years, was surely in part due to
the fact that it exhibited a tendency for its overall response to flatten
when placed on top of a mixing console – its predominant position of use.
Figure 8.12 shows the gradual change in an NS10’s response as a mixing
console and room are brought into its proximity. From these results it
should be apparent that mounting mixing loudspeakers on a meter bridge
or on pedestals are not alternative options. A mixing console will augment
the low frequencies but a pedestal will not. The decisions must be made
according to the designers’ intentions, and the local boundary conditions
presented by the rooms unless the monitors are self-powered, and fitted
with tilt and roll-off controls to compensate for the acoustic loading differences. Far too many people, even professional mixers, fail to realise that
the loudspeaker and its mounting conditions cannot be separated. No fixed
response loudspeaker is suitable for all mounting conditions.
The NS10’s popularity was also probably due to the fast and uniform
decay of its time response. Figure 8.13 shows a selection of waterfall plots
from nine different mixing monitors. The similarity of the plots of the
254 Loudspeakers
a)
10
dB
Flush Mounted (
Free Field
(
0
)
)
–10
100
1000
Frequency (Hz)
10000
100
1000
Frequency (Hz)
10000
100
1000
Frequency (Hz)
10000
100
1000
Frequency (Hz)
10000
b)
10
dB
0
–10
c)
10
dB
0
–10
d)
10
dB
0
–10
Figure 8.12 a) Response of idealised loudspeaker: flush mounted (dashed line) and freefield (solid line). b) Response of Yamaha NS10M, outside, flown 4 m from floor and wall.
c) As b), but mounted on a mixing console metre bridge (all flow 4 m from ground).
d) As c), but with the mixing console on the floor in a reasonably controlled room.
Note how the overall response gradually changes – (b) shows a response rather similar to the
free-field response in (a), whereas (d) shows a response more similar to the flush-mounted
response in (a)
Form follows function 255
NS10M and Auratone 5C are too close to be mere coincidence. The Auratone was one of the first, internationally used ‘references’ – originally used
as a small loudspeaker reference in the days when the large monitors were
still the most commonly used mixing loudspeakers. The NS10s very largely
displaced the Auratones when they arrived on the scene in the early 1980s.
They exhibited a considerably wider frequency response and significantly
more output capability, yet still maintained the response characteristics
that made the Auratone 5C so popular. The deeper consequences of their
responses will be discussed further in Chapter 11, but it can be seen from
Figures 8.12 and 8.13 that their responses were tending towards flat and
fast when placed on top of mixing consoles, and these two characteristics
are conducive to good mixing. Basically, if one could ignore the colouration, and check the low frequencies on other systems, the NS10s and 5Cs
told many mixing engineers what they needed to know in order to make a
good balance of instruments and reverberation.
The twin demands of lowering production costs and maximising the
commercial acceptance of the mixes have led to a situation where by far
the majority of music is mixed on relatively small monitor systems, a selection of which is shown in Figure 8.14. Although fashion plays a big role
in the choice of which loudspeakers to use, and some commonality of
choice is still to be found, there are nonetheless many individual choices
made by different people, and it is not by any means unusual to hear
discussion between people who cannot understand how each other can
use their loudspeakers of choice. Many of the differences come down to
different hierarchies of priorities and methods of working – which both
(9) Auratone 5C
(29) Roland DS-50A
(30) SLS S8R
(31) Spender SA300
(31) Studer A5
(33) Tannoy A600
(34) Tannoy Reveal
(35) Westlake BBSM-5
(36) Yamaha NS10M
Figure 8.13 Nine waterfall plots – all of close-field monitor loudspeakers in an anechoic
chamber
256 Loudspeakers
a)
b)
c)
Figure 8.14 Three families of studio monitor loudspeakers. a) Dynaudio Acoustics systems
b) Quested Monitoring systems. c) Westlake Audio systems
Form follows function 257
ultimately translate to individual ways of thinking about the work. Mixingloudspeaker characteristics can be separated into parameters such as spectral uniformity, dynamic performance (transients), distortion, sound-stage
imaging, off-axis performance (very relevant in less controlled rooms),
ambience reproduction (transparency), and, of course, the overall impression. However, the order of these characteristics will not be the same for
all people. And, what is more, work and leisure requirements may be very
different. Many top recording engineers, mixers and producers do not use
the same loudspeakers at home that they use in the studios, even though
the sizes of the loudspeakers may be similar. At work, they need to hear
all the problems; at home, they simply want to enjoy the music. But another
reason for the difference is because, in general, almost all serious mixing
will be done in rooms with a reasonable degree of acoustic control and
a lot of equipment, whereas acoustic control usually does not take much
precedence in the designs of their homes, and domestic furniture tends to
be rather acoustically different to mixing consoles and equipment racks.
The object of the exercise is therefore to do mixes in a professional environment which will translate to a domestic environment. The recording
engineers’ homes also furnish them with a means of listening as other people listen, which helps them to get another perspective on their work. For
these reasons, mixing monitors for use in studios have developed along
their own course.
In a report presented in 2004 relating to the selection of a new ‘standard’
choice of monitors for the BBC 2 , the author acknowledged; “Loudspeakers
are a sensitive topic on which many people have very different views . .”
Despite this, however, in an organisation such as the BBC, with over 600
sound control rooms, some standardisation is necessary because the staff
need to move around from room to room, but always need to know what
they are listening to. They also use rooms which are rather more dead
than most domestic rooms because ‘Critical assessment of sound quality
cannot be carried out in rooms with large areas of specularly-reflecting
surfaces and long and uneven reverberation times, however attractive they
might be architecturally2 ’. As we will discuss later, domestic loudspeakers
must deal with these conditions, but they really cannot replace professional
loudspeakers if a good degree of consistency of sound quality is required
when used in typical mixing environments.
The BBC carried out their tests in rooms with a mid-band decay time
of about 0.2 seconds, which is quite typical of modern control rooms, but
it is much lower than is normally to be found in most domestic rooms.
The listening tests were carried out during a period of three weeks, by
eleven ‘democratically chosen’ representatives of the staff – all very experienced listeners – on a total of 28 pairs of loudspeakers. In the ‘Summary
and Conclusions’ of the abovementioned report it stated “Inevitably, the
final outcome was not entirely clear-cut.” The tests were made using large,
medium and small loudspeakers, without the listeners knowing the identity of any of them. It is interesting to note that no set of three from
any one manufacturer stood out from the rest in either quality or family
resemblance. The best family resemblance of a large, medium and small
loudspeaker was of mixed manufacturer.
258 Loudspeakers
8.3.1 Location dilemmas
The main purpose of the mixing monitors is to reliably enable the mixing
personnel to achieve musically and timbrally balanced mixes. Working in
the close-field, if the loudspeakers are too small and their low frequency
responses are too restricted, then the lower octaves may be leading an
uncontrolled life of their own due to the inability to monitor them. Adding
shelf equalisation to an instrument at 80 Hz may give rise to unintentional rises at 30 or 40 Hz, leading the mixing personnel to believe that
they have obtained the desired tonal balance which subsequently, when
played on larger loudspeakers, turns out not to be the case. The use of
larger loudspeakers for the mixing may mean pedestal mounting, behind
the mixing console, but unless the back of the console is heavily treated
with absorbent material, the reflexions from the rear surface can ricochet
around the room, affecting the clarity and stereo imaging. This concept of
‘mid-field’ monitoring also brings more of the room acoustics into the listening equation, and the omnidirectional low frequencies will rarely be as
flat as from monitors flush mounted in the wall, which do not suffer from
the reflexions of rear radiation and the subsequently response irregularity
due to interference at the listening position. Neither will the low frequencies from mid-field monitors be as likely to be as flat as the ones that
are available (to a more restricted degree, of course) from loudspeakers
mounted in the close-field, where the direct sound dominates the overall
response. The whole situation is full of frequently irreconcilable compromises, and great experience may be required in deciding just how the most
workable compromises can be achieved.
There is, of course, no fixed response for all mixes. The mixes are, above
all, artistic interpretations of the performances which they encapsulate, so
if a certain type of loudspeaker leads a certain mixer or producer to achieve
their desired results, then those loudspeakers will, for them, be excellent
mixing monitors, even though for other people they might be considered
to be unusable. Nonetheless, in general, achieving a smooth response at
the listening position is still a highly desirable goal.
Mixing monitors are therefore a means to an end, and not an end in
themselves. They are tools, and just as with any other tool, such as a tennis
racquet or a pair of football boots, different models may suit different
individual styles of use and personal comfort. However, it is indeed rare
to find normal domestic hi-fi loudspeakers in use as mixing monitors, or
typical mixing monitors in use as domestic hi-fi loudspeakers, because they
are used quite differently and in acoustically different circumstances. But
in a growing number of cases, yet another type of loudspeaker has been
introduced into the chain to try to interface better the professional and
domestic worlds, which we shall now look at in a little more detail.
8.4 Mastering loudspeakers
Historically, the last stage of the quality control of the recording process,
both artistic and technical, was the disc cutting, when the tapes were transcribed to cellulose acetate discs. From these discs the stampers would
Form follows function 259
be made, by processes of electroplating, which would in turn mould the
vinyl records for sale in the shops. Once all the settings had been decided
upon, and a written record had been made for future reference, an acetate
test cut could be taken home, or to the record company offices, to assess
the sound in known, domestic-type conditions, which were considered to
be more representative of end-user conditions than the machinery filled
space of the disc cutting room. If all sounded well, the engineers or producers could return to the cutting room, adjust the equipment once more to
the settings which had been written down, and a master disc could be cut
and sent to the factory. (It was important not to play this disc, as the soft
acetate was easily damaged.) If it was felt that some adjustment needed to
be made to the sound, then the appropriate changes could be made to the
settings of the equalisers or compressors before the final disc was cut.
Reference acetates were also frequently cut to assess tracking, because
what could be cut on to disc was not always able to be played back on
cheaper domestic equipment. The cheaper cartridges could not always keep
their styli in the grooves if they were too heavily modulated, and customers
would return the discs to the shops if ‘the needle jumped’, which could be
very expensive for the record companies in lost sales. Vinyl discs therefore
always had to be made to a realistic lowest common denominator, and it
was not only the stylus tracking which made this necessary. In the 1970s
and early ’80s most domestic loudspeakers were not capable of supplying
high levels of low frequencies, so excessive bass levels could either cause
distortion on playback or cause the listeners to turn down the bass on the
tone controls of their equipment. In neither case would they be hearing
what the people recording the disc were intending them to hear, so the
artistic intention of the disc could not be fulfilled. Once again, it would
be an acetate test disc that would usually be used to confirm the overall
domestic compatibility of the musical mix.
With the advent of the compact disc, the greater capabilities of digital
recording introduced low frequency response possibilities that were never
available from vinyl discs or tape cassettes, and the domestic loudspeaker
manufacturers began to respond with more robust loudspeaker systems
which could highlight the new advantages of digital recording. Music mixes
then needed to be prepared for multi-format release, on vinyl disc, compact
disc and tape cassette, and producers still wanted to know, as ever, what
the mixes would sound like on the radio. The early 1980s therefore began
to see the birth of a new concept within the recording chain; the concept
of the mastering studios, where all of these questions could be resolved.
Mastering engineers tend to always work in the same place – their own
dedicated mastering room. Their rooms, equipped with their own choices
of loudspeakers and equipment become their references. During the course
of a year, many more recordings will usually pass through a mastering room
than a mixing room, and the recordings which a mastering engineer deals
with are likely to vary, in terms of musical styles and recorded quality, much
more than the recordings worked on by a mixing engineer. Consequently,
mastering engineers gain much experience about how a very wide range of
recordings sound in their own, personal rooms. In general, mastering rooms
are much more sparsely equipped than mixing rooms. There is usually
260 Loudspeakers
no mixing console between the loudspeakers and the listeners, and what
furniture there may be tends to be of an open and not very reflective nature.
Mastering is the last chance to solve problems, or at least to be aware of
them before the music goes to the factories and the shops. It is therefore
necessary at this stage to be able to listen critically, both artistically and
technically. With experience, mastering engineers get to know the relationship between how things sound in their own rooms and how things sound
in a wide range of circumstances in the outside world.
Mastering rooms often have acoustic properties somewhere between the
typical studio control room acoustics and typical (if such a thing exists)
domestic replay circumstances. The monitor systems which they use are
frequently of wider frequency range than many mixing monitors, because
the mastering personnel need to be able to look for things that have been
neglected in the mixing circumstances, and they often do this by using
larger loudspeakers which are either not of the reflex design, or are reflex
boxes with very low tuning frequencies. Mastering monitors can often
afford to be larger because they do not need to fit into the spaces left
after the mixing console and equipment racks have been installed – both
of which are very necessary for mixing purposes. A typical mastering room
is shown in Figure 8.15.
The great tendency is to use free-standing loudspeakers, because many
mastering engineers feel that these are more typical of the way in which the
music will be perceived in the domestic circumstances. The larger boxes
and lower low frequency responses facilitate the assessment of the low
frequency colouration, and reduce the masking effect which can cover lowlevel detail when reflex cabinets of a higher tuning frequency are used.
Furthermore, the mastering studios need to be able to cope with whatever
work comes to them, and if some work is of a very high quality, extended
low frequency nature, they need to be able to hear it at its best, because
guessing is not what mastering engineers are paid for. Their job, to a very
Figure 8.15 A typical mastering room arrangement. Optimum Mastering, Bristol, UK, with
engineer Shawn Joseph and a pair of large PMC transmission lines
Form follows function 261
great degree, is to give confidence to the rest of the people who have
been working on the performances, recording, mixing and editing of the
music, and also to the record companies who may be distributing it. For the
above reasons, mastering loudspeakers tend to be of an audiophile high
fidelity quality, which are capable of being used in rooms with an acoustic
which is often less controlled than the studios in which the mixes have
been made. Mastering monitors are not required to support the stresses of
solo’d drums or bass guitars, so they generally do not need to be as robust
as recording or mixing monitors. This fact can allow mastering engineer’s
greater flexibility in their choice of loudspeakers.
From time to time, however, one encounters mastering studios which are
more like a recording studio control room, but with some notable modifications. The room shown in Figure 8.16 is based on a control room design,
but with the loudspeakers mounted in such a way to maximise the accurate
listening area, as no compromises need to be made to accommodate a
mixing console. The flush-mounted loudspeakers, although of a type used
in smaller control rooms, will normally not be used at control room levels,
because mastering engineers tend to work at domestic levels, so the high
frequency roll-off that would be applied if they were in a recording studio
(as discussed in Section 8.2) is left flat. The owner of the mastering room
shown in Figure 8.16 is a former recording engineer who feels the need to
be able to refer to a more typical, recording-style, full-range monitor when
needed, and uses a smaller set of monitors as a secondary reference. As in
all matters associated with loudspeaker choice, no absolute, hard and fast
rules apply, though strong trends are apparent.
Figure 8.17 shows yet another mastering room. In this case the monitors
consist of loudspeakers on stands but with a dedicated sub-woofer below
each one. These sub-woofers come into use below about 80 Hz, where the
directional characteristics of the auditory system are very poor. This allows
the mastering engineer to use full-range monitors, but of smaller physical
size than those shown in Figure 8.15. The room is used for much work in
Figure 8.16 A mastering room prepared for a future, centre-front loudspeaker
262 Loudspeakers
Figure 8.17 Super Audio Mastering – Chagford, Devon, UK
surround sound, and the owner felt that five large, full-range loudspeaker
boxes would cause too many acoustic problems if they were surrounding
him at close range; especially when only working in 2-channel stereo.
However, it is important to note that the sub-woofers are not used with
any arbitrary bass management system. They are only used for extending
the low frequency responses of the loudspeakers which are mounted above
them. There are therefore five sub-woofers for five loudspeaker channels.
There is a significant difference between the responses of small cabinets
with sub-woofers below, and larger full-range, integrated cabinets when
free-standing in rooms. Although the on-axis responses may be the same
in either case, the greater mid/high frequency diffraction of the smaller
cabinets gives rise to more reverberant energy in those frequency bands
than would arise from generally larger cabinets. In semi-reverberant conditions, typical of many mastering rooms, this gives rise to a better balanced
reverberant response compared to the somewhat bass-heavy reverberation
which is typical from the larger cabinets, whose greater front baffle areas
restrict the mid/high-frequency diffraction. Obviously, though, in a more
absorbent general acoustic, the difference would be less noticeable at the
listening position, so once again the choice of loudspeaker designs is very
closely linked to the rooms in which they will be used.
It is often said by mastering engineers that the loudspeakers which are
used for the great majority of music mixing are not sufficiently revealing
of low-level details, whereas mixing engineers say that the loudspeakers
typically used for mastering are difficult to use for mixing because they
do not interface well with the equipment distribution of a mixing studio.
They also often speak about the difficulty of mixing on loudspeakers which
reveal too much detail, because the information overload becomes an
obstacle to concentrating on the mix, and that smaller loudspeakers give
a more close approximation to typical end-use conditions. It is interesting
to remember that in the 1960s and early 1970s, the people who mixed the
music were often referred to as balance engineers, and that musical balance
is the essence of good mixing.
What is very clear therefore is that whilst recording, mixing and
mastering can all be accomplished on one set of loudspeakers in one
room, there are operational and financial reasons why the use of different
Form follows function 263
loud speakers and acoustic conditions can be beneficial at each stage of
the process, and that recordings which have passed through those different
stages are perhaps better prepared for the very wide range of circumstances
in which they will ultimately be heard in peoples’ homes.
8.5 Domestic loudspeakers
The scope of domestic loudspeaker design and performance is enormous.
Some of the audiophile designs cost more than even the largest recording
monitors, whilst the smallest and cheapest are perhaps those in a typical
‘ghetto blaster’ or portable music centre. All, however, ostensibly serve one
purpose – to give enjoyment to the listeners when reproducing music, either
recorded or via live broadcast. The range is vast because the degree of
importance which people give to listening to music is also very great, from
fanatical to inconsequential, and also because the homes in which music
will be heard can be architecturally very different. It was recognised a long
time ago that many Californian designers of hi-fi loudspeakers aimed for
different low frequency alignments than many British designers, because
the typical wooden framed houses of California responded very differently
to the musical signals than did the solid, stone or brick houses in the UK.
Rooms which are heavily endowed with soft furnishing will be absorbent
in the higher frequency ranges. As most domestic listening takes place in
the far-field, where the reflected response dominates the direct response
from the loudspeakers, a loudspeaker with a brighter anechoic response
may sound better balanced in some homes than a loudspeaker with a
flatter axial response. Loudspeakers placed against walls or near to corners
will exhibit a much reinforced bass response compared to loudspeakers
which are placed away from reflective boundaries. A flat loudspeaker may
therefore sound bass heavy when close to a reflective boundary, so a choice
of loudspeaker with a reduced low frequency response may sound more
balanced in such circumstances. In many cases, for reasons of domestic
harmony, loudspeakers may have to be placed in conditions which would
not suit those having flat anechoic responses, so the range of different
loudspeakers available to the public can offer a choice to select a model
which best matches the circumstances of use and the affordable price range.
It is therefore essential to judge domestic loudspeakers at home for final
assessment, unless the acoustic conditions and mounting conditions in the
showroom are very close to the conditions of use. And, of course, one
should never be reluctant to use any tone controls on the amplifiers to
make a final adjustment to taste. The concept that the tone controls should
be left flat for a maximally accurate sound to be heard is absurd, unless
the listener lives in identical conditions to those in which the recordings
were mixed or mastered.
Low colouration, low non-linear distortion, a smooth frequency response
which tends towards flat in conditions of use, and an adequate dynamic
range are all common goals for either recording, mixing, mastering or
domestic hi-fi loudspeakers. However, the fact that in the latter case the
acoustic conditions of the rooms in which they will be used will almost
never be based on the requirements for the loudspeakers; the loudspeakers
264 Loudspeakers
must be chosen to suit the rooms, whereas in the former, professional
cases the rooms are often treated to accommodate the loudspeakers. For
this reason, whereas professional loudspeakers tend towards similarity, the
domestic loudspeakers tend towards diversity. The first book mentioned in
the Bibliography at the end of this chapter deals with the subject in more
depth, and those 500+ pages only deal with high performance loudspeakers,
which gives an indication of the scope of domestic loudspeaker design.
Taste is also an allowable parameter in the selection of domestic loudspeakers to a much greater degree than in professional loudspeaker choice.
As was mentioned earlier in the chapter, most professionals in the music
recording industry do not use at home the loudspeakers that they use at
work. Very few people, except some audiophile die-hards, want to hear
every error and distortion in a recording when they are listening for pleasure. There is therefore an incentive for the manufacturers of domestic
loudspeakers to make products which sound pleasant, even at the expense
of accuracy. This is a totally reasonable situation in the design of products which are, after all, intended to be used for enjoyment. Nevertheless,
the same basic principles apply to the majority of the four categories of
loudspeakers discussed so far. On the other hand, for the final group of
loudspeakers to be discussed in this chapter, sounding pleasant is their only
function, and in their design just about everything that we have discussed
so far is about to be turned on its head.
8.6 Musical instrument loudspeakers
As mentioned at the beginning of the chapter, loudspeakers for musical
instrument amplification are part of a music production process, not a
reproduction process. Reproduction by loudspeakers can be classified as
a situation where the acoustical output is intended to accurately represent
the electrical input. Conversely, in music production loudspeakers, the
controlling factor is the subjectively desirable nature of the output sound,
irrespective of its relationship to the electrical input signal.
A bass guitar, for example, has a very dynamic output. The peak-tomean ratio of the signal is very great, and if a bass guitar is directly injected
into a mixing console, without passing through a musical instrument
amplifier, it is almost obligatory to compress its dynamic range. If this were
not done it would have difficulty blending in a balanced way with the other
instruments of the ensemble. Reproduction on domestic equipment would
be difficult, because even at reasonable volume levels the peaks could be
stressing the entire analogue portion of the playback system. Therefore,
when performing live, and not having the advantage of access to electrical
compressors, it is often left to the loudspeakers, themselves, to exercise
some dynamic range control. Furthermore, the loudspeakers used with
amplifiers for musical instruments have often been developed hand-inhand with the instruments themselves, and hence have also been designed
to enhance the tonal quality of the instruments. To this end, they have often
been designed to introduce linear and non-linear distortions which lead to
subjectively desirable colouration, and employ dynamic range compression
Form follows function 265
a)
b)
c)
Figure 8.18 Relationship between coil length and magnetic gap length. a) Short-coil/long-gap.
b) Long-coil/short-gap. c) Equal coil/gap length
to add punch to the sound. All of these qualities are, of course, anathema
to the designers of loudspeakers for high quality music reproduction.
Figure 8.18 shows three types of magnetic gap and coil proportions
which can be used for low frequency drivers. Example a) shows a shortcoil – long-gap design. This concept is perhaps the best for low distortion
reproduction, because the coil remains in the gap and crossing the same
number of flux lines throughout its range of travel. It is also apparent that
the coil is in good thermal proximity with the large magnet assembly, so it
can easily lose the heat which its resistance dissipates. The drawback to this
design is predominantly cost, because of the large quantities of magnetic
materials which are needed. Example b) shows the opposite approach, the
long-coil – short-gap design. In this case, half of the coil is outside of the
gap at any one time during its entire range of movement. This is good
in terms of linearity of motion with drive signal, but it is bad in terms of
efficiency and heat loss from the voice coil. The efficiency is poor because
only a proportion of the energy put into the coil is acting on the magnetic
flux lines crossing the gap, due to the fact that much of the coil always
remains out of the magnetic gap. It is poor in terms of heat dissipation
both because only half of the coil is surrounded by metal, to conduct the
heat away, and, compared to the design shown in a), because there is less
metal to do the conducting. However, less magnetic materials are used, so
cost of production can be considerably reduced. In the cases of examples
a) and b) the linearity can be excellent, but example a) tends to have the
slight advantage.
In example c) the coil and gap are the same length. Production costs
can be kept low, and efficiency can be kept high, but it can be appreciated
266 Loudspeakers
that almost as soon as the coil begins to move, it begins to leave the gap.
Once it begins to move out of the gap, less turns of the coil are influenced directly by the magnetic flux lines crossing the gap, although the
fringing effect which extends beyond the gap will ameliorate the effect
of the abrupt movement out of the gap. The result of this motion is that
as more current is applied to the coil, it has less proportional effect as a
driving force. The driving force is therefore not linear in its relationship
to the drive current, so the acoustic output will be compressed in relation to the electrical input, and harmonic distortion will also be generated.
For high quality music reproduction these effects would be disastrous, but
they can be highly desirable in their effect on the sound of electric or
electronic musical instruments, and even some amplified acoustic instruments, blues harmonica being one obvious example.
It is also essential in the design and construction of loudspeakers for high
fidelity sound reproduction that the cones behave as closely as possible to
pure pistons, or that any break-up which does exist decouples sections of
the cone in order to control the directivity at higher frequencies. Normally,
for high fidelity drive units, either strong, heavy, straight sided cones are
used (where the weight is also useful for lowering the resonant frequency),
or deep profile cone shapes can be applied. If more sensitivity and an
extended high frequency response are required, a lighter weight curvilinear
cone shape can be employed. These forms are as shown in Figure 8.19.
The latter shape facilitates the decoupling of the outer regions of the cone
at high frequencies, leaving the central area and the dome as the principle
radiating areas, thus improving the control of the directivity whilst still
a)
b)
c)
Figure 8.19 Cone profiles – they each serve best for different purposes. a) Ribbed, straightsided – thickness and ribbing employed to increase rigidity. b) Deep, straight-sided – smaller
apex angle employed to increase rigidity. c) Curvilinear – curved profile employed to aid
decoupling of outer region of cone
Form follows function 267
preventing the break-up modes from circulating around the cone. At low
frequencies, a straight sided, light-weight, shallow angle cone would not
be desirable for high fidelity use, because it would lack the stiffness to
act as a good piston. However, a straight sided, light-weight cone may be
exactly appropriate for some musical instruments, where the extra sensitivity gives more volume per watt of amplifier power, and the colouration
from the reduced stiffness can enhance the tonal response. Cone depth
(apex angle) can also be chosen to move resonances into desirable regions.
Light, shallow cones can exhibit rising, peaky, mid-range responses, which
can be excellent for electric guitar amplification, despite being awful for
high fidelity purposes.
What is more, high fidelity loudspeakers are generally intended to be
used ‘sensibly’, but musical instrument loudspeakers may be purposely
overloaded on many occasions to achieve certain sounds. For this reason, the suspension systems, as well as the voice-coil/magnetic-gap designs,
may be used to limit the cone movements and offer some degree of
self-protection from overload. Inevitably, this means the use of nonlinear suspensions, which add characteristic sound qualities that would
be impossible to accept in a world of high fidelity, yet they may also
add further characteristic tone qualities of a desirable nature to a musical instrument loudspeaker. In fact, once all of these ‘defects’ have come
together in the right balance of qualities and quantities to produce their
own, classic sounds, it can be very difficult for the drive unit designers to ‘improve’ the construction without losing the magic sound. Their
sound can be something very difficult to define in technical terms, but
the musicians can recognise even the slightest change from the original
item. The Celestion company, for example, who produced 12 inch loudspeakers for the classic Vox (blue chassis) and Marshall (silver chassis)
guitar amplifiers of the 1960s have had to find sources of exactly the
same materials in order to make the same loudspeakers 40 years later.
No amount of research and engineering or computer analysis has been
able to achieve the same sounds from different designs. Conversely, their
current high fidelity products are considered to be much superior to their
products of the 1960 and 1970s, and none of the older designs remain in
production.
8.6.1 Cabinet designs
In the glory days of amateur high fidelity, when almost all recordings were
in mono, an enormous quantity of ‘patent’ cabinet designs were written
about. Before the advent of stereo gave a whole new dimension to the
spaciousness of the reproduction, many strange loudspeaker designs were
offered in an attempt to bring more life to the reproduction, and to generally enhance the sensation of ‘being there’. Clearly, by the very fact that
they were designed to enhance the reproduction, they could not, strictly
speaking, be called high fidelity, but many of the designers claimed otherwise. Their point of view was that if the designs gave a greater sensation
of being at the performance, then that in itself was a greater fidelity to
the overall musical experience, even if it was not provable by objective
measurement. The fact that many, current, portable music players have
268 Loudspeakers
‘stereo enhance’ and ‘super maxi bass’ facilities on them would seem to
prove their case, at least when listening for pure pleasure is the goal, and
when the basic reproduction is not the best that hi-fi stereo can offer. And
it must also be said that many, modern, domestic surround systems are
more likely to produce a pleasant sensation rather than anything which
could be claimed to be a lifelike reality.
As stereophonic domestic music reproduction began to reach much better standards, in the late 1960s, many of the eccentric designs which had
previously been offered began to disappear. In stereo, where the spacial
enhancement was much less necessary, the strange designs only proved
to be sources of annoying colouration, and the fact that they were not
capable of producing true high fidelity became very apparent. However,
not long after they had begun to fade from the hi-fi scene, some of them,
such as the Karlson Coupler, from the 1950s, shown in Figure 8.20, began
to be re-discovered by the makers of musical instrument amplifiers. In this
new guise, where the concept of fidelity did not exist, the strange cabinets
could freely and justifiably contribute their special sound enhancement
characteristics to the realm of sound production. The original claim for
the Karlson enclosure was that it de-tuned the normal resonance of the
rear radiation path, making it responsive over a broad band, but objective
measurement could largely only show that it produced response irregularities, and little else. It was also recommended for use with full-range
front chamber
port from rear
chamber to
front chamber
rear chamber
flared exit
to room
driver
mounting
baffle
Figure 8.20 The Karlson Coupler, from the early 1950s
Form follows function 269
loudspeakers, but it is hard to see how severe colouration could be avoided
due to resonances and reflexions in the cavity in front of the drive unit.
It is unimaginable to be listening to modern day CDs via such an absurd
‘design’, yet in the 1970s it made a big come-back as a popular and successful bass guitar loudspeaker, where its own sound was deemed to be
very favourable, and such enclosures continue to be used to this day for
instrument amplifiers.
It is therefore very difficult to give specific guidelines for the design of
cabinets for musical instrument amplification, because what sounds good
is good; although it might be good for some players and their particular instruments but not good for others. It is also difficult to give target
responses for overall performance, because good musical sounds, at their
production stage, do not follow many set rules. Designers may well also
break the accepted hi-fi standards when it comes to wiring the drive units
in the cabinets, such as wiring woofers in series, specifically to reduce
the damping and enhance the resonances and colouration. This idea may
be further extended by using valve amplifiers without any negative feedback on the output stage. This raises the output impedance, and reduces
the damping still further. Undersized output transformers may also be
employed, to give rise to saturation and ‘overdrive’ effects at high levels.
In fact, guitar amplifiers and loudspeakers are crafted more by artistry
than by science, but so is the music which they help to create.
Summary
The recording chain from the musicians to the music buying public consists
of five very different links. At each stage, the demands on the loudspeakers
are different, and even if a perfect loudspeaker did exist, the circumstances
of its application would render it non-optimal in many situations where
specialised needs exist. Although the fundamental requirements are the
same for the reproduction loudspeakers, the specific balance of characteristics can change to quite a large degree—very much so in terms of physical
size. However, once we enter the world of musical instrument amplification, many of even the fundamental requirements change drastically, and
what can be an absolute taboo for reproduction can be highly desirable
for sound production, such as using 12 inch (300 mm) loudspeakers up to
6 or 7 kHz, for example. This not only goes for the loudspeaker drive
units themselves, but also for the cabinets, the wiring, and the design of
the amplifier output stages.
References
1 Newell, P., ‘Recording Studio Design’, Appendix 1, Focal Press, Oxford, UK
(2003)
2 Walker, R., ‘The Selection of Loudspeakers for BBC Radio & Music’, Proceedings of the Institute of Acoustics, Vol 26, Part 8, pp 93-106, Reproduced Sound
20 conference, Oxford, UK (2004)
270 Loudspeakers
Bibliography
1 Colloms, M., ‘High Performance Loudspeakers’, 6th Edition, John Wiley & Sons,
Chichester, UK (2005)
2 Fletcher, H., Munson, W.A., ‘Loudness: Its Definition, Measurement and Calculation’, Journal of the Acoustical Society of America, Vol 5, p 82, (October
1933)
3 Robinson, D.W., Dadson, R.S., ‘A Redetermination of the Equal-Loudness Relations for Pure tones’, Journal of Applied Physics, Vol 7, p 156, UK (May 1956)
4 ISO226, ‘Normal Equal-Loudness Level Contours’, International Standards
Organisation, (1987)
Chapter 9
Subjective and objective assessment
9.1 The general situation
The human hearing system is quite extraordinarily sensitive and complex.
It has a frequency range of around eleven octaves if one considers physical
sensation as part of the process, and a dynamic range such that the lowest
audible sounds have power levels of only 10−12 compared to the loudest
sounds before the threshold of pain in the ears. That is a power ratio of
one million, million times (one trillion in American English). At the lowest
detectable sound pressure levels, the lateral movement of the ear drum,
(or tympanic membrane) is less than the diameter of a hydrogen molecule,
and if the average ear were only 9 or 10 decibels more sensitive, we would
experience a permanent hissing sound due to the detection of the Brownian
(random) motion of the air molecules. The signal processing of sounds
by the brain is also a remarkably refined process. It is thus little wonder
that when we reproduce music via the relatively crude devices described
in Chapter 2 we are rarely fooled into believing that we are listening to
the real instruments.
Nevertheless, back in 1990 David Moulton made the case that loudspeaker reproduction has now reached a stage where, at least with many
musical styles, it should be recognised as something in its own right1 . Music
is now being created on loudspeakers for reproduction by loudspeakers,
and much of this music exists in no other form. For many musical creations
there was never, at any place or any time, a complete performance of
the music as recorded. The late Richard Heyser, the ‘father’ of the ‘Time
Delay Spectrometry’ measuring system said that in order to really enjoy
stereo reproduction, one has to willingly suspend one’s belief in reality.
We must therefore ask ourselves if we are really trying to reproduce a
sense of ‘being there’ at the original performance, or is there a ‘being
there’ at the reproduction, which may be far more exciting than any live
performance could ever be, because it must be accepted that some reproducible music simply could never be performed live. Are we now, as David
Moulton asked, so accustomed to reproduction via loudspeakers that the
loudspeakers, themselves, have become the greatest musical instrument of
our time?
We seem now to have two separate outlooks on loudspeakers for music
reproduction: ‘the closest approach to the original sound’, as the Acoustical Manufacturing Company put in their advertisements in the 1940s, or
‘the best sound that we can possibly get’, with ‘best’ being highly arbitrary. Nevertheless, it seems that from whichever viewpoint the subject
272 Loudspeakers
is approached, the general requirements tend to be rather similar: wide
bandwidth, low distortion, adequate sound pressure level, fast transient
response, low colouration, and so forth. The degrees to which the levels
of discrepancies of each aspect of the response are acceptable may vary
with the musical styles and the listeners’ preferences, but John Watkinson’s
point of view, that the only criterion we have for the accuracy of a loudspeaker system is the sensitivity of the human hearing system2 , seems to
be quite valid. He went on to say that if a reproduction system is more
accurate than the human hearing system’s error detection threshold, then
it needs no further improvement. Nonetheless, that is a difficult goal to
achieve when we consider what was discussed in the opening paragraph of
this chapter. As shown in Chapter 7, the human hearing system is dealing
with wavelengths from as great as around 20 metres to as small as about
1.5 centimetres, a ratio of over 1000 to 1. By contrast, the eye has to deal
with almost a one octave range of visible light spectrum, a wavelength ratio
of less than 2:1.
Strictly speaking, we would only need one test for a perfect loudspeaker:
its ability to perfectly reproduce a delta function supplied electrically to
its input terminals. A delta function, otherwise known as a Dirac function,
or impulse, contains all frequencies in a very fixed phase relationship, and
its waveform is shown in Figure 9.1. Unfortunately, no mechanical system
can start and stop instantaneously, so this waveform can never be perfectly
reproduced. A delta function reproduced by a good loudspeaker is shown
in Figure 9.2, and the degree of reproduction error is patently obvious.
Unfortunately, we cannot glean all the information that we need from
a visual inspection of the delta function response, so we tend to use a
series of individual measurements which highlight particular aspects of a
response. Some of them show behaviour in the frequency domain, whilst
others show behaviour in the time domain. From them we can build up a
picture of how a loudspeaker is responding to its electrical input stimulus,
and shortcomings in the response can be assessed.
9.2 Test signals and analysis
The most well known aspect of any loudspeaker performance is the
magnitude of the frequency response, which appears in just about every
advertising leaflet for loudspeakers. In fact, the full frequency response also
needs to show the associated phase response, and from the full response
every linear aspect of a loudspeaker performance can be derived. A system
may be said to be linear if the output contains no frequencies which do not
exist in the input signal. A roll-off, or any other deviation from flatness in
the frequency response, can be called a linear distortion. A system is said to
be non-linear when frequencies exist in the output which were not present
in the input signal. For example, if a pure sine wave were to be fed to the
input terminals of a loudspeaker, and the measured output showed small
amounts of response at twice the frequency and three times the frequency,
then those additional frequencies would be the second and third harmonics of the input frequency, and the loudspeaker would thus be generating
non-linear distortion; in this case harmonic distortion. If the loudspeaker
Subjective and objective assessment 273
Figure 9.1 Evolution of the Dirac delta function (reproduced from Lighthill, 1964)
In a delta-function one can imagine the energy in a unidirectional signal being gradually
narrowed, and each time that it narrows the amplitude increases until, in extremis, it becomes
a pulse of infinite height and infinitesimal width
is fed with multiple input frequencies, anywhere from two upwards, then
a non-linear system would also produce sum and different tones. In such
a case, if the input were to be fed with 1 kHz and 4 kHz, for example,
outputs would be noticed also at 1 + 4 kHz, or 5 kHz, and 1 − 4 kHz, or
3 kHz. The products can also further create their own sum and difference
tones, and also inter-react with the original tones, producing frequencies
such as 3 kHz + 4 kHz (7 kHz), 5 kHz + 1 kHz (6 kHz) and so forth. Whilst
harmonic distortions in themselves are not necessarily unpleasant, because
all musical sounds are rich in harmonics, the sum and difference products,
known as intermodulation distortion, can be grossly offensive to the ear.
274 Loudspeakers
1
Level
0.5
0
–0.5
–1
0
5
10
15
20
Time (ms)
Figure 9.2 Loudspeaker reproduction of an impulse
The Dirac delta-function when reproduced by a loudspeaker inevitably becomes
bi-directional and smeared in time, due to the imperfect reproduction
They may or may not coincide with musical harmonics, and they tend to
build up into a noise-like signal which accompanies the music. Briggs, in
his book Sound Reproduction, published in the 1950s, summed up the
situation beautifully in a short quotation from Milton with which he introduced his chapter on intermodulation distortion – “ dire was the noise
of conflict.”3 In fact, Gilbert Briggs was so disturbed about the problem of
intermodulation distortion that he invited a more knowledgeable specialist,
one N.C. Crowhurst, to write the chapter in the Third Edition of the book.
In the Second Edition, published in 1950, Briggs had quoted Shakespeare
in the chapter on intermodulation which he had written himself (Briggs,
that is; not Shakespeare!):
Find out the cause of this effect;
Or rather say, the cause of this defect,
For this effect defective comes by cause.
Hamlet, Act II, Scene 2.
Over 50 years later, intermodulation distortion is still a significant problem, and we still have no simple way to measure it in an easily interpretable
way which intuitively relates to all its audible implications.
Time domain representations of performance are less frequently published, and even less widely understood by loudspeaker users. Nevertheless,
they are essential aspects of the analysis of loudspeakers because the phase
response, which in concert with the amplitude response is sufficient to
define all linear aspects of performance, is very non-intuitive. Phase is very
abstract; it is a relationship between things, and cannot exist alone. Time
domain representations include waveform responses, such as Dirac (delta)
and Heaviside function responses (impulse and step-function responses),
acoustic source plots which show group delay against frequency, and cepstrum plots, which are useful for finding reflexion and diffraction problems
Subjective and objective assessment 275
in otherwise complex signals. It is perhaps useful, now, to look at all of
these representations and their implications step by step.
9.2.1 Frequency response plots
Figure 9.3 shows a frequency response plot of the axial response of a
loudspeaker, derived from a pink noise signal and a dual channel analyser
which compared the direct electrical input with the acoustic output, in an
anechoic chamber via a measuring microphone. Both the amplitude and
phase responses are shown, and it can be seen how there can be no deviation from a straight line in either curve without a corresponding deviation
in the other. This is the characteristic of a minimum phase response as
discussed in Chapter 7.
Figure 7.19 shows clearly how the amplitude response plots change as
equalisation is introduced into a system. Almost everybody reading this
book will understand the significance of the amplitude part of the plot, and
how ideally, for perfect reproduction the line should be as flat as possible
and as wide as possible. From an objective point of view the magnitude
plot tells the engineers much about the uniformity, or otherwise, of the
pressure amplitude response with respect to different frequencies, and
consequently, if those design aims have been achieved.
Subjectively, it has long been considered that the magnitude of the pressure amplitude response (the frequency response in everyday language)
is the most significant measure of a loudspeaker’s performance, and yet
TRANSFER IMPEDANCE
DATE: 19-7-88
MODULUS
SAMPLE TYPE: 2A
PHASE
HORN LENGTH: 277 mm, D1: 26 mm, D2: 150 mm
0
FREQUENCY Hz
5000
Figure 9.3 A full frequency response
The frequency response of a mid-range horn loudspeaker
The vertical divisions represent 10 dB in amplitude or radians in phase (360 degrees/
2 = about 57 degrees). It can be seen how every change in the upper, pressure amplitude
plot is accompanied by a corresponding deviation in the lower, phase plot
276 Loudspeakers
no loudspeakers are truly flat. Smooth deviations from flatness are generally acceptable, and are easily grown accustomed to by listeners who
are familiar with the loudspeakers. Many mastering engineers consider
extreme flatness to be nice if it can be achieved without other compromises being made, but not essential, because a smooth frequency response
deviation is a linear distortion which can be compensated for both mentally and electrically without having to pay the penalty of side effects. On
the other hand, abrupt changes or irregularities in the frequency response
are definitely undesirable. They not only introduce colouration which will
only affect music with dominant signal content in the region of the irregularity, but they almost always imply that something else is wrong in the
system, and that the abrupt changes are only side-effects of whatever that
something else may be. The physics of loudspeaker design really does not
permit abrupt changes in frequency response without other consequences,
so smoothness is a very desirable characteristic of a curve, perhaps more so
than general flatness with an abrupt change somewhere. Abrupt changes
are usually accompanied by time response anomalies.
Figure 9.4 shows a series of off-axis plots, both in the vertical and horizontal planes. Their significance is twofold. Firstly, any persons listening
off-axis (that is, away from the line which is typically perpendicular to the
centre of the face of the loudspeaker cabinet), will hear a response which
is characterised by the respective plots in the horizontal and vertical directions. [Note that in a multi-way loudspeaker system it can be very difficult
to determine exactly where on the face of the cabinet is the exact acoustic
centre of propagation.] The acoustic centre of the loudspeaker shown in
Figure 8.6(a) is rather obvious, but the acoustic centre of the loudspeaker
shown in Figure 8.6(c) is not obvious at all. The second significance of offaxis frequency responses is that any reflexions which return to the listening
position from off-axis radiations will be affected not only by the frequency
response of the reflective surface, which for a plastered brick wall would be
acceptably flat, but also by the frequency balance radiated in that direction
from the loudspeaker. Many, large, multi-way monitor systems do exhibit
poor off-axis responses, a price sometimes paid to allow for other design
benefits, which is one reason why so many professional control rooms have
rather absorbent side-walls that will not return reflexions to the listening
position, or geometry that tends to direct this energy into absorbers after
the first bounce.
Until now we have been looking at plots of anechoic responses, but once
the room response becomes involved in the proceedings, the loudspeakersonly responses tend to get corrupted. Figure 9.5 shows the response of a
loudspeaker in an anechoic chamber, and Figure 9.6 shows the response of
the same loudspeaker placed on top of a mixing console in a typical small
control room. The changes can be seen to be gross, but a measuring microphone is not a pair of ears and a brain. The ability of the ear to know when
it is still receiving a smooth direct sound, despite all the chaos surrounding
it, is something quite impressive. Moreover, human beings live and work
in reflective environments, so if the response corruption is not excessive
the irregularities are accepted as what they are – room effects. However,
if the room reverberation or response decay time becomes significant, it
can mask low-level detail in the sound, so the room decay time is an
Subjective and objective assessment 277
10
0
–10
Axial Response
dB
15 degrees
–20
30 degrees
45 degrees
60 degrees
–30
–40
20
100
1000
10000
Frequency (Hz)
Horizontal directivity
10
0
–10
Axial Response
dB
15 deg. up
–20
30 deg. up
15 deg. dn
30 deg. dn
–30
–40
20
100
1000
10000
Frequency (Hz)
Vertical directivity
Figure 9.4 Horizontal and vertical directivity plots, showing the responses on-axis and at
various angles off-axis
important factor where detailed monitoring is required. The acceptability
or otherwise of room effects on loudspeaker responses may depend on the
principal reason for listening, such as to the recording quality, or to the
performance.
The phase of the frequency response is something which is more useful
in engineering processes rather than as something that relates to clearly
audible effects, except to say that gross phase errors will be discernible as
time response effects.
9.2.2 Waterfall plots
A good general grasp of the performance of loudspeakers can be made
from a visual assessment of their waterfall plots. These show a three
278 Loudspeakers
Yamaha NS10M
100
dB SPL for 2.83 V @ 1 m
90
80
Axial Response
70
2nd Harmonic
3rd Harmonic
4th Harmonic
60
5th Harmonic
50
40
30
20
100
1000
10000
Frequency (Hz)
Figure 9.5 Anechoic measurement of frequency response
10
dB
0
–10
100
1000
10000
Frequency (Hz)
Figure 9.6 Console-top measurement of frequency response
The same loudspeaker as measured in Figure 9.5, but on top of a mixing console in a
typical home-studio control room
axis representation of time against frequency against level, as shown in
Figure 9.7. In effect, a waterfall plot is a series of pressure amplitude
plots taken a few milliseconds apart and displayed by superimposition by
computer after the input stimulus has been stopped. An ideal loudspeaker
system, which could reproduce an accurate delta function, would show
only the top line of the plot – the zero milliseconds line – because the
decay would be instantaneous. As explained earlier though, no mechanical
system can start and stop instantaneously, and the waterfall plots show
how the decay takes place, frequency by frequency. A large selection of
waterfall plots are shown in Figure 11.1 which are very informative. They
show, without any shadow of a doubt, why virtually all loudspeaker systems sound different to one another: none of the responses decay in the
same way.
Subjective and objective assessment 279
Figure 9.7 A waterfall plot
The cascading lines are the frequency (pressure) responses at 2 millisecond intervals after
the cessation of the input stimulus (simulated) at time = 0 milliseconds. Various resonances
can be seen continuing to ring until about 40 milliseconds
Subjectively, a long decay tail sounds exactly like what it is; resonance. Figure 9.8 shows the waterfall plots of two different loudspeakers
of more or less the same size, a) being a sealed box and b) a reflex
enclosure. The box concepts are dealt with in Chapter 3, and the implications are dealt with in Chapter 11, but the general tendency is for
the loudspeaker with the faster decays to sound tighter in the bass; the
longer decays sound rounder. Balances between bass guitars and bass
drums tend to be more reliable and compatible with a range of other
loudspeakers when mixed on faster decaying loudspeakers, because the
resonances of the individual instruments are heard in a more realistic
proportion with each other. Resonant loudspeakers will add their own
characteristics to the sound, so it becomes difficult to judge exactly what
part of the bass sound is due to the instruments alone, and which part
is due to the loudspeakers. Relatively few top mastering engineers use
reflex cabinets, and those who do use them tend to use relatively large
cabinets with resonances very low down in the audible frequency range.
It is believed by the authors that the long-lived and widespread use of
the Aurotone 5C and Yamaha NS10 loudspeakers for rock music mixing was largely because of their rapid decays which were uniform with
frequency. Even though their frequency responses in anechoic chambers were far from flat, they tended to flatten in the bass region when
placed on top of mixing consoles due to the reduction in the radiating
angle. Nevertheless, they were still rather bass light, but the accurate
time response meant that the relative levels of bass instruments were
not confused by resonances, so if the mix was deemed to be bass heavy
on larger loudspeakers, it was a relatively simple matter to equalise the
mix with a reduction of bass frequencies and still maintain the instrumental balances. This process is often not possible when the balance
between the instruments has been confused by loudspeaker resonances.
This is especially problematical when the resonant frequencies of the loudspeaker reflex port timing is above the 41 Hz fundamental frequency of
280 Loudspeakers
a)
b)
Figure 9.8 Waterfall plots of two loudspeakers. a) A small sealed-box loudspeaker with a
relatively rapid delay. b) A small reflex loudspeaker with a considerably longer decay at low
frequencies than at mid and high frequencies
the lowest note on a conventional 4-string bass guitar or double bass (the
E-string).
Whether such instruments are recorded flat, or stylised by the use of
equalisation and signal processing, the final sound must be judged to
be suitable for reproduction via a wide range of loudspeakers. This is
clearly a difficult task with the situation that exists. The responses shown
in Figure 11.1 all represent loudspeakers designed for professional music
recording and all were measured in the same anechoic chamber. The situation in domestic reproduction rooms and with non-professional loudspeakers is obviously more diverse. Whilst research has been done both
by JBL and Genelec on finding the mean frequency response of a wide
range of listening conditions, no such work seems to have been carried out
to find the mean, most representative waterfall plot. It transpires that the
mean frequency response (or at least the pressure response) is substantially flat, and many critical listeners also consider that loudspeaker decay
times should also be uniform with frequency. Mastering engineers certainly
seem to choose predominantly low decay-time loudspeakers – a choice
which they have mostly made by ear – as they have found them to aid in
the making of more consistent decisions, but the lack of any industry-wide
guidelines on response decays is a great pity.
Subjective and objective assessment 281
9.2.3 Harmonic distortion
Harmonic distortion plots cannot be generated from noise signals nor
complex waveforms. The only practical method of producing a plot such as
the one shown in Figure 9.9 is to send to the loudspeaker a sine wave tone
which continuously sweeps up in frequency, covering the entire audible
frequency range, and use a set of tracking filters which are spaced at
one, two, three and four octaves above the principal tone. The outputs
of these filters are the second, third, fourth and fifth harmonics of the
input tone, and their relative levels can be given in percentages or decibels,
which are compared below:
0 dB
−10 dB
−20 dB
−30 dB
−40 dB
−50 dB
−60 dB
−70 dB
100%
30%
10%
3%
1%
0.3%
0.1%
0.03%
Hence, for example, in a loudspeaker which produces 0.3% of harmonic
distortion, the distortion products would be 50 dB below the main signal.
Another method, perhaps more commonly used, it to measure the level of a
single tone, repeated at several different frequencies, and then to measure
what remains each time when the frequency of the drive tone is filtered
out of the response. This yields a ‘total harmonic distortion plus noise’ or
THD + N figure for each single frequency that is measured, but THD + N
10
0
–10
Axial Response
–20
2nd Harmonic
dB
3rd Harmonic
4th Harmonic
–30
5th Harmonic
–40
–50
–60
20
100
1000
Frequency (Hz)
Figure 9.9 On-axis pressure amplitude and harmonic distortion
10000
282 Loudspeakers
has consistently failed to relate well, subjectively, to the perceived sound
from loudspeakers. Below 50 Hz it seems to be very doubtful that second and third harmonic distortion levels as high as 5% are audible, and
it seems questionably whether levels as low as 0.25% are audible at any
frequency. The ‘maximum operating level’ for magnetic flux on analogue
tape recorders was set for many years around the 3% distortion level, and
some really beautiful sounding recordings were made on those machines.
Furthermore, despite the fact that electronic systems, such as amplifiers,
with the above levels of distortion could not even be considered for high
fidelity use, they may, in some circumstances, make tonally rich sounding
guitar amplifiers; so they may not be accurate, but they are not necessarily unpleasant sounding. There is also an enormous range of microphone
preamplifiers on the market, all sold on the basis of their characteristic
sounds, which effectively means their characteristic distortions. These distortions are considered desirable by many people during the recording process, although for monitoring purposes it is obviously undesirable to colour
the sound or the concept of monitoring the recording would not be valid.
Nonetheless, and again as mentioned in Chapter 6, such distortions are
also considered to be desirable for musical instrument amplification, so
we therefore need to face the problem of deciding what level of harmonic
distortion is accepted as ‘non-intrusive’ for each piece of equipment in turn.
The problem with harmonic distortion as a quality measure in itself is
that harmonics of a low order (2nd , 3rd , 4th can actually be quite pleasant
sounding, and not unmusical at all. All instruments produce large quantities
of harmonics, sometimes even more than their fundamental tones, so the
question was often asked as to how the ear could detect 0.2% of harmonic
distortion from an amplifier reproducing an instrument whose tone was
itself perhaps 80% or more of harmonics. The answer must lie in the
differences in the mechanisms which produce the harmonics, and in what
other ways those mechanisms manifest themselves.
A musical instrument produces harmonics from the break-up of its parts
into separately resonating sections, which vibrate independently whilst
they also vibrate as part of the whole. Figure 9.10 shows a representation
of a string breaking into second, third, and fourth harmonic modes, and
Figure 9.11 shows the vibrational patterns of a metal plate. Note the perfectly symmetrical behaviour. A harmonic analysis of the sound would be
likely to show only frequencies which were harmonically related to the
fundamental resonance.
When an amplifier produces harmonics, the mechanisms involved are
totally different. Harmonics are produced as a result of the transfer function
of the amplifier being non-linear, as shown in Figure 9.12, and by other
means which are totally alien to natural vibrations, such as the crossover
distortion mentioned in Chapter 6. Loudspeakers, also, behave entirely
differently to either musical instruments, strings or plates because, at least
for sound reproduction purposes, they are usually designed not to break
up into separately moving sections, and they are unlike amplifiers because
their moving parts have mass, and hence momentum when in motion. They
also have non-linear stiffness in their suspension systems, and, amongst
other things, they may have non-linear Bl products, where the drive force
is not uniform because of the inconsistent relationship between the static
Subjective and objective assessment 283
Figure 9.10 Vibrational modes in strings
Representation of a string vibrating, and showing how it can break up into multiple segments at harmonic intervals in response to stimuli at those frequencies
magnetic field (B) and the length of coil (l) when being driven by the
voice coil.
In fact, harmonic distortion is not a good measure of such subjective
subtleties. Some loudspeakers can have 10 dB of difference in harmonic
distortion levels yet they may sound very similar, or vice versa. During
listening tests carried out by the authors in 19894 , in an attempt to group
according to sonic similarity a selection of twenty mid-range drive units,
harmonic distortion performance failed to show any relationship to the
pattern of similarity groupings. The fact is that harmonic distortion is really
the benign face of non-linear distortion, it is usually the intermodulation
distortion which really offends the ear.
9.2.4 Intermodulation distortion
This subject has been investigated in depth by Czerwinski, Voishvillo and
their co-investigators who have tried to make representations of analyses
which relate measured intermodulation products with sonic perceptions56 .
The problem with measuring these distortions is that they are so dependent upon circumstances that it has always been difficult to define them.
Intermodulation distortion can change dramatically with level, with the
frequency range of the music, with the crest factor of the music (the peak
to average relationship) and with many other parameters. Generally, the
more complex the musical signal, the more offensive is the intermodulation, as every frequency interacts with every other frequency and with the
products of the intermodulation, which in turn intermodulate with themselves. For this reason, a loudspeaker system may sound totally acceptable
on relatively simple musical signals, but may sound rather unpleasant with
an orchestral crescendo or a heavy concentration of guitars. At the same
time, it may well be the case that the perception of the purely harmonic
distortion, even up to the higher harmonics, if the intermodulation distortion could be separated out, could be totally inoffensive. However,
the harmonic and intermodulation products cannot be separated, because
284 Loudspeakers
Figure 9.11 Vibrations in plates
An insight into diaphragm break-up. Nineteenth century experiments on vibrations in
metal plates [From ‘On Sound’ by John Tyndall, Longmans Green & Co, London, (1895).
Reprinted by Dover Press – highly recommended reading, and still in print]
Subjective and objective assessment 285
10 dB
0
20,000
10,000
Frequency in Hz
IM Spectrum, industry standard amplifier using quasi-complementary circuitry
10 dB
0
10,000
20,000
Frequency in Hz
Figure 9.12 Non-linear transfer functions
The two transfer functions show very significant differences in intermodulation distortion
in two amplifiers whose harmonic distortion figures are very similar to each other. The four
highest peaks are the four frequencies of the drive signal. All the other spikes are distortion
products of intermodulation
they are products of the same non-linear processes. Nevertheless, it is
unfortunately misleading that the harmonic distortion, which can easily
be measured, should so frequently get blamed for the undesirable sounds
which are really a result of the intermodulation distortion, which cannot
be so easily quantified. As no simple relationship exists between harmonic
and intermodulation distortions, neither one can be extrapolated from the
other.
286 Loudspeakers
0
–20
dB –40
–60
–80
20
50
100
200
500
1k
2k
5k
10k
20k
Frequency, Hz
Figure 9.13 Spectrum of a 20-component logarithmic multi-tone signal
Figure 9.12 showed the greatly different levels of intermodulation and
harmonic products of two amplifiers whose harmonic distortion products,
alone, were measured to be very similar. Traditionally, intermodulation
has been measured by pairs of tones, say 1 kHz and 5 kHz, but the results
have never been particularly representative of any sonic characteristics of
the systems under test. The tests shown in Figure 9.12 used four input
tones, however, multi-tone signals using ten or twenty frequencies, specially
chosen give rise to the widest spread of intermodulation products, can
give a visual display of results which intuitively relate much better to
what is heard. A twenty tone spectrum is shown in Figure 9.13, and its
corresponding waveform is shown in Figure 9.14, which looks quite typical
of a musical signal. In fact, statistically, it is also very representative of
a real musical signal7 . The response of a bass driver to a ten tone signal
is shown in Figure 9.157 . The reason why intermodulation distortion is so
audibly offensive can clearly be seen from this graphical presentation. Bear
in mind that a distortion-free system would exhibit only the ten vertical
lines of the stimulus signal, similar to the twenty, clean lines shown in
Figure 9.13. The mass of sum and difference tones shown in Figure 9.15 are
like a noise signal which changes dynamically and spectrally according to
the stimulus. On a music signal it would be heard as a loss of transparency
and openness in the sound, and a loss of low level detail. If the density
of intermodulation products from only ten sine-wave tones is as high as
shown in Figure 9.15, then it is easy to appreciate that a complex musical
signal would produce an underlying, signal-related hash that could take
the sweetness out of the music and mask room-sounds.
The fact that intermodulation distortion is the real enemy of both
musicality and fidelity has been known since the very early days of
loudspeakers8 , but it is still so hard to quantify it in any meaningful way
simply because it is dependent upon so many dynamic factors, and its
Subjective and objective assessment 287
0
2
4
6
8
10
Time, mc
Figure 9.14 Waveform of a 20-component logarithmic multi-tone signal
110
dB, SPL
90
70
50
30
10
20
50
100
200
500
1k
Frequency, Hz
Figure 9.15 Sound pressure reaction of a loudspeaker (long coil, short gap) to multi-tone stimulus. The peak level of the input signal corresponds to X max = 4 mm. The solid curve shows
the level of distortion products averaged in a one-third-octave-wide rectangular sweeping
window
subjective offensiveness is signal dependent to a much greater degree than
is the case for harmonic distortion. The fact that the two types of distortion
share the same origins is easily demonstrated by the use of two tones, one
fixed in frequency and the other variable. If the two tones are different,
288 Loudspeakers
the spectral lines on a frequency analysis would show the harmonics, plus
the sum and difference tones. If the variable frequency source were to be
swept to the same frequency as the fixed tone, the pattern of modulation
products would change until with the two tones at the same frequency,
only the harmonics would be evident. However, where intermodulation
is concerned the products are dependent upon so many factors that no
truly meaningful figure of ‘merit’ has been devised to unequivocally define
intermodulation distortion performance. To quote from Czerwinski et al,
“High-order nonlinearity is very sensitive to the level of the input signal.
An increase in input signal which produces a negligible effect on low-order
[harmonic] products can wake up the ‘evil forces’ of nonlinearity, releasing
an unfathomable number of high-order intermodulation product ‘piranhas’
to tear the flesh of the reproduced sound to pieces”6 .
It has puzzled many people for many years why relatively low levels of
high-order harmonic distortion – 5th , 6th , 7th etc – have been associated with
poor sound quality. The principal explanation has been that the higher
harmonics are not musically related to the signal, but the very low levels
of these distortions have not corroborated this idea when they have been
added artificially to sine waves, where they have tended to be inaudible
at levels which prove to be offensive on music. Czerwinski et al offer the
explanation that the low levels of high-order harmonics are, in fact, just
tips of high-order intermodulation distortion ‘icebergs’. It obviously does
not bode well to be metaphorically sailing amongst icebergs in a sea full
of piranhas! But that has been the reality of intermodulation distortion –
a largely hidden, unquantifiable, yet dangerous enemy.
Distortion mechanisms which give rise to similar levels of harmonic
distortion may yield greatly differing levels of intermodulation distortion,
and this fact is surely at the root of the long acknowledged lack of any
robust correlation between harmonic distortion measurements and subjective audio quality. Having said that, it is obvious that a loudspeaker
producing 75% of total harmonic distortion (THD) at 1 kHz would not be
considered to be high fidelity, but once we get into the low single figures
at low frequencies, or below 0.5% at higher frequencies, then a loudspeaker with 10 dB less THD than another may well not guarantee that
it would sound more musically accurate, even when their linear parameters were relatively similar. On the other hand, multi-tone intermodulation
distortion presentations have begun to reveal good correlation between
pure-sounding loudspeakers and clean-looking displays.
9.2.5 Delta-functions and step-functions
A delta-function is shown in Figure 9.16. It is a unidirectional impulse
containing all frequencies, and of infinitesimal duration. The response to
a delta function defines the full frequency response of any linear system.
Mathematically speaking, the delta function is the derivative of the Heaviside function, also known as the step-function. The main problem with
using a delta function (also known as a Dirac function, or impulse) in
acoustic measurements is that it has very little low frequency content; having a spectrum rising by 3 dB per octave, like white noise. This results in
a tendency towards poor signal to noise ratios at low frequencies, where
Subjective and objective assessment 289
Amplitude
1
0
–1
0
5
10
15
20
Time (ms)
Figure 9.16 A Dirac delta-function, or impulse
Amplitude
1
0
–1
0
5
10
15
20
Time (ms)
Figure 9.17 A Heaviside step-function
air conditioning noise, ventilation noise and traffic rumble can prejudice
the low frequency response accuracy of the acoustic measurement. The
step-function (or Heaviside function), shown in Figure 9.17, contains much
more low frequency energy. The fact that by processes of either integration or differentiation, either one can be transformed into the other makes
the step-function a better option for acoustic measurements, even if it is
the impulse response that is ultimately required. Numerous step-function
responses are shown in Chapters 10 and 11.
A simple circuit for a rudimentary step-function generator is shown
in Figure 9.18. If this signal is applied 15 or 20 times to the input of
an amplifier (sufficient to allow for an averaging process to disregard
extraneous noises) with about 5 seconds each of ‘on’ and ‘off’ time, then
by means of the FFT processing of a dual channel recording of the direct
electrical output of the box and the loudspeaker output via a measuring
microphone, the full frequency response of the transfer function of the
system can be obtained. The pressure amplitude response, phase response,
waterfall plots, acoustic source plots, cepstrum plots, impulse response and
waveform response can all be derived from the step-function. Listening to
290 Loudspeakers
Isolator
switch
1.5 volt
battery
Momentary action
push switch
1kΩ
level
adjust
to output
connector
Figure 9.18 A step-function generator
This circuit will emulate quite well the waveform shown in Figure 9.17. For low impedance
loads, such as direct connection to loudspeaker drivers, the potentiometer should be set to
maximum. A good quality potentiometer should be used
the DC ‘thuds’ can also be quite revealing. A highly damped loudspeaker
in an absorbent room will produce a very ‘tight’ impact. In many small
control rooms, using small, reflex loudspeakers, the step function tends to
sound like an ‘ideal’ bass drum – round and warm, yet solid. This exposes a
dangerous situation for making decisions about bass drum/bass guitar/bass
synthesiser sounds, because it suggests that much of the perceived sound is
likely to be that of the loudspeaker and/or room, and that the ‘great’ sound
is not on the recording. To get a better idea of what the step function really
sounds like, it can be listened to on a pair of good quality headphones if a
reference in anechoic conditions and via fast loudspeakers is not available.
The step function, used in this way, will also expose resonances from
things such as open ended cable tubes in the control room, tubular steel
mixing console frames, fire extinguishers, furniture resonances, window
pane resonances and many other problems that ideally should not be in a
critical listening environment. Figure 9.19 shows the response of a control
room with open cable tubes in the floor. Although not obviously audible
on a pink noise signal, the step source rendered their presence plainly
audible to anybody in the room.
If a battery is used as a step source by coupling it and decoupling it
directly to a passive loudspeaker system the effects will not be symmetrical, because during the ‘on’ phase, the battery will be connected across
the loudspeaker terminals, and its low internal resistance will damp the
loudspeaker resonance. On the other hand, when the battery is disconnected, the loudspeaker input terminals will be left open circuit, so the
voice coil(s) of the low frequency driver(s) will be left unterminated and
free to resonate. The sound of the on and off cycles may therefore sound,
Subjective and objective assessment 291
10
0
–10
dB
–20
–30
20
40
60 ms
80
100
20
100
1000
10000
Frequency (Hz)
Figure 9.19 Cable tube resonances exposed by a switch box as described in Figure 9.18.
Resonances are clearly visible at about 70 Hz and 110 Hz due to open cable tubes in the
control room floor. The resonances were clearly audible on step-function excitation
and measure, quite different. However, when the signal is supplied to the
loudspeaker via a power amplifier, the low impedance of the output is
permanently connected across the loudspeaker terminals, so the positive
and negative signals should be much more similar. Bear in mind though
that if a 11/2 volt battery is used as a step source and connected to the
input of a power amplifier for loudspeaker testing purposes, the amplifier
should have a flat response down to DC, or the amplifier’s roll-off would
affect the loudspeaker’s true low frequency response.
It should also be borne in mind that the human ear does not always hear
the positive and negative pulses in the same way due to its own polarity
asymmetry. For this reason a positive-going output from a mixing console
or other music source should produce a forward (towards the listener)
movement of the loudspeakers diaphragm(s). Although the effect is subtle,
if this ‘absolute phase’ connection is not respected it can give rise to altered
perception of the music.
And beware! Not all loudspeakers or drive units or amplifiers give a
positive-going output from a positive-going input at their red terminals or
signal ‘hot’ input connectors. Many JBL loudspeakers still follow an older
standard where the application of a positive voltage to the red terminal
causes a movement of the diaphragm inwards, towards the magnet. It is
difficult for long-established manufacturers to change protocols without
creating havoc in their replacement parts markets. Quad and Tannoy are
other famous brands who have used this reversed standard, and some
eastern manufacturers have copied the lead of such exalted names. As a
general rule it is important to either check the manuals and data sheets or
physically test any unfamiliar equipment.
The original reason for this old standard of absolute phase was to
maintain the phase of the source. For example, a voice pronouncing a
‘p’ would expel air from the mouth, which would push the microphone
292 Loudspeakers
diaphragm inwards. It therefore followed that in order to maintain the
positive pressure in the listening room, the loudspeaker should go outwards
(i.e. in anti-phase to the microphone), which is perfectly logical! Some
older designs of amplifiers also reverse polarity from input to output, and
sometimes this was done to ‘correct’ older loudspeaker standards, so it is
always best to check any unknown device for its relative polarity of input
and output.
Back on the subject of delta functions and step functions, it is important
to note that they should be applied conservatively in terms of level, because
subsequent FFT (Fast Fourier Transform) analysis will break down in the
presence of distorted signals. The peak of a delta function is so narrow that
it can clip without apparently affecting its shape. A clipped spike may look
very similar to an un-clipped spike on an oscilloscope, but their frequency
contents would be very different. Delta functions are also not very easy to
generate in a pure form, but the response can be calculated via the inverse
FFT from a white or pink noise signal. White noise also suffers from the
poor signal to noise ratio at low frequencies, because of its 3 dB octave
(10 dB per decade) rising response. That is, the level at 20 kHz would be
down by 3 dB at 10 kHz (or 10 dB down by 2 kHz). At 20 Hz; which is
10 octaves (or 3 decades) below 20 kHz, the response would be 30 dB down.
Pink noise, with a flat power spectrum, is a more practical alternative, and
from a dual channel recording (one channel straight from the source and
the other via a measuring microphone) exact replicas of the step-function
and delta-function waveforms can be derived via the inverse FFT. About
2 minutes of noise should be recorded to allow the averaging-out of any
extraneous noises.
It is remarkable to think that Fourier, the French mathematician, calculated this relationship in the early 19th century, around 1807. In fact,
he was so far ahead of his time, and the means of proving the concept
practically were still over a century away, that his teacher and mentor, the
renowned mathematician Laplace, until his death refused to believe that
Fourier’s work on these transforms could be correct. Laplace even went
so far as to try to discredit Fourier over this issue, but powerful computers
have proved his concept beyond question.
Dirac and Heaviside also derived their functions long before the days of
transistors or digital computers. One cannot help but wonder at the power
of such brains – or whatever it was that they were taking! A selection of
step-function responses are shown on short time scales in Figure 9.20. The
variability of transient responses should be evident from inspection of the
plots. The more similar the waveform is to the electrical input waveform
of Figure 9.17, the better will be the transient response of the system.
9.2.6 Acoustic source plots
Whereas the delta and step function responses look at representation of
time against amplitude, another way of looking at the time response of a
signal is to look at it in terms of time against frequency. This, of course is
what is displayed on the horizontal plane of a waterfall plot, which shows
the response decay of a system. We can look at the system attack in this
Subjective and objective assessment 293
a)
SPL
0
Time (ms)
6
Response of a two-way monitor system
b)
SPL
0
Time (ms)
6
Response of electrostatic loudspeaker
c)
SPL
0
Time (ms)
6
Response of Tannoy Dual-Concentric
d)
SPL
0
Time (ms)
6
Response of large, widely used 2-way studio monitoring system
Figure 9.20 Step function responses on short time-scales
domain via an acoustic source plot. As the speed of sound at any comfortable listening temperature is around 340 metres per second, time can
therefore be converted into equivalent distance. The acoustic source plots
shown in Figure 9.21 show the responses of two systems, one a sealed box
and the other a reflex enclosure of roughly similar dimensions. It was discussed in Chapter 5 how any filter or resonant system must suffer a ‘group
delay’, where not all the frequencies pass through the system with the same
294 Loudspeakers
a)
4
3
m
2
1
0
–1
20
100
1000
10000
Frequency (Hz)
b)
4
3
m
2
1
0
–1
20
100
1000
10000
Frequency (Hz)
Figure 9.21 Acoustic source plots
Acoustic source plots of the same two loudspeakers whose waterfall plots were shown in
Figure 9.8, showing that not only does the reflex enclosure (b) exhibit a longer decay than
(a), but also that the low frequencies from loudspeaker (b) effectively emanate from a point
over 3 metres behind the physical position of the box. The low frequencies emanate from an
apparent point only one metre behind the sealed box (a)
speed. The acoustic source plots show how the different frequency delays
give rise to the effect of some frequencies apparently emanating from points
somewhere behind the physical location of the loudspeaker cabinets. Some
frequencies in a complex sound, after passing through an entire system,
actually emanate from the loudspeaker later than other frequencies, despite
them all having entered the electrical input simultaneously. The low frequencies from the sealed box shown in Figure 9.21(a) can be seen to apparently
arrive from a metre behind the face of the cabinet, which corresponds to
a delay of about 3 milliseconds, which equates to effectively emanating
from about 1 metre behind the force of the loudspeaker. The reflex cabinet
shown in Figure 9.21(b) shows a much greater signal delay at low frequencies
due to the resonant nature of the box. Here, a 50 Hz signal appears to emanate
from a source about 3 metres behind the actual location of the cabinet,
which shows the delay in the transient attack with respect to a similar sized
sealed box. Obviously, the low frequencies do not really arrive from behind
the loudspeaker, but the concept is a useful way of visualising the effect of
the group delay on the low frequency components of a transient signal.
Subjective and objective assessment 295
Group delay (milliseconds)
4
3
2
1
0
500
1k
2k
4k
8k
Frequency (Hz)
Figure 9.22 The Blauert and Laws criteria for the perception of group delays
Many manufacturers refer to the Blauert and Laws criteria, shown in
Figure 9.22. Blauert and Laws determined their results from listening tests,
and concluded that any acoustic source plots falling below the line would
not be audibly distinguishable in terms of group delay, alone. However,
group delays never occur alone, so assumptions about such things should
be made with great caution. Effectively the steeper the low frequency
roll-off for any given 3 dB down point, the greater will be the group delay
and the further behind the physical source will be the apparent source of
the low frequency content of a sound.
In some publications the acoustic source has been referred to as the
‘acoustic centre’, but that term is now generally agreed to refer to the
point on a loudspeaker front baffle which most closely corresponds to
the measurement axis on which the arrivals from the single or multiple
drivers would arrive with the most coherent phase relationship. (See subSection 9.2.1.)
9.2.7 Cepstrum analysis
The word cepstrum is an anagram of spectrum. Cepstrum analysis results
in plots shown in terms of time against non-dimensional decibels which
quantify the gamnitude (an anagram of magnitude). In the world of the
cepstrum, phase becomes saphe, high pass filters become long pass lifters,
harmonics become rahmonics. Power cepstra were developed in the early
1960s for the enhancement of the detection of echoes from earthquakes
in vibrationally noisy environments 9 . The repeated signals become more
evident after the inverse Fourier transform of the logarithmic power spectrum, which effectively treats the spectrum as though it were a waveform.
Figure 9.23 shows a series of pressure amplitude responses of a loudspeaker
with a discrepancy between the on and off-axis responses in the region
296 Loudspeakers
a)
10
0
–10
Axial Response
15 degrees
30 degrees
45 degrees
60 degrees
dB
–20
–30
–40
20
100
1000
10000
Frequency (Hz)
Horizontal Directivity
b)
10
0
–10
dB
Axial Response
15 deg. up
30 deg. up
15 deg. dn
30 deg. dn
–20
–30
–40
20
100
1000
10000
Frequency (Hz)
Vertical Directivity
Figure 9.23 On and off-axis pressure responses
Above 4 kHz there can be seen response irregularities in the on-axis response which are
not evident in the off-axis responses
around 5-8 kHz, where the on-axis irregularities are not present in the
off-axis responses. The cepstrum analysis shown in Figure 9.24 shows a
reflexion around 0.4 milliseconds (400 microseconds), which suggests that
the problem is one of diffraction from the cabinet edges at a distance of
about 7 cm from the centre of the tweeter. One millisecond represents
34 cm at the speed of sound. Four hundred microseconds therefore represents 34 × 0.4 cm, or 13.6 cm. The half distance, there and back would be
13.6 ÷ 2, or 6.8 cm, and the centre of the tweeter was, in fact, about 7 cm
from the top and one side of the cabinet.
Cepstrum analysis is not therefore something which directly relates to
what we hear (which is not surprising considering its abstract nature) but
it can be a powerful tool for diagnosing the sources of complex problems
(which is also not surprising considering its original application).10
Subjective and objective assessment 297
Gamnitude (dB)
4
3
2
1
0
0
1
2
3
4
Quefrency (ms)
Power Cepstrum
Figure 9.24 The power cepstrum
A strong, single reflexion is evident at about 400 ms, indicating a diffraction problem with
the loudspeaker represented in Figure 9.23
9.2.8 Modulation transfer functions
The ubiquitous ‘frequency response’ plots show the pressure amplitude
which a loudspeaker generates at each frequency, or in each defined
frequency band, in response to a flat input signal. In many cases, as
will be shown in Chapter 11, this simple pressure measurement may fail
to reveal many other measured response and sonic differences between
loudspeakers. Taken to an extreme, we could scramble the overall phase
response by measuring a loudspeaker in a reverberation chamber, and
adjust it to give a flat response, but the intelligibility of speech or the
resolution of detail in music would be hopelessly lost.
For this reason, in reverberant spaces such as railway stations and airport
terminals, a measurement of intelligibility known as a speech transmission index (STI) is often employed which is used to indicate the clarity
with which the spoken word would be likely to be heard amongst the
background noise and reverberation. Using similar techniques, a system of
modulation transfer function (MTF) measurement can be used to indicate
the degree of accuracy with which a loudspeaker is reproducing the information content in a musical signal.
Thought of another way, imagine a frequency response like a lettercount in this paragraph. We could individually count all the numbers of the
letters a, b, c, d etc, and end up with a table such as a = 28, b = 9, c = 13 etc.
If we then shuffled the letters around into one giant anagram, a subsequent
letter count would still provide the same result as before; a = 28, b = 9,
c = 13 etc, but depending on the degree to which we mixed up the letters,
the information content of the paragraph would gradually be lost.
When resonances or group delays within loudspeaker systems or their
crossovers and amplifiers smear the time response of a signal, a flat pressure amplitude response may still be achievable, but the onsets of all the
components of the music will not arrive in the correct temporal order.
They will all arrive, but out of sequence due to phase response errors, so
298 Loudspeakers
an information content loss would be experienced which would equate to
shuffling letters around in a paragraph. Fine detail in the musical sounds
would be lost, and the jumbled signals would produce other artefacts which
were not a part of the original signal. In Chapter 11 is a discussion of the
application of this concept to loudspeaker box tunings and port resonances,
but here it may be interesting to see how this MTF concept can be applied
to room acoustics.11
Figure 9.25 shows the comparison of results from a high resolution, full
range, flush-mounted monitor system, at a distance of one metre and four
metres in the highly damped control room of a music recording studio.
The MTF measures the accuracy of response, frequency by frequency,
in terms of its fidelity to the input waveform – ‘1’ being perfect and ‘0’
representing no similarity between input and output. It is evident from
Figure 9.25 that the control room is not giving rise to any significant loss
of information content as the sound waves cross the room, because there
is very little difference between plots (a) and (b). [And no; despite the oft
heard criticisms about absorbent rooms being oppressive, the room is not
oppressive to be in because there is plenty of reflective surface area sited
where the loudspeakers cannot ‘see’ it, but where it can add adequate life
to the speech and movements of people within the room.]
The tests were then repeated using a pair of small loudspeakers in a
studio recording/performing room having a relatively neutral acoustic character. Figure 9.26 shows the results, and it can be seen how the MTF drop
(information loss) from 1 metre to 4 metres is clearly apparent. Figure 9.27
shows the results of moving the tests into a granite-walled, acoustically live
room, using the same loudspeaker and microphone as for Figure 9.26. It
is plainly apparent that even at a distance of only one metre, the response
has already been significantly degraded with respect to the one metre measurements in the more neutral room. It is also apparent from Figure 9.25
how the full-range, high-resolution, flush-mounted (and expensive) professional monitor system shows more generally detailed information content
(a higher MTF at all frequencies) than the small, inexpensive, yet popular
‘studio monitor’ used for Figures 9.26 and 9.27.
1
1
0.8
0.8
0.6
MTF
MTF
9.2.8.1 Application of room equalisation
A number of companies are now offering monitor systems which purport to
deal with the room problems by means of active or adaptive equalisation,
to restore a flat frequency response even in relatively uncontrolled rooms.
(a) d = 1m
0.4
0.6
(b) d = 4 m
0.4
0.2
0.2
0
0
31
40
50
63
80
Frequency Band (Hz)
100
125
31
40
50
63
80
Frequency Band (Hz)
Figure 9.25 Flush-mounted, full-range monitors in a control room
100
125
1
1
0.8
0.8
0.6
MTF
MTF
Subjective and objective assessment 299
(a) d = 1m
0.4
0.6
(b) d = 4 m
0.4
0.2
0.2
0
0
31
40
50
63
80
Frequency Band (Hz)
100
31
125
40
50
63
80
Frequency Band (Hz)
100
125
1
1
0.8
0.8
0.6
0.6
MTF
MTF
Figure 9.26 Small loudspeakers in a studio performing room
0.4
0.2
0.4
0.2
(a) d = 1m
0
(b) d = 4 m
0
31
40
50
63
80
Frequency Band (Hz)
100
125
31
40
50
63
80
100
Frequency Band (Hz)
125
Figure 9.27 Small loudspeakers in a granite-walled, live room
The implication from the publicity often seems to be that room acoustic
problems can now be dealt with by signal processing, and also that the
highest standards of monitoring clarity can be achieved in less than wellacoustically-designed rooms.
In general, the phase response of a room/loudspeaker system can be
separated into minimum-phase (-shift) and excess-phase (-shift) components, as discussed in Section 7.9. The minimum-phase components of the
response are given rise to by anything which affects the response in a more
or less instantaneous way – such as the extra loading on the diaphragm,
and the consequent bass boost, when a loudspeaker is placed in a corner.
Excess phase effects result from time-shifted events, such as group delays in
crossover outputs (where the high frequency and low frequency outputs of
the filters suffer different signal delays) or reflexions which interfere with
a loudspeaker response after returning from a distant surface. In the case
of any minimum-phase response modification, the amplitude equalisation
will automatically tend to correct the phase errors, and hence the time
response (transient response) will also be improved. On the other hand,
an excess-phase response will often not have its phase response improved
as the amplitude response is flattened, and so its transient response may
even be made worse due to time smearing as the amplitude component of
the frequency response is flattened.
Figure 9.28 shows the MTFs for the wide-range, high resolution monitor
in the highly-damped control room (as shown in Figure 9.25). In this
case, its response has been flattened in a computer by the application
of a ‘perfect’ real-time filter, which also employed a 12 dB/octave filter
below 20 Hz to prevent wild, out-of-band correction responses. In terms
of the MTF, little has changed between Figures 9.25 and 9.28, either at
one metre or at four metres. The average MTF has not changed. In the
1
1
0.8
0.8
0.6
MTF
MTF
300 Loudspeakers
(a) d = 1m
0.4
0.2
0.6
(b) d = 4 m
0.4
0.2
0
0
31
40
50
63
80
Frequency Band (Hz)
100
31
125
40
50
63
80
Frequency Band (Hz)
100
125
1
1
0.8
0.8
0.6
MTF
MTF
Figure 9.28 Large loudspeakers in a control room – after correction
(a) d = 1m
0.4
0.2
0.6
(b) d = 4 m
0.4
0.2
0
0
31
40
50
63
80
Frequency Band (Hz)
100
31
125
40
50
63
80
Frequency Band (Hz)
100
125
1
1
0.8
0.8
0.6
0.6
MTF
MTF
Figure 9.29 Small loudspeakers in a performing room – after correction
0.4
0.2
0.4
0.2
(a) d = 1m
(b) d = 4 m
0
0
31
40
50
63
80
Frequency Band (Hz)
100
125
31
40
50
63
80
Frequency Band (Hz)
100
125
Figure 9.30 Small loudspeakers in a granite room – after correction
case of Figure 9.29, however, which shows the result of ‘perfect’ real-time
equalisation to the smaller loudspeaker in the well-controlled studio room,
(as shown previously in Figure 9.26) the MTF response at one metre has
been significantly improved by the equalisation, but the response at four
metres distance has hardly been improved at all. The results for the same
loudspeaker in a stone room, after equalisation to flatness, are shown in
Figure 9.30, where it can be seen that the MTF response has also been
improved at one metre, but the response at four metres has barely been
affected.
These results suggest that the new breed of room-equalised loudspeaker
systems can work well at short distances, but that the far-field response
in the room may/will not benefit in terms of the resolution of detailed
information content, even though the frequency response may appear to
be quite flat. In other words, such equalisation may improve the sound for
Subjective and objective assessment 301
the person close to the loudspeakers, but on the sofa a few metres away
the MTF response may remain as bad as ever, or worse! It would appear
that only well-designed room acoustics can provide and maintain a large,
flat, high-resolution listening area.
All rooms, unless highly absorbent, affect the transmission of information from a loudspeaker to a listener, and even at low frequencies the
loss of information content (detail) can be significant. In well-designed
listening/control rooms of low decay time (which, once again, need not be
oppressive to be in if reflective surfaces are strategically placed) the loss
of information content is minimal. However, the overall responses in less
well treated rooms can be improved considerably by modern equalisation
processes, but only, it would seem, at relatively short distances from the
loudspeakers. Room equalisation does not, in general, significantly reduce
the loss of signal information at greater distances.
What the evidence presented here is highlighting is that the flattening
of the ‘frequency response’ is not necessarily restoring low level detail and
low frequency information accuracy. In fact, as the amplitude part of the
frequency response is being flattened, the phase response may be suffering
degradation. This may make it easier to achieve a correct musical balance
for a mix, but it may not do anything to improve the assessment of things
such as the fine structural detail or the transparency of the room sounds
within the recordings.
Once we get into the lower MTF regions at low frequencies, experience
has shown it can become more difficult to balance percussive and more
continuous sounds, such as bass guitar to bass drum balances. A good MTF
and a fast transient response at low frequencies therefore remain essential
features of a good mixing environment.
Clearly, this type of insight into loudspeaker and room responses
requires techniques such as MTF analysis in order to be able to confirm and
see what ears have been telling people for decades, but which many ‘conventional’ established forms of loudspeaker measurement systems have
signally failed to reveal.
9.2.8.2 A D-to-A dilemma
A further point should also be raised about mid-priced loudspeaker systems
which incorporate digital equalisation. The quality of the D to A converters
should be considered when thinking about using them. A good quality pair
of D to A converters for monitoring a recording made via good quality
A to D converters costs around 1000 euros/dollars or more. Clearly, on
entire loudspeaker systems costing only 1000 euros/dollars, and having
digital inputs, the converters used in the electronics will probably cost
nearer to tens of dollars. When auditioning different converters using these
loudspeakers, this situation could (and in fact does) lead to conclusions
such as: “When we made comparisons, the mid-price A to D converters
sounded just as good as the super-expensive ones”. Such conclusions could
easily be drawn when monitoring via mid-price monitor systems which use
digital equalisation systems and low-cost D to A converters in acoustically
untreated or inadequately treated rooms.
John Watkinson raised this issue when he suggested that the resolution
of a loudspeaker system could be tested by reducing the bit rate of a
302 Loudspeakers
digital signal until the loss became noticeable12 . The loudspeakers making
audible the smallest bit-rate reductions being the ones with the greatest
resolution of fine detail. Although some holes can be picked in this argument, the basic concept does seem to hold water. In practice, the problem
which this highlights is that if the limitations of the D to A conversion
of the monitor system, or poor MTFs due to bad room acoustics, lead
to bad decisions about the choice of A to D converters, the deficiency
will be forever locked into the recording. Conversely, excellent A to D
conversion, even if not revealing itself on all reproduction systems, will be
fully enjoyable by those who do listen to the recordings via high quality
reproduction chains. However, measurement systems for accurately predicting subtle sonic differences in A-to-D and D-to-A conversion are still
not well-defined, and no simple, powerful tool is yet readily available.
Nevertheless, it should be rather self-evident that if any D to A converters
in the monitor system are not of the highest quality, then they will limit
the ability to monitor the quality of any other converters in the recording
chain. Cheap, quality-control monitors with digital inputs are therefore,
effectively, a contradiction in terms.
9.3 Sound fields and human perception
Once all the objective testing has been completed, the ultimate assessment
of the quality of a loudspeaker intended for musical use must be made by
the ear. Unfortunately there are some aspects of perceived loudspeaker
quality which do not easily lend themselves to objective measurement, yet
which are important aspects of perceived quality. No matter how good a
recording may be, and no matter how good its reproduction in terms of spacial imaging and definition, one incontrovertible fact is that its reproduced
sound-field will bear little resemblance to the sound-field of the original
instrument. Of course, if the music is an electronically based creation,
where no real instruments ever existed other than the electronic system
itself, then the loudspeaker playback on the original monitor system on
which it was mixed is the definitive sound field. However, a loudspeaker
reproduction of a cello recording will inevitably give rise to a huge spacial
distortion in terms of the sound field. A bowed cello radiates sound from
a large area, and in a very complex manner. Walking round a cello whilst
it is being played, a listener may experience a small reduction in the high
frequencies when passing immediately behind the cellist, whose body will
tend to cast a high frequency shadow, but otherwise the tone would be
perceived to be relatively independent of position. The source is very
distributed, with many parts of the instrument radiating a wide range of
frequencies at the same time. The sound field pattern from the instruments
contrasts sharply with that from any loudspeakers radiating a reproduction
of a recording of the same instrument.
The recording microphone is a pressure transducer, or a pressure gradient transducer if of figure-of-eight pattern, which responds to the radiated
sound received at the small place that the diaphragm occupies, and converts the sound pressure changes into an electrical signal. In stereo, with
two microphones, a two-channel signal can be recorded which can convey
Subjective and objective assessment 303
to the ear of a centrally placed listener, via loudspeakers or headphones,
enough information to give a sensation of the source positions in terms of
left and right, but not in terms of height. Once these signals are reproduced
via multi-driver loudspeakers, the ‘no-height’ information is also separated
into frequency bands. All the high frequencies above a certain crossover
point will come from two points (the tweeters), perhaps no more than 3 cm
in diameter, spaced at the extreme left and right of the sound-field. The
composite high frequency sound pressure is thus beamed at the two ears
in two separate rays, from two points in space, with no height information.
Compare this to listening to the instruments of a string quartet or a rock
group. The sound sources are multiple and are distributed in width and
height. High frequencies arrive from the entire drum kit, with the cymbals
above ear height and the snare drum below, or with the violin above and
the cello below. If the recordings were made in an anechoic chamber, then
played back in a reflective room, comparison to the live performance at
the same place in the same room would show many differences. The real
instruments would each be located at different places with regard to the
nodes and anti-nodes of the room modes. Conversely, the phantom images
of the recorded instruments would all originate only from the two loudspeaker positions, and only the nodes and anti-nodes relevant to the two
places occupied by the two loudspeakers could affect the overall response.
A phantom central image of a guitar would not couple to the room at its
phantom position, but at each loudspeaker position. Therefore a pair of
loudspeakers would send a signal to the ears from two places, whereas a
real group of musicians would send their sound to the ears from many
individual positions. In reflective/reverberant conditions, a pair of loudspeakers would couple to the room acoustics at only two places, whereas a
group of musicians would each couple to the room in a different way, and
even the individual drums in a kit would couple differently to the room
modes, and each produce their own unique reflexion patterns and timings.
Given the extreme sophistication of the human hearing system it would be
stretching the imagination to even hope that such differences between live
music and music reproduced via loudspeakers could go unnoticed.
[The pinnae of the ears (the ear flaps) are highly refined devices which
collect sound in different ways from different horizontal and vertical directions. The sound pressure differences at the entrances to the ear canals are
therefore not merely the differences that would occur if microphones were
placed in the same location in the absence of a head, torso and pinnae.
A pair of ear canals receives cues about the directions of sounds in the
horizontal and vertical planes which are not available to a pair of microphones, and as such the composite responses are not the same. By the
use of dummy heads with ear flaps, binaural recordings of great spacial
sensitivity can be made for playback over close-fitting earphones, but such
recordings will not work via loudspeakers because the head, torso and
pinnae of the listener would introduce a second set of processing which
would confuse the delicate information in the binaural recording.]
The ears therefore receive a different set of cues from the distributed set
of sources than from a phantom sound stage created by two sources, and
the resulting sound-field distortion can lead to great perceptual differences.
As loudspeakers cannot three dimensionally reproduce the reality of a live
304 Loudspeakers
performance, we must therefore look at loudspeaker reproduction as a
performance in its own right. The question then to be asked is how well
the loudspeakers can transmit the emotions which were generated by the
original performance. Given that the musicians were likely to be using the
tones of their instruments to manipulate the sensations which they were
intending to convey, it would seem obvious that their timbral subtleties
should be preserved as accurately as possible. However, exactly how that
timbral fidelity can be achieved may depend on certain compromise decisions, but the optimum compromise for one set of instruments may not
be optimum for a different set of instruments. The compromises for large
loudspeakers with great source areas may be different from the compromises which seem most apt for smaller, more compact sources, but even
the differences between those sources may be dependent on the musical
genre. Furthermore, to create an appropriate rendition of any given piece
of music in different room acoustics may also favour one set of loudspeaker
design compromises over another.
When music is created by electronic or electric sources, it is itself created
on loudspeakers for reproduction by loudspeakers. One presumes that the
loudspeakers on which the music is finally mixed are the reference for
the timbre and balance of the instruments, but the question arises as to
how to choose those loudspeakers. Are they to be chosen to give the
widest range of options for the recording personnel, or are they to be
chosen to be the most appropriate to enable the widest range of likely
domestic loudspeakers to reproduce the intentions of the producers in the
majority of circumstances? This dilemma often leads to the use of different
recording and mixing loudspeakers, as was discussed in Chapter 8.
There are in fact some market tendencies which do exist. Leaving aside
the audiophiles for now, and also leaving aside the people for whom music
is just something to fill the empty air, there is a tendency, for people who
choose their loudspeakers by careful listening before buying, to choose
different loudspeakers depending upon the type of music that they mostly
listen to. People who like orchestral music tend to buy different loudspeakers to those who like rock music. In fact, there is also a tendency
for recording engineers who work principally with classical music to use
different monitor loudspeakers to those who record rock music. What is
more, there are traceable similarities between the recording/mixing and
domestic listening loudspeakers used by each group.
The orchestral/acoustic music listeners tend to value loudspeakers with
low non-linear distortion, low colouration and a smoothly rolling-off low
frequency response, coupled with wide and smooth directivity to give rise
to plenty of the lateral reflexions which are necessary to produce a sense
of spaciousness. Pinpoint stereo positioning is often low on their agenda,
because in the reflective and reverberant acoustics of a concert hall, no
precise positional localisation is possible at a live concert; and neither is
it usually considered to be desirable, because it would imply an acoustic
that could not support the spaciousness – the two things are generally
mutually exclusive. On the rock music side, flat low frequency responses
are often valued, even if they cut-off quite abruptly. Colouration is to some
degree acceptable because instruments are often so heavily equalised in
the recording and mixing processes that no real reference exists. Heavy
Subjective and objective assessment 305
percussion and transient signals are commonplace, so high sound pressure
level capabilities are often required, and as the audibility of small amounts,
or even not so small amounts, of non-linear distortion is doubtful on
such high impact recordings, non-linear distortion levels may be tolerable
which would be too high for classical music enthusiasts. Relatively narrow
directivity may also be deemed to be desirable for rock music enthusiasts
because too many room reflexions can detract from the transient impact
of the fast changing music. However, all of the above-above-mentioned
items are tendencies, only, and will not apply in all circumstances.
Of course for a price, if money is no great object, very many of the most
desirable properties could be reasonably incorporated into one design, but
it would not be cheap and it would not be small. At 2006 prices, if one
were prepared to pay 2000 euros per pair of 50 litre boxes, one could
begin to approach a compatible design if the room acoustics could also be
reasonably contoured to requirements. Unfortunately though, it is sad to
say that even people in some supposedly professional parts of the music
industry consider such costs and sizes to be beyond their circumstances. In
such cases, it is really important to understand that when compromises are
made when using cheaper and smaller loudspeakers, they may not be as
suited to some music or rooms as they are to others, so any reference which
they provide may not be as robust or broad-based. Further implications of
mix compatibility will be discussed in Chapter 10, but in general, within
reason, as loudspeaker costs and sizes increase, and rooms become better
controlled, the easier it is to achieve a more universal set of monitors.
Small, cheap loudspeakers, if they are good at all, tend only to be good
for a limited range of circumstances and uses.
It is therefore difficult to be too rigid in trying to determine threshold
levels for ‘good’ performance when considering the implications of the
various characteristics discussed in Section 9.2 because what is optimal for
any given size of loudspeaker will depend upon its use. Ultimately, the
goal of listening to music is to enjoy it, so what gives pleasure has value,
even if it can be technically argued against. However, in general, the closer
that one can get to technical excellence, the overall sonic performance of a
loudspeaker usually improves, and it is surely incumbent on a professional
recording industry to be fully aware of what is on a recording, even if
99.9% of the purchasers of the end products are not going to hear the
subtleties. The music buyers can invest in their domestic entertainment
systems according to the degree that they are important in their lives, but
professional attitudes are more demanding. If nothing else, professional
pride requires that the end users should not become aware of recording
errors that passed unnoticed through the recording and mixing process.
9.3.1 Further perceptual considerations
The fact that our pinnae, middle ears, inner ears and brains are unique to
each of us introduces aspects of physiology and taste into the questions
of loudspeaker parameter optimisation. Culture and ethnicity also have
a bearing on the subject. When concentrating on listening to music, all
human beings tend to react with the side of the brain which relates to them
being right or left handed. When listening in a relaxed way, the tendency
306 Loudspeakers
is for the activity to switch to the opposite hemisphere. Mongoloid races,
such as Japanese, tend to process western music with one half of the brain
and oriental-style music with the other half of the brain13 .
Dr Diana Deutsch, at the University of San Diego, California, published
finding showing that the place of our birth, irrespective of being from local
descendants or not, can affect our musical perception. The median pitch of
the language and accent with which we first learn to speak can fix certain
aspects of our musical perception for the rest of our lives, and may even
affect the perception of complex pitch sequences in terms of whether we
hear them to be rising or falling14 . Southern English and Californian populations were shown to perceive a tri-tone pitch sequence in opposite ways.
During listening tests at the Institute of Sound and Vibration Research,
a band-limited, anechoic recording of an acoustic guitar chord was perceived by some listeners to change its notational inversion when played
through different loudspeakers, whilst other listeners heard the same chord
notation but a change in the timbre15 .
During the installation of a monitor system in London in the late 1980s,
there arose a situation with two well respected recording engineers who
could not agree on the ‘correct’ amount of high frequencies from a monitor loudspeaker system which gave the most accurate reproduction when
compared to a live cello. They disagreed by a full 3 dB at 6 kHz, but this
disagreement was clearly not related to their own absolute high frequency
sensitivities because they were comparing the sound of the monitors to
a live source. The only apparent explanation for this is that because the
live instrument and the loudspeakers produced different sound fields, the
perception of the sound-field was different for each listener. Clearly, all the
high frequencies from the loudspeaker came from one very small source,
the tweeter, whilst the high frequency distribution from the instrument
was from many points on the strings and various parts of the body. The
‘highs’ from the cello therefore emanated from a distributed source having
a much greater area than the tweeter. Of course, the microphone could
add its own frequency tailoring and one-dimensionality, but there would
seem to be no reason why this should differ in perception from one listener
to another.
During research in the late 1970s, Belendiuk and Bulter16 concluded
from their experiments with 45 subjects that “there exists a pattern of
spectral cues for median sagittal plane positioned sounds common to all
listeners”. In order to prove this hypothesis, they conducted an experiment in which sounds were emitted from different, numbered, loudspeakers, and the listeners were asked to say from which loudspeaker the
sound was emanating. They then made binaural recordings via moulds of
the actual outer ears of four of the listeners, and asked them to repeat
the test, via headphones, of the recordings made using their own pinnae.
The headphone results were very similar to the direct results, suggesting
that the recordings were representative of ‘live’ listening. Not all the subjects were equally accurate in their correct choices, though, with some, in
both their live and recorded tests, scoring better than others in terms of
identifying the correct source position. Very interestingly, when the tests
were repeated with each subject listening via the pinnae recordings of the
three other subjects in turn, the experimenters noted, “that some pinnae,
Subjective and objective assessment 307
in their role of transforming the spectra of the sound-field, provided more
adequate (positional) cues than do others”. Some people who scored
low in both the live and recorded tests, using their own pinnae, could locate
more accurately via other peoples’ pinnae. Conversely, via some pinnae,
none of the subjects could locate very accurately. However, for all the
subjects, listening through their own pinnae sounded most natural to each
of them.
Interestingly, some people do claim to hear height information in twochannel stereo recordings which can carry no such information, but this is
an effect of their own pinnae being stimulated in different ways by different
loudspeakers and mounting conditions. Such people really do hear height
in the stereo images, but only as an artefact of their own pinnae, and not
of the recordings or the loudspeakers.
Given these differences, and all of the aspects of frequency discrimination, distortion sensitivity, spectral response differences, directional
response differences, psychological differences, environmental differences,
cultural differences, and so forth, it would be almost absurd to expect
that we all perceive the same balance of characteristics from any given
sound. True, whatever we each individually hear is natural to each one of
us, but when any reproduction system creates any imbalance in any of its
characteristics, as compared to a natural event, the aforementioned human
variables will inevitably dictate that any shortcomings in the reproduction
system may elicit different opinions, vis-à-vis the accuracy of reproduction,
from different people. So, to the question of whether it is more important
to reduce the harmonic distortion in a system by 0.2%, or the phase accuracy by 15 degrees at 15 kHz could well be an entirely personal matter,
which could be task related, music related or room related, or even related
to a person’s psycho-physical make-up.
In fact, it could also be experience related. Human beings have a great
tendency to acclimatise themselves to familiar sounds. If we go into a
strange house, we often note the change in the sound of our voices, yet
in our own homes we rarely notice a change from going from outside to
inside, because we are so used to it. People who have been working for
years on a certain genre of loudspeaker also have a tendency to hear music
in relation to the way that they are accustomed to hearing it. It is hard to
say whether people make some choices about loudspeakers because they
suit their concept of what sounds right to them, or because they have a
recognisably familiar sound that they feel comfortable with. In the realms
of acoustic music, if a listener is also a regular concert-goer, the reference
of the general sound of live instruments is always in the back of their
mind as a reference, but with heavily processed music, only the people in
the control room at the time of the mixing really know what the sound
should be like. People can and do get accustomed to how a wide range of
non-acoustic music sounds on their own loudspeakers, then presume that
that is how everything should sound. [Conversely, I had a recording which
I liked very much and had played it on many systems, the better ones
of which yielded a remarkably rich yet obviously natural drum sound. By
chance, several years later, and on a different continent, I met the mixing
engineer, and told him what I thought of the recording. “Natural?”, “I had
308 Loudspeakers
to e.q. the hell out of it to get that sound!” he exclaimed. So we have to
be very careful about our supposed references. P.N.]
Despite all of the complications of human perception, objective analysis of loudspeakers is fundamental for keeping the progress on the rails
because subjectivism has far too many variables. Toole speaks of a circle
of confusion17 , where recordings considered to be ‘good’ are used to assess
loudspeakers, which are used to make recordings, which are made to assess
loudspeakers, which are used to make recordings ad infinitum.
If this is done in conjunction with continued reference to objective loudspeaker measurements, it is perhaps one of the only means that we have
to refine our assessments, but Toole’s implications were that this has often
been a ‘circle of testing’ which has occurred too often without the strict
objective constraints. Where, for example, domestic loudspeakers of average quality have been the de facto reference, and monitoring loudspeakers
have been chosen which give the best compatibility with this arbitrary reference. Then the new sounds recorded via this system become the reference
recordings, and so forth. Some marketing people may actually applaud
this, but professionally it is a loose practise.
Moulton1 discusses listening in the living room, the bedroom, the car,
on headphones, on the ‘ghetto blaster’ in the street, then concludes that
in order to sound compatible on all these irreconcilably different playback
systems, a recording must be:
a) comparatively simple spacially and texturally
b) limited in note-to-note dynamic range
c) exaggerated in spacial characteristics that do not become significantly
degraded timbrally when summed into mono and,
d) must not depend on their musical effect for any frequencies outside of
a range from 80 Hz to 10 kHz
The latter requirement dispenses with three whole octaves of the audible
range – octaves where the ‘power’ and ‘air’ are to be experienced. Even
people who cannot hear tones above 10 kHz can still usually hear when
the 10 to 20 kHz band is cut, so if we were to monitor only to this lowest common denominator, we would be robbed of much of the musical
experience when listening on audiophile systems. Working like this does
no justice to either the art, the technology or the science. The discerning
listeners deserve more.
Whilst the 80 Hz to 10 kHz brigade are unquestionably the bread and
butter of the industry, the artistes, the dedicated professionals and the
audiophiles are the great driving force that keeps it fresh and interesting. Said Roederer, “Music is not a waveform, but a psychological and
spiritual construct within the mind. The waveform and its physical dimensions are simply carriers of musical information”18 . Yet, that waveform is
best defended from corrupting influences if the objective performance of
a loudspeaker is designed to best convey it. Despite the subjective assessment being the ultimate arbiter of any loudspeaker’s performance, it is
only by objective means that we can keep focussed on the engineering
targets, without which, and by subjective means only, we would surely
become lost.
Subjective and objective assessment 309
It may well be that the dynamic ebb and flow of the music, the subtle
timing differences and other characteristics are better exhibited by some
loudspeakers than by others, but these are things for which we have no
reliable, measurable descriptors. However, the overwhelming tendency is
for a loudspeaker which scores highly in all the objective measurement
regimes detailed in Section 9.2 to show the musical characteristics in a more
artistic and exciting light. Nevertheless, it must always be the case that
until we have perfection, we will always be faced with different balances
of compromises serving some situations better than others.
References
1 Moulton, D., ‘The Creation of Musical Sounds for Playback Through Loudspeakers’, AES 8th International Conference, The Sound of Audio, Washington
DC, USA (1990)
2 Watkinson, John; ‘The Jitter Bug’, Resolution, Vol 1, No 4, UK (October 2002)
3 Briggs, G., ‘Sound Reproduction’, Third Edition, p 174, Wharfedale Wireless
Works, Bradford, UK (1953)
4 Newell, P., Holland, K. R., ‘Do All Mid-Range Horn Loudspeakers have a
Recognisable Characteristic Sound?’ Proceedings of the Institute of Acoustics,
Vol 12, Part 8, pp 249–258, Reproduced Sound 6 conference, Windermere,
UK (1990)
Also in: Newell, P., ‘Studio Monitoring Design’ Chapter 12, p 200, Focal Press,
Oxford UK (1995)
5 Czerwinski, E, Voishvillo, A., Alexandrov, S., Terekhov, A., ‘Multitone Testing
of Sound System Components – Some Results and Conclusions, Part 1: History and Theory’, Journal of the Audio Engineering Society, Vol 49, No 11,
pp 1011–1048 (November 2001)
6 Czerwinski, E., Voishvillo, A., Alexandrov, S., Terekhov, A., ‘Multitone Testing of Sound System Components – Some Results and Conclusions, Part 2:
Modeling and Application’, Journal of the Audio Engineering Society, Vol 49,
No 12, pp 1181–1192 (December 2001)
7 Voishvillo, A., ‘Assessment of Loudspeaker Large Signal Performance –
Comparison of Different Testing Methods and Signals’, Presented at the 111th
AES Convention, New York, USA (November/December 2001)
8 Janovsky, W., ‘The Audibility of Distortion’ (in German), Elek, Nochr.-Tech,
Vol 6, pp 421–430 (Nov 1929)
9 Bogert, B. P., Healy, M. J. R, Tukey, J. W., ‘The Quefrency Analysis of Time
Series for Echos: Cepstrum, Pseudo-Autocovariance, Cross-Cepsrum and Saphe
Cracking’, in Rosenblatt, M., (editor), Proceedings of the Symposium on Time
Series Analysis, pp 209–243, Wiley, New York, USA (1963)
10 Holland, K. R., ‘Use of Cepstral Analysis in the Interpretation of Loudspeaker
Frequency Response Measurements’ Proceedings of the Institute of Acoustics,
Vol 15, Part 7, pp 65–72 (1993)
11 Holland, K., Newell, P., Castro, S. and Fazenda, B., “Excess Phase Effects and
Modulation Transfer Function Degradation in Relation to Loudspeakers and
Rooms Intended for the Quality Control Monitoring of Music”. Proceedings of
the Institute of Acoustics, Vol 27, Part 8, Reproduced Sound 21, (2005)
12 Watkinson, J and Salter, R., “Modelling and Measuring the Loudspeaker as an
Information Channel”, presented to the ‘Reproduced Sound 15’ conference of
the Institute of Acoustics, Stratford-on-Avon, UK (November 1999)
13 Davis, D., Davis, C., ‘Sound System Engineering’, Second Edition p 9, Focal
Press, Oxford, UK (1997)
310 Loudspeakers
14 Deutsch, D., ‘Paradoxes of Musical Pitch’ in Scientific American, Vol 267, No 2,
pp 70–75 (August 1992)
15 Newell, P., ‘Studio Monitoring Design’ Chapter 5, Section 5.6, Focal Press,
Oxford, UK (1995)
16 Belendiuk, K., Butler, R. A., ‘Directional Hearing under Progressive Impoverishment of Binaural Cues’ Sensory Processes, 2, pp 58–70 (1978)
17 Toole, F., ‘Art and Science in the Control Room’ Proceedings of the Institute
of Acoustics, Vol 25, Part 8, Reproduced Sound 19 conference, Oxford, UK
(2003)
18 Roederer, J. G., ‘Introduction to the Physics and Psychophysics of Music’ 2nd
Edition, pp 11–12, Springer Verlag, New York, USA (1979)
Bibliography
1 Voishvillo, A., ‘Assessment of Nonlinearity in Transducers and Sound Systems
—From THD to Perceptual Models’, presented at the 121st convention of the
Audio Engineering Society, San Francisco, USA (October 2006)
Chapter 10
The mix, the music and the monitors
10.1 Physics or psychology?
The recording personnel in many small studios seem endlessly to be searching for that magic pair of loudspeakers that they can trust for whatever
type of music they mix on them. They swear by one pair of loudspeakers
as being their ultimate reference, then after the first mix that fails to sound
as good on another system – say at home, or in the A&R department
office – they lose all faith in them and seek a new ‘reference’. Until they
find that new reference, they may live in a state of unease, and even panic,
as their perceived anchor to ‘reality’ loses its grip. Why such well-trusted
loudspeakers could suddenly lose their authority has long puzzled many
people, but the fact is that the loudspeakers, themselves, rarely are the
sources of the problems. They usually have not changed at all between
the days when they were used to make the ‘magic’ mixes and the days
when the mixes were not perceived to travel so well. As often as not, the
problem lies not in the loudspeakers, but in the music, as we shall see
later. However, many other things can also change along the way, such as
the perception of the recording engineers who are using them. They often
seem to pass through the following phases during the period of use of any,
one type of loudspeaker system:
1)
2)
3)
4)
First audition – forming an initial opinion.
Getting to know them – evaluating and refining the opinion.
Increase in worries about minor aspects of the sound.
Boredom with the sound and doubts about its ‘accuracy’.
In so many instances, after finding a new, favourite loudspeaker, people
say that they have finally found a monitor to which they can accurately
refer their recordings and mixes, only to find that six months later they
again declare them to be ‘wrong’ and unusable. If in reality nothing in the
control room had changed in six months, and it is very doubtful that a pair
of good quality loudspeakers would have changed their characteristics in
such a short time of use, then the only thing which could have changed is
the way in which the users were perceiving the sound.
Sounds exist only in peoples’ brains. We all hear differently – we all
perceive the sounds differently – so it is difficult to compare musical perceptions, and no doubt we all have our individual hierarchies of priorities
in terms of what is important in any given musical rendition. Furthermore,
312 Loudspeakers
almost any experienced recording engineer or producer would freely admit
that on any given day, the ‘accuracy’ of the monitor system or the ‘rightness’ of a mix can seem to be dependent upon things such as the general
mood the day before, or how well they have slept. Less experienced people, however, often believe that their hearing system is always accurate
and ‘highly tuned’. If, one day, a monitor system does not sound ‘right’ to
them, or even when somebody else tells them that they do not sound right,
they call people in to carry out a thorough test of the system, and it is
often some absurd response change, carried out by the person or persons
called in to make the adjustments, which ultimately placates them. But
perhaps something is heard with the new settings that were not noticed
the day before, so in the minds of the recordists, this signifies that more
detail is now being perceived. The confirmation by measurement that all
was previously well with the loudspeakers frequently does nothing to deter
the requests for something to be changed.
In fact, quite often, rather than the measurements confirming that all
was well, they can induce a sense of even greater insecurity, because some
recording staff may feel that their comments were not being listened to,
and that their integrity and reputation were being undermined. At this
point something must be found so that honour and credibility can be
restored. Therefore, under growing pressure to come up with something,
and whilst being influenced by what are often misleading descriptions of
the perceived problems, perhaps some illogical change will be made to the
monitoring response which nonetheless seems to provide a credible ‘realignment’ of the loudspeaker. The change has a novelty value which brings
a new ‘reality’ with it. Honour has also been satisfied, because a problem
was found and rectified, yet the probability is that in almost all cases, no
physical problem existed and no aspect of the loudspeaker response had
actually changed until the adjustment was made. The only problem that
the adjustment really fixed was the one in the mind of the person reporting
the problem, and it possibly, in reality, took the loudspeaker response in
a direction away from absolute accuracy.
So what underlies this sort of insecurity and variability of perception?
There is little doubt that mood can affect perception. The stress resulting
from a rejection of a mix by a recording company can certainly deflate the
confidence, especially of less experienced sound recordists, and once doubt
and insecurity sets in it develops a momentum of its own. Nevertheless,
the problem under discussion here is too frequent and widespread to be
simply a case of a confidence crisis, because even when good moods are
restored for all parties, the problem of the mix being incompatible between
a number of loudspeaker systems may still remain, even though other
mixes done on the same monitor system may not have suffered from the
same problem.
10.2 The musical dependence of compatibility
The symptoms of a very common problem tend to be that a mix which was
done on a certain monitor system, in which the mixing personnel used to
have great confidence, and which sounded great in the control room, did
The mix, the music and the monitors 313
not sound good on the radio, or in some other important reference place.
They then compare this situation to that of a mix which had been done
some months earlier, (of a different piece of music – in almost all cases)
on the selfsame monitor system, which sounded great in all the places in
which it had been checked.
The perceived implication is normally that if the earlier mix sounded
good in the control room, and then proceeded to sound good in several
other ‘trusted’ locations, then it must be the case that the later mix, which
did not sound good in the other locations, must have been incorrectly
mixed. This is usually thought to be due to a changed control room monitor
system performance misleading the mixing personnel into making erroneous judgements. However, if a new monitor system is used, and a more
compatible mix results, it almost never seems to be the case that anybody
then bothers to remix the earlier music, which showed good general compatibility, on the new reference system, and then play it back in the other
reference places to see if it still sounded good on all the systems. This is
a crucial test, because the musical source material can be very influential
in terms of the compatibility between loudspeaker systems. It could be
the case that the musical arrangement was the source of the compatibility
problems. This fact can easily be demonstrated. Two monitor systems in
a control room can often be adjusted to sound almost identical on one
voice or instrument, only to then sound very different from each other on
a different musical signal.
It is also common knowledge that some music, mixed by certain people
in certain famous studios, seems to sound good wherever it is played,
yet many mixes, done by lesser mortals, only sound good on a few types
of loudspeaker. Many people seem to think that some special skills or
equipment are being used in the recording, mixing or mastering processes
by the people producing the ‘sound good anywhere’ mixes. They believe
that they must have some special, ‘truthful’, monitor systems, and wonder
what they can be. But what people often fail to remember is that the top
people in the top studios are also often working with very highly skilled and
experienced musicians, who also have a lot of experience in how to achieve
well-arranged, musically balanced recordings, which show a remarkable
degree of tolerance to minor level or equalisation changes.
When working in recording studios, up until the early 1970s, an
almost universally present member of the recording team was the musical
arranger. Things were worked out and rehearsed in advance, and each
instrument had its own place in both the time and the frequency domains.
It was very much a part of the job of the musical arranger to make sure
that instruments did not clash with one another either in terms of time,
pitch, or timbre. However, as things have progressed, the recording process had gradually become somewhat more anarchic, and this had led to
mixes in which many instruments may be fighting for the same time and
frequency spaces. They need to be so delicately balanced in order to sound
‘right’ that even minor differences in any aspect of the response of another
loudspeaker system can be sufficient to render the balance unsatisfactory.
Quite arbitrarily, the loudspeakers on which music is mixed can often be
declared to be inaccurate, but from the plots of Figure 11.1, we can see
quite clearly how no loudspeakers are technically accurate.
314 Loudspeakers
10.2.1 Sine waves and pink noise
Let us think of the compatibility problem this way. If we put a mid frequency sine wave into five good quality loudspeakers in turn, then adjust
all the levels to give the same sound pressure, it is probable, unless serious
distortion is present in any of the systems, that the sine wave will sound
the same in each case. The sine wave represents just about the simplest
signal source that could be used. Now let us go to the other extreme,
and use a signal that contains all frequencies, such a pink noise. Almost
certainly, even after the most careful adjustments, the pink noise would
sound noticeably different when reproduced by each of the five different
loudspeakers – its tone colour would certainly change – and it may even
sound different if played alternately through the two loudspeakers of a
matched stereo pair.
The significance of this, in musical terms, is that the more that a musical
mix tends towards a noise signal (in many cases this means the more
complicated that it becomes) the more it will tend to sound different
when switched from one loudspeaker to another. A lightly blown flute
will therefore tend to sound more similar when reproduced by a wide
range of loudspeakers than would be the case for a fuzz guitar. The latter
could noticeably change in timbre, or even in pitch, even when played on
relatively similar loudspeakers.
So, the more information that exists in a musical mix, the more of it there
is to get upset by minor response differences. Clean and simple mixes,
or mixes of music which is well arranged in terms of the temporal and
frequency distribution of the different musical parts, will tend to be more
robust than mixes which are highly congested and/or heavily processed.
Many of the recordings of Dire Straits always seem to sound musically
balanced no matter on whatever systems they are played, from an audiophile hi-fi system to a hotel radio alarm clock. Further consideration of
their excellent musical arrangements surely goes some way to explaining
why this is the case. This situation can puzzle many people who have gone
to great lengths to ensure that their monitors are well set up, and they
are very respectably flat when analysed with pink noise. However, as discussed in Chapter 9, there is far more to a loudspeaker response than its
steady-state pressure amplitude response.
10.3 Real responses vs. preconceived ideas
There is a tendency in much of the music recording world to believe that
the responses of all ‘good’ loudspeakers are more or less the same, and that
it is merely the precise application of their proprietary construction techniques which makes the minor differences between them, but the reality is
somewhat brutally different, as Figures 10.1 to 10.5 show. The plots show
five aspects of the responses of a Yamaha NS10M and two of its ‘competitors’ in the field of close-range music monitoring. These measurements
were all made in one, fixed position in the same, large, anechoic chamber.
Even before any room response anomalies could be considered, such as
those given rise to by directivity differences, the simple, on-axis, anechoic
The mix, the music and the monitors 315
b)
dB SPL for 2.83V @ 1m
a)
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Axial Response
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dB
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Frequency (Hz)
Figure 10.1 Pressure amplitude and harmonic distortion responses of three loudspeakers.
a) Yamaha NS10M. b) Genelec S30D. c) SAE TM160A
responses of the three loudspeakers, as shown in Figure 10.1, are different
to the point of absurdity if they are all ostensibly for the same sort of
professional use. The levels of harmonic distortion are also quite different.
Given their disparate responses, there is simply no way that a wide range
of musical mixes could sound similar when alternately played on each of
the three loudspeakers, but the degree to which they do sound different
may well be largely a question of instrumentation and arrangement, rather
than simply a matter of the balance of the mix.
Figure 10.2 shows the acoustic source plots of the same three loudspeakers referred to in the previous paragraph. As each metre on the
vertical scale represents about 3 milliseconds, it can be seen that from
the Yamaha the 50 Hz component of the signal is delayed by about 4
ms (about 1.3 metres).From the SAE the delay is around 6ms, and for
the Genelec, the delay is in the order of ten milliseconds. The plots of
Figure 10.2 show the delay in the attack of the low frequencies, but by contrast, Figure 10.3 shows the delay in the decays. The waterfall plots show
how the different frequencies decay in response to any signal which excites
316 Loudspeakers
b)
a)
m
4
4
3
3
2
m
1
2
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Frequency (Hz)
c)
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Figure 10.2 Acoustic source plots. a) Yamaha NS10M. b) Genelec S30D. c) SAE TM160A
the loudspeakers. Again, the temporal response variations are enormous.
On these plots, the 60 Hz component from the Yamaha is 30 dB down by
20 ms; the Genelec is barely down by 30 dB even after 100 ms, and the
SAE response lies somewhere in-between. How can a bass drum sound the
same on each loudspeaker? These longer responses can play havoc with
the balance between bass drums and bass guitars.
Figure 10.4 shows an electrical step function. An easy way of generating
such a function would be to connect a 11/2 volt battery to the input terminals
of a loudspeaker – active or passive. Figure 10.5 shows the time response
(which is in fact the waveform response) of the same three loudspeakers as
shown in Figures 10.1 to 10.3 when subjected to a step-function stimulus.
Once again, the resulting waveforms are very different. They could hardly
be expected to sound the same, and indeed they do not sound the same.
How a mix would ‘travel’ from one pair of these loudspeakers to another
would depend on the musical arrangement, the frequency range which
the music covered, and many other factors. The musical style, or genre,
may determine on which loudspeakers the mix was deemed to sound most
right, and this may, in turn, lead people to false conclusions about which
loudspeaker was generally most right. Surely, though, such vaguearies can
hardly be considered to be a desirable part of any ‘reference monitoring’
process. From Figures 10.1 to 10.3 it is easy to understand how pink noise
would sound very different if played through each pair of loudspeakers in
turn. It should be equally easy to appreciate how spectrally complex music
would suffer a similar fate.
With such a widely varying range of loudspeakers in use as so-called
‘references’, there is little wonder that no, one, mix, done on any set of
The mix, the music and the monitors 317
a)
10
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c)
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Frequency (Hz)
Figure 10.3 Waterfall plots. a) Yamaha NS10M. b) Genelec S30D. c) SAE TM160A
318 Loudspeakers
Amplitude
1
0
–1
0
5
10
15
20
Time (ms)
Figure 10.4 An electrical step-function waveform
a)
b)
1
Amplitude
Amplitude
1
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Time (ms)
15
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c)
Amplitude
1
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Time (ms)
Figure 10.5 Step-function responses of the three loudspeakers shown in Figures 10.1 to 10.3.
a) Yamaha NS10M. b) Genelec S30D. c) SAE TM160A
monitor loudspeakers, can be expected to sound equal on all of them. Nevertheless, a well-distributed musical balance, of well-arranged music, can
go some considerable way to ameliorate the problems, but much modern
music is very complex. Especially when music has been produced entirely
on one set of loudspeakers, it is inevitable that it will tend to sound wrong
on many other systems in many different rooms. The fact that so many
different references are available seems to devalue the very concept of
their use as references. Furthermore, the ear, itself, especially as part of an
overall system of musical perception, has also been shown to be a rather
The mix, the music and the monitors 319
variable reference, and it is usually only a combination of experience and
confidence which can solve this problem. This is exactly what people are
usually paying for when they engage the services of a reputable mastering
engineer.
It is also interesting to note that in general, classical recordists tend to
use different loudspeakers to rock music recordists. This fact serves to
highlight how far we are from perfection in loudspeaker design, because
a perfect loudspeaker would be an incontrovertible reference, unless, that
is, the buyers of one type of music recording had a general trend towards
all using a specific genre of imperfect loudspeaker in their homes, and to
which it seemed appropriate to make mixing compromises. To some extent
this case actually exists, with the vast majority of domestic listeners to rock
music using small, bass reflex enclosures, the problems of which will be
discussed further in the next chapter.
It seems to be the case that highly experienced and successful recording
personnel stick tightly to their chosen monitor systems, and they are very
reluctant to change them – even when they know them to be lacking.
Conversely, many inexperienced recording personnel provide the bread
and butter for the mid-priced monitor loudspeaker industry, rushing to
change their references every time that somebody complains about the
failure of a mix to travel well. The reality is that in the latter case, the
problem usually lies in the music and the mix, and not in the loudspeakers.
A robust musical arrangement, well played and well mixed, will travel.
A complex mix of a poor arrangement will probably not fare so well.
Acknowledgement
This chapter was partly inspired by the following paper which, although
on a different subject, highlighted many parallel concepts.
Bailey, Mark; ‘Perception of Music: The Element of Surprise’, Proceedings of the Institute of Acoustics, Vol 24, Part 8, Reproduced Sound 18
conference, Stratford-upon-Avon, UK (November 2002)
Chapter 11
Low frequency and transient response
dilemmas
11.1 The great low frequency deception
Recording industry publications often contain advertisements proclaiming
the true and lifelike responses of ‘accurate’ small monitor systems. If only
from the sheer quantity of such advertising, it is entirely reasonable that
many people would be led to believe that accurate low frequency reproduction from small boxes at quite high monitoring levels was an easily
achievable goal, but the reality is rather different. At realistic listening
levels for recording studio or mastering use, the low frequency response of
small loudspeakers cannot be as accurate in terms of frequency response
and transient response as that of a good large system, flush mounted in
the front wall of a well-controlled room. The laws of physics simply will
not allow it.
Various techniques can be used to flatten and extend the low frequency
pressure amplitude of loudspeakers in small-to-medium-sized cabinets, but
what so many people are unaware of is the degree to which these methods
of response extension can distort the time responses of the systems, and
mask considerable amounts of the low-level detail which a complex musical
signal may contain. The magnitude of the problem is clearly depicted in
Figure 11.1, from which it can be seen that of the 38 specimens tested,
when the time, frequency and pressure responses are viewed together, no
two out of the 38 plots look the same. It can also be added, without fear
of contradiction, that no two loudspeakers sound the same, either. Using
these loudspeakers as monitoring references therefore is more a question
of interpretation rather than anything absolute.
The variability between these ‘reference’ loudspeakers is made all the
more alarming when one considers two further points. Firstly, that all
the measurements shown in Figure 11.1 were made in the same position in
the same, large 611 m3 anechoic chamber. Obviously, when one uses these
loudspeakers in typical control rooms or domestic rooms, the responses
will be further adulterated. Secondly, it must be appreciated that amongst
the 38 examples are some very fine loudspeakers, in fact all were submitted
for test by manufacturers who were proud of what they had achieved,
and all were presented as professional music-monitoring loudspeakers.
Therefore, as these loudspeakers represent ‘the higher end’ of loudspeaker
production, it is lamentable to think how poor the responses can be at
Low frequency and transient response dilemmas 321
the lower end of the market. Furthermore, it should also be obvious that
if these plots represent the best that such famous manufacturers can do,
then we are not dealing with any problems that can be easily solved. So,
perhaps we should now look at the implication of what the plots represent,
and analyse the problems step by step.
11.1.1 The air spring
Moving coil loudspeakers in boxes are volume-velocity sources. The acoustic output is the product of the area and the velocity of the diaphragm, so,
for any given output, either a large volume of air can be moved slowly,
or a small volume of air can be moved quickly. Let us say that, for a
given SPL, the diaphragm of a 15 inch (380 mm) woofer in a 500 litre
box moved 2 mm peak to peak. With an effective diaphragm radius of 61/2
inches, which is about 160 mm, (we do not count the surrounds as part
of the radiating area), the radiation area would be 80000 mm2 . Moving
2 mm peak to peak means moving 1 mm from rest to the peak in either
direction, so the unidirectional displacement would be 80000 × 1 mm3 or
80000 mm3 . This is equal to 0.08 litres, so the static pressure in a 500 litre
box would be compressed (if the cone went inwards) by 0.08 litres, or by
one part in 6250 of the original volume.
For the same SPL, a 6 inch (150mm) loudspeaker in a 10 litre box would
still need to move the same amount of air 80000 m3 . However, with an
effective piston radius of only 21/2 inches, or 65 mm, the cone travel would
need to be about 12 mm peak to peak, or 6 mm in either direction, so
it would also need to travel six times faster than the cone of the 15 inch
loudspeaker, (i.e. 6 mm instead of 1 mm in the same period of time for
any given frequency). What is more, the displacement of 80 000mm3 (0.08
litres) in a box of only ten litres would represent a pressure change in the
box of one part in 125 of the original volume, compared to one part in 6250
in the 500 litre box. The air compression inside the box would therefore
be 50 times greater than that in the 500 litre box, and there are several
consequences of these differences.
Anybody who has tried to compress the air in a bicycle pump with their
finger over the outlet will realise that air makes an effective spring. They
will also realise that the more the air is compressed, the more it resists
the applied force, and the bicycle pump can rarely be compressed much
more than about half way. The force needed to compress the air by each
subsequent cubic centimetre increases with the compression, so the process
is not linear. In the case of the 15 inch and 61/2 inch cones referred to above,
the cone in the small box would have a much harder job to compress the air
by 1/125th of its volume than the cone in the large box, which only needs
to compress the air by 1/6250th part in our previous example. (Cone size
is irrelevant, here – only the volume displacement matters.) Large boxes
therefore tend to produce lower distortion at low frequencies, because the
non-linear air compression is proportionally less. The concept is shown
diagrammatically in Figure 11.2.
The non-linearity of the air spring can perhaps also be better understood
when one considers that it would take an infinite force to compress 1 litre of
air to zero volume, yet it would take only a moderate force in the opposite
322 Loudspeakers
(2) ADAM S2A
(1) Acoustic Energy AE2
(3) Alesis M1 Active
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(18) JBL LSR32
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(20) KRK V8
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(21) KSdigital ADM-2
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(15) HHb Circle 3P
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(19) K&H 0198
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(14) Hafler TRM8
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(12) FAR DbW-80
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(11) DAS Monitor 6
(16) HHb Circle 5A
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(9) Auratone 5C
(8) AVI Pro9
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(10) Behringer TRUTH B2031
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(6) ATC T16 Active
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(5) ATC SCM20A
(4) Apogee CSM-2
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Figure 11.1 Waterfall plots of the anechoic responses of 38 loudspeakers
10000
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ms
dB
Low frequency and transient response dilemmas 323
(22) Mackie HR824
(23) Meyer HM-1S
(24) Minipod
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(33) Tannoy A600
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(32) Studer A5
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(25) M&K MPS-150
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Figure 11.1 Continued
direction to rarefy it to 2 litres. The forces needed for a given change in air
volume in each direction (in this case ±1 litre) are thus not equal, so the
restoring forces applied by the air on the compression and rarefaction half
cycles of the cone movement are also not equal. The non-linear air-spring
forces thus vary not only with the degree of displacement, but also with the
direction of the displacement. Changing air temperatures inside the boxes
also add more complications of their own, and waste-heat from the voice
Volume in litres
324 Loudspeakers
1
1/2
1/3
1/4
0
10
20
30
40
Pressure in newtons per square centimetre
Figure 11.2 Boyle’s law
Each pressure change of 10 newtons produces progressively less change in the volume of the
gas. The process is therefore not linear, and can give rise to harmonic distortion
From this it can be seen that the more that a gas is compressed, the more it will resist
further compression. The line passing through the cylinders is a curve, not a straight line, and
this gives rise to the non-linear distortion (principally harmonic distortion) due to the backloading on the diaphragm of a low frequency driver. In a big box, the relative compression is
less, so for any given displacement the non-linear distortion due to the effect of the air spring
will also be less
coils when the loudspeakers are being driven by a musical signal ensures
that the temperature of the air will change during use. Therefore, for any
given SPL, loudspeakers in small boxes tend to produce more distortion
than similar loudspeakers in larger boxes.
11.1.2 Size, weight and sensitivity
The main controlling factor for the extension of the low frequency response
of a loudspeaker system is its resonant frequency, because the low frequency response of any conventional loudspeaker system will begin to fall
off quite rapidly below the resonant frequency. There are systems which
drive the loudspeakers well below resonance, with the application of electronic compensation, but they can run into problems of cone excursion
limitations, and are not in widespread use. The resonance is a function of
the stiffness of the air spring formed by the air inside the box, coupled
with the moving mass of the loudspeaker cone/coil assembly. The fact that
the air inside a small box presents a stiffer spring than the air in a larger
box, (because it is proportionally compressed more for any given volume
displacement) means that it will raise the resonant frequency of any driver
mounted in it, compared to the same driver in a larger box (i.e. loaded by
a softer spring). The only way to counter this effect, and to lower the resonant frequency to that of the same driver in a larger box, is to increase the
mass of the cone/coil assembly. [Imagine a guitar string; if it is tightened,
Low frequency and transient response dilemmas 325
the pitch will increase. Maintaining the same tension, the only way to lower
the note is to thicken the string, i.e. make it heavier.]
The problem that one now encounters is that to move the heavier cone,
in order to displace it by the same amount as a lighter cone in a larger
box, more work must be done, so more power will be needed from the
amplifier. The sensitivity of a heavy cone in a small box is therefore less
(for the same resonant frequency and bass extension) than for a lighter
cone in a larger box. If the sensitivity is to be maintained in a smaller box,
by using the same weight of cone and coil, then inevitably the resonant
frequency will be forced upwards. So, as the box size decreases, either the
bass extension or the sensitivity (or both) will be reduced. The only way
to maintain the bass extension and the sensitivity is to increase the size of
the box or the size of the magnets.
Larger boxes often tend to use larger drive units. A large diaphragm will
tend to be heavier than a smaller one, and the large diaphragm may also
need to be heavier to maintain its rigidity, as discussed in Section 7.2.2. This
would suggest a lower sensitivity in free air, but larger drive units often
also have larger magnet systems, which can easily restore the sensitivity,
and a larger radiating area, in itself, increased the radiation efficiency, as
was discussed in Section 7.2.2. Nevertheless, in small boxes, the greater
pressure changes may require stiffer, heavier cones, in order not to deform
under high pressure loads, so the efficiency can again be caused to reduce.
Once more, a bigger magnet could be an answer, but it may not be a simple
task to use a bigger magnet because it could seriously obstruct the free
air movement behind the cone, and it could reduce the internal volume of
the box, hence further stiffening the spring and again raising the resonant
frequency, which could only be offset by making the cone assembly even
heavier. If this were the case, the extra weight of the cone would have to
be compensated for by using more power to drive it, and because putting
in more power means that it would probably need a bigger (and heavier)
voice coil to take the extra power, it could therefore need even more power
to restore the output. So, now it should be becoming obvious that there
are just so many things which conspire against the extended low-frequency
performance of small boxes. There is no way out – we just keep going
round in circles.
Let us now consider two actual loudspeakers of similar frequency range
but very different size. A small loudspeaker such a the ATC SCM10 would
need to be driven by almost 200 watts in order to give the same SPL at
one metre as the double 15 inch (380 mm) woofered UREI 815 receiving
one watt of input. The two loudspeakers are shown in Figure 8.11. As has
just been discussed, reducing the box size demands that either the low
frequency response will be reduced, or the sensitivity will be reduced. High
sensitivity and good low frequency extension can only be achieved in large
boxes. If the ATC seeks to achieve a good low frequency extension in a
small box, then the sensitivity must be low; the air-spring physics dictates
that this must be so. The ATC SCM10 has a box volume of about 10 litres;
the UREI 815 contains almost 500 litres. Given that they cover the same
frequency range, the sensitivity difference of about 22 dB is the result –
hence the ATC needing almost 200 watts to sound as loud as the UREI
receiving one watt.
326 Loudspeakers
11.1.3 Further consequences of small size
When small cones move far and fast, they also tend to produce more
Doppler distortion (or frequency modulation), and this problem is often
exacerbated by the small woofers being used up to higher frequencies than
the large woofers, which can make the Doppler distortion more noticeable.
The high frequencies are being radiated from a diaphragm which is moving
backwards and forwards with the low frequency signals. (For more about
Doppler distortion see the Glossary.)
Long cone excursions also mean more movement in the cone suspension
systems (the surrounds and the spiders), which also tend to be non-linear in
nature as cone excursions increase. That is, the restoring forces are rarely
uniform with distance travelled. This tends to give rise to higher levels of
intermodulation and harmonic distortion than would be experienced from
larger cones of similar quality, moving over shorter distances. The larger
movements also require greater movement through the static magnetic
field of the magnet system, which tends to give rise to greater flux distortion
and, even more audible, non-linear Bl profile distortions.
Furthermore, the reduced sensitivity of the smaller boxes means that
more heat is expended in the voice coils compared to that produced in the
voice coils of larger loudspeakers for the same output SPLs. This problem
is even further aggravated by the fact that the smaller loudspeakers have
greater problems in dissipating the heat, because there is less air surrounding them in the smaller boxes. This can lead to thermal compression, as the
hotter the voice coil gets, the more its resistance increases, so the less power
it can draw from the amplifier for any given output voltage. The resulting
power compression produces yet more distortion products, so it can clearly
be seen that the distortion mechanisms acting on small loudspeakers are
far greater than those acting on similarly engineered large loudspeakers.
And even that is not all; small cones rapidly punching thought the air can
produce turbulence, which can be a source of strange noises due to the
shearing of the air at the edges of the cone. There are thus many reasons
why large-coned drivers moving over short distances tend to produce less
distortion than smaller ones, of similar quality, moving over larger distances. All of these reasons militate against the low frequency performance
of small loudspeakers.
11.2 Commercial solutions
The commercial pressures on loudspeaker manufactures tend to come from
people who are largely ignorant of these problems. The typical customers
demand more output of a wider bandwidth from ever smaller boxes, so
loudspeaker manufactures try to rise to the challenge. One example of a
technique used to augment the low frequency output is to use a reflex
loaded cabinet, (as described in Chapter 3) with one or more tuning ports.
In these systems, the mass of air inside the ports resonates with the spring
which is created by the air trapped within the cabinet. If the resonant
frequency is chosen to be just below where the driver response begins to
roll-off, then the overall response can be extended. The resonance in the
Low frequency and transient response dilemmas 327
tuning ports begins to radiate sound just where the drivers begins to lose
their output, and so the overall response can be extended downwards.
The effective extension of the low frequency response by means of reflex
loading also increases the loading on the rear of the driver as resonance
is approached. This helps to limit the cone movement and to protect the
drivers from overload. Unfortunately though, once the frequencies pass
below resonance, the air merely pumps in and out through the ports, and
all control of the cone movement is lost. In many active monitor systems,
electrical high-pass filters are used to sharply reduce the input power to the
drivers at frequencies below the cabinet resonance frequency. This enables
higher acoustic output from the loudspeaker systems within their intended
bandwidth of use, without the risk of overload and mechanical failure due
to high levels of programme below the resonance. By such means, a flat
pressure amplitude response can be obtained to a lower frequency than
with a sealed box of the same size, and the maximum SPL can be increased
(typically 3–4 dB for similar sized boxes) without risking drive unit failure,
but there is a price to be paid for these gains. The phase response will be
compromised, and hence the uniformity of the time (transient) response
will tend to be lost.
11.2.1 The time penalty
It must be understood that a resonant system can neither start nor stop
instantly. The time response of reflex loaded loudspeakers therefore tends
to be longer than that of similar sealed box versions, which means that
transients will be smeared in time: the impulse response will be longer.
Moreover, the effect of the electrical high-pass filters is to further extend
the impulse response, because the electrical filters are also resonant (tuned)
circuits. In general, the steeper the filter slope for any given frequency,
the longer it will ring. More effective protection therefore tends to lead
to greater transient smearing. Figure 11.3 shows the low frequency decay
of a sealed box loudspeaker, with its attendant low frequency roll off.
Figure 11.4 shows the low frequency response of an electrically protected
reflex cabinet of somewhat similar size. Clearly the response shown in
Figure 11.4 is flatter until a lower frequency, but a flat frequency response
is not the be-all and end-all of loudspeaker performance. Note how the
response between 20 Hz and 100 Hz has been caused to ring on, long after
the higher frequencies have decayed.
Figure 11.5 shows the corresponding step-function responses, and
Figure 11.6 the acoustic source plots. These plots clearly show the time
response of the reflex cabinets to be significantly inferior to the sealed
boxes. The low frequencies from the reflex enclosure arrive later (as can
be seen from Figure 11.6), and take longer to decay (as can be seen from
the decay tails in Figure 11.5), which both compromise the ‘punch’ in the
low frequency sound. Figure 11.7 compares the two plots of Figure 11.6
with the acoustic source plot of a large, wide-band, flush-mounted studio
loudspeaker system in a well-controlled room. From this comparison it
should be obvious why the NS10M (and Auratone 5C before it) earned a
reputation as a punchy little ‘big’ monitor.
328 Loudspeakers
10
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60 ms
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Figure 11.3 Waterfall plot of a small, sealed-box loudspeaker (NS10M)
10
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10000
Frequency (Hz)
Figure 11.4 Waterfall plot of a small reflex (ported) enclosure of similar size to the loudspeaker whose response is shown in Figure 11.3
A sealed box cabinet will exhibit a 12 dB per octave roll-off below
resonance, but a reflex enclosure will exhibit a 24 dB per octave roll-off
when the port output becomes out of phase with the driver output. As the
system roll-offs are often further steepened by the addition of electrical
protection filters below the system resonance, sixth, and even eighth order
roll-offs (36 dB and 48 dB per octave, respectively) are quite common.
With such protection, some small systems can produce high output SPLs
at relatively low frequencies, but the time (i.e. transient) accuracy of the
responses may be very poor. We will return to this topic in the next sections
of this chapter.
Low frequency and transient response dilemmas 329
a)
b)
Yamaha NS10M
Tannoy A600
1
Amplitude
Amplitude
1
0
–1
0
–1
0
5
10
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15
0
Time (ms)
5
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20
Time (ms)
c)
Amplitude
1
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Time (ms)
Figure 11.5 Step function responses corresponding to the waterfall plots shown in Figures 11.3
and 11.4, compared to the electrical input signal shown in (c). Note how rapidly the NS10 (a)
returns to a flat line on the zero amplitude level
Inevitably, the different resonances of the different systems will produce musical colourations of different characters. This may not be a
serious problem for use in domestic listening, but such inconsistency of
colouration does little to help the confidence of the users in recording studios. If a mix sounds different when played on each system,
then how does one know which loudspeaker is most right, or when the
musical balance of the mix is correct? The resonances of the sealed
boxes tend to be better controlled, and are usually much more highly
damped than their reflex-loaded counterparts. This leaves the magnitude of the frequency response of sealed boxes as their predominating audible characteristic, but it is usually the time responses of reflex
enclosures (related to the ‘phase’ part of the frequency response) which
give rise to their different sonic characters. There is considerable evidence to suggest that the many years of use of the Auratone 5C
and Yamaha NS10Ms as mixing monitors has been due to their rapid
response decays. It can be seen from their response plots (Numbers 9
and 36 in Figure 11.1) that all the frequencies decay at an equal rate –
none can be seen to be hanging on after the other frequencies have
disappeared.
A simple roll-off in the low frequency response of a loudspeaker used for
mixing is in itself not a great problem, because any wrong decisions about
a balance can usually be corrected by equalisation at a later date, such
as during mastering. As previously stated in other chapters, an error in
330 Loudspeakers
a)
4
3
m
2
1
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–1
20
100
1000
10000
Frequency (Hz)
b)
4
3
2
m
1
0
–1
20
100
1000
10000
Frequency (Hz)
Figure 11.6 Acoustic source plots corresponding to the waterfall plots shown in Figures 11.3
and 11.4
In these plots the low frequency response delay is shown in terms of from how many
metres behind the loudspeakers the low frequencies are apparently emanating. As each metre
corresponds to about 3 milliseconds, it can be appreciated how the low frequencies from
behind the sealed box (a) arrive much more ‘tightly’ with the rest of the frequencies than
they do in the case from the reflex cabinet
the time response, such as that added by tuning port and filter resonances,
can lead to misjudgements especially between the percussive and tonal
low frequency instruments, such as bass drums and bass guitars, whose
relative levels cannot be adjusted once they have been mixed together. The
time response errors of the loudspeakers will have led to erroneous mixing
decisions which cannot be unscrambled. The concept will be treated in a
more definitive manner in Section 11.7.
11.2.2 The transient trade-off
A problem therefore exits in terms of how we can achieve flat, uncoloured,
wide-band listening at relatively high sound pressure levels from ten-litre
boxes. At the moment, basically, the answer is that we cannot do it. Just
as there is a trade-off between low frequency extension, low frequency
sensitivity/efficiency (see Glossary) and box size; there is also a trade-off
between low frequency SPL, bass extension, and transient accuracy if bass
reflex loading and electrical protection are resorted to in an attempt to
Low frequency and transient response dilemmas 331
a)
4
3
2
m
1
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20
100
1000
10000
Frequency (Hz)
b)
4
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m
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Frequency (Hz)
c)
4
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m
2
1
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100
1000
10000
Frequency (Hz)
Figure 11.7 Acoustic source plots of Figure 11.6 compared to the acoustic source plot of a
large, flush-mounted, studio monitor loudspeaker. a) A 700 L, wide-range, flush-mounted
studio monitor loudspeaker. b) A Yamaha NS10M. c) A popular, small, reflex-loaded, closefield loudspeaker system. Note how the response of the NS10M mimics that of the large
monitor loudspeaker system. There is therefore little wonder that the NS10M has a reputation
for having a ‘rock and roll punch’
defeat the box size limitations. In effect, the bass extension is gained at
the expense of transient accuracy.
We therefore have a state of affairs whereby, at low SPLs, good low frequency extension can be achieved from small boxes, but the non-linearity of
the internal air-spring can lead to high distortion when the cone excursions,
and hence the high degrees of internal pressure changes, become significant. Suspension and magnet system non-linearities can add further problems, and remember also that in a small box there often exists the problem
332 Loudspeakers
of how to get rid of the heat from the voice coil. Thermal overload and
burnout are always a problem at high SPLs due to the high power necessary to overcome the limitations of the poor system efficiency. Larger,
higher-sensitivity systems not only produce less heat for any given SPL,
but also are much better at dissipating it. They thus win on both counts.
From the waterfall plots of Figures 11.3 and 11.4 it can be seen that,
whatever the box type, the decay is never instantaneous. There is always
a slope to the time representation, which in these plots is depicted by
the time ‘slices’. One can imagine the slope of the plot in Figure 11.3
continuing below the ‘floor’ formed by the frequency and time axes, with
the lines of the ‘waterfall’ continuing to cascade down. The question has
often been asked whether the electrical flattening of the low frequency
response would inevitably lengthen the time response, even with the sealed
boxes – effectively extending the response on the time scale as the level
was brought up from below the ‘floor’ on the amplitude (vertical) scale.
In truth, the tendency is for the flattening of the amplitude response to
shorten the time response (i.e. steepen the slope) by means of its correction
of the phase response errors which are associated with the roll-off. This
means that a large or small sealed box, equalised or not, would still exhibit
a much faster time response than a reflex enclosure. Figure 11.8 shows the
comparative effect.
Unfortunately, the type of equalisation shown in Figure 11.8 is not a practical option, because even at very low sound pressure levels, the excursion
limits of a small drive unit would be exceeded at the lowest frequencies,
and the drive-power levels would double every time that an extra 3 dB
of boost was applied. Figure 11.8 only serves to show how, in principle,
corrective equalisation would beneficial to the entire time/frequency/phase
response.
It seems reasonable that the more extended bass response of reflex
enclosures may well be valuable to ‘vibe’ the musicians during the recording
process, where concentration is more on achieving a good performance
rather than necessarily looking at the subtleties of each sound. However,
during the mixing process, another, more critical view is required, and
hence perhaps a different set of loudspeakers. At the mastering stage, the
requirements for sonic transparency can become even more critical, and
hence we have arrived at the sort of differentiation of uses described at
length in Chapter 8.
There are those who say that very fast time responses are not necessary
from loudspeakers, because their decay times are considerably shorter than
many of the rooms in which most of them will be used. However, what
they fail to realise is that the small loudspeakers are usually being used
in the close-field, which is normally considered to be within the critical
distance where the direct sound and room sound are equal in level. It
therefore follows that if one is listening in the close-field, the responses of
the loudspeakers will predominate in the total response. Indeed, this is one
of the principal reasons for the use of close-field listening. The room decay
will therefore not totally mask the loudspeaker decay, except in rooms
which are so live that the close field extends only a matter of centimetres
from the loudspeakers, but such rooms would hardly be appropriate for
monitoring.
Low frequency and transient response dilemmas 333
a)
10
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80
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Frequency (Hz)
b)
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60 ms
10000
Frequency (Hz)
Figure 11.8 Time vs. frequency – the effect of equalisation on a sealed box loudspeaker.
a) Waterfall plot showing the effect on the time response of electrically flattening the response
of an Auratone 5C. Although the response is now flatter down to a lower frequency than
the reflex enclosure shown in Figure 11.4, the time response has not been extended – the
decay is much more rapid. Unfortunately, such equalisation is not a practical solution because
the loudspeaker would overload even at low SPLs. Compare this plot with the unequalised
response shown in (b), from which it can be seen that the time response has not been
lengthened in the slightest by the corrective equalisation
11.3 The evolution of the desk-top monitor
It came as a bit of a shock during interviews with some highly respected
recording personal to find not only how little they knew about loudspeakers, but also how little they cared about knowing what was going on inside
the boxes. They seemed only to be interested in whether they worked, or
334 Loudspeakers
not, for their own decision-making during recording or mixing sessions.
In effect, it seems that they have largely given up trying to understand
a subject which usually appears to be cloaked in so much mystery. The
problem with this is that it provides very little feedback to the loudspeaker
designers, and the trend towards aggressive marketing of the products also
does little to increase the breadth of understanding of the users.
Somewhat disturbingly, even the designers of many professional
loudspeaker system are under the influence of powerful marketing pressures. When they receive instructions from their paymasters to design a
new loudspeaker, sound quality can be as low as fourth or fifth on the list
of design priorities. Things such as to be 100 euros a pair cheaper than
the perceived competition, an eye-catching design that will look good in
advertisements, comparable size to a competitor, and to be louder than the
nearest competing models are often typically seen to be more important
than absolute sound quality by the largely all-powerful marketing/sales
people, even in a supposedly professional recording industry.
However, despite this, mastering engineers, recording engineers, producers and musicians have been able to find some common paths, which,
even if they have not been clearly marked by technical guidelines, have
nevertheless been leaving some clear sonic footprints. Look, for example
at Figure 11.9. How many users of Auratones and NS10s have ever realised
that they possessed such similar frequency responses, (at least below 6 kHz)
or how different their ‘inverted V’ anechoic frequency responses were
from most other loudspeakers? The waterfall plots shown in Figure 11.10
(which show pressure amplitude against time against frequency) are also
very similar, as are the step function responses shown in Figure 11.11.
These plots help to explain why such a large number of recording engineers
and producers moved to the NS10 as a louder and deeper replacement for
their trusted Auratone 5Cs. The NS10 basically gave them more SPL and
more bass than the Auratones, but the general characteristics of the sound
remained the same. The reasons why only became apparent about 20 years
after the switch had taken place by the judgement of ears, alone1 .
The plots in Figure 11.9 are anechoic chamber responses, and it is clear
that in the frequency domain they are not flat with frequency. Technically,
they seem wrong, but sonically, at least for achieving a musical balance
between instruments, many users find them to be right when used in their
typical console-top locations, the effect of which on the pressure response
was shown in Figure 8.12.
Let us consider the implications of Figure 8.12(a), shown again, here,
as Figure 11.12. The solid line shows the predicted response of a loudspeaker such as an NS10M in a free-field (as in an anechoic chamber). The
shape is not unlike the measured anechoic responses of the NS10M and
the Auratone 5C, as were shown in Figure 11.9. The broken line shows
the predicted response when such a loudspeaker is flush mounted in a
wall. When one considers that the NS10M was originally designed as a
bookshelf loudspeaker, the logic behind its anechoic response should now
be clearly apparent. In fact, if sited next to any large reflective surface,
such as the top surface of a large mixing console when placed on its meter
bridge, the response would also tend towards that of the broken line.
Figure 11.13 shows the actual response of an NS10M on a meter bridge in
Low frequency and transient response dilemmas 335
a)
10
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dB
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Frequency (Hz)
b)
10
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dB
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20
100
1000
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Frequency (Hz)
Figure 11.9 Comparisons of pressure amplitude responses of the NS10M and the Auratone 5C
loudspeakers. a) NS10 anechoic frequency response plot. b) Auratone 5C anechoic frequency
response plot. Note the general similarity of the frequency responses (apart from the peak at
8 kHz in the Auratone’s response). The fact that they are not flat is also worthy of note
a typical recording environment. Obviously the desk (console) tops cause
many response irregularities, but, the general tendency towards an overall
response flatness is also very apparent in Figure 11.13. The low frequency
response has clearly been augmented, and what is more it has been augmented in a non-resonant manner that does not affect the rate of decay of
the low frequencies.
The great significance of this is that if a loudspeaker which had a flat anechoic response were to be similarly positioned, it would also be subjected to
the same type of response modifications, and so would tend to produce an
excess of low frequencies. This is the reason why many active loudspeakers
have bass frequency adjustment switches, with recommended settings for
different mounting conditions. With passively crossed-over loudspeakers,
this flexibility in response correction is only usually achievable by the
use of external equalisers, but it is seldom a practical solution. Low frequency response controls can be incorporated into an active design for
a few cents, but a dedicated equaliser with the sonic transparency necessary for high quality monitoring may be vastly more expensive than the
336 Loudspeakers
a)
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60 ms
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Frequency (Hz)
b)
10
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60 ms
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Frequency (Hz)
Figure 11.10 Comparison of the waterfall plots of the NS10M and the Auratone 5C
loudspeakers. a) Waterfall plot of NS10M. b) Waterfall plot of Auratone 5C. By 20 milliseconds after the wideband excitation has ceased, the response at almost all frequencies has
decayed below the −40 dB level. This is not the case with most small reflex loudspeakers, of
which the plot of Figure 11.4 is more typical
loudspeakers with which they are being used. This tends to discourage their
use. Obviously, the use of a cheaper equaliser, with its own sonic character,
would be an absurd choice if accurate monitoring were the goal. Passively
crossed-over loudspeakers therefore tend to be best chosen with responses
appropriate for their conditions of mounting, but a large proportion of the
people involved in the recording world seem not to understand this rather
important point.
The upshot of this is that loudspeakers get located in positions that
are physically practical for working, but which may not be conducive to
Low frequency and transient response dilemmas 337
a)
Amplitude
1
0
–1
0
5
10
15
20
15
20
Time (ms)
b)
Amplitude
1
0
–1
0
5
10
Time (ms)
Figure 11.11 Comparison of the step-function responses of the NS10M and Auratone 5C
loudspeakers. a) NS10M step function. b) Auratone 5C step function. By 8 milliseconds after
the impulsive excitation, the responses have decayed to a flat line. Again, this is not typical of
most loudspeakers of which, once again, the step-function response shown in Figure 11.5(b)
is perhaps more typical
10
dB
Flush Mounted (
Free Field
(
0
)
)
–10
100
1000
10000
Frequency (Hz)
Figure 11.12 Response of an idealised loudspeaker, of similar size to an NS10M, under
different conditions of mounting
The solid line shows the free-field response, and the dotted line shows the expected response
if flush-mounted
338 Loudspeakers
10
dB
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100
1000
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Frequency (Hz)
Figure 11.13 Response of a Yamaha NS10M loudspeaker on top of a mixing console meter
bridge in a typical, small control room
Note the general tendency towards an overall flat response. The irregularities are desk-top
reflexions, which would tend to similarly affect the responses of any loudspeakers so mounted
optimising the flatness of the low frequency response, and usually no
measures are subsequently taken to correct the overall response. A small
bookshelf loudspeaker, for example, will be acceptably flat, in wideband
terms, when mounted on a meter bridge of a suitably sized mixing console, but the consequent comb-filtering due to the desk-top reflexions will
reduce the sonic openness and transparency. (The effect of the reflexions
can be seen in the irregularity of the response shown in Figure 11.13).
These latter two aspects could be restored by positioning the loudspeakers
behind the console, on pedestals, but then the low frequency reinforcement
would be lost and the bass response would fall off more rapidly. Neither
situation is therefore ideal. In the case of pedestal mounting, because the
low frequency roll-off is a result of the lack of loading on the bass driver, it
could be equalised by a suitably sonically neutral equaliser. [Note that this
is not a room response problem, which could not be properly corrected by
means of equalisation, but rather it is a loudspeaker air-loading problem,
which can legitimately be equalised]. The equaliser would, in this case, correct the loudspeaker response in terms of both amplitude and phase, but
unfortunately it would also reduce the headroom, so overloads would be
likely at lower than normal volume levels. This is therefore not perceived
to be a useful solution.
From this discussion it should be apparent that a loudspeaker mounted
on the meter bridge of a mixing console, in a control room, could not be
expected to perform similarly when placed on pedestals in a mastering
room. So, this is one clear example of why mastering engineers may need
different loudspeakers to the ones used in recording studios – they use them
differently. What is more, it must be fully understood that loudspeakers
which are to be mounted on pedestals tend to need a flatter anechoic low
frequency response than loudspeakers which will be mounted in walls, next
to walls, or on meter bridges. A loudspeaker with a fixed, passive crossover
and with a flat anechoic frequency response is therefore not suitable for
meter bridge mounting.
Low frequency and transient response dilemmas 339
11.4 The great time deception
The problems discussed so far in this chapter would appear to be at the root
of the frequent observation by mastering engineers that the recordings from
the studios with less-experienced personnel frequently display incorrect
balances between the bass instruments. If a loudspeaker exhibits a resonant
low frequency response, it will add this resonance to the response of the
instrumental sounds that it is reproducing. This may be of little significance
to a resonant instrument like a bass guitar, but it may very distinctly alter
the character of a tight, fast-decaying, percussive bass drum sound. The
added resonant energy could mislead the mixing personnel into believing
that the bass drum was louder in the mix than was actually the case. They
would hence balance the instruments with the bass drum lower than it
should be with respect to the bass guitar. When it comes to the mastering
stage, little can be done to rectify the situation, because the equalisers or
compressors usually cannot act on the bass drum without also acting on
the bass guitar. The only solution may be to go back to the studio and do
another mix with more bass drum, and incur whatever extra expenses and
wasted time that may be involved.
Conversely, if a mix was done on loudspeakers with fast, low-frequency
decays, albeit deficient in bass extention, the situation may not be so bad.
If the instruments were balanced between themselves, a simple equalisation
process (taking off whatever low frequency had been added due to the lack
of bass on the mixing loudspeakers) could return the overall response to
that which the recording staff thought that they had at the time of mixing.
But it is the errors in the loudspeakers’ time responses which are the great
deceivers in so many cases, and the mixing errors which they lead people
to make are often unable to be corrected by any currently known signal
processing device.
It still seems to be the case that too many loudspeaker manufactures
who make products specifically aimed at the music recording market are
paying too much attention to the flattening of the pressure amplitude of
the frequency response and too little attention to the shortening of the
time responses. This could, at least in part, be down to the fact that the
anechoic response flatness sells loudspeakers by looking good in brochures,
whereas a short time response does little to sell the loudspeakers because
99% + of the users are unaware that a time response problem even exists.
This is a pity, because we now have the evidence available to show how
important the fast decay of a time response is to the sonic neutrality of a
system2 .
11.5 Resonant tails and one-note bass
Figure 11.14 shows the frequency responses of ten different small
loudspeakers, all ostensibly designed for use as small monitors in recording studios3 . It can be seen how the responses below 200 Hz are all quite
different. Numbers 1 and 2 are sealed boxes, which roll off naturally at
12 dB per octave. Number 1 is a larger box than Number 2, so it typically exhibits a flatter response to a lower frequency before the roll-off
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Low frequency and transient response dilemmas 341
begins. The eight subsequent plots all show the responses of loudspeakers
which have used different acoustic or electro-acoustic means to attempt to
maintain the flatness of the response to lower frequencies than would be
achievable if the boxes had been sealed. Number 10 exhibits a response
not unlike Number 1, albeit with a steeper roll-off, but in a rather smaller
box than that of Number 1.
Figure 11.15 shows another series of plots. These show the responses
of six of the loudspeakers shown in Figure 11.14, but after excitation with
a burst of four cycles of 60 Hz. The ‘order’ referred to in the captions
below each of the plots relates to the overall rate of low frequency rolloff: each ‘order’ represents 6 dB per octave. Whilst there is nothing in
Figure 11.14 to suggest that there could be any significant problem with the
means that have been used to extend the flatness of the on-axis responses,
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342 Loudspeakers
Figure 11.15 begins to cast doubt on their validity. Note what happens as
the box resonances are used to extend the low frequency flatness, and the
electrical filters are applied in order to prevent over-excursion of the cones
at frequencies below those of the box resonances. Number 1, a simple
sealed box, shows a relatively straightforward decay at 60 Hz. But look at
the ported enclosures, Numbers 5 and 7. The port tunings are not high Q,
so their resonances are rather broad. This means that they can be excited
by other frequencies which are reasonably close to their own resonant
frequencies. The four cycles of 60 Hz are sufficient to excite the nearby
port resonances, and it can be seen that as the 60 Hz excitation (at the
top of the plots) decays, the electro-acoustical resonances continue to ring
on. In effect, the decay of the excitation note shifts in frequency. In the
cases of Numbers 8 and 9, double resonance can be seen to continue, with
the initial excitation frequency bifurcating into separate resonant decays.
If the excitation was a musical signal, then these resonances may not relate
to the musical input. They may even be very discordant.
Of course, this can also happen in ‘boomy’ rooms, where room resonances are excited at frequencies nearby the original musical input. Some
concert halls or performance stages are notorious for their ‘out of tune’
decays, which can be quite noticeable and undesirable during acoustic performances. In the cases of large, often multi-purpose rooms, the problems
can be difficult to treat, due to the sheer, physical scale of the treatments,
but in loudspeakers the problems are surely the result of either ignorance
or inappropriate engineering design. Clean-sounding bass is hardly likely to
be heard from loudspeakers which are generating their own low-frequency
signatures.
11.6 The masking of detail
Another aspect of loudspeaker resonances is their tendency to mask detail
in the signal. Figure 11.16 shows representations of the reproduction of a
modulated noise signal. This was a pseudo-random noise with a bandwidth
from 35 Hz to 70 Hz, modulated by a 10 Hz sine wave. The process was
not unlike that which is used to measure speech intelligibility in voice
evacuation systems (Speech Transmission Indices – STI and RASTI). In
these plots, the shallower the modulation depth, the more the loudspeaker
is likely to mask low frequency detail – or bass articulation as it may
be referred to. The sealed box, with the second order roll-off, shows a
modulation depth of around 32 dB (from 50 dB, down to 18 dB). The
sealed box with an electrical protection filter (Number 3) reduces this to
about 26 dB. By the time we get to the ported enclosure with the second
order electrical protection filter, the modulation depth is down to about
14 dBs.
As the boxes become progressively more tuned and protected, the detail
in low level signals can become progressively more lost. Once again, larger,
sealed boxes perform much better.
Low frequency and transient response dilemmas 343
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Figure 11.16 Averaged, convolved, modulated noise via six different loudspeakers
11.7 Theoretical equalisation and excess phase
Figure 11.17 shows the waterfall plots of the anechoic, on-axis responses
of the same ten loudspeakers represented in Figure 11.14. They are all
boxes of reasonably similar size. It can be seen that the low frequency
resonances tend to increase in their decay time as the order of roll-off
increases. Due to the general irregularity of the frequency responses, it
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Figure 11.17 Waterfall plots of the same anechoic responses as shown in Figure 11.14
dB
Low frequency and transient response dilemmas 345
is hard to accurately compare one response with another. Nevertheless,
it should be easy to appreciate that each loudspeaker would be likely to
lead mixing personnel to make different level and equalisation decisions
with respect to the low frequency instruments in their musical mixes. So, in
terms of references, they are clearly not compatible. The big question is, to
what degree would the mixing misjudgements made on each loudspeaker
be correctable?
If people make different equalisation decisions at the mixing stage, then
it should be possible to reverse them at the mastering stage if the decisions were global, that is, if extra bass was added to most low frequency
instruments, or a little extra top was added. However, as was discussed in
Section 11.4, if people have been led into equalisation or level decisions
due to time response irregularities in the monitors, then those decisions
are idiosyncratic to those monitors only, and may not relate well to the
balance as heard in the mastering rooms. For the purposes of a research
paper for a conference on acoustics, an attempt was made to ‘do what the
mastering engineer would do’, by trying to equalise the response of the ten
loudspeakers represented in Figure 11.17, and to try to see what was left in
the response if they were all equalised to a common flatness3 . Figure 11.18
shows that the results after the minimum phase portions of the frequency
responses (the parts which are correctable in their phase responses as they
are corrected in their amplitude responses) were ‘normalised’ by a digital
computer. The idea behind this being that if all of the loudspeaker responses
could be equalised to be flat, then the mixes done on all of them should
subsequently be equalisable back to flat.
All of the upper traces of the ten plots shown in Figure 11.18 can be
seen to be more or less equal, but the rates of decay have not been made
uniform. Although the top line of the response of Number 3 is very similar
to the top line of Number 8, the continuing resonance of loudspeaker
Number 8 would undoubtedly lead to a more smeared, coloured, resonant
sound in the bass response, and a probable perception of more bass, all
due to time domain artefacts which have no solution in the frequency
domain (i.e. by equalisers). No matter how flat the frequency responses of
these loudspeakers can be made, the fact remains that their time response
discrepancies would still lead to different mixing decisions. So, the implication, here, is that the loudspeakers which can be equalised flat in the
frequency domain, without any significant hang-over in the time domain,
should tend to lead mixing personnel into subsequently equalisable mixes.
Judgemental errors made on loudspeakers which show resonant hangover, even after frequency response flattening, would tend to need to be
re-mixed. In other words, given non-perfect loudspeakers, the ones which
can be equalised closer to ‘perfection’ in both the time and frequency
domains will tend to lead to more correctable mixes at the mastering stage.
11.8 Modulation transfer-function and a new type of frequency
response plot
Fashions and marketing can have a huge influence on the loudspeaker
buying public. This is especially worrying when the loudspeakers will not
346 Loudspeakers
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Figure 11.18 Waterfall plots of the excess-phase responses of the loudspeaker responses
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Low frequency and transient response dilemmas 347
simply be used for the enjoyment of listening to music, but rather will be
used, supposedly, to try to mix to some reference standard. If we don’t
use some at least reasonably standard conditions for music mixing, then
what is there for a ‘high-fidelity’ domestic systems to be faithful to? In
the Concise Oxford Dictionary, ‘fidelity’ is defined as ‘strict conformity
to truth or fact; exact correspondence to the original’. But how can one
conform in the home if the original sources of references are so variable?
Taste, of course, comes in to this question, but so many of the tonal balance
difference between music recordings in the shops are due to the wide
variability of monitoring conditions. Something more revealing than the
frequency response graphs has long been needed, and the MTF concept,
introduced in Chapters 7 and 11, can be used to give much more insight
into the potential sonic accuracy of different loudspeakers.
Traditionally we have relied on the modulus of the frequency response
(commonly referred to as simply the frequency response) as the standard of
reference, but it should be clear from Figure 11.1 that even two loudspeakers with similar ‘top lines’ on the waterfall plots can hardly be expected to
sound the same if the remainder of the decaying responses are so difference. Something more was needed to define the low frequency responses,
so research was undertaken to try to adopt Speech Transmission Index
(STI) techniques to look at the ability of loudspeakers to convey the full
information content of the signals4 . The STI is a means of calculating the
voice modulation carrying the message through the general background
noise. The idea proposed for the research was to use the concept of a typical
modulation transfer function (MTF) calculation to determine how much
detail could be carried on a low frequency signal without being blurred
by resonances or distortions. To investigate this, the impulse responses of
the loudspeakers were convolved with a modulated noise signal; a pseudorandom noise with a bandwidth of about 35 to 70 Hz, modulated by a 10
Hz sine wave. The results are shown in Figure 11.19, three of which are
taken from the same group of results shown in Figure 11.16.
A sealed box exhibits a second order roll-off (12 dB/oct) below the
resonant frequency of the system. Adding a first order, high-pass electrical
protection filter yields a third order roll-off (18 dB/oct). A ported enclosure
typically shows a fourth order (24 dB/oct) roll-off below resonance, and
adding a second order protection filter results in a sixth order (36 dB/oct)
roll-off. As can be seen from Figure 11.19, as the order of roll-off increases,
the modulation depth reduces. In the cases shown, the depth varies from
about 28 dB for the simple sealed box to only about 14 dB for the sixth
order ported system. This indicates that bass detail is being lost in the
ported systems, especially the ones with the added electrical protection
filters. Nevertheless, although this shows what is happening, it still does
not provide and easily describable accuracy measure. What was needed
was a means by which to demonstrate not only the flatness of the response
but also the accuracy with which the detail in the overall signal was being
preserved.
Obviously, the modulation depth of the 20 to 30 Hz region of a loudspeaker whose response is already 40 dB down by those frequencies is
not going to play much part in the subjective assessment of the sound, so
a way had to be found to cross-correlate the modulation accuracy with
348 Loudspeakers
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depth decreases. In other words, the information content in the signal decreases
the useful response of each system. A level of 85 dB SPL was chosen as
a typical listening level, then the loudspeaker responses were convolved
with an inverse of the minimal audible field curve (MAF) from the typical
Robinson-Dadson curves for the sensitivity of human hearing – as shown
in Figure 8.4 – similar to the well-known Fletcher-Munson curves. This
yielded a compromise between response flatness and modulation accuracy.
The plots of Figure 11.20 show the resultant MTF curves for the same four
loudspeakers as in Figure 11.19. The MTF (vertical) scale is marked from
0 to 1. Zero would represent a response with no relation to the input signal, and 1 would represent perfect reproduction. The graphs are therefore
plots of reproduction accuracy versus frequency. They are not frequency
response plots; however, from them it can be seen which loudspeakers
keep the highest MTF accuracy down to the lowest frequencies, so they
are, in effect, low frequency quality response plots.
Whilst the ‘frequency response’ plots of Figure 11.14 would suggest
that the ported enclosure with the fourth order roll-off would be a much
better monitor loudspeaker than the simple sealed box shown in plot Number 2, the plots of Figure 11.20 show that the small sealed box maintains
Low frequency and transient response dilemmas 349
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Figure 11.20 MTF results for the four example loudspeakers at a level of 85 dB SPL and
incorporating compensation for minimum audible field (MAF)
a response accuracy, in terms of detail in the sound, down to a lower
frequency than the fourth order ported box. In these plots, the total area
below the curve is effectively a measure of response quality, whereas in
Figure 11.14, the area below the curve only represents level; irrespective
of whether that level is of anything connected with the music, or not, as
shown by the extraneous resonant frequencies in Figure 11.15, which only
serve to swamp the detail in the musical signal.
Of course, for anybody buying a loudspeaker from the advertising
brochures, the response of the ported fourth order enclosure in Figure 11.14
would seem to greatly improve upon the response of the simple sealed
box in the same figure. Even typical in-room response measurements on
a spectrum analyser would tend to support that case, yet the results in
Figure 11.20 would tell a rather different story, with the accuracy of reproduction, (looked at from a broader perspective than simply the sound
pressure level) favouring the simple sealed box. The sixth order ported
cabinet, which shows an almost similarly extended ‘frequency response’
in Figure 11.14, comes off much worse in Figure 11.20, suggesting that it
produced ‘artificial’ bass, which would not be consistent with the concept
of accurate reproduction.
This system of low frequency response assessment is the subject of
continuing research. The whole point of the exercise is to try to define
which loudspeakers are monitoring the musical signals which are being
delivered to them, and which ones are ‘inventing’ their output. As previously stated, a ‘truthful’ loudspeaker, even if it is short on overall bass
level, will tend to give rise to mixes which can be corrected at the mastering
stage, or even by the tone controls on domestic hi-fi systems. Conversely,
350 Loudspeakers
a loudspeaker which shows a poor MTF response, no matter how flat its
‘frequency response’ may appear, may well give rise to mixes which are
the results of deceptions in the time domain, or the ‘smudging’ of the fine
detail in the sounds being reproduced. Such loudspeakers are likely to
give rise to mixes which are not correctable by means of equalisation in
the later stages of production, and lost detail is something that simply will
not be heard. Obviously, no judgements can be made about things which
can not be heard, and so artistic opportunities may be lost. Loudspeakers
with poor MTFs are scrambling the message, whereas a loudspeaker with
a good MTF but a low-frequency roll-off is simply reducing the level of
the message at those frequencies, hence the possibility of a correction by
subsequent low frequency equalisation of the mix.
11.9 Summing-up
In this chapter it has been demonstrated how the fundamental principles
of electro-acoustics dictate that loudspeaker cabinets and low frequency
drive units need to be large if extended low frequency responses are to be
achieved with good system sensitivity and low distortion. It is possible to
trade size for sensitivity, low-frequency extension for transient accuracy,
or sensitivity for low frequency extension, but it is not possible to simultaneously maximise the performance in terms of low frequency extension,
low distortion, high system sensitivity and fast transient response except
in large boxes. Furthermore, it has also been shown how fine detail in
the sound may be lost when resonant systems are used to extend the low
frequency responses or protect drivers from over-excursion.
Also, in general, loudspeakers with lower order low-frequency roll-offs
tend to offer more precise transient accuracy than higher order designs.
In terms of response accuracy it is always beneficial to extend the low
frequency response as far as possible, but whilst minimising the ultimate
slope of roll-off. If this can only be done at suitable listening levels from
small cabinets by means of employing resonant cabinets, it means that
they can never achieve the overall low frequency response accuracy of
well-designed large cabinets, because only large cabinets can exhibit low
order roll-offs and high SPLs at very low frequencies. Furthermore, it has
been shown that mixes which have been carried out using loudspeakers
with low-order roll-offs and high SPLs are more readily equalisable at a
later date if the overall frequency response is deemed to be inappropriate
for the music. Conversely, bass drum/bass guitar balances deemed to be
incorrect after having been mixed on resonant loudspeaker systems show
a tendency towards being less correctable due to simultaneous time and
frequency domain errors.
Well-designed larger loudspeaker boxes will win on almost all aspects of
reproduction, which is why the more reputable mastering engineers tend to
avoid relying on small loudspeakers when an accurate, overall assessment
of a recording is required.
Always remember the incontrovertible truth: size is important!
Low frequency and transient response dilemmas 351
References
1 Newell, P. R., Holland, K. R., Newell, J. P., ‘The Yamaha NS10M: Twenty Years
a Reference Monitor. Why?’ Proceedings of the Institute of Acoustics, Vol 23,
Part 8, pp 29–40; Reproduced Sound 17, Stratford- upon-Avon, UK (2001)
2 Newell, P. R., Holland, K. R., Mapp, P., ‘The Perception of the Reception of a
Deception’, Proceedings of the Institute of Acoustics, Vol 24, Part 8, Reproduced
Sound 18, Stratford- upon-Avon, UK (2002)
3 Holland, K. R., Newell, P. R., Mapp, P., ‘Steady State and Transient Loudspeaker
Frequency Responses’. Proceedings of the Institute of Acoustics, Vol 25, Part 8,
Reproduced Sound 19, Oxford, UK (2003)
4 Holland, K. R., Newell, P. R., Mapp, P., ‘Modulation Transfer Functions - a
Measure of Loudspeaker Performance’. Proceedings of the Institute of Acoustics,
Vol 26, Part 8, pp 107–115; Reproduced Sound 20, Oxford UK, (2004)
Copies of the above papers can be obtained from the Institute of Acoustics,
(UK), Tel. +44 1727 848195, Fax, +44 1727 850553 or email [email protected]
The full set of response plots can also be obtained from Reflexion Arts, S.L.,
Tel. +34 986 481155, Fax +34 986 413412, or by e-mail, [email protected]
Chapter 12
The challenges of surround sound
The choice of loudspeakers for use with surround-sound systems is never
easy. One problem is that the concept of surround means so many different things to so many different people. Except for professional cinema
applications, where Dolby and THX, along with a few other companies,
have laid down strict guidelines, the rest of the world of surround exists in
near chaos. Even in professional, industry magazines, recording engineers
and producers, who ought to know better, can be seen promoting the idea
that there are no rules, so everybody should do it in their own way. Well;
if there are no rules in the studios, then where are the references for the
domestic reproduction systems to comply with?
The majority of this confusion stems from the fact that modern, musiconly surround sound was never conceived and controlled purely by the
music business, but has developed as an adjunct to other surround technologies which have developed for their own purposes, and which were
never primarily intended to be capable of audiophile quality music reproduction. Exactly how best to deal with the subject of the recording and
reproduction of music in surround is something which is still very controversial; even in professional circles.
In domestic applications, we have to accept that in the majority of
cases one loudspeaker arrangement will be used for home cinema and
the reproduction of music-only SACDs and DVDs in surround. This is a
very unsatisfactory situation, but it would be totally unrealistic to expect
people to have ten or more loudspeakers in their lounges. Firstly, therefore,
it may be beneficial to look at the reasons for the undesirability of the
above circumstances by looking at a range of professional surround mixing
circumstances. This will also establish a more global understanding before
embarking on a more detailed discussion of the requirements of each
individual loudspeaker.
12.1 Surround sound in professional studios
Surround sound, in the guise of quadrophonics, first came to prominence
in the early 1970s. The concept of the use of close-field monitors had not
yet become widespread, so the first quadrophonic control rooms tended
to consist of the two front halves of the then normal stereo control rooms
placed face to face. A 1970s-style quadrophonic room is shown in Figure 12.1.
There was some pressure at the time to spell the word quadraphonic, with an
‘a’, which was said to be more etymologically correct, but the compatibility
The challenges of surround sound 353
X
Window or door
system
Typical plan view
absorbent bass traps strategically
located to try to confound the
build up of the most problematic
modes
‘trap’ entrances
Absorbent rear
‘trap’
Y
.
A 1979s studio built according to the above principles
Vertical cut through X-Y
Figure 12.1 A quadrophonic control room from the 1970s
In effect, the room consists of the two front walls of a stereo room placed face to face. Note
that the front loudspeakers are flush-mounted, above the windows, but the rear loudspeakers
are mounted above the soffits of the machine alcoves – another source of asymmetry
with stereophonic and monophonic led to a tendency to use the ‘o’ spelling.
However, when The Who released their famous film Quadrophenia, that
seemed to kill off the ‘a’ spelling. It was in such uncertain conditions
and the battles of the format wars that quadrophonics sprung into life.
In those days, quite frankly, the sound in most cinemas was bad. Dolby,
to their great credit, began to specify that cinemas which used the Dolby
processed soundtracks should comply to certain standards. Dolby understood the limitations of the phase-matrixed quadrophonic music systems,
(which were not convincing the record-buying public to purchase many
quadrophonic music systems) but they saw the possibilities of stabilising
the centre-front image in cinema presentations by using one of the four
quadrophonic channels in the centre-front position, effectively making a
three-channel frontal stereo sound-stage. The remaining channel they fed
to multiple rear and side loudspeakers, all supplied with the same signal,
to give the effect of a distributed source of ambiental sound. This was
the Dolby Stereo system. The quadrophonic and Dolby Stereo layouts are
354 Loudspeakers
30°
30°
90°
90°
90°
90°
Mono Surround
Basic Quadrophonics
Dolby Stereo 4.0
(Pro-Logic)
Figure 12.2 Comparison of quadrophonic and Dolby Stereo formats, both using four channel
matrix-encoded signals
shown in Figure 12.2. Both systems used phase-matrixed analogue recordings, which exhibited very poor separation between channels, and ‘logic’
enhancement systems were usually employed to improve the inter-channel
discrimination. (Some vinyl disc systems used high frequency carriers, for
the rear channels, instead of phase matrixing, but they were fraught with
problems.) The quadrophonic music systems of the 1970s used four identical loudspeakers, but the Dolby Stereo system required large loudspeakers
of controlled directivity behind the screen, and multiple, small, restricted
bandwidth, wide-dispersion loudspeakers for the surround channel, to maximise the audience coverage and the sense of spaciousness. Therefore, at
this very first bifurcation, the loudspeaker requirements for four channel
surround had already changed.
Around this time, still in the mid 1970s, Tomlinson Holman proposed,
for domestic playback, the use of dipole (figure of 8) loudspeakers for
the surround channels1 . Even at this very early stage, many people were
beginning to realise that the 360 degree distribution of primary instruments
was not suitable for a great deal of music, and that the rear channels were
often better employed for ambience. The use of dipoles in this position,
as shown in Figure 12.3, with their nulls facing the listeners, ensured that
sub
5 channel surround
using dipole surrounds
Figure 12.3 Dipole surround loudspeakers
The challenges of surround sound 355
only the sound that reflected from the walls would be heard, thus creating
a well diffused ambient surround field.
Figure 12.4 shows a reasonably similar idea, proposed by Fosgate2 , but
using bipolar loudspeakers instead of the dipoles proposed by Holman.
Again, the loudspeakers are generally facing away from the listener, and
in the drawing each side of the surround uses 3 drivers – a pair in the
side cabinets and one in the rear cabinet. There was also in the proposal
a means of creating four channels from the rear pair, in order to further
diffuse the ambience. In the above configuration there are no true nulls, as
there are in Figure 12.3, but only the low frequencies will radiate directly
to the listener. The middle and high frequencies will tend to be received
via reflexions only.
Another attempt at providing a diffuse side/rear surround field is shown
in Figure 12.5. This method has been used in small film dubbing and video
post-production studios3 . In this case the conventional box loudspeakers
are mounted so as to face mathematically derived diffuser panels which
are fixed to the walls. Once again the low frequencies will radiate omnidirectionally, but the middle and high frequencies can only arrive at the listening position via the diffusers. A variation on this theme, using naturally
diffuse sources, is shown in Figure 12.6. This system uses distributed mode
loudspeakers as single surround sources on each side wall 4 . Figures 12.1
to 12.6 clearly show how professional and domestic systems have both
developed around concepts which have used some very different types of
left
side
right
side
le
ft
re
ar
r
ea
tr
h
rig
Figure 12.4 Bipolar surround, proposed by Fosgate, using processors to decode seven channels
processed from five
Figure 12.5 A five-channel format using wall-mounted diffusers to disperse the sound from
the conventional rear loudspeakers. (After David Bell)
356 Loudspeakers
sub
Figure 12.6 Diffuse surround sources – NXT DML panels
loudspeakers to try to create the desired illusion. Unfortunately, with so
many concepts in use – and we have barely begun discussing them – it
should already be apparent that compatibility problems are to be expected
between the mixing and domestic playback environments.
In cinemas, the environments are usually well controlled, in order to conform to standards which ensure reasonable commonality with the dubbing
theatres – the studios in which the film soundtracks are mixed. Although
this book is not intended to be about cinema and video systems, it is necessary to look at them here so that their influence on the development
of domestic entertainment systems can be better understood. For many
people, since the beginning of the 21st century, the playback of music
recordings in the home has only been via their home theatre systems,
which are primarily geared to the reproductions of film and video soundtracks, but it must be clearly established that there is no single type of
loudspeaker which can serve for all purposes. The monopoles, dipoles and
bipoles represented in Figures 12.2, 12.3 and 12.4 are fundamentally different radiating sources, as are the diffuse sources shown in Figures 12.5
and 12.6, and the T.V./video style systems shown in Figure 12.7. There is
no possibility of these diverse sources producing identical sounds. Consequently, if music is not mixed on systems of the same general concept as
the reproduction systems, then the reproduction cannot be anything other
than compromised. The resulting sound may be pleasing, and may even be
desirable, but it will not be ‘high-fidelity’ in the sense that a good domestic
stereo system, well positioned in an appropriate room, will be expected to
radiate a sound which is very close in its balance and timbre to that which
120°
– 60°
R Surround
120°
– 60°
L Surround
30° 30°
HDTV study group-Japan
Single or multiple surround sources
5 Channel 3-2
A home cinema format
Figure 12.7 Incompatible domestic formats
The challenges of surround sound 357
was being heard by the recording personnel at the time of mixing. With
surround sound, the variables are so many that the degree of fidelity which
we have come to expect in stereo is rarely achievable.
12.2 Cinema sound
Feature films, in general, are mixed specially for the big screen, where
there is an important psychological correlation between picture size and the
appropriate sound pressure level. Figure 12.8 shows a behind-the-screen
installation of a mixing room (dubbing theatre) equipment for either 5.1,
6.1 (Dolby EX, with left, centre and right surround channels) or 7.1, the
Sony Dynamic Digital Sound (SDDS) system. The surround loudspeakers
are 12 JBL 8340A cabinets, specially designed for use as cinema surround
loudspeakers. A smaller 5.1 room, using JBL behind-screen loudspeakers is
shown in Figure 12.9. Rooms such as these are used for the final mix, usually
Figure 12.8 A cinema studio monitor wall for Sony SDDS 7.1 surround
Figure 12.9 Auditel ‘Audi A’, in Paris, France, using a JBL cinema system
358 Loudspeakers
Figure 12.10 The ‘Kyoto’ control room at Eurosonic, Madrid, Spain, designed by
Sam Toyashima. The room is used for mixing stems for film soundtracks. The surround
loudspeakers are pedestal mounted at the sides and rear of the room. The large, right-front
monitor is the black rectangle at the left of the photograph. The console-mounted loudspeakers are for stereo television mixing
from ‘stems’ (or pre-mixes) of music, dialogue and effects. In many cases,
however, the music is mixed in smaller rooms without screens. Such a room
is shown in Figure 12.10. This room has a large, Quested frontal monitor
system in a room designed by Sam Toyashima. The surround loudspeakers
are pairs of smaller Genelec monitors, on pedestals, in an L-shaped, side
and rear configuration. The monitor system is essentially flat, with a small
high frequency roll-off in typical music recording studio style.
Once the music stems go to the dubbing theatres to be mixed with the
dialogue and effects, the surround/front balance will be readjusted to the
cinema environment. What is more, the overall sound will be re-equalised,
because after the perforated projection screen has been placed in front of
the loudspeakers, the response at the mixing positions is adjusted to the
‘X-curve’, as shown in Figure 12.11. Mixing will normally take place with
peak levels reaching 105 dBC or more at the listening position. A picture
of a life-sized tank, firing a shell with a ‘bang’ at 85 dBC would simply not
sound credible, so large sounds go with large screens. Bearing in mind that
when played in the home on a small screen, even 85 dBC may be considered to be too loud for the neighbours, a quick glance at the equal loudness
curves shown in Figure 8.4 will reveal that the perception at 80 dB and 100
dB is quite different. Film protocol demands that the mix be done at the
same level as the cinema presentations, so that the perception of relative
frequency balance can be accurately assessed, unlike the music mixing process, where no such control exists. For home cinema release, the soundtrack
may have to be re-equalised, not only because of the lower probable level
of reproduction, but also because many home systems do not reproduce
with an X-curve equalisation. (For more on the X-curve see the Glossary).
A typical domestic playback system is shown diagrammatically in
Figure 12.12, conforming to the ITU775 recommendation. When a film
is played back on such a system, using loudspeakers of typical domestic
The challenges of surround sound 359
dB relative response
a)
+10
0
–10
2
3 4 5 678910 1.5 2
3 4 5 678910 1.5 2
100
1,000
3 4 5 678910 1.5 2
10,000
Frequency (Hz)
2
0
–2
–4
–6
–8
–10
–12
40
50
63
80
100
125
160
200
250
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000
5000
6300
8000
10000
12500
16500
1/3-octave-band electroacoustic frequency response, dB
b)
Figure 12.11 The X-curve. a) ISO Bulletin 2969 – recommended response curve for motion
picture loudspeaker systems. b) The X-curve for cinema monitoring, to be measured spacially
averaged in the far-field of the sound system with quasi-steady state pink noise and lowdiffraction (small) measuring microphones. The room volume must be at least 200 m3 (6000
cubic feet). The curve is additionally adjusted for various room volumes, as per SMPTE 202
ITU.R 3/2
30°
110°
+/–10°
30°
110°
+/–10°
Allows for 100°–120° rear
loudspeaker angles
Figure 12.12 ITU.R 775, 3/2
360 Loudspeakers
nature, the overall perception is bound to change because the type and
distribution of the loudspeakers are different to those on which most films
are mixed. Very little source material is therefore specifically mixed for
reproduction on home theatre systems. In audio-visual presentations, the
changes in the perception of the soundtracks tends to be compensated for
by the strong domination of the eyes over the ears. The small screen also
tends to require less low frequencies in the sound. However, when we
listen to music-only mixes, there are no such distractions, and the lack of
fidelity can be conspicuous.
12.3 Music mixing
Unlike in the cinema world, no standard mixing conditions have ever been
enforced for music mixing, and recommendations have been ignored in
the majority of instances or, at best, have only been respected in certain aspects. There has been a free-for-all which has continued unchecked
largely because the domestic surround sound systems have been predominantly cinema/video orientated, and music mixes have been accepted in
a compromised form by people who were unwilling to accept a separate,
music-only system at home. The lack of any clear domestic trends of high
fidelity music orientated surround systems has not encouraged recording
studio owners to invest in specialised surround-sound mixing facilities, so
the studios, themselves, are therefore tending not to give any clear leads.
In many cases there have been few clear-cut decisions about whether music
should be mixed four-channel, five-channel, or five-channel plus a discrete
low frequency channel. (5.1 as it was dubbed by Tom Holman.) The argument for four channels has been put forward by many people who have
felt that the centre-front channel is compromised in many 5.1 domestic
systems, because of the conflict between the loudspeaker and the video
screen vying for the same spot. Considering the fact that the centre-front in
music mixes is the location for many lead vocals and primary instruments,
the risk of compromising it has led many music mixers to continue to make
phantom centres from the front left and right channels to avoid the risk of
the mix being ruined by playback through systems with inadequate centre
channels. In most cases, the front left and front right loudspeaker will,
indeed, be the best loudspeakers in any set up.
Another body of opinion has been avoiding mixing vocals in the centre channel because of the equalisation changes which are noticed if the
recording is ‘folded down’ to four or two channels due to the asymmetrical or symmetrical reception by the ears of a phantom centre or discrete
centre image respectively. The problem is shown in Figure 12.13, from
which it can be seen how the signals arriving from 30 degrees either side
of centre front suffer a path length difference of about 10 cm between the
nearest and furthest ear from each loudspeaker. As discussed in Chapter 5,
arrival delays between two drivers will give rise to a cancellation at the
ear around the frequencies which arrive in the region of 180 degrees out
of phase. Conversely, the sound from one loudspeaker will suffer the same
cancellation effects if the ears are displaced so that the arrival of the wavefront is not simultaneous at the two ears. Consequently, a phantom centre
The challenges of surround sound 361
central, mono
source
left loudspeaker
of a stereo pair
equal path length
to each ear,
therefore no
cancellations
will occur
path length to right ear
is considerably longer
than to the left ear:
of such a degree that
a cancellation will result
around 2 kHz. The
signal from the right
loudspeaker cannot
help to fill in the response
dip, as it suffers from
the same problem,
only in reverse
head of listener
Figure 12.13 Path length anomalies for phantom central images
image will suffer from some cancellation in the region of around 2 kHz.
When making decisions about equalisation of the phantom centre-front
instruments or voices, this dip is automatically taken into account. When
listening to the same sounds through a discrete centre-front channel, no
such arrival delay dip occurs, so, for any given sound, the equalisation decisions would be different when mixing with a discrete or a phantom centre.
This has led some people to complain that the sounds which they are accustomed to recording and monitoring via a stereo pair of loudspeakers sound
too present when monitored through a discrete, centre-front loudspeaker.
They therefore opt to use phantom centre-front images in order to try to
maintain better equalisation compatibility when the surround mixes are
heard in normal, two-channel stereo.
The other big dilemma is often whether to mix to 5 or 5.1 channels –
that is, with or without the sub-woofer as a dedicated channel. In reality,
the sub-woofer channel has little to do with music mixing. The .1 was a
cinema invention to provide extra headroom for low frequency effects,
such as during explosions. In music, there is really no equivalent function,
so five-channel mixing tends to be the norm. When listening to a ‘pseudo
5.1’ system which is really a five-channel system with a bass management
system feeding a common sub-woofer, there will be perceptual differences
as compared to listening on five full-range loudspeakers, due both to the
mono low-bass and to the arrival time anomalies that will be experienced
in all but the very centre of the array. The perception will also be likely to
change significantly with changes in the frequency below which the content
of the five channels was filtered and sent to the sub-woofer. There is no
standard frequency of cross-over into sub-woofer(s).
362 Loudspeakers
12.4 Sub-woofers – discrete and managed
To get the best out of any sub-woofer, the cabinet needs to be large.
The sub-woofers shown in Figure 12.8 are real sub-woofers, designed to
outperform even the 600 litre cabinets of the five main loudspeaker systems, which easily reach down to 20 Hz themselves. With ten 15 inch
loudspeakers in the five 600 litre cabinets, and with reflex ports tuned
to 20 Hz, the low-frequency output of this main system, alone, is quite
prodigious. Each of the sub-woofers visible in the photograph consists of a
McCauley 6174, eighteen inch driver (460 mm), with a free-air resonance
of 20 Hz and a sensitivity of 94 dB for one watt (2.83V) at one metre. The
frequency range is quoted by the manufacturers as 15 Hz to 800 Hz and the
rated power capacity is 800 watts. The boxes are also of 600 litre capacity,
with one driver in each box, and are reflex tuned to 16 Hz. They are constructed from a sandwich of 2 layers of 19 mm chipboard with a 5 kg/m2
plasticised bituminous deadsheet in-between, and lined with a sandwich
of 20 mm felt/3.5 kg deadsheet/20 mm felt. The boxes are also internally
braced in all three axes, and are surrounded by 10 cm of concrete. The
40 mm-long voice coil allows a cone travel in any one direction of 15 mm
under a constant force factor (Bl), and a 25 mm unidirectional travel with
reduced Bl before mechanical limitations arise. The total cone excursion
can therefore reach 50 mm (2 inches) peak to peak. Each drive unit weighs
over 16 kg, and the ferrite magnet alone, of 13000 gauss, weighs almost
12 kg, and has a Bl factor of 15.3 tesla.
This system is being explained in detail because it is a professional
sub-woofer, intended to deliver high quality sound at cinema levels, day
after day, year after year. The response decay is rapid and uniform in
the frequency bandwidth of use. The loudspeakers have no characteristic
‘boom’ to their sound. Their positioning at the junction of the front wall and
the floor effectively mounts them in quarter space (or space) as explained
in Chapter 7. This effectively raises the sensitivity by 6 dB compared to the
quoted 94 dB in free space. The use of two drivers, side by side, increases
the loading on the cones still further, and the mutual coupling so achieved
adds another 3 dB to the low frequency sensitivity, yielding 103 dB for
1 watt at 1 metre for the pair of cabinets. Structural losses are kept low
by making both the floor and monitor wall out of thick concrete. The
listening distance in this room is about 8 metres, so the ‘double distance
rule’ (stating that the SPL falls by 6 dB every time the distance from the
source is doubled, [see Chapter 7]) would mean that 103 dB at 1 metre
would fall by 18 dB at 8 metres, to 85 dB. Each multiplication of the power
by 10 adds 10 dB to the SPL, so 1000 watts (10 × 10 × 10) would deliver
30 dB more than the 85 dB for 1 watt. The maximum peak short-term SPL
to be expected on rare occasions in cinema would not exceed 115 dBC,
so the 1600 watts rms rating of the pair of loudspeakers (or 3200 watts
for 10 milliseconds) gives the system adequate damage tolerance. At all
normal cinema levels, the loudspeakers are working well within their low
distortion range, and, as high level peaks are always short-lived, thermal
compression is not a factor. The amplifiers driving the sub-woofers are
Class AG, made by Neva Audio in St Petersburg, Russia, and can deliver
2000 watts into 8 ohms. The above description outlines the lengths that one
The challenges of surround sound 363
needs to go to outperform the low frequency response of a good, medium
to large sized studio monitor system.
Purely in terms of high fidelity, when mixing music in surround on a
monitor system using five, full-range loudspeakers, it is best to use their
own low frequency capability rather than a separate sub-woofer, because
the five discrete sources can give better spacial perception, a seamless
response because no low frequency crossover is involved, a tighter and
better spacially distributed transient response, and an overall low frequency
sound quality that outperforms the majority of commercial sub-woofers.
In fact, in many studios which are used to mix music stems for cinema, and
where some low frequencies may be mixed to a separate sub-bass (Low
Frequency Effects [.1]) channel, the low frequency feed is often distributed
across the flush-mounted front loudspeakers, instead of feeding a discrete
sub-woofer of commercial design, precisely because the LF response of the
main system is likely to be better than that of a commercial sub-woofer.
However, as will be discussed later, there are other concerns which may
lead to other decisions about the best option for mixing formats.
There can also be some confusion caused by the different meanings of
LFE as have been applied to sub-woofer use. In the Dolby Digital (Dolby
Surround) language, LFE stands for the Low Frequency Effects channel
that is the discrete (.1) channel of low bandwidth, used in addition to
the 5 main channels. Conversely on many music monitoring systems, the
LFE is the Low Frequency Extension provided by the sub-woofer, whose
feed is derived from a bass management system which re-directs to the
sub-woofer the low frequency content of the five principal channels, below
the frequency where the five main loudspeakers begin to roll-off in their
frequency response. The two concepts are very different. In the former
case, the five main channels are full range, and the LFE channel may at
times operate up to 500 or 1000 Hz, although normally the upper limit
is more likely to be around 120 Hz. In the latter case, the sub-woofer
should ideally only operate below 80 Hz, or the low frequencies will be
localised by the ear to the position of the sub-woofer. A further concept
of Low Frequency Enhancement also exists, in the form of an optionally
reproducible low frequency effects channel for digital television, but whose
content is not essential to the overall programme. We therefore have LFE
standing variously for Low Frequency Effects Extension, or Enhancement.
There is little or no commonality between the three concepts, and some
implementations are optional. So much for standardisation.
Dolby now recommend a sub-woofer distribution for cinema use as
shown in Figure 12.14, with one woofer placed 33% of the distance from
one side wall, and the other woofer placed 20% of the distance from the
other side wall. This gives rise to a more or less central image, without
either risking the localisation of the effects channel to one side of the
cinema or symmetrically driving the room modes from a central location.
However, in home use, one single sub-woofer is normally used whose
frequency response is limited by a crossover, the frequency of which is
determined by the low frequency response of the five main loudspeakers. Somewhat absurdly, this can be as high as 400 Hz when used with
mini-satellite loudspeakers. In such cases, localisation of many low frequency sounds to the ‘sub’-woofer in inevitable. For discerning listeners,
364 Loudspeakers
×
80%d
33 1/3%d
×
20%d
66 2/3%d
ROOM WIDTH (d)
Figure 12.14 Sub-woofer siting for cinema installations
Dolby recommendations for siting two sub-woofers; one of them one fifth of the room
width from one side wall, the other one third of the room width from the other side wall. This
not only avoids both the localisation of the sound to a single sub-woofer placed off-centre,
but also avoids the symmetrical driving of the strongest room modes by the central placement
of the sub-woofer(s)
the crossover to a sub-woofer must be kept below 80 Hz, and lower if
possible, or spacial information will be lost and localisation of sound to
the sub-woofer will occur. [However, see Section 12.6.]
Obviously, when we listen to five discrete channels we localise sounds at
their sources, but a system with a bass management system will re-distribute
the low frequencies, sometimes with odd consequences. For example, a synthesizer located in the left rear loudspeaker may sound strange if its output
above 200 Hz comes from the left rear and the output below 200 Hz comes
from the front-located sub-woofer. Again, this may in many cases sound
acceptable, but it is not high fidelity inasmuch as this was probably not what
the music producer intended. However, some mixes are actually carried out
with bass management systems because some mixing personnel feel that this
is more typical of how the majority of people will listen at home. This is
a market-led approach, rather than a high fidelity approach, but there will
be justification for this idea in Section 12.6, on grounds of sheer practicability.
12.5 Size versus performance compromises
The low frequency decay of a good studio loudspeaker system is shown
in Figure 12.15. The response extends quite low, and the decay is fast
and uniform with frequency. In general, such a response is only possible
with relatively large boxes, but compactness has been a very desirable
characteristic of loudspeakers for surround systems, because the domestic
practicality or social desirability of placing five or six large cabinets in
a dwelling space is not good. Even in professional studios, the lack of
universally accepted surround formats for music mixing has made owners
reluctant to invest heavily in surround control rooms. For this reason, many
stereo rooms have been adapted for surround use by the installation of
free-standing systems. Again, for reasons of practicality in rooms already
containing much other equipment, many studios have opted to use rather
small loudspeakers.
The challenges of surround sound 365
10
0
–10
dB
–20
–30
200
400 ms
600
20
100
1000
Frequency (Hz)
Figure 12.15 Responds decay of a full-range loudspeaker in an acoustically well-controlled
room
A single sub-woofer must handle the low frequencies from five channels,
and so needs to have the same acoustic output capability as that of all five
principal loudspeakers connected in phase and receiving the same signal.
By its very nature, a sub-woofer is required to have an extended low frequency
response, but to achieve this in a small box with the sensitivity necessary in
order not to burn up with the sheer electrical input power needed to handle the combined output of five channels is, as we saw in Chapter 11, a
great conflict of requirements. The sensitivity problem has been addressed
by some manufacturers by the use of bandpass cabinets and horn loaded
cabinets, but each only addresses part of the overall response shortfall.
The bandpass concept was described in Chapter 3. These systems tend
to exhibit multiple resonances, as it is the resonant effects that help to augment the sensitivity and flatten the pressure amplitude response over the
desired band. The response of one such cabinet is shown in Figure 12.16. The
waterfall plot shows a flat response for just over an octave, but the decay
shows a degree of resonance that would not be conducive to tight, highimpact bass sounds. The step function response in the same figure shows
just how slow the attack is. The response actually builds up with time,
rather than immediately starting to decay. Neither the attack nor the decay
could really be deemed to be concordant with the concept of high fidelity.
Figure 12.17 shows the response of a horn-loaded cabinet intended
for use as a sub-woofer. Typical of the high acoustic loading presented
to the diaphragm by the horn, the time response is characterised by a
fast attack, as shown in the step function plot, and a fast decay which
is clearly observable in the waterfall plot. Unfortunately, the bass extension is rather poor because the horn mouth needs to be proportionate
to the wavelength in order to couple the horn to the room, as explained
in Chapter 4. Once again, when size is kept small, we have a trade
off between bass extension and a clean transient response. Therefore, a
small, high-fidelity, high sensitivity sub-woofer is a contradiction in terms.
366 Loudspeakers
10
0
–10
dB
–20
–30
100
200 ms
300
1000
100
20
Frequency (Hz)
Amplitude
1
0.5
0
–0.5
–1
0
5
10
15
20
Time (ms)
Figure 12.16 Waterfall plot and step-function plot of a typical bandpass sub-woofer in an
anechoic chamber
‘Woofer’, perhaps, but sub-woofer only if a low fidelity transient response
can be tolerated. A horn-loaded loudspeaker which is a true sub-woofer
is shown in Figure 12.18, but small it is not. Nevertheless, in some cases,
the corner placement of a horn-loaded sub-woofer may go some way to
extending the low-frequency output, but it will exite all the possible room
modes, and hence may provoke severe room resonances. This would, of
course, defeat the object of using the loudspeaker with the better transient
response.
The need for small size in order to be marketable has led to an emphasis on the multichannel spacial sensations, and relatively little has been
openly discussed about the ways in which many loudspeaker performances
have dropped vis-à-vis older loudspeakers intended for stereo. There is a
tendency for surround to compromise absolute fidelity for the extra sensation of space, but the excitement of the spaciousness can be short lived
once the absolute fidelity loss is recognised. Loudspeaker manufacturers
are obviously going to make what they can sell, and if super hi-fi surround
systems appeal to only a very small market, then the bigger market will
be primarily catered for. There has been a general recognition that the
The challenges of surround sound 367
10
0
–10
dB
–20
–30
100
200 ms
300
20
100
1000
Frequency (Hz)
Amplitude
1
0.5
0
–0.5
–1
0
5
10
15
20
Time (ms)
Figure 12.17 Waterfall plot and step-function plot of a horn-loaded sub-woofer in an anechoic
chamber
Figure 12.18 A concrete horn, under the stage, loads a cabinet with four 18 inch (450 mm)
low frequency drivers. The response is essentially flat down to 20 Hz, and 120 dBC on the
dance-floor is achieved with ease and reliability. The mouth size is 4 m × 1 m
368 Loudspeakers
vast majority of domestic users will use ‘satellite and sub-woofer’ systems,
and much effort has gone into finding means by which the low frequency
cabinets can be positioned and controlled in order to get a real improvement in the LF response, even beyond that which could be expected from
good stereo loudspeakers in the same rooms. This concept will be further
explored in the next section.
12.6 Compound sub-woofers and electronic control
Whilst no electronic signal processing system can be expected to
outperform the excellent acoustic treatment of rooms, it is entirely justifiable to recognise that good rooms are expensive and rare. For this reason,
some loudspeaker manufacturers have seen a real need for a means of
deriving a decent low frequency performance in acoustically poor rooms,
and the use of separate (sub-) woofers can be a real advantage in such
circumstances as exist in many domestic listening rooms. Toole gave a
good overview of the situation in his 2003 paper, ‘Art and Science in the
Control Room’5 . He made the observation that below about 100 Hz, room
resonances can be controlled electro-acoustically, although response dips
cannot be equalised. Between about 100 Hz and 300 Hz, mounting geometry, adjacent boundaries, and strong solitary reflexions can cause problems
that defy simple electronic cures, and most probably need to be dealt with
acoustically. Above 300 Hz, the loudspeaker dominates, so there is no
substitute for using good, well-mounted drivers here.
Below 100 Hz, in small rooms, such as many sound control rooms and
domestic listening rooms, the number of resonant modes will be few, and
mostly well separated. This gives rise to great spacial variation and amplitude response variation. A listener seated at an antinode of a resonance will
hear a greatly augmented response, whereas at a node the response would
be diminished, perhaps almost to the point of cancellation. The perceived
frequency response of a loudspeaker driving the room from a boundary
would therefore be dependent upon the listening/receiving position. Conversely, a loudspeaker placed at a node of a resonance would be incapable
of driving the mode at that frequency, whereas when placed at an antinode
it would strongly drive the resonance. Hence, any given loudspeaker in
any given room being measured or listened to at any given point in the
room would exhibit a low-frequency response which was entirely position
dependent, and likely to vary wildly from place to place unless the room
was heavily damped, i.e. acoustically dead.
Back in the days of mono recording it was customary to find a
loudspeaker position which drove a room in the most uniform manner
achievable, and then find a listening position with the flattest overall
response. Stereo complicated matters, because the relationship between
the driving and the listening positions was fixed by the ideal equilateral
triangle which needed to be maintained between the two loudspeakers
and the listener(s). Finding three relatively flat positions was much more
difficult than finding just two, especially when the three needed to maintain the equilateral triangle geometry. The extra degree of difficulty led to
the development of highly specialised design concepts for stereo control
The challenges of surround sound 369
and listening rooms, some examples of which are shown in Figure 12.19.
All of the rooms shown are asymmetrical from front to back: the end
that generates the sound is in all cases acoustically different from the
end which receives the sound. This works fine for stereo, but for multichannel surround sound, where the rear channels may carry significant
programme information, and not just ambience, this approach will not
suffice. Dr Toole argues that in anything but very highly damped rooms
with enormous bass absorption systems, the ability to obtain a flat lowfrequency response from five full-range loudspeakers is beyond us. In
fact, the authors of this book came to a similar conclusion in a 2004
conference paper, when discussing the concept of how to make a symmetrical room for surround sound with individual loudspeaker responses as
good as can be achieved in a stereo room, especially with flush-mounted
monitors6 .
Toole is convinced that the five full-range loudspeaker option, when
used below 80 to 100 Hz, can only lead to appalling bass responses in
anything other than anechoic chambers, especially when one considers all
the possibilities of the combinations of loudspeakers which may be radiating simultaneously whilst supporting some of the many possible phantom sound stages. He maintains that the bass summation is not only a
cost-saving measure, but is a superior way to reproduce bass in non-ideal
rooms.
Given this concept of mono bass below 80 Hz, a technique for achieving a
flat, in-room response already exists, with the use of a combination of four
distributed sub-woofers whose responses are modified by signal processing
and parametric equalisation, both in the form of individual equalisation and
global equalisation. This can bring an overall loudspeaker/room response
to within about 3 dB of flat over a wide listening area. Moreover, the fact
that room modal responses, as opposed to reflexions, are of a minimum
phase nature, this amplitude correction will also tend to correct the phase,
and hence the time response. Toole has been most insistent that this is
the only practical solution for domestic surround sound listening, and, as
such, it only makes sense to monitor the same way in the studio control
rooms, because almost nobody will hear the mixes reproduced in a totally
discrete way. On the other hand, Holman7 has argued that stereo subwoofers can be essential in order to create a greater sense of spaciousness,
and advocates the positioning of a sub-woofer half way down each side of
the room. The authors of this book agree with both of them, hence the
title of their aforementioned 2004 paper – Surround Sound – The Chaos
Continues6 . Spaciousness and flatness cannot both be maximised in the
same system; except, of course, in an anechoic chamber!
Shortly before the publication of this book, Floyd Toole published
a paper in the Journal of the Audio Engineering Society in which he
expanded further on the concepts of low frequency responses for surround
systems8 . Dr. Toole has said that in his opinion, if room modes can be
actively suppressed by processed multiple woofers, and a relatively flat,
uniform, low frequency sound field can be achieved in less than perfect
rooms, then achieving this in mono below 80 Hz may well be significantly
more desirable than the extra spacial effects of stereo low frequencies
370 Loudspeakers
a)
fabric covered openings
to allow direct sound from
monitors to enter absorbent
cavities
reflective panels to give
life to the room without
creating direct reflexions
from the loudspeakers
absorbent/reflective nature of
rear wall adjusted to suit desired
room conditions
Front half (more or less)
of room to be relatively
dead at all but the
lowest frequencies
b)
DEAD END
Highly diffusive rear
section of room. To
create an ambient
life in the general
acoustic without
causing confusing
specular reflexions.
LIVE END
c)
hard wall
Full-range
absorbers
Figure 12.19 a) Typical room in the style of Wolfgang Jensen. b) Live-end, Dead-end
control room. c) Non-environment control room. d) BBC-style, controlled reflexion room.
e) Ishii/Mizutoni listening room. f) An IEC listening room
The challenges of surround sound 371
d)
Right-hand
source
Listener
Left-hand
source
Acoustic absorption
e)
reflectors
absorbant
material
hard
wall
f)
carpet on the floor
Figure 12.19 Continued
Furniture
Pictures (thick frames)
Drapes
Optional absorbent treatment
372 Loudspeakers
which must suffer modal irregularities. There is a lot of reason in what
he says.
12.7 System considerations
What must be understood is that surround sound is not simply stereo
plus another dimension. Surround sound is something totally different,
and needs to be assessed as such. As we have already seen from
Figure 12.19, the stereo rooms will not adapt well to discrete surround
sound, although they can work quite well if the surround channels are
restricted to ambience. This reappraisal of rooms for surround use, with
careful juxtapositioning of diffusive and absorptive surfaces, evenly distributed around the room, also requires a reappraisal of loudspeaker performances. In many professional stereo rooms, the axial response of a
loudspeaker tends to be paramount, because off-axis irregularities can, in
many cases (although not all applications) be controlled by absorption.
However, in surround rooms, loudspeakers often tend to need to exhibit
very smooth off-axis responses, because of the wider distribution of diffusively reflective surfaces in the room. They also need a wider directivity
pattern in the horizontal plane because the listening positions tend to be
broader than stereo listening areas. Figure 12.20 a) shows how a producer
and engineer may experience essentially the same overall balance in a
stereo listening room, but in surround, they may have to be side-by-side,
otherwise the producer would remain too close to the rear loudspeakers.
This is another argument for the use of the centre-front channel, because
it can anchor the stereo centre image even for off-centre listeners, thus
allowing two people to hear essentially the same mix when sat side-by-side.
(However, there is also a good argument for larger mixing rooms, where
small positional changes will less affect the perception!)
In Figure 12.20 b) the rear, P2 position is not valid because the person
sitting there would hear too much of the rear channels in proportion to the
front channels. The left side, P1 position would work reasonably well if
the front sound stage was anchored with the central images coming from
the centre loudspeaker. However, if a phantom central image were to be
used, the person at position P1 , would predominantly only hear it coming
from the left loudspeaker, due to the precedence effect and the earlier
arrival time of the signal from the left loudspeaker. (Unfortunately, this
means that the decision whether to use discrete centre or phantom centre
may be dictated by something as arbitrary as the size of the mixing room.)
The precedence effect, or the ‘law of the first wavefront’ means that for
the arrival of two similar signals, varying in arrival time between about
1 millisecond and 40 milliseconds, the perceived direction of the source
will be from the direction of the first sound to arrive, unless the level of
the later arriving sound is 6 or 8 dBs higher. In reality, for a centrally
panned image, the later arriving sound will also be lower in level, because
it will be arriving from further away, so the directional pull to the earlier
sound will be reinforced. Similar sounds arriving within less than about 700
microseconds (0.7 ms) will not be so affected, and sounds arriving more
than about 60 ms apart will be heard as two separate sounds – a sound
The challenges of surround sound 373
a)
b)
E
P1
E
P
P2
Figure 12.20 a) In a stereo room, given a suitably absorbent rear wall, the engineer and
producer at positions E and P would hear essentially the same mix. The only significant
difference would be a slightly reduced level at position P. b) In a surround room there are no
positions where two people can hear the same balance. Relative to the engineer’s position (E)
position P1 would experience a left-heavy mix, and P2 a rear-heaving mix
Only large rooms can resolve this problem, but, ironically, the current trend is towards
smaller rooms
and its echo. There are ‘grey areas’ between 0.7 and 1 millisecond, and
40 and 60 milliseconds, which can depend on the nature of the signal and
individual perceptions. For this reason, Dolby Digital Surround systems in
cinemas have a delay, adjusted to circumstances, on the signals fed to the
surround channels so that if any sound exists in all loudspeakers, then even
for people at the back of the cinema, the behind-the-screen loudspeaker
signals will always arrive first. This keeps the action located on the screen.
However, the music industry does not apply such delays because the rear
channels may be used for discrete instruments, and not just ambience.
What is more, in some cases, the cinema surround loudspeaker arrays
are also tapered in level, becoming lower towards the back of the theatre.
There will always be a level reduction from the frontal loudspeakers as
a listener moves towards the rear, so a corresponding level reduction in
the surround loudspeakers can help to prevent the surround sounds from
dominating the more important screen sounds. A 4 dB taper from the
frontmost to the rearmost surround loudspeakers is about the maximum
which can be used before the surround distribution would itself become
compromised. In the configuration shown in Figure 12.20 b), with only
single loudspeakers on each of the rear channels, no such tapering would
be possible, so the front/rear balance would depend upon the listening
position. Room reflexions can help to ameliorate the problem, but smooth
off-axis responses are essential if the reflexions are to be returned with an
evenly distributed energy balance, or substantial colouration of the sound
would be experienced.
For the above reasons it can be very difficult in small rooms to find
positions where two or more people can enjoy similar listening experiences
from surround sound systems, especially when the use of the centre channel
has not been fully exploited for reasons of lack of faith in the end-users’
choice of adequate centre-front loudspeakers. In larger rooms, which allow
374 Loudspeakers
greater distances between the loudspeakers, the relative time and level
differences are generally less, so a larger area can usually be achieved
where a more common listening experience can be realised. However, as
always, when the distance from the loudspeaker to the listener is increased,
the room acoustics come more into play. If the room acoustics cannot be
changed, then loudspeakers may be chosen with more suitable directivity
patterns, but this would, of course, also change the relationship of the direct
to ambient sound. There are no easy solutions to problems of ‘universal’
surround sound.
Loudspeakers that are good for stereo are therefore by no means necessarily good for multi-channel systems. The loudspeaker directivities and
total power responses need to be considered in relation to room acoustics and the size and orientation of the designated optimal listening areas.
The question of whether five surround channels will be used for the free
distribution of instruments or as a frontal stereo sound-stage plus ambient
rear-channels is another factor which will greatly influence loudspeaker
choice. Quite clearly, a system using monopole front loudspeakers with
dipole rears whose nulls are facing the listeners will not be capable of
giving equal reproduction perception to a guitar, for example, panned from
one type of loudspeaker to the other. Conversely, a symmetrical system
which can do this may be unable to exhibit the same enveloping ambience
as the dipole. When considering true high fidelity in surround sound, the
choice and the positioning of the loudspeaker is greatly more complicated
than the corresponding choices in stereo.
Unfortunately, it is also the case that very few studios are as well
prepared for surround as they are for stereo, and the people doing the
surround mixes are generally much less sure of what to do, which is not
surprising when surround can mean so many things to so many different people. Some, who perhaps should know better, even applaud the
free-for-all, no rules approach in the name of artistic freedom, but, as was
mentioned in the opening paragraph of this chapter, if there is no reference standard at the time of mixing, then how are the domestic listeners
to know what loudspeaker arrangement is most appropriate to reproduce
the intended sound of any given mix?
The range of loudspeakers which are currently used in the control rooms
where music surround mixing takes place is wildly variable, as are the
control room acoustics. There is no degree of standardisation even vaguely
approaching that of film dubbing theatres, and no companies such as Dolby
or THX to ‘enforce’ the standards. As previously explained, rooms which
are optimised for stereo are not optimal for surround, and loudspeakers
which are optimal for use in good surround use may not be optimal for
stereo. Mixes done for cinema are not optimally reproducible on domestic
surround systems which are optimised for music, and vice versa. Music
which has been mixed on five, discrete, full-range loudspeakers will not
be optimally reproduced on ‘home theatre’, bass managed systems. High
fidelity music-only surround and home cinema systems are very different.
This is both unfortunate and disappointing, because very few people will
be prepared to purchase, or live with, two completely separate systems.
However, for people who are happy to listen to all their music via MP3
coding perhaps this discussion about surround loudspeaker optimisation is
The challenges of surround sound 375
superfluous, yet unless there is a public demand for quality, the industry
will stagnate, and the whole artistic process of music production will be
demotivated such that creativity will surely suffer. The lack of general
awareness about the whole question of loudspeaker suitability for surround
sound is, in itself, only adding to the confusion.
References
1 Holman, Tom., ‘New Factors in Sound for Cinema and Television’, Journal of
the Audio Engineering Society, Vol 30, Nos 7/8, pp 529–539 (July/August 1991)
2 Fosgate, James; matrix engineer and designer of the Dolby ProLogic II system
3 Chase, Jason., ‘Hi-Fi or Surround, Part Two’, Audio Media, European edition,
Issue 92, pp 122–6 (July 1998)
4 Newell, P.R., Holland, K.R., and Castro, S.V., ‘An Experimental Screening Room
for Dolby 5.1’, Proceedings of the Institute of Acoustics, Reproduced Sound 15
conference, Vol 21 Part 8, pp 157–66 (1999)
5 Toole, Floyd E., ‘Art and Science in the Control Room’, Proceedings of the
Institute of Acoustics, Vol 25, Part 8, Reproduced Sound 19 conference, Oxford,
UK (2003)
6 Newell, Philip R., Holland, Keith R., ‘Surround Sound – The Chaos Continues’,
Proceedings of the Institute of Acoustics, Vol 26, Part 8, pp 135–147, Reproduced
Sound 20 conference, Oxford, UK (2004)
7 Holman, Tomlinson., ‘5.1 Surround Sound – Up and Running’, Focal Press,
Oxford, UK (2000)
8 Toole, Floyd., ‘Loudspeakers and Rooms for Sound Reproduction – A Scientific
Review’, Journal of the Audio Engineering Society, Vol 64, No 6, pp 461–476
(June 2006)
Glossary of terms
This glossary has been rolled forwards from previous work by the authors,
with some new additions specifically relating to the text of this book.
Experience has shown that although some of the terms may be familiar
to many readers, they have often been misunderstood or misused. This
glossary attempts to clarify the definitions of the terms, at least as used in
British English.
Acausal filter
A filter applied, usually digitally, which has advanced knowledge of the
signal arriving, via delaying the main signal on which it is intended to act –
effect before cause through prior knowledge of the cause. See Causal filter.
Active systems
Filters or loudspeaker systems, for example, where an external power
source needs to be applied as well as the drive signal. A filter based on
semiconductors or valves, driven from an external battery or mains supply,
and placed ahead of a power amplifier in a loudspeaker system is an
example of an active filter. See Passive systems.
Anechoic chamber
A room that is designed to simulate free-field acoustic conditions by
means of the placement of highly absorbent materials on all surfaces. The
absorbent materials are usually in the form of wedges pointing into the
room. This arrangement ensures that sound waves arriving at the room
edges are maximally absorbed for all angles of incidence. The lower frequency limit of anechoic performance is set by the length of the wedges,
which are effective down to a frequency where the wedge length is equal
to one-quarter wavelength. However, what little reflexions still exist will
return more weakly from the distant walls of the larger anechoic chambers
than from the nearer walls of a smaller chamber using similar wedges.
Variously known as anechoic rooms or free-field rooms.
See also Semi-anechoic chamber and Hemi-anechoic chamber.
Glossary of terms 377
A to D
Analogue to Digital converter. A device using a highly stable internal clock
which samples the audio voltage waveform at a rate higher than at least
twice the highest frequency of interest, and puts out a digital binary signal
that represents the voltage level of each sample. For example, to sample
a maximum frequency of 8 kHz, the sampling rate would need to be in
excess of 16,000 samples per second. See also D to A.
Audio frequency range
The range of frequencies over which the human ear is sensitive is usually
considered to be from 20 Hz to 20 kHz. A number of commonly used
frequency ranges are listed below. The span of frequencies quoted for each
range should not be treated as exact; they are included as an approximate
guide only.
Name
Frequency range
Infrasonic
Very low
Low
Lower mid
Mid
Upper mid
High
Very high
Ultrasonic
0–20 Hz
15–50 Hz
20–250 Hz
200–1000 Hz
250 Hz–5 kHz
2–6 kHz
5–20 kHz
15–25 kHz
20 kHz–1013 Hz
Back e.m.f.’s
The electromotive forces (voltages) which are generated in a loudspeaker
system by the mechano-magnetic interactions. They superimpose on the
drive signal (forward e.m.f.) but are usually largely damped by the energy
sinking (absorbing) action of the low output impedance of an amplifier,
which thus provides a high damping factor. Excessive impedance in loudspeaker cables, for example, can reduce this damping effect, and hence
in such systems the back e.m.f.’s would play a greater part in the overall
response of the system.
Bookshelf loudspeaker
A genre of domestic orientated loudspeakers whose low frequency
responses are aligned to try to achieve a flat far-field response when the
loading provided by a wall is taken into account, as would typically be the
case when a loudspeaker was mounted on a bookshelf.
Causal filter
A filter in which the effect takes place after the cause. See Acausal filter.
378 Loudspeakers
Cellular
Composed of cells, which can be either open or closed. In closed cell
foams, for example, each cell acts like a small balloon. When compressed
or distorted the air trapped inside cannot escape, and so the cell acts as
a good spring but a poor sound absorber. Open cell foams are generally
poorer springs but better acoustic absorbers. (For equal densities.)
Close field
The region close to a sound source, such as a loudspeaker, in which the
sound field is largely that due to the source, and is little affected by the
room reflexions, resonances, or reverberation. See also Near field.
Codec (code-decode)
An algorithm for allowing data compression in digital systems, usually in
accordance with psychoacoustic phenomena, which allows maximum data
compression with minimum acceptable (perceptually/subjectively dependent) audible degradation of the reconstructed sound.
Damping
Damping refers to any mechanism that causes an oscillating system to lose
energy. Damping of acoustic waves can result from the frictional losses
associated with the propagation of sound through porous materials, the
radiation of sound power, or causing a structure with internal losses to
vibrate.
dBA
A weighted (filtered) measurement scale where the filter curves are roughly
the inverse of the 40 phon contour of equal loudness. The scale was principally developed to relate to the subjective annoyance of noise around
the 30–50 dB SPL ear sensitivity at mid frequencies, by correcting the high
and low frequency measured levels to the same subjective level as the mid
frequencies. (See Figure 8.4.)
D to A
Digital to Analogue converters receive digitally coded signals, representing
voltage waveforms, and by means of clocking and filtering, produce an
analogue output voltage that should be as close a representation as possible
of the waveform represented by the digits. See also A to D.
dBC
Similar to dBA but based on the inverse of the 80 phon contour of equal
loudness, relating more to the subjective frequency balance at typical music
listening levels. The low frequency response of the dBC curve is almost flat.
Deadsheets
Limp membranes having considerable inertia but little stiffness. They are
widely used for the mechanical damping of acoustic waves. Those used in
loudspeaker construction are normally between 3 and 15 kg/m2 .
Glossary of terms 379
Decibel
The standard unit of measure for level, or level difference. One tenth part
of a bel. Multiplying a given quantity by 1.26 (to two significant figures)
will give an increase in level of one decibel.
For example: 1 W × 126 = 126 W (+1 dB relative to 1 W); 126 W × 126 =
159 W (+2 dB relative to 1 W); 159 W × 126 = 200 W (+3 dB relative to
1 W). It must be borne in mind that in all cases, a decibel represents a
power ratio.
Decibels and sound pressure level (SPL)
Many observable physical phenomena cover a truly enormous dynamic
range, and sound is no exception. The changes in pressure in the air due to
the quietest of audible sounds are of the order of 20 Pa (20 micro-pascals),
that is 0.00002 Pa, whereas those that are due to sounds on the threshold of
ear-pain are of the order of 20 Pa, a ratio of one to one million. When the
very loudest sounds, such as those generated by jet engines and rockets,
are considered, this ratio becomes nearer to one to one thousand million!
Clearly, the usual, linear number system is inefficient for an everyday
description of such a wide dynamic range, so the concept of the bel was
introduced to compress wide dynamic ranges into manageable numbers.
The bel is simply the logarithm of the ratio of two powers; the decibel is
one tenth of a bel.
Acoustic pressure is measured in pascals (newtons per square metre),
which do not have the units of power. In order to express acoustic pressure
in decibels it is therefore necessary to square the pressure and divide it
by a squared reference pressure. For convenience, the squaring of the
two pressures is usually taken outside the logarithm (a useful property of
logarithms); the formula for converting from acoustic pressure to decibels
can then be written:
2
p
p
decibels = 10 × log10 =
=
20
×
log
10
p0
p20
where p is the acoustic pressure of interest and p0 is the reference pressure.
When 20 Pa is used as the reference pressure, sound pressure expressed
in decibels is referred to as sound pressure level (SPL). A sound pressure
of 3 Pa is therefore equivalent to a sound pressure level of 103.5 dB, thus:
3
SPL = 20 × log10
= 1035 dB
20 × 10−6
The acoustic dynamic range above can be expressed in decibels as sound
pressure levels of 0 dB for the quietest sounds, through 120 dB for the
threshold of pain, to 180 dB for the loudest (severely ear-damaging) sounds.
Decibels are also used to express electrical quantities, such as voltages
and currents, in which case the reference quantity will depend upon the
application (and should always be stated).
380 Loudspeakers
When dealing with quantities that already have the units of power, such as
sound power or electrical power, the squaring inside the logarithm is unnecessary and the ratio of two powers, W1 and W2 expressed in decibels is then
10 × log10
W1
W2
Distributed mode loudspeaker (DML)
A type of loudspeaker where the motor system excites a plate of high
modal density. The source is diffuse and acts like neither a piston nor a
point source. Radiation takes place from both sides of the panel, but the
response is not typically that of a more conventional dipole, even when the
panel is unbaffled. The stereo imaging is not as good as with conventional
loudspeakers, but the response tends to be less disturbed by the room
acoustics. Such loudspeakers can be advantageous as the ambient rear
channels of a surround loudspeaker system, for example.
Doppler distortion
Frequency modulation dependent on the speed with which a source of
sound is either approaching or receding from a listening position. The most
common example is perhaps that of a train whistle, or horn, which suddenly
drops in pitch as the listening position is passed. The whistle exhibits a
constant frequency of output, but when it is approaching the listening
position, the period between the cycles is compressed as the arrival delay
shortens with time. As the source approaches, effectively the wavelength
is shortened. This gives rise to the impression that a higher frequency is
being emitted. The time of arrival for each subsequent cycle is reduced
as the train approaches because it is emitted from a point nearer to the
listener than was the previous cycle. Once the listening point is passed, the
opposite effect occurs, with each subsequent cycle emanating from a more
distant position, lengthening the wavelength and hence suffering a greater
arrival delay. The frequency is thus perceived to have lowered. The degree
of pitch change is dependent upon the relative speed of the sound source
and the listener. (C. J. Doppler, 1842.)
Efficiency of loudspeakers — See Sensitivity and efficiency
Eigenfrequency
Frequency of the Eigentones (see below).
Eigentones
The natural resonant tones of a space (or any other resonant system, in
fact), ‘eigen’ being German for ‘own’. A room’s own tones. If a room is
driven (excited) by a noise signal containing all frequencies, then all the
eigentones will be driven. When the drive signal is terminated, however,
only the eigentones will continue to ring-on, the decay rate being a function
of size and total absorption. If a room is driven by a musical signal, only
the eigentones that correspond to frequencies in the musical signal will be
driven, and then only those eigentones will ring on when the music stops.
Glossary of terms 381
The eigentones thus dictate which frequencies will ring-on when the drive
signal is stopped, but the input signal determines which eigentones are
driven. Eigentone is another term for resonant mode. (See Mode.) If a
room is driven at a frequency that does not correspond with an eigentone
(mode), then the room response will decay more rapidly, once the drive
signal has been stopped, than the frequencies which correspond with the
eigentones. This is why widely spaced room modes give rise to uneven overall responses in a room. Frequencies corresponding to eigentones (modes)
will be reinforced or cancelled, depending on source and receiver position, but other frequencies will be unaffected. See Standing waves and
resonances.)
Euro (E)
The European currency unit, roughly equivalent to 1.25 US dollars in 2006.
During the reading of the first draught of this book for assessment by the
publishers, a referee requested that the currencies used in the text should be
converted to one standard unit, such as the euro or the U.S. dollar. In reality, this proved difficult to achieve in any meaningful manner because the
wild fluctuations of the currencies would lead to distorted senses of values
outside of the local territory of that currency. In mid 2001, the euro would
buy 87 cents of a U.S. dollar. By mid 2004 it would buy 1 dollar 34 cents,
a rise in value of over 50 percent. Consequently, reference in this book to
things manufactured in the USA is given in dollars, and to things made in
Europe, in euros. Where any other currencies are stated, some means of
assessing the relative value at the time referred to will be given in the text.
Far-field
The far-field is the region in which the radiation from a loudspeaker, or
other acoustic source, can be considered equivalent to that of a point
source, and in which the sound pressure and velocity reduce by 6 dB for
each doubling of distance from the source.
Feedback
1 The instability that occurs when the output from a microphone is reproduced by a loudspeaker system, the output of which arrives back at the
microphone. Regenerative feedback develops when the overall gain is
greater than 1. Also known as ‘howlround’.
2 The instability that occurs when an output of an electrical amplification
system is re-applied to its input.
3 A term used by orchestral musicians to describe the way in which they
hear the output from their own instruments reinforced via reflexions in
their performance space. When fed to them via loudspeakers or headphones, the usual term is foldback.
4 Negative feedback (phase reversed) is used in electronic amplifier circuitry to reduce distortion.
Fourier Transform
The mathematical transform linking the time domain representation of a
signal to its frequency domain representation. Application of the Fourier
382 Loudspeakers
Transform to a signal (waveform) reveals the frequency components in
terms of their magnitude and relative phase (the Spectrum). Application of the inverse Fourier Transform to the spectrum yields the original
waveform.
Frequency
The rate of change of phase with time. The number of complete cycles per
unit interval of time for a sinusoidally time-varying quantity. The repetition
rate of any cyclic event. Unit: Hertz: (Hz); previously measured in units of
cycles per second (c.p.s.), and even earlier in half-vibrations per second.
Frequency response
The response of a system in terms of its amplitude and phase response.
See (Pressure) amplitude response and Phase response.
Group delay
The frequency dependent response delay through electrical or mechanical
systems which are given rise to by phase distortions. The group delay is
related to the degree of phase shift.
Haas effect
H. Haas, 1951. See Precedence effect.
Hemi-anechoic chamber
An anechoic chamber with one hard boundary in which the sound sources
can be embedded. Equates to 2 space – hemispherical radiation.
Impedance
A combination of resistance and reactance. Symbol Z. The ratio of pressure
to velocity in acoustic systems, or voltage to current in electrical systems,
expressed at a given frequency. (See also Resistance and Reactance.)
Infrasonic
Relating to frequencies below approximately 20 Hz. See Subsonic.
Intensity
‘Sound intensity’ is a very specific term, and represents the flow of acoustic
energy. It is measured in units of watts per square metre, and should not
be confused with either sound power level (SWL), sound pressure level
(SPL) or loudness, but it is associated with the sound intensity level (SIL).
Interference field
See Standing wave field.
Kinetic energy
Energy of motion. Energy possessed by a body due to its motion, which
can be converted to other forms of energy through the application of a
braking force.
Glossary of terms 383
Linearity
A system can be said to be linear when the output contains only the frequencies applied to the input. A falling amplitude response with frequency
is therefore a linear distortion. Such a response is NOT non-linear, as may
be erroneously stated in many advertisements. See Non-linearity.
Loss factor
The reciprocal of the Q-factor. See Q-factor.
Magnetostriction
The property of some materials, for example iron, of expanding and contracting due to the influence of an applied magnetic field.
Microphone directivity patterns
Most microphones consist of a small diaphragm that moves in response
to changes in the pressure exerted on it by a sound wave; the diaphragm
motion is then detected and converted into an electrical signal.
The simplest form of microphone is one that has only one side of the
diaphragm exposed to the sound field. If the diaphragm is sufficiently small,
such a microphone will respond equally to sounds from all directions, and
is termed ‘omni-directional’.
A microphone which has both sides of the diaphragm open to the sound
field will only detect the difference between the pressures on the two sides.
When a sound wave is incident from a direction normal to the diaphragm,
there will be a short delay between the pressure on the incident side and
that on the far side, and the microphone responds to the resultant pressure
difference. When a sound wave is incident from a direction in line with the
diaphragm, the same pressure is exerted on both sides of the diaphragm
and the sound is not detected. This arrangement results in a ‘figureof-eight’ or dipole directivity pattern.
If an omnidirectional microphone element and a figure-of-eight microphone element are mounted close together and their outputs summed, the
resultant directivity pattern will lie between the two extremes of omnidirectional and figure-of-eight patterns. If the sensitivities of the two elements are the same, the combined directivity pattern is known as cardioid,
because of its heart shape. Various other patterns, such as hyper-cardioid
and super-cardioid are achieved by varying the relative sensitivities of
the omni-directional and figure-of-eight elements. Similar directivity patterns can be realised using only one microphone element. The microphone
diaphragm is mounted at one end of a short tube, and the delay introduced
to one side of the diaphragm by the tube gives rise to an approximation to a cardioid directivity pattern. More complex directivity patterns
can be achieved by using more than two elements; the SoundField microphone, for example, has four elements that can be combined in a variety
of ways.
384 Loudspeakers
Minimum phase and non-minimum phase
A minimum phase signal/system is one in which the phase shift associated
with the amplitude response is the minimum that can be allowed whilst
still exhibiting the properties of a causal system (one in which the output
never arrives before the input). As there is a strict relationship between
amplitude and phase in such systems, correcting either one will inevitably
tend to correct the other. The low frequency response boost given rise to by
the flush mounting of a loundspeaker in a wall is an example of a minimum
phase response change, which therefore can be equalised to restore the
free-field response in terms of both amplitude and phase (and hence it will
also restore the time [transient] response). The essential factor is that no
appreciable delay is involved between the generation of the signal and the
effect of whatever is influencing it. If there is no appreciable delay, then
there can be no appreciable phase-shifts, hence minimum-phase, or more
fully, minimum phase-shift.
‘Non-minimum phase’ responses are those where amplitude correction,
alone, cannot correct any phase disturbances. The far-field response of a
loudspeaker in a reflective room is an example of a non-minimum phase
effect. Here, there is a delay between the signal generation by the loudspeaker and the superimposition of the boundary reflexions on the overall
response. Reflexion arrival times create phase irregularities, which are
frequency and distance (time) dependent, so no simple manipulation of
the amplitude response of the source can adequately compensate for the
complex disturbances.
Another example of a non-minimum phase effect is in the combination of
the various outputs of crossovers. In any filter circuits, either mechanical or
electrical, there are inherent Group delays for any signal passing through
them. The amount of group delay increases as the filter frequency lowers,
and as its order (6, 12, 18, 24, etc. dB/octave) increases. A crossover will
thus have different group delays associated with each section, and when the
outputs are recombined, they will not produce an exact replica of the input
signal. For this reason, conventional equalisation cannot be used to correct
for response errors at crossover points. Amplitude correction will lead to
further phase distortion, and hence time response errors. In practice, most
crossovers above first-order are non-minimum phase devices.
Mode
A special pattern of vibration whose position remains invariant, as when a
travelling wave and its reflexions superimpose themselves between two or
more boundaries such that the peaks and troughs in the waveform coincide,
and appear static. See Standing wave field.
Modes and resonances
Sound consists of tiny local changes in air density that propagate through
the air as a wave motion at the speed of sound. The speed of sound is
around 340 metres per second at normal room temperature and, although
it is temperature dependent, it is independent of variations in the ambient
pressure, and is the same at all frequencies. The frequency of a sound
Glossary of terms 385
wave is measured in cycles per second (c/s or cps) known more usually
these days as hertz (Hz), and is usually represented by the symbol f . The
distance that a sound wave travels in one cycle at any frequency is known
as the wavelength, represented by the symbol (lambda), and has the
units of metres. The speed of sound is represented by the symbol c. The
relationship between wavelength, frequency and the speed of sound is
simple; wavelength is equal to the speed of sound divided by the frequency,
or = c/f . Therefore, for example, a sound wave at a frequency of 34 Hz
has a wavelength of 340/34 = 10 m.
As a sound wave propagates away from a source in a room, it will expand
until it reaches a reflective room boundary, such as a wall, from which
it will reflect back into the room. The reflected wave will continue to
propagate until it reaches other boundaries from which it will also reflect.
If there is nothing in either the room or the boundaries to absorb energy
from the wave, the propagation and reflexion will continue indefinitely,
but in practice some absorption is always present and the wave will decay
with increasing time. The point on the cycle of a sound wave (the phase of
the wave) when it reaches the boundary depends upon the distance to the
boundary and the frequency of the wave.
A rigid boundary will change the direction of propagation of an incident
sound wave, but will maintain its phase, so the phase of a reflected wave
can be calculated from the total distance propagated from the source. If this
total distance is equal to a whole number of wavelengths, then the wave will
have the same phase as it started with. When two boundaries are parallel to
each other, a sound wave will reflect from one boundary towards the other,
and then reflect back again to where it started, continuing back and forth
until its energy is dissipated. If the distance between the boundaries is such
that the ‘round trip’ from the source to the first boundary, on to the second
boundary, and back to the source is a whole number of wavelengths, then
the returning wave will have the same phase as the outgoing wave, and
will serve to reinforce it. This situation is known as resonance. Resonances
can also occur due to reflexions from multiple boundaries; the necessary
requirement being that the sound wave eventually returns to a point with
the same phase as when it left. One can imagine a whole set of possible
combinations of reflexions in a typical room that allows the wave to return
to its starting point, and therefore a whole set of frequencies for which
resonance will occur. In fact, in theory, every room has an infinite number
of possible resonances.
As stated above, if there is nothing in the room or the boundaries to absorb
energy from a sound wave, a short duration sound pulse (or transient),
emitted from a source will propagate around the room indefinitely. Of
the infinite number of possible paths that the wave can take, only those
that correspond to resonances at frequencies contained in the pulse will
be continually reinforced; all other paths will not be reinforced. After a
short time, the resulting sound field can be thought of as simply a sum
of all of the resonances that have been excited. These resonant paths are
known as the natural modes of the room, and the resonant frequencies
386 Loudspeakers
are known as the natural frequencies, or ‘eigentones’, of the room; both
are determined uniquely by the room geometry. ‘Eigen’ is German for
‘own’, so the eigentones are a room’s own particular, natural, resonance
frequencies.
When sound absorption occurs within the room or boundaries, resonant
modes still exist, but the wave will decay at a rate determined by the amount
of absorption. To maintain a given sound level in a room in the presence
of absorption, the source needs to be operated continuously, at a level
dependent upon both whether or not resonant modes are being excited
and the amount of absorption present. When the sound source emits a
transient signal in the presence of absorption (for example, switching off a
continuous signal), many different paths – not just resonant modes – will
be excited, but after a short time, only the resonant modes will remain
(because they tend to have less absorption); the room will ‘ring’ at the
resonance frequencies until the modes decay. The reverberation time of
a room is a measure of the average rate of decay of the sound in the
room when an otherwise continuous sound source is switched off; it is the
time taken for the sound level to fall to minus 60 dB relative to its initial,
continuously excited, level. As the amount of absorption is increased, the
sound level at the resonant frequencies will reduce, but the bandwidth
of each mode (the range of frequencies over which the mode can be
excited to a significant degree) will increase. When the boundaries are fully
absorbent, the room modes no longer exist (an anechoic chamber).
When sounds such as speech or music are heard in a room, the level of
the continuous components of the sound will be determined by whether or
not they coincide with any room resonances that are excited. The transient
components will ‘hang on’ at the resonance frequencies after the transient
has gone. It should also be understood that the perception of the modal
activity is not uniform within the space, because of the spacial distribution
of the nodes and antinodes.
Mutual coupling
Mutual coupling is the term used to describe the interaction between two or
more sound sources radiating the same signal. If the diaphragms are receiving different, uncorrelated inputs, then the output power summation will
be simply that of the output of the different diaphragms. However, if the
diaphragms are receiving the same input, then for frequencies whose wavelengths are greater than eight times the distance between the diaphragms
(i.e. the diaphragms are less than one-eighth of a wavelength apart) the
outputs will be substantially in-phase at any point in the room. The radiated pressures (not powers) will then superimpose, giving rise to a 6 dB
increase in SPL for each doubling of the radiating area if the diaphragms
are radiating the same power. This implies four times the output power,
yet, when the radiated powers are equal but the radiated signals are uncorrelated (i.e. totally different signals) only a 3 dB SPL increase (due to the
simple power summation) would result. Where a close boundary reflects a
wave back on to the radiating surface of a diaphragm, the effect is the same
as if a second diaphragm were radiating the same signal – the mirrored
Glossary of terms 387
room analogy – and so the diaphragm radiated twice the power that it
would do if moved away from the boundary.
This seemingly 1 + 1 = 4 situation is due to the fact that, for a given
diaphragm velocity, the power output is proportional to the diaphragm
radius raised to the fourth power. Doubling the diaphragm area therefore
yields a fourfold increase in power. The increased low frequency radiating
efficiency of large diaphragms can be thought of as being due to all the
individual parts of the diaphragm mutually coupling. The pressure radiated
by one part of the diaphragm resists the movement of the adjacent parts.
The increase in radiation resistance on a mass-controlled diaphragm, typical of a heavy woofer (whose movement can be considered independent of
the local air pressure), gives rise to increased work being done, by having
a greater pressure of air to push against, so more power is radiated.
As the frequency of radiation rises, or the loudspeakers (or the loudspeaker and a reflective surface) are sited further apart (i.e. the diaphragms
are separated by more than one-eighth of a wavelength), the coupling
becomes less in-phase so the radiation boost reduces. As the frequency
or separation distance continues to rise, regions of in and out of phase
interference will result, giving rise to a combined output power response
as shown in Figure 7.11. Only for a listener on the central plane between
the loudspeakers will the 6 dB pressure summation be maintained.
In a reverberant room, the output from a pair of stereo loudspeakers reproducing a central mono signal will sum by 6 dB on axis, at all frequencies,
but the reverberant field will be driven by the combined power response,
as shown in Figure 7.11b). The overall sound, therefore, will be darker
(with more low frequencies) than that from a central mono source radiating the same signal and receiving the same input power as the mutually
coupling pair.
Much more on this subject can be found in Reference [1]. at the end of
the Glossary.
Near field
There are two quite distinct and separate definitions of the near field of
a source of sound; one is related to the geometry of the source whilst the
other has to do with the rate of expansion of radiating waves. The region
beyond both near fields is known as the far field.
The geometric near field is defined as that region close to a source
where the sound pressure does not vary as the inverse of the distance from
a source. The extent of the geometric near field is dependent upon the
detailed geometry of the sound source and is finite only at frequencies
where the wavelength is shorter than a typical source dimension (for a
circular piston this is when the wavelength is equal to the piston diameter);
there is no geometric near field at lower frequencies. A point source does
not have a geometric near field at any frequency.
The acoustic near field (or hydrodynamic near field) is defined as that
region close to a source where the air motion (velocity field) does not vary
388 Loudspeakers
as the inverse of the distance from a source, although the acoustic pressure
may. The extent of the acoustic near field is inversely proportional to
frequency: it is large at low frequencies and small at high frequencies. The
sound field radiated by a point source has a sound pressure that varies as
the inverse of distance from the source at all frequencies and distances.
The air motion only varies as the inverse of distance in the far field. For
practical sources, the extent of the acoustic near field is affected also by
source geometry.
Decisions relating to the proximity of a listener to a close-field monitor
should be made by considering the geometric near field only; the ear, being
essentially a pressure sensitive organ, is insensitive to the presence of the
acoustic near field.
Newton
A standard unit of force; symbol N. Easy to remember examples are that
one newton is roughly equal to a weight (on the earth’s surface) of 100 g,
and that an apple of medium size is attracted to the earth by a force of
around one newton. A force of one newton bearing down on a spring
would be applied by a 100 g weight on the surface of the earth.
Non-linearity
A system is said to be non-linear when the output contains frequencies
which were not present in the input signal, and are not due to system noise.
Harmonic distortion, intermodulation distortion and rattles are sources of
non-linearities. A system exhibiting any of these is said to be non-linear.
See Linearity.
Noise weighting curves (dBA, etc.)
The human ear does not have a flat frequency response; a low frequency
noise will generally sound quieter than a higher frequency noise having
the same sound pressure level. A measurement of sound pressure level
therefore does not yield an accurate measurement of perceived loudness
unless the frequency content of the noise is taken into account. Noise
weighting curves are used to convert sound pressure level measurements
into an approximation of perceived loudness, by discriminating against low
and high frequency noises. The most commonly used noise-weighting curve
is known as A-weighting. An A-weighting curve is simply a filter with a
response that rises with increasing frequency up to 2kHz, above which it
falls off gently.
The frequency response of the human ear changes with changes in sound
pressure level (see Figure 8.4), so different weighting curves are required
for different levels. The dBA curve was developed for signals having loudness below 40 phon, the dBB curve was intended for somewhat higher
levels. At levels over about 80 phon, the dBC curve should be used. Other
curves are also in use, such as dBD, which can be used for high level
industrial noise, and dBG, which is used for infrasonic and very low frequency noise assessments.
Glossary of terms 389
The widespread use of the dBA curve for the assessment of noise can
give rise to poor results in situations when another weighting curve is
more appropriate. Only at about 1 kHz and 6 kHz do all the curves agree.
Between 3 and 4 kHz, errors of up to 10 dB can be found, and at low frequencies, the A-weighting curve can over-assess or under-assess noise nuisance levels by up to 20 dB, depending upon level. The dBA curve is often
used at relatively high levels; a purpose that it was never intended for, and is
not suited to, but sometimes this needs to be done for comparison purposes.
In any case, noise weighting should only be applied when one requires an
approximation to the perceived loudness of a sound; it is therefore of most
use in noise assessment. Noise weighting should never be applied when
absolute values of sound pressure are required; in the measurement of
loudspeaker frequency response, for example. Here, a flat measurement
(unweighted) should be used.
Objective and subjective assessment
In acoustics in general, and in audio in particular, there is often some disagreement between that which our measurements tell us and that which we
hear. In audio, objective assessment involves measuring the performance
of a piece of equipment using instruments, and comparing this performance
with a desired specification. Subjective assessment, however, involves auditioning the equipment under carefully controlled conditions and assessing
particular aspects of the sounds that are heard. The successful assessment
of the quality or suitability of a piece of audio equipment therefore, ideally,
needs both approaches. Objective assessment is more easily carried out in
the laboratory, or during production runs, than subjective assessment. To
make a reliable and repeatable subjective assessment usually requires the
ears of a number of subjects, and hence, often, a large amount of time.
Particulate
Relating to particles. Particulate motion = motion of the particles.
Pascal
A pressure of one newton per square metre. See Newton.
Passive systems
Systems, such as filters, without any source of external power other than
the signal energy itself. An inductor/capacitor filter immediately before a
loudspeaker drive unit is an example of a passive filter. See Active systems.
Phase response
The relative phase of the input and output signals as a function of frequency.
Phon
A unit of perceived loudness, such that a given change in the phon level
would always produce an equal, subjective loudness change, irrespective of
the actual SPL change. The contours in Figure 8.4 represent phon levels,
which it can be seen do not relate directly to the physical sound pressure
levels.
390 Loudspeakers
Pink noise
Filtered white noise (reducing 3 dB/octave with frequency) which yields
equal energy per octave.
Pinna
Plural: pinnae. The outer part of the ear that projects outside the head.
The ear flap.
Potential energy
The energy of position; such as imparted on a body by raising it in a gravity
field. The energy concentrated in a spring is also potential energy.
Precedence effect
Also referred to as the Haas effect, and the law of the first wavefront. When
two short-duration sounds are heard in rapid succession, the tendency is
for the second sound to be psychoacoustically suppressed. The pair of
sounds is perceived as one sound, coming from the direction of the first
arriving source. The precedence effect operates when the second sound
arrives within approximately 0.7–40 ms after the first sound.
The affect can often be overridden if the second sound is 7–15 dB higher
in level than the first sound.
(Pressure) amplitude response
The ratio of the output amplitude of a system divided by the amplitude of
the input as a function of frequency. When sound pressure is involved, the
term ‘pressure’ is prefixed: for electrical or mechanical systems, the term
‘amplitude response’ suffices.
Psychoacoustics
Unlike the related discipline of acoustics, which is concerned with the
physics of sound, psychoacoustics is the science of the perception of sound,
particularly by humans. The stereo illusion, the cocktail party effect and
the perception of pitch are all examples of psycho-acoustic phenomena.
PVA
Poly-vinyl acetate. A water-based adhesive that is water resistant once dry.
Q-factor
A measure of the sharpness of the peak in a resonant system. It is defined as
Q=
f res
Bh
where
f res = resonant frequency
Bh = the half-power bandwidth of the resonance
Glossary of terms 391
Reactance
A reactive system is one which stores and releases energy without loss.
Inductors and capacitors are reactive. Symbol X. The phase quadrature
part of Impedance, q.v. Reactance can be thought of as the resistance to
the flow of AC, as exhibited by inductors and capacitors, and is highly
frequency dependent.
Resistance
Anything which impedes the flow of energy in such a way that the losses
are dissipated (more usually into heat, but also into work). Symbol R. The
in-phase part of an impedance q.v. Resistance acts equally on AC and DC
currents, independent of frequency.
Semi-anechoic chamber
A room in which the absorption is incomplete, and contains a residual
reflected component that can be corrected for during measurement analysis. See Anechoic chamber.
Sensitivity and efficiency
The efficiency of a loudspeaker is the proportion of total radiated sound
power relative to the total electrical input power. The sensitivity is usually
measured over a limited frequency band — usually in the centre of the
loudspeakers’ flat range of operation — at one metre distance and with
an input of 2.83 volts. [Some early systems of measurement used 1 mW of
input power at 30 feet distance.]
Efficiency is given as a percentage, whereas sensitivity is measured in dB
SPL for one watt at one metre (2.83 volts into 8 ohms). The input signal
is usually pink noise, suitably band-limited to suit the operating range of
the loudspeaker or driver in question.
A complication arises in the specification of the sensitivity of compression
drivers because the horns to which they are connected, by virtue of their different directivity patterns, distribute the radiated output power over different areas. It is therefore better to consider a combined driver/horn system
as one unit before specifying the sensitivity, because the axial sensitivity
will fall as the total area over which the sound is distributed is increased.
Shuffler
A type of circuit used in headphone reproduction to try to create interaural cross-correlation to simulate the effect of loudspeaker listening. This
is done in an attempt to produce a frontal sound stage, because the stereo
sound stage is generally inside or above the head of a listener when using
headphones. Pre-World War II, the word was also used for other purposes,
relating to middle/side (M & S) microphone matrixing.
Sine wave (and its frequency content)
A sine wave is a graph of the value of a single frequency signal against time.
Strictly speaking, for a signal to consist to a single frequency, the sine wave
must have existed for all time, as any change to the amplitude of the signal,
such as during a switch-on or switch-off, gives rise to the generation of other
frequencies: this has important implications for audio. Most audio signals
392 Loudspeakers
contain pseudo-steady-state sounds, such as notes played on an instrument.
When these sounds are reproduced by an imperfect audio system, the
excitation of any resonances in the reproduction chain will depend upon
the frequency content of the signal. During a long note, the signal may
be dominated by a few discrete frequencies, such as a set of harmonics,
and the chances of resonances being excited are slim. However, during the
start and stop of the note, a range of frequencies is produced, above and
below those of the steady-state signal, and the chances of resonances being
excited are increased. This phenomenon leads to the apparent pitch of the
note being ‘pulled’ towards the frequency of any nearby resonance during
the start, and particularly the end, of the note.
Sound Power Level (SWL)
The level of sound power, expressed in decibels, relative to a stated reference value. The unit is the decibel referenced to 1 picowatt (1 pW).
Sound Pressure Level (SPL)
The unit is the decibel, referenced to 0 dB SPL at 20 micro-pascals 20 Pa.
It is defined by 20 log10 prms /pref . Sound Pressure Level, or SPL, doubles
or halves with every 6 dB change, unlike the sound power, which doubles
and halves with 3 dB change, because the power relates to the square of
the pressure. In the acoustic and electrical domains, sound power equates
to electrical power and SPL to voltage. Subjective loudness tends to double
or halve with 10 dB changes: 10 dB higher being twice as loud, and 10 dB
lower being half as loud. See also Intensity. Ten decibels relates to a ten
times power change.
Squawker
Term of American origin for a mid-range loudspeaker – onomatopoeically
relating to the sound of a large bird such as a seagull or macaw.
Standing wave field
The pattern of wave superposition that occurs in a reflective environment,
whereby the distribution of peaks and troughs in the response throughout
the space appear to be stationary. See Mode.
Standing waves and resonances
Standing waves occur whenever two or more waves having the same frequency and type pass through the same point. The resultant spatial interference pattern, which consists of regions of high and low amplitude, is
‘fixed’ in space, even though the waves themselves are travelling.
Resonant standing waves only occur when a standing wave pattern is set
up by interference between a wave and its reflexions from two or more
surfaces. And, when the wave travels from a point, via the surfaces, back to
that point, it is travelling in the original direction. And, when the distance
travelled by this wave is equal to an exact number of wavelengths. The
returning wave then reinforces itself, and if losses are low, the standing
wave field becomes resonant.
Glossary of terms 393
The simplest resonant standing wave to visualise is that set up between
two parallel walls spaced half a wavelength apart. A wave travelling from a
point towards one of the walls is reflected back towards the other wall, from
which it is reflected back again in the original direction. As the distance
between the walls is one half of a wavelength, the total distance travelled
by the wave on return to the point is one wavelength; the wave then travels
away from the point with exactly the right phase to reinforce the next cycle
of the wave. If the frequency of the wave or the distance between the walls
is changed, a standing wave pattern will still exist between the walls, but
resonance will not occur.
It should be stressed that standing waves always exist when like waves
interfere, whether a resonance situation occurs or not, and that the common
usage of the term ‘standing wave’ to describe only resonant conditions is
both erroneous and misleading. That is, all resonant modes are standing
waves, but all standing waves are not resonant modes. See also, Eigentones.
Step-function
Alternative names are ‘unit step function’ ‘Heaviside step function’ and
‘Heaviside function’. (O. Heaviside, 1892.)
Hx = 0 for x < 0
Hx = 1 for x > 0
Its value at x = 0 is not defined. The alternative notation ux is more
common in signal processing.
Subsonic
This, in British English at least, is an aerodynamic term meaning below the
speed of sound (as opposed to Supersonic). Its use implying below 20 Hz
is incorrect.
Compare:
Infrared with ultraviolet
Latin: sub – under, super – on top of, above
Infra – below, ultra – beyond
Conventionally, ‘sub’ usually pairs with ‘super’ and ‘infra’ with ‘ultra’. (See
Infrasonic.)
Supersonic
An aerodynamic term meaning above the speed of sound. Its use relating
to beyond the frequency range of hearing is archaic. Ultrasonic is the term
now used for frequencies above the range of human hearing.
Transfer function
Alternative term used (at least in electro-acoustics, although not in all
subjects) for the frequency response. What you get out relative to what
you put in. A flat frequency response implies a flat transfer function.
Transient response
The response of a system to an impulsive input signal. An accurate time
(transient) response requires an extended frequency response and a smooth
394 Loudspeakers
phase response. A low frequency amplitude response roll-off, for example,
will give rise to the lengthened time (transient) responses, as shown in
Figures 6.3 and 6.4. The more the frequency response is curtailed, either in
terms of frequency of turnover or steepness of slope, the more the transient
response will be smeared in time.
Tweeter
Term of American origin for a high-frequency loudspeaker, onomatopoeically imitating the high-pitched ‘tweet-tweet’ sound made by small
birds.
Ultrasonic
Relating to frequencies above approximately 20 kHz. Some authorities
limit the term to a maximum of 1013 Hz, beyond which the term ‘hypersonic’
is used. Hypersonic is also used in aerodynamics, relating to speeds beyond
five times the speed of sound.
Weighting
The pre-multiplication of data by a set of weighting factors. A bias applied
to improve measurement compatibility with subjective assessment.
White noise
A random noise signal containing all frequencies. Statistically the response
has equal energy per bandwidth in hertz. For example, 20 Hz to 25 Hz
(5 Hz bandwidth) would have equal energy to the band from 1000 Hz to
1005 Hz (also a 5 Hz bandwidth), and hence on a spectrum analyser shows
a response rising 3 dB per octave as the frequency rises.
Woofer
Term of American origin for a low frequency loudspeaker – onomatopoeically relating to the deep bark, or ‘woof’ of a large dog.
X-curve
An empirically derived curve for the equalisation of monitor systems in
the cinema industry. The curve is shown in Figure 12.11, and is used, somewhat flexibly, according to room size and decay time to improve the sonic
compatibility of the perceived frequency response. Due to many reasons,
of which not all the mechanisms or implications are fully understood, the
frequency balance of the soundtracks tend to become brighter sounding
as the room size increases, and/or the decay time increases. Thus, a large
room with a longer decay time, using a flat monitor response, would be
perceived to be over-bright when compared to the sound in a smaller room
with a shorter decay time.
Reference
1 Borwick, John, Loudspeaker and Headphone Handbook, 3rd Edn, Chapters 1
and 9, Focal Press, Oxford, UK and Boston, USA (2001)
Thanks to Professor James Angus for verifying the accuracy of this glossary.
Index
A.D.A.M Audio, 50, 52
ABR (Auxiliary Bass Radiator), 81
Absolute phase, 291
Acausal responses, 220, 224–5, 376
Acoustic centre, 276, 295
Acoustic impedance, 7, 99, 196
Acoustic labyrinths, 76, 77
Acoustic lenses, 117
Acoustic Research, 71
Acoustic source plots, 274, 289,
292–3, 315
Acoustic suspensions, 71
Acoustical Manufacturing
Company, 271
Air conditioning, 246
Air, weight of, 1
Alnico, 22, 37
Amplifier classes, see Biasing class
Anechoic chambers, 196–7, 376
Angus, Professor James, 394
Antinode, 210, 211, 236, 303, 368
Aquaplas, 28
ATC SCM10, 252, 325
Audibility of phase (rate of change
of), 155
Auditory nerves, 153
Auratone 5C, 232, 255, 297, 327,
329, 334
AX1, 112
AX2, 110, 112–13, 118, 121
Axis tilting, 128
Back-EMF, 171, 173, 377
Baffle:
finite, 65
general, 65
infinite, 65, 88
open, 65
Bailey, A. R., 78, 80
Bailey, Mark, 319
Bandpass enclosures, 82, 365–6
Bass-guitar/bass-drum balances, 279,
290, 301, 330, 339, 350
Bass management, 361, 363–4
BBC, 27, 168, 257
Belendiuk and Butler, 306
Beryllium, 43, 47, 244
Bessel filters, 137
Bextrene, 27
Bi-wiring, see Multi-cabling
Biasing class, 158
Bipolar junction transistors (BJTs),
163, 164
Bipole radiators, 355–6
Bl non-uniformity, 282–3
Blauert and Laws criteria, 295
Blumlein, Alan Dower, 216
Bookshelf loudspeakers, 92–3,
338, 377
Boyle’s law, 324
Bradbury, L. J. S., 80
Break up, 24, 43, 282
Briggs, Gilbert, 3, 274
Brownian motion, 271
Butterworth filters, 68, 137
Cabinet, construction of, 87
Cabinet lining materials, 76–7, 86–7
Cabinet tuning, 72, 81
Cables, gauge of, 167
Cables, length of, 167–8
Campbell, Alex, 146
Capacitance of cables, 168
Causal responses, 225, 377
Celestion loudspeakers, 28, 267
Centre-front channels, 360–1, 372–3
Centring device, 23, 25–6
Cepstrum analysis, 118, 289, 295–7
Characteristic impedance, 101, 239
Cinema sound systems, 357–60
Class A, 159–61, 163, 180–1
Class A Sliding bias, see Sliding bias
Class A
Class AB, 161, 163, 181
Class AG/AH, 163, 245
396 Index
Class B, 160
Class C, 161
Class D, 161–3
Class G, 163
Class H, 163
Close-field, 13, 248–9, 258,
332, 378
Cobalt, 37
Colloms, Martin, 28, 87, 188
Colouration, 51, 56, 87, 118, 218,
263–4, 267–9, 276, 282, 304,
329, 373
Comb filtering, 99–100
Compact disc, 259
Compensation networks, 154
Compression drivers, 45, 160
Compression ratio, 45, 101
Computer aided design, 246
Concise Oxford Dictionary, 347
Cone profiles, 266–7
Cone sag, 33
Cones, solid, 25
Congo, 22, 37
Conjugate networks, 138
Constant voltage sources, 166–7, 326
Converters–D to A, A to D, 147,
149, 162, 189, 194, 223,
301–2, 377–8
Critical damping, 67
Critical distance, 249, 332
Crossover distortion, 160–1, 245, 282
Crossover points, choice of, 242
Crossovers:
active, 124, 142–3
digital, 146–7
first-order, 131, 142
fourth-order, 136, 142, 243
high-order, 136–7
inductive, 124
inductor/capacitor, 129–30
Linkwitz-Riley, 136, 142, 243
mechanical, 124
passive, 124, 142, 145, 154, 164, 173,
246–7, 335–6
phase response of, 134–7
reconstruction problems, 125,
226, 299
resistor/capacitor, 130
second-order, 133
third-order, 134
Crowhurst, N.C., 274
Current sheet, 49–50
Cut-off frequency, see Horns
loudspeakers
Czerwinski, Eugene, 174, 283, 288
Damping, 70, 87, 172, 269, 378
Damping factor, 167–8
d’Appolito layout, 243
DCW (Directivity Control
Waveguide), see Waveguides
Deadsheet, 87, 362, 378
Decibel, 379
Delta function, 272, 274, 278, 288–92
Deutsch, Dr Diana, 306
Diffracted waves, 90
Diffraction:
effects, 88, 262
horns, see Horns loudspeakers
sources, 88–9, 92
Diffusers (acoustic), 242, 355
Digital response correction:
of loudspeakers, 220, 301
of rooms, 226, 298–9
Dipole radiators, 59, 200, 210,
355–6, 374
Dirac function, see Delta function
Dirac, Paul, 292
Directivity, 102, 241–3
Directivity factor (Q), 198
Directivity index (DI), 198
Disc cutting, 258
Distributed mode loudspeakers
(DMLs), 51, 53, 55–6, 61, 355
Dither, 189
Dolby, 352–3, 363, 374
Dolby Digital (Surround), 363, 373
Dolby EX, 357
Dolby Stereo, 353
Dome loudspeakers, 40, 121
Domes:
hard, 43
rigid, 43, 248
soft, 43, 248
Doppler distortion, 107, 326
Double distance rule, 201, 207
Driver stages, 164
Drone cones, see ABR (Auxiliary
Bass Radiator)
Dynamic Class A, 161, 245
Dynamic impedance, 246
Efficiency, see also Electroacoustic
efficiency; Radiation efficiency
Electrical protection filters, 327–8,
342, 347
Electroacoustic efficiency, 10, 96,
101, 391
Electromagnetic interference
(EMI), 162
Index 397
Electrostatic loudspeakers, 58–63, 151,
200, 210
EMI (the EMI company), 216
Emilar EK175, 118
Equal loudness contours, 235
Equalisation, one-third octave band,
225, 233
Excess phase, 226, 299, 343
Fahy, Professor Frank, 1
Ferrofluids, 39, 44
Fidelity – definition of, 347
Field coil, 22
Figure-of-eight radiators, see Dipole
radiators
Flare discontinuities, 104, 109, 118
Flare rate, 97, 121
Flare shape, 97
Fletcher-Munson curves, 270, 348
Flush mounting, 88, 91, 211, 233,
254, 261
FM Acoustics, 247
Fosgate, James, 355
Fourier, 292
Fourier transform, 225, 292, 381
Frequency-band splitting, 164–5,
188, 192
Frequency—definition of, 213, 382
Frequency response:
full, 157, 272, 275
magnitude of, 156, 272
plots, 275
Frindle, Paul, 189–90
Genelec, 120, 220–2, 280, 358
Gerlack, 48
Glaser, Ronald, 190
Grille losses, 92
Group delay, 128, 146–7, 220, 226, 274,
293–5, 299, 382
Guitar amplifiers, 267, 282
Haas effect, see Precedence effect
Hair cells, damage to, 250
Harmonic distortion, 157–8, 272,
281, 283
Heaviside function, see
Step-function
Heaviside, Oliver, 154, 292
Height—apparent perception of, 307
Heil air-motion transformer, 50, 52
Heil, Dr Oskar, 51
Hemi-anechoic chambers, 196,
197, 382
Heron, Dr Ken, 51
Heyser, Richard, 271
Hitachi, 163
Holman, Tomlinson, 354–5, 360, 369
Hooke’s Law, 34
Horns loudspeakers:
catenoidal, 121–2
conical, 97, 99
constant directivity, 104
cut-off frequency, 99–100, 108, 122
diffraction, 119
exponential, 98, 100, 103
folded, 123
general, 19, 45, 96, 243
hyperbolic, 121–2
hypex, 121
low frequency, 113, 365–7
materials of construction, 119–20
multicellular, 119–20
radial/sectoral, 103, 118–19
vestigal, 120
Human hearing system, 271
Hysteresis, 34, 43
Impedance, 7, 9, 159, 382
Impedance analogy, 13, 16
Impulse, see Delta function
Inductance of cables, 167–8
Inductive coupling, see Crossovers
Infinite baffle, see Baffle; Sealed box
loudspeakers
Inner suspension, 23
Instantaneous current capacity, 158
Institute of Sound and Vibration
Research (ISVR), 112, 146, 306
Intermodulation distortion, 29, 47,
157–9, 164, 192–3, 273, 283, 288
Ionic loudspeakers, 57
Isobaric loudspeakers, 84
ITU775, 358–9
JBL, 117, 221, 280, 291, 357
JBL L100, 26
JDF, 247
ka, 10
Karlson Coupler, 268
Katz, Dr Shelley, 55
KEF, 33, 55–6, 87
KEF Uni Q, 128, 131
Kellogg, E., 2, 39
Kelly, Stanley, 49
Kinoshita monitors, 145
Kinoshita, Shozo, 247
Korg, 56
Krell amplifiers, 164
398 Index
Laplace, Marquis de, 292
Lateral reflexions, 304
Layered Sound, 55–6
Leslie tone-cabinet, 151
LFE, 363
Linear distortion, 157, 264, 276
Linear system, 3, 272
Lining materials, see Cabinet lining
materials
Litz wire, 170, 188, 193
Live-End, Dead-End rooms, 218
Lodge, Sir Oliver, 2
Loudspeaker:
basic groupings, 229
definition of, 1
orientation of, 219
power ratings, 153
sensitivity/efficiency, 246, 330
Low frequency alignments, 68, 75, 81,
243, 263, 320, 338, 347–8
Magnetic gap and coil proportions, 265
Marginal stability, 168
Marshall amplifiers, 267
Masking of detail, 342
Mastering, 258–63, 276, 279–80, 319,
329, 339, 345, 349
Meter bridge (console top) mounting
of loudspeakers, 92, 253, 334, 338
Meyer HD2, 121
Mid-field monitors, 258
Minimum audible field, 348
Minimum-phase responses, 140, 220–1,
224–6, 275, 299, 384
Mirrored room analogy, 205
Mobility analogy, 13
Mode, see Resonant mode
Modulation transfer function (MTF),
222, 297–302, 345–50
Mongoloid races, 306
Monopole sources (radiators), 210, 374
MOSFET, 163–4
Motional feedback, 226
Moulton, David, 271, 308
Moving coil cone loudspeakers,
9, 22, 39
Multi-cabling, 191, 193, 247
Multi-tone testing, 174, 286–8
Multiamplification, 192–3, 247
Mutual coupling, 205, 215, 386–7
Near-field, 12, 248–9, 387–8
Negative feedback, 170, 183, 269
Neodymium magnets, 23, 37
New Transducers Ltd, 51
Node, 210, 303
Noises:
from equipment (physical), 224
in signals, 157
Non-environment rooms, 218
Non-linear distortion, 47, 157, 162,
174, 230, 239, 264
Non-linear system, 272, 285, 323, 388
Non-minimum-phase responses, 140,
146, 220, 223–6, 384
Norcross, S. G., 223
NXT, 51
Off-axis energy, 242, 276, 296, 373
Ohm’s law, 14
Olson, H. F., 49, 88
Oxygen-free copper (OFC), 180
Pan-pot, 215–16
Parasitic cones, 124, 127
Particle velocity, 7, 51
Passive radiator, see ABR (Auxiliary
Bass Radiator)
PCM, 162
Pedestal mounting, 338
Pendulum, 208
Perception relative to SPL, 231, 251
Permendur, 37
Phantom images, 212, 215–17
Phase, 274, 277, 289, 297, 327, 329
Phase dispersion, 11
Phase distortion, 156, 226
Phase inverters, see Reflex enclosures
Phase shift, 156–7
Phase slope, 156
Phasing plug, 47–8, 115
Piezoelectric transducers, 57
Pink noise, 292, 390
Pinnae, 303, 305, 307, 390
Piston radiators, 99, 239, 243
Planar loudspeakers, 63
Plane wave, 7, 104
Plates, vibrations in, 282
PMC (Professional Monitor
Company), 78, 260
Polyamplification, 192–3
Power amplifier, 151, 237
Power cables, 246
Power ratings of amplifiers, 154
Precedence effect, 217, 372, 390
Pressure source, 210
Progressive wave, 7, 104
Pulsating sphere, 40
PWM, 162
Pythagorus’ theorem, 17
Index 399
Q (directivity factor), see Directivity
factor (Q)
Q (quality factor), 65, 68–9, 73, 81,
136, 390
Quad Electrostactic Loudspeaker, 62
Quad ESL 63, 61
Quadrophonics, 352–4
Quartz cells, 57
Quested HM415, 247
Quested Loudspeakers, 358
Radiation efficiency, 96, 99, 101,
239, 325
Radiation impedance, 202, 205
Radio frequency interference
(RFI), 188–9
Radiola Model 104, 3
Rare earth magnets, 22–3, 37
Rattles, 157
Reactance:
of capacitor, 12, 16
general, 7
of inductor, 12, 16
Reactive impedances, 7, 171
Reflex cabinets, 71, 200, 260,
326, 328–9
Reflex enclosures, 71
Reflex loading, 71, 239, 326
Resistance, 391
Resonance, free air, 35, 73
Resonant frequency, 87, 239, 324
Resonant mode, 209–10, 236, 303,
366–8, 384–6
Resonant systems, 18, 71, 279, 327
Reverberation chambers, 197, 199,
214, 297
RG59 cable, 174, 180
Ribbon loudspeakers, 48
Rice, C., 239
Ring radiator, 42, 44–5
Robinson-Dadson curves, 235,
270, 348
Rochelle salt, 57
Rocking motion, 44
Roederer, J.G., 308
Roll-offs:
at high frequencies, 233
orders of, 129–37, 328, 339, 341,
343, 347
phase effects, 155
Room equalisation, 298–301
Room modes, see Resonant mode
Samarium magnets, 23, 37
Schottky, 48
SDDS, 357
Sealed box loudspeakers, 65, 67, 76–7,
80, 200, 328–9, 342
Semi-anechoic chambers, 196, 391
Sensation of fidelity, 56, 267
Siemens, Werner, 2
Skin effect, 170
Slew rate, 154
Sliding Bias Class A, 160–1
SLS Loudspeakers, 50
Small, Richard, 123, 139
Solid State Logic, 189–90
Sony Oxford R3, 189–90
Sound, 1
Sound field distortion, 303
Sound fields, 238, 302, 306
Sound power, 96
Sound pressure, 1
Spaciousness, 304
Speaking tubes, 201
Specific acoustic impedance, 7
Speech transmission index (STI), 297,
342, 347
Speed of sound:
in air, 1, 105, 147
in other materials, 147
Sphere, surface area of, 197
Spider, 23, 25, 32–3, 39, 326
Standing waves, 99–100, 209, 392
Step-function, 154–5, 274, 288, 316
Step-function generator, 154, 289, 316
Step response, 128
Stereo, original patent, 216
Stretching pressure, 97–9
Strings, harmonic break-up, 282
Sub-woofers:
compound, 368–9
general, 361–8
mono, 85, 361, 365
multiple, 262, 363
stereo, 85, 361
Sum and difference tones, 273
Super Class A, 160–1
Super position, principal of, 105
Surround loudspeakers (in
cinemas), 373
Surrounds (of loudspeaker
diaphragms), 30–1
Suspension, inner, see Spider
Tannoy, 143, 152
Tannoy Dual Concentric
loudspeakers, 45, 107, 111–12,
115, 128, 134, 244
Target functions, 139–40, 240
400 Index
TD 2001, 111, 118, 174, 244
Terekhov, Alexander, 174
THD+N, 281
Theile, Neville, 139
Thermal compression, 239, 243,
246, 326
Thomas, Peter, 78
THX, 352, 374
Titanium, 43, 121
Toole, Dr Floyd, 308, 368–9
Toyashima, Sam, 358
Transient headroom, 245
Transient response, 69, 75, 154–5,
164, 225–6, 245–6, 292, 299,
327, 350, 366, 393–4
Transmission lines, 76, 200
Transparency, 286, 301
Tuning ports, 326–7
Turbulence, 116, 326
UREI 815, 252, 325
UREI horns, 128
Valve (tube) amplifiers, 151, 164,
168, 269
Velocity component, 208
Vented boxes, see Reflex enclosures
Villchur, Edgar, 71
Voice coil, 22–3, 35, 147, 332
Voice coil former, 35
Voice coil temperatures, 35, 37,
39–40, 332
Voight, Paul, 3
Voishvillo, Alexander, 174, 283
Voltage-controlled amplifiers
(VCAs), 189
Volume-velocity sources, 9, 210,
239, 321
Vox AC30, 28, 267
Waste heat, 30, 237, 239, 243, 252,
265, 323, 326, 332
Waterfall plots, 255, 277, 289, 315,
322–3, 332, 344, 346
Watkinson, John, 272, 301
Wattless power, 17
Waveform steepening, 105–6
Waveguides, 92, 115, 120–1, 245
Wavelength, 126, 213
Wedges, anechoic, 196
White noise, 292, 394
Work, 19
X-curve, 235, 358–9
Yamaha NS10M, 92, 164, 232, 253,
255, 279, 327, 329, 334
Zobel filter, 189
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