Audio Power
Design Handbook
Audio Power
Design Handbook
Third edition
Douglas Self MA, MSc
An imprint of Elsevier Science
Linacre House, Jordan Hill, Oxford OX2 8DP
225 Wildwood Avenue, Woburn MA 01801-2041
First published 1996
Reprinted 1997, 1998
Second edition 2000
Reprinted 2000
Third edition 2002
Copyright © 1996, 2000, 2002, Douglas Self. All rights reserved
The right of Douglas Self to be identified as the author of this work has
been asserted in accordance with the Copyright, Designs and Patents Act
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A catalogue record for this book is available from the British Library
ISBN 0 7506 56360
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Printed and bound in Great Britain
1. Introduction and general survey
2. History, architecture and negative feedback
3. The general principles of power amplifiers
4. The small signal stages
5. The output stage I
6. The output stage II
7. Compensation, slew-rate, and stability
8. Power supplies and PSRR
9. Class-A power amplifiers
10. Class-G power amplifiers
11. FET output stages
12. Thermal compensation and thermal dynamics
13. Amplifier and loudspeaker protection
14. Grounding and practical matters
15. Testing and safety
Chapter 1
Introduction and general survey
The economic importance of audio amplifiers
There are no practical textbooks
Knowledge assumed
Origins and aims
The study of amplifier design
Some new findings in amplifier design
A snapshot of the technology
No inspiration from IC technology
Aimed at discrete amplifiers
Amplifiers are now designable
Misinformation in audio
Science and subjectivism
The Subjectivist position
A short history of subjectivism
The limits of hearing
Articles of faith: the tenets of subjectivism
The length of the audio chain
The implications
The reasons why
The outlook
Technical errors
The performance requirements for amplifiers
Power output and load capability
Frequency response
Damping factor
Absolute phase
Chapter 2
History, architecture and negative
A Brief History of Power Amplifiers
Power amplifier architectures
The three-stage structure
The two-stage amplifier structure
Power amplification classes
Variations on Class-B
AC and DC coupled amplifiers
The advantages of AC-coupling
The advantages of DC-coupling
Negative feedback in power amplifiers
Some common misconceptions about negative feedback
Amplifier stability and NFB
Maximising the NFB factor
Linearising before adding NFB
Chapter 3
The general principles of power
How a generic power amplifier really works
The advantages of the conventional
The eight distortions
The performance of a standard power amplifier
Determining open-loop non-linearity
Direct open-loop gain measurement
The use of ‘model’ amplifiers
The concept of the Blameless amplifier
Chapter 4
The small signal stages
The role of the input stage
Three kinds of differential input stage
BJTs versus FETs for input stages
Singleton versus differential input stages
Measuring input stage distortion in isolation
Importance of input stage balance
Use of current-mirrors
Constant-gm degeneration
Radical methods of improving linearity
Input stage cascoding
Input noise and how to reduce it
Input balance and DC offset
The input stage and the slew-rate
The voltage-amplifier stage
Measuring VAS distortion in isolation
VAS operation
VAS distortion
Linearising the VAS: active-load techniques
Enhancements to the basic VAS
The importance of voltage drive
The Balanced VAS
The VAS and the manipulation of open-Loop bandwidth
Manipulating open-loop bandwidth
Chapter 5
The output stage I
Classes and devices
The distortions of the output
Harmonic generation by crossover distortion
Comparing output stages
The Emitter-Follower output configuration
The Complementary-Feedback-Pair output configuration
Quasi-Complementary output stages
Output triples
Triple EF output stages
Distortion and its mechanisms
Large-signal distortion
The load-invariant concept
The LSN mechanism
Doubled output devices
Better output devices
Feedforward diodes
Trouble with triples
Loads below 4 Better 8- performance
A practical load-invariant design
The latest findings
Crossover distortion
Switchoff distortion
Thermal distortion: why it doesn’t exist
Thermal distortion in a power amp IC
Selecting the appropriate output stage
Closing the loop: distortion in complete amplifiers
Chapter 6
The output stage II
Distortion 4: non-linear loading of the VAS
Distortion 5: incorrect decouple grounding
Distortion 6: the induction of non-linear currents
Distortion 7: incorrect feedback connection point
Distortion 8: feedback capacitor distortion
A complete Class-B power amplifier
Chapter 7 Compensation, slew-rate, and stability
Compensation in general
Dominant-pole compensation
Lag compensation
Including the output-stage: inclusive Miller compensation
Nested feedback loops
Two-pole compensation
Output networks
Amplifier output impedance
Minimising amplifier output impedance
Zobel networks
Output inductors
The output inductor value
Cable effects
Crosstalk in amplifier output inductors
Reactive loads and speaker simulation
Resistive loads
Loudspeaker load modelling
Reactive and loudspeaker loads
Single-speaker load
Two-way speaker loads
Enhanced loudspeaker currents
Amplifier instability
HF instability
LF instability
Speed and slew-rate in audio amplifiers
The basics of amplifer slew-limiting
Slew-rate measurement techniques
Improving the slew-rate
Simulating slew-limiting
Slewing limitations in real life
Some additional complications
Further improvements and other configurations
Chapter 8
Power supplies and PSRR
Power supply technologies
Simple unregulated supplies
Linear regulated supplies
Switch-made power supplies
Design considerations for unregulated supplies
Mains transformers
Fusing and rectification
RF emissions from bridge rectifiers
Power supply-rail rejection
A design philosophy for rail rejection
Positive supply-rail rejection
Negative supply-rail rejection
Chapter 9
Class-A power amplifiers
An introduction to Class-A
Class-A configurations and efficiency
Output stages in Class-A
Quiescent current control systems
A novel quiescent current controller
A complete Class-A power amplifier
Trimodal power amplifiers
Load impedance and operating mode
On Trimodal biasing
Class-A/AB mode
Class-B mode
The mode-switching system
Thermal design
A complete Trimodal power amplifier
The power supply
The performance
Further possibilities
Chapter 10
Class-G power amplifiers
The principles of Class-G
Introducing series Class-G
Efficiency of Class-G
The biasing requirements
The linearity issues of series Class-G
The static linearity
Practical Class-G design
Controlling small-signal distortion
The performance
Deriving a new kind of amplifier: Class-A + C
Adding two-pole compensation
Further variations on Class-G
Chapter 11
FET output stages
The characteristics of power FETs
Power FETs versus bipolar transistors (BJTs)
Insulated-Gate Bipolar Junction Transistors (IGBTs)
Power FET output stages
The FET/bipolar linearity comparison
FETs in Class-A stages
Chapter 12
Thermal compensation and thermal
Why Class-B quiescent conditions are critical
The accuracy required
Basic thermal compensation
Assessing the bias errors
Thermal simulation
Modelling the EF output stage
Modelling the CFP output stage
The integrated absolute error criterion
Improved thermal compensation: The emitter-follower stage
Improved thermal compensation: The CFP output stage
A better CFP sensor position
A junction-temperature estimator
A junction estimator with dynamics
Variable-tempco bias generators
Creating a higher tempco
Ambient temperature changes
Creating a lower tempco
Current compensation
Thermal dynamics in reality
Early effect in output stages
Chapter 13 Amplifier and loudspeaker protection
Categories of amplifier protection
Semiconductor failure modes
Overload protection
Electronic protection
Plotting the protection locus
Simple current-limiting
Single-slope VI limiting
Dual-slope VI limiting
Simulating overload protection
Catching diodes
DC-offset protection
Relay protection and muting output control
Distortion in output relays
Output crowbar DC protection
Protection by power-supply shutdown
Thermal protection
Powering auxiliary circuitry
Chapter 14
Grounding and practical matters
Audio Amplifier PCB design
Rail induction distortion
The mounting of output devices
Single and double-sided PCBs
Power supplies
Power amplifier PCB layout details
The audio PCB layout sequence
Miscellaneous points
Amplifier grounding
Ground loops: how they work and how to deal with them
Class I and Class II
Mechanical layout and design
Convection cooling
Mains transformers
Wiring layout
Semiconductor installation
Chapter 15
Testing and safety
Testing and fault-finding
Safety requirements
I wish to dedicate this book to my parents Russell and Evelyn, and
to all the friends and colleagues who have given me help,
information and encouragement while I was engaged in its writing.
In particular I want to acknowledge the active assistance and
collaboration of Gareth Connor in the quest for the perfect
amplifier, and the fortitude of Peter King in enduring many rambling
expositions of my latest thoughts on the subject.
The design of power amplifiers exerts a deep fascination all of its own in
both amateur and professional circles. The job they do is essentially simple,
but making a reliable high-performance circuit to do it well is surprisingly
difficult, and involves delving into all kinds of byways of electronics.
Perhaps this paradox is at the root of the enduring interest they generate.
Reliable information on power amplifier design is hard to find, but in this
book, I hope to fill at least some of that need.
It is notable how few aspects of amplifier design have received serious
scientific investigation. Much of this book is the result of my own research,
because the information required simply was not to be found in the
published literature.
In the course of my investigations, I was able to determine that power
amplifier distortion, traditionally a difficult and mysterious thing to grapple
with, was the hydra-headed amalgamation of seven or eight mechanisms,
overlaying each other and contributing to a complex result. I have evolved
ways of measuring and minimising each distortion mechanism separately,
and the result is a design methodology for making Class-B or Class-A
amplifiers with distortion performance so good that two or three years ago
it would have been regarded as impossible. The methodology gives
pleasingly reliable and repeatable results with moderate amounts of
negative feedback, and insignificant added cost. It is described and
explained in detail here.
This leads to the concept of what I have called a Blameless amplifier, which
forms a benchmark for distortion performance that varies surprisingly little,
and so forms a well-defined point of departure for more ambitious and
radical amplifier designs. The first of these I have undertaken is the Trimodal
amplifier (so-called because it can work in any of the modes A, AB and B,
as the situation requires) which is fully described in Chapter 9.
Apart from the major issue of distortion and linearity in power amplifier
design, I also cover more mundane but important matters such as reliability,
power supplies, overload and DC-protection, and so on. In addition there
is unique material on reactive loading, unusual forms of compensation,
distortion produced by capacitors and fuses, and much more. I have
provided a wide and varied selection of references, so that those interested
can pursue the issues further.
Sometimes controversies arise in audio; in fact, it would be truer to say that
they have become endemic, despite a lack of hard facts on which genuine
differences of opinion might be based. Although audio power amplifiers are
in many ways straightforward in their doings, they have not escaped the
attentions of those who incline more to faith than science. In my writings,
I simply go where the facts lead me, and my experiences as an amateur
musician, my work designing professional mixing consoles, and my studies
in psychology and psychoacoustics have led me to the firm conclusion that
inexplicable influences on audio quality simply do not exist, and that any
serious book on amplifier design must start from this premise.
I have done my best to make sure that everything in this book is as correct
as theory, simulation, practical measurement and late-night worrying can
make it. The basic arguments have been validated by the production of
more than twenty thousand high-power Blameless amplifiers over the last
two years, which is perhaps as solid a confirmation as any methodology
can hope to receive. If some minor errors do remain, these are entirely
my responsibility, and when alerted I will correct them at the first
I hope this book may be interesting and useful to the amplifier designer and
constructor, be they amateur or professional. However, it is my fondest
wish that it may stimulate others to further explore and expand the limits of
audio knowledge.
Douglas Self
Introduction and general
The economic importance of power amplifiers
Audio power amplifiers are of considerable economic importance. They
are built in their hundreds of thousands every year, and have a history
extending back to the 1920s. It is therefore surprising there have been so
few books dealing in any depth with solid-state power amplifier design.
The first aim of this text is to fill that need, by providing a detailed guide to
the many design decisions that must be taken when a power amplifier is
The second aim is disseminate the results of the original work done on
amplifier design in the last few years. The unexpected result of these
investigations was to show that power amplifiers of extraordinarily low
distortion could be designed as a matter of routine, without any
unwelcome side-effects, so long as a relatively simple design methodology
was followed. This methodology will be explained in detail.
To keep its length reasonable, a book such as this must assume a basic
knowledge of audio electronics. I do not propose to plough through the
definitions of frequency response, THD and signal-to-noise ratio; this can
be found anywhere. Commonplace facts have been ruthlessly omitted
where their absence makes room for something new or unusual, so this is
not the place to start learning electronics from scratch. Mathematics has
been confined to a few simple equations determining vital parameters such
as open-loop gain; anything more complex is best left to a circuit simulator
you trust. Your assumptions, and hence the output, may be wrong, but at
least the calculations in-between will be correct . . .
Audio Power Amplifier Design Handbook
The principles of negative feedback as applied to power amplifiers are
explained in detail, as there is still widespread confusion as to exactly how
it works.
Origins and aims
The core of this book is based on a series of eight articles originally
published in Electronics World as ‘Distortion In Power Amplifiers’. This
series was primarily concerned with distortion as the most variable feature
of power amplifier performance. You may have two units placed side by
side, one giving 2% THD and the other 0.0005% at full power, and both
claiming to provide the ultimate audio experience. The ratio between the
two figures is a staggering 4000:1, and this is clearly a remarkable state of
affairs. One might be forgiven for concluding that distortion was not a very
important parameter. What is even more surprising to those who have not
followed the evolution of audio over the last two decades is that the more
distortive amplifier will almost certainly be the more expensive. I shall deal
in detail with the reasons for this astonishing range of variation.
The original series was inspired by the desire to invent a new output stage
that would be as linear as Class-A, without the daunting heat problems. In
the course of this work it emerged that output stage distortion was
completely obscured by non-linearities in the small-signal stages, and it
was clear that these distortions would need to be eliminated before any
progress could be made. The small-signal stages were therefore studied in
isolation, using model amplifiers with low-power and very linear Class-A
output stages, until the various overlapping distortion mechanisms had
been separated out. It has to be said this was not an easy process. In each
case there proved to be a simple, and sometimes well-known cure, and
perhaps the most novel part of my approach is that all these mechanisms
are dealt with, rather than one or two, and the final result is an amplifier
with unusually low distortion, using only modest and safe amounts of
global negative feedback.
Much of this book concentrates on the distortion performance of amplifiers.
One reason is that this varies more than any other parameter – by up to a
factor of a thousand. Amplifier distortion was until recently an enigmatic
field – it was clear that there were several overlapping distortion
mechanisms in the typical amplifier, but it is the work reported here that
shows how to disentangle them, so they may be separately studied and
then with the knowledge thus gained, minimised.
I assume here that distortion is a bad thing, and should be minimised; I
make no apology for putting it as plainly as that. Alternative philosophies
hold that as some forms of non-linearity are considered harmless or even
euphonic, they should be encouraged, or at any rate not positively
discouraged. I state plainly that I have no sympathy with the latter view; to
Introduction and general survey
my mind the goal is to make the audio path as transparent as possible. If
some sort of distortion is considered desirable, then surely the logical way
to introduce it is by an outboard processor, working at line level. This is not
only more cost-effective than generating distortion with directly-heated
triodes, but has the important attribute that it can be switched off. Those
who have brought into being our current signal-delivery chain, i.e. mixing
consoles, multi-track recorders, CDs, have done us proud in the matter of
low distortion, and to wilfully throw away this achievement at the very last
stage strikes me as curious at best.
In this book I hope to provide information that is useful to all those
interested in power amplifiers. Britain has a long tradition of small and very
small audio companies, whose technical and production resources may not
differ very greatly from those available to the committed amateur. I hope
this volume will be of service to both.
I have endeavoured to address both the quest for technical perfection –
which is certainly not over, as far as I am concerned – and also the
commercial necessity of achieving good specifications at minimum cost.
The field of audio is full of statements that appear plausible but in fact have
never been tested and often turn out to be quite untrue. For this reason I
have confined myself as closely as possible to facts that I have verified
myself. This volume may therefore appear somewhat idiosyncratic in
places; for example FET output stages receive much less coverage than
bipolar ones because the conclusion appears to be inescapable that FETs
are both more expensive and less linear; I have therefore not pursued the
FET route very far. Similarly, most of my practical design experience has
been on amplifiers of less than 300 W power output, and so heavy-duty
designs for large-scale PA work are also under-represented. I think this is
preferable to setting down untested speculation.
The study of amplifier design
Although solid-state amplifiers have been around for some forty years, it
would be a great mistake to assume that everything possible is known
about them. In the course of my investigations I discovered several matters
which, not appearing in the technical literature, appear to be novel, at least
in their combined application:
The need to precisely balance the input pair to prevent second-harmonic
The demonstration of how a beta-enhancement transistor increases the
linearity and reduces the collector impedance of the Voltage-Amplifier
An explanation of why BJT output stages always distort more into 4 than 8 .
Audio Power Amplifier Design Handbook
In a conventional BJT output stage, quiescent current as such is of little
importance. What is crucial is the voltage between the transistor
Power FETs, though for many years touted as superior in linearity, are
actually far less linear than bipolar output devices.
In most amplifiers, the major source of distortion is not inherent in the
amplifying stages, but results from avoidable problems such as induction
of supply-rail currents and poor power-supply rejection.
Any number of oscillograms of square-waves with ringing have been
published that claim to be the transient response of an amplifier into a
capacitive load. In actual fact this ringing is due to the output inductor
resonating with the load, and tells you precisely nothing about amplifier
The above list is by no means complete.
As in any developing field, this book cannot claim to be the last word on
the subject; rather it hopes to be a snapshot of the state of understanding at
this time. Similarly, I certainly do not claim that this book is fully
comprehensive; a work that covered every possible aspect of every
conceivable power amplifier would run to thousands of pages. On many
occasions I have found myself about to write: ‘It would take a whole book
to deal properly with . . .’ Within a limited compass I have tried to be
innovative as well as comprehensive, but in many cases the best I can do
is to give a good selection of references that will enable the interested to
pursue matters further. The appearance of a reference means that I consider
it worth reading, and not that I think it to be correct in every respect.
Sometimes it is said that discrete power amplifier design is rather
unenterprising, given the enormous outpouring of ingenuity in the design of
analogue ICs. Advances in op-amp design would appear to be particularly
relevant. I have therefore spent some considerable time studying this
massive body of material and I have had to regretfully conclude that it is
actually a very sparse source of inspiration for new audio power amplifier
techniques; there are several reasons for this, and it may spare the time of
others if I quickly enumerate them here:
A large part of the existing data refers only to small-signal MOSFETs,
such as those used in CMOS op-amps, and is dominated by the ways in
which they differ from BJTs, for example in their low transconductance.
CMOS devices can have their characteristics customised to a certain
extent by manipulating the width/length ratio of the channel.
In general, only the earlier material refers to BJT circuitry, and then it is
often mainly concerned with the difficulties of making complementary
circuitry when the only PNP transistors available are the slow lateral
kind with limited beta and poor frequency response.
Many of the CMOS op-amps studied are transconductance amplifiers,
i.e. voltage-difference-in, current out. Compensation is usually based on
Introduction and general survey
putting a specified load capacitance across the high-impedance output.
This does not appear to be a promising approach to making audio power
Much of the op-amp material is concerned with the common-mode
performance of the input stage. This is pretty much irrelevant to power
amplifier design.
Many circuit techniques rely heavily on the matching of device
characteristics possible in IC fabrication, and there is also an emphasis
on minimising chip area to reduce cost.
A good many IC techniques are only necessary because it is (or was)
difficult to make precise and linear IC resistors. Circuit design is also
influenced by the need to keep compensation capacitors as small as
possible, as they take up a disproportionately large amount of chip area
for their function.
The material here is aimed at all audio power amplifiers that are still
primarily built from discrete components, which can include anything from
10 W mid-fi systems to the most rarefied reaches of what is sometimes
called the ‘high end’, though the ‘expensive end’ might be a more accurate
term. There are of course a large number of IC and hybrid amplifiers, but
since their design details are fixed and inaccessible they are not dealt with
here. Their use is (or at any rate should be) simply a matter of following the
relevant application note. The quality and reliability of IC power amps has
improved noticeably over the last decade, but low distortion and high
power still remain the province of discrete circuitry, and this situation
seems likely to persist for the foreseeable future.
Power amplifier design has often been treated as something of a black art,
with the implication that the design process is extremely complex and its
outcome not very predictable. I hope to show that this need no longer be
the case, and that power amplifiers are now designable – in other words it
is possible to predict reasonably accurately the practical performance of a
purely theoretical design. I have done a considerable amount of research
work on amplifier design, much of which appears to have been done for
the first time, and it is now possible for me to put forward a design
methodology that allows an amplifier to be designed for a specific
negative-feedback factor at a given frequency, and to a large extent allows
the distortion performance to be predicted. I shall show that this
methodology allows amplifiers of extremely low distortion (sub 0.001% at
1 kHz) to be designed and built as a matter of routine, using only modest
amounts of global negative feedback.
Misinformation in audio
Few fields of technical endeavour are more plagued with errors, misstatements and confusion than audio. In the last twenty years the rise of
controversial and non-rational audio hypotheses, gathered under the title
Audio Power Amplifier Design Handbook
Subjectivism has deepened these difficulties. It is commonplace for hi-fi
reviewers to claim that they have perceived subtle audio differences which
cannot be related to electrical performance measurements. These claims
include the alleged production of a ‘three-dimensional sound-stage and
protests that the rhythm of the music has been altered’; these statements are
typically produced in isolation, with no attempt made to correlate them to
objective test results. The latter in particular appears to be a quite
impossible claim.
This volume does not address the implementation of Subjectivist notions,
but confines itself to the measurable, the rational, and the repeatable. This
is not as restrictive as it may appear; there is nothing to prevent you using
the methodology presented here to design an amplifier that is technically
excellent, and then gilding the lily by using whatever brands of expensive
resistor or capacitor are currently fashionable, and doing the internal wiring
with cable that costs more per metre than the rest of the unit put together.
Such nods to Subjectivist convention are unlikely to damage the real
performance; this is however not the case with some of the more damaging
hypotheses, such as the claim that negative feedback is inherently harmful.
Reduce the feedback factor and you will degrade the real-life operation of
almost any design.
Such problems arise because audio electronics is a more technically
complex subject than it at first appears. It is easy to cobble together some
sort of power amplifier that works, and this can give people an altogether
exaggerated view of how deeply they understand what they have created.
In contrast, no-one is likely to take a ‘subjective’ approach to the design of
an aeroplane wing or a rocket engine; the margins for error are rather
smaller, and the consequences of malfunction somewhat more serious.
The Subjectivist position is of no help to anyone hoping to design a good
power amplifier. However, it promises to be with us for some further time
yet, and it is appropriate to review it here and show why it need not be
considered at the design stage. The marketing stage is of course another
Science and subjectivism
Audio engineering is in a singular position. There can be few branches of
engineering science rent from top to bottom by such a basic division as the
Subjectivist/rationalist dichotomy. Subjectivism is still a significant issue in
the hi-fi section of the industry, but mercifully has made little headway in
professional audio, where an intimate acquaintance with the original
sound, and the need to earn a living with reliable and affordable
equipment, provides an effective barrier against most of the irrational
influences. (Note that the opposite of Subjectivist is not ‘Objectivist’. This
term refers to the followers of the philosophy of Ayn Rand.)
Introduction and general survey
Most fields of technology have defined and accepted measures of
excellence; car makers compete to improve MPH and MPG; computer
manufacturers boast of MIPs (millions of instructions per second) and so on.
Improvement in these real quantities is regarded as unequivocally a step
forward. In the field of hi-fi, many people seem to have difficulty in
deciding which direction forward is.
Working as a professional audio designer, I often encounter opinions
which, while an integral part of the Subjectivist offshoot of hi-fi, are treated
with ridicule by practitioners of other branches of electrical engineering.
The would-be designer is not likely to be encouraged by being told that
audio is not far removed from witchcraft, and that no-one truly knows what
they are doing. I have been told by a Subjectivist that the operation of the
human ear is so complex that its interaction with measurable parameters
lies forever beyond human comprehension. I hope this is an extreme
position; it was, I may add, proffered as a flat statement rather than a basis
for discussion.
I have studied audio design from the viewpoints of electronic design,
psychoacoustics, and my own humble efforts at musical creativity. I have
found complete scepticism towards Subjectivism to be the only tenable
position. Nonetheless, if hitherto unsuspected dimensions of audio quality
are ever shown to exist, then I look forward keenly to exploiting them. At
this point I should say that no doubt most of the esoteric opinions are held
in complete sincerity.
The Subjectivist position
A short definition of the Subjectivist position on power amplifiers might
read as follows:
Objective measurements of an amplifier’s performance are unimportant
compared with the subjective impressions received in informal listening
tests. Should the two contradict the objective results may be
Degradation effects exist in amplifiers that are unknown to orthodox
engineering science, and are not revealed by the usual objective tests.
Considerable latitude may be employed in suggesting hypothetical
mechanisms of audio impairment, such as mysterious capacitor shortcomings and subtle cable defects, without reference to the plausibility of
the concept, or the gathering of objective evidence of any kind.
I hope that this is considered a reasonable statement of the situation;
meanwhile the great majority of the paying public continue to buy
conventional hi-fi systems, ignoring the expensive and esoteric high-end
sector where the debate is fiercest.
It may appear unlikely that a sizeable part of an industry could have set off
in a direction that is quite counter to the facts; it could be objected that
Audio Power Amplifier Design Handbook
such a loss of direction in a scientific subject would be unprecedented. This
is not so.
Parallel events that suggest themselves include the destruction of the study
of genetics under Lysenko in the USSR [1]. Another possibility is the study of
parapsychology, now in deep trouble because after some 100 years of
investigation it has not uncovered the ghost (sorry) of a repeatable
phenomenon [2]. This sounds all too familiar. It could be argued that
parapsychology is a poor analogy because most people would accept that
there was nothing there to study in the first place, whereas nobody would
assert that objective measurements and subjective sound quality have no
correlation at all; one need only pick up the telephone to remind oneself
what a 4 kHz bandwidth and 10% or so THD sounds like.
The most starting parallel I have found in the history of science is the
almost-forgotten affair of Blondlot and the N-rays [3]. In 1903, Rene
Blondlot, a respected French physicist, claimed to have discovered a new
form of radiation he called ‘N-rays’. (This was shortly after the discovery of
X-rays by Roentgen, so rays were in the air, as it were.) This invisible
radiation was apparently mysteriously refracted by aluminium prisms; but
the crucial factor was that its presence could only be shown by subjective
assessment of the brightness of an electric arc allegedly affected by N-rays.
No objective measurement appeared to be possible. To Blondlot, and at
least fourteen of his professional colleagues, the subtle changes in
brightness were real, and the French Academy published more than a
hundred papers on the subject.
Unfortunately N-rays were completely imaginary, a product of the
‘experimenter-expectancy’ effect. This was demonstrated by American
scientist Robert Wood, who quietly pocketed the aluminium prism during
a demonstration, without affecting Bondlot’s recital of the results. After this
the N-ray industry collapsed very quickly, and while it was a major
embarrassment at the time, it is now almost forgotten.
The conclusion is inescapable that it is quite possible for large numbers of
sincere people to deceive themselves when dealing with subjective
assessments of phenomena.
A short history of subjectivism
The early history of sound reproduction is notable for the number of times
that observers reported that an acoustic gramophone gave results indistinguishable from reality. The mere existence of such statements throws
light on how powerfully mind-set affects subjective impressions. Interest in
sound reproduction intensified in the post-war period, and technical
standards such as DIN 45–500 were set, though they were soon criticised
as too permissive. By the late 1960s it was widely accepted that the
requirements for hi-fi would be satisfied by ‘THD less than 0.1%, with no
Introduction and general survey
significant crossover distortion, frequency response 20–20 kHz, and as
little noise as possible, please’. The early 1970s saw this expanded to
include slew-rates and properly behaved overload protection, but the
approach was always scientific and it was normal to read amplifier reviews
in which measurements were dissected but no mention made of listening
Following the growth of subjectivism through the pages of one of the
leading Subjectivist magazines (Hi-Fi News), the first intimation of what
was to come was the commencement of Paul Messenger’s column
Subjective Sounds in September 1976, in which he said: ‘The assessment
will be (almost) purely subjective, which has both strengths and weaknesses, as the inclusion of laboratory data would involve too much time
and space, and although the ear may be the most fallible, it is also the most
sensitive evaluation instrument.’ Subjectivism as expedient rather than
policy. Significantly, none of the early instalments contained references to
amplifier sound. In March 1977, an article by Jean Hiraga was published
vilifying high levels of negative feedback and praising the sound of an
amplifier with 2% THD. In the same issue, Paul Messenger stated that a
Radford valve amplifier sounded better than a transistor one, and by the
end of the year the amplifier-sound bandwagon was rolling. Hiraga
returned in August 1977 with a highly contentious set of claims about
audible speaker cables, and after that no hypothesis was too unlikely to
receive attention.
The limits of hearing
In evaluating the Subjectivist position, it is essential to consider the known
abilities of the human ear. Contrary to the impression given by some
commentators, who call constantly for more psychoacoustical research, a
vast amount of hard scientific information already exists on this subject,
and some of it may be briefly summarised thus:
The smallest step-change in amplitude that can be detected is about
0.3 dB for a pure tone. In more realistic situations it is 0.5 to 1.0 dB. This
is about a 10% change [4].
The smallest detectable change in frequency of a tone is about 0.2% in
the band 500 Hz–2 kHz. In percentage terms, this is the parameter for
which the ear is most sensitive [5].
The least detectable amount of harmonic distortion is not an easy figure
to determine, as there is a multitude of variables involved, and in
particular the continuously varying level of programme means that the
level of THD introduced is also dynamically changing. With mostly loworder harmonics present the just-detectable amount is about 1%, though
crossover effects can be picked up at 0.3%, and probably lower. There
is certainly no evidence that an amplifier producing 0.001% THD
sounds any cleaner than one producing .005% [6].
Audio Power Amplifier Design Handbook
It is acknowledged that THD measurements, taken with the usual notchtype analyser, are of limited use in predicting the subjective impairment
produced by an imperfect audio path. With music, etc. intermodulation
effects are demonstrably more important than harmonics. However, THD
tests have the unique advantage that visual inspection of the distortion
residual gives an experienced observer a great deal of information about
the root cause of the non-linearity. Many other distortion tests exist which,
while yielding very little information to the designer, exercise the whole
audio bandwidth at once and correlate well with properly-conducted tests
for subjective impairment by distortion. The Belcher intermodulation test
(the principle is shown in Figure 1.1) deserves more attention than it has
received, and may become more popular now that DSP chips are
One of the objections often made to THD tests is that their resolution does
not allow verification that no non-linearities exist at very low level; a sort
of micro-crossover distortion. Hawksford, for example, has stated ‘Lowlevel threshold phenomena . . . set bounds upon the ultimate transparency
of an audio system’ [7] and several commentators have stated their belief
that some metallic contacts consist of a net of so-called ‘micro-diodes’. In
fact, this kind of mischievous hypothesis can be disposed of using THD
I evolved a method of measuring THD down to 0.01% at 200 microvolts
rms, and applied it to large electrolytics, connectors of varying provenance,
and lengths of copper cable with and without alleged magic properties. The
method required the design of an ultra-low noise (EIN = –150 dBu for a 10
source resistance) and very low THD [8]. The measurement method is
shown in Figure 1.2; using an attenuator with a very low value of resistance
to reduce the incoming signal keeps the Johnson noise to a minimum. In no
case was any unusual distortion detected, and it would be nice to think that
this red herring at least has been laid to rest.
Interchannel crosstalk can obviously degrade stereo separation, but the
effect is not detectable until it is worse than 20 dB, which would be a
very bad amplifier indeed [9].
Phase and group delay have been an area of dispute for a long time. As
Stanley Lipshitz et al have pointed out, these effects are obviously
perceptible if they are gross enough; if an amplifier was so heroically
misconceived as to produce the top half of the audio spectrum three hours
after the bottom, there would be no room for argument. In more practical
terms, concern about phase problems has centred on loudspeakers and
their crossovers, as this would seem to be the only place where a phaseshift might exist without an accompanying frequency-response change to
make it obvious. Lipshitz appears to have demonstrated [10] that a secondorder all-pass filter (an all-pass filter gives a frequency-dependant phaseshift without level changes) is audible, whereas BBC findings, reported by
Figure 1.1
Basic principle of
Belcher intermodulation
Audio Power Amplifier Design Handbook
Figure 1.2
THD measurements
at very low levels
Harwood [11] indicate the opposite, and the truth of the matter is still not
clear. This controversy is of limited importance to amplifier designers, as
it would take spectacular incompetence to produce a circuit that included
an accidental all-pass filter. Without such, the phase response of an
amplifier is completely defined by its frequency response, and vice-versa;
in Control Theory this is Bode’s Second Law [12], and it should be much
more widely known in the hi-fi world than it is. A properly designed
amplifier has its response roll-off points not too far outside the audio band,
and these will have accompanying phase-shifts; there is no evidence that
these are perceptible [8].
The picture of the ear that emerges from psychoacoustics and related fields
is not that of a precision instrument. Its ultimate sensitivity, directional
capabilities and dynamic range are far more impressive than its ability to
measure small level changes or detect correlated low-level signals like
distortion harmonics. This is unsurprising; from an evolutionary viewpoint
the functions of the ear are to warn of approaching danger (sensitivity and
direction-finding being paramount) and for speech. In speech perception
the identification of formants (the bands of harmonics from vocal-chord
pulse excitation, selectively emphasised by vocal-tract resonances) and
vowel/consonant discriminations, are infinitely more important than any
hi-fi parameter. Presumably the whole existence of music as a source of
pleasure is an accidental side-effect of our remarkable powers of speech
perception: how it acts as a direct route to the emotions remains profoundly
Articles of faith: the tenets of subjectivism
All of the alleged effects listed below have received considerable
affirmation in the audio press, to the point where some are treated as facts.
The reality is that none of them has in the last fifteen years proved
susceptible to objective confirmation. This sad record is perhaps equalled
only by students of parapsychology. I hope that the brief statements below
are considered fair by their proponents. If not I have no doubt I shall soon
hear about it:
Introduction and general survey
Sinewaves are steady-state signals that represent too easy a test for
amplifiers, compared with the complexities of music.
This is presumably meant to imply that sinewaves are in some way
particularly easy for an amplifier to deal with, the implication being that
anyone using a THD analyser must be hopelessly naive. Since sines and
cosines have an unending series of non-zero differentials, steady hardly
comes into it. I know of no evidence that sinewaves of randomly varying
amplitude (for example) would provide a more searching test of amplifier
I hold this sort of view to be the result of anthropomorphic thinking about
amplifiers; treating them as though they think about what they amplify.
Twenty sinewaves of different frequencies may be conceptually complex to
us, and the output of a symphony orchestra even more so, but to an
amplifier both composite signals resolve to a single instantaneous voltage
that must be increased in amplitude and presented at low impedance. An
amplifier has no perspective on the signal arriving at its input, but must
literally take it as it comes.
Capacitors affect the signal passing through them in a way invisible to
distortion measurements.
Several writers have praised the technique of subtracting pulse signals
passed through two different sorts of capacitor, claiming that the non-zero
residue proves that capacitors can introduce audible errors. My view is that
these tests expose only well-known capacitor shortcomings such as
dielectric absorption and series resistance, plus perhaps the vulnerability of
the dielectric film in electrolytics to reverse-biasing. No-one has yet shown
how these relate to capacitor audibility in properly designed equipment.
Passing an audio signal through cables, PCB tracks or switch contacts
causes a cumulative deterioration. Precious metal contact surfaces
alleviate but do not eliminate the problem. This too is undetectable by
tests for non-linearity.
Concern over cables is widespread, but it can be said with confidence that
there is as yet not a shred of evidence to support it. Any piece of wire passes
a sinewave with unmeasurable distortion, and so simple notions of intercrystal rectification or ‘micro-diodes’ can be discounted, quite apart from
the fact that such behaviour is absolutely ruled out by established materials
science. No plausible means of detecting, let alone measuring, cable
degradation has ever been proposed.
The most significant parameter of a loudspeaker cable is probably its
lumped inductance. This can cause minor variations in frequency response
at the very top of the audio band, given a demanding load impedance.
These deviations are unlikely to exceed 0.1 dB for reasonable cable
constructions (say inductance less than 4 µH). The resistance of a typical
Audio Power Amplifier Design Handbook
cable (say 0.1 ) causes response variations across the band, following the
speaker impedance curve, but these are usually even smaller at around
0.05 dB. This is not audible.
Corrosion is often blamed for subtle signal degradation at switch and
connector contacts; this is unlikely. By far the most common form of
contact degradation is the formation of an insulating sulphide layer on
silver contacts, derived from hydrogen sulphide air pollution. This typically
cuts the signal altogether, except when signal peaks temporarily punch
through the sulphide layer. The effect is gross and seems inapplicable to
theories of subtle degradation. Gold-plating is the only certain cure. It costs
Cables are directional, and pass audio better in one direction than the
Audio signals are AC. Cables cannot be directional any more than 2 + 2 can
equal 5. Anyone prepared to believe this nonsense won’t be capable of
designing amplifiers, so there seems no point in further comment.
The sound of valves is inherently superior to that of any kind of
The ‘valve sound’ is one phenomenon that may have a real existence; it has
been known for a long time that listeners sometimes prefer to have a certain
amount of second-harmonic distortion added in [13], and most valve
amplifiers provide just that, due to grave difficulties in providing good
linearity with modest feedback factors. While this may well sound nice, hifi is supposedly about accuracy, and if the sound is to be thus modified it
should be controllable from the front panel by a ‘niceness’ knob.
The use of valves leads to some intractable problems of linearity, reliability
and the need for intimidatingly expensive (and once more, non-linear) ironcored transformers. The current fashion is for exposed valves, and it is not
at all clear to me that a fragile glass bottle, containing a red-hot anode with
hundreds of volts DC on it, is wholly satisfactory for domestic safety.
A recent development in subjectivism is enthusiasm for single-ended
directly-heated triodes, usually in extremely expensive monoblock systems. Such an amplifier generates large amounts of second-harmonic
distortion, due to the asymmetry of single-ended operation, and requires a
very large output transformer as its primary carries the full DC anode
current, and core saturation must be avoided. Power outputs are inevitably
very limited at 10 W or less. In a recent review, the Cary CAD-300SEI triode
amplifier yielded 3% THD at 9 W, at a cost of £3400 [14]. And you still need
to buy a preamp.
Negative feedback is inherently a bad thing; the less it is used, the better
the amplifier sounds, without qualification.
Introduction and general survey
Negative feedback is not inherently a bad thing; it is an absolutely
indispensable principle of electronic design, and if used properly has the
remarkable ability to make just about every parameter better. It is usually
global feedback that the critic has in mind. Local negative feedback is
grudgingly regarded as acceptable, probably because making a circuit
with no feedback of any kind is near-impossible. It is often said that high
levels of NFB enforce a low slew-rate. This is quite untrue; and this
thorny issue is dealt with in detail on page 46. For more on slew-rate see
also [15].
Tone-controls cause an audible deterioration even when set to the flat
This is usually blamed on phase-shift. At the time of writing, tone controls
on a pre-amp badly damage its chances of street (or rather sitting-room)
credibility, for no good reason. Tone-controls set to flat cannot possibly
contribute any extra phase-shift and must be inaudible. My view is that they
are absolutely indispensable for correcting room acoustics, loudspeaker
shortcomings, or tonal balance of the source material, and that a lot of
people are suffering sub-optimal sound as a result of this fashion. It is now
commonplace for audio critics to suggest that frequency-response inadequacies should be corrected by changing loudspeakers. This is an
extraordinarily expensive way of avoiding tone-controls.
The design of the power supply has subtle effects on the sound, quite
apart from ordinary dangers like ripple injection.
All good amplifier stages ignore imperfections in their power supplies, opamps in particular excelling at power-supply rejection-ratio. More nonsense has been written on the subject of subtle PSU failings than on most
audio topics; recommendations of hard-wiring the mains or using goldplated 13 A plugs would seem to hold no residual shred of rationality, in
view of the usual processes of rectification and smoothing that the raw AC
undergoes. And where do you stop? At the local sub-station? Should we
gold-plate the pylons?
Monobloc construction (i.e. two separate power amplifier boxes) is
always audibly superior, due to the reduction in crosstalk.
There is no need to go to the expense of monobloc power amplifiers in
order to keep crosstalk under control, even when making it substantially
better than the –20 dB that is actually necessary. The techniques are
conventional; the last stereo power amplifier I designed managed an easy
–90 dB at 10 kHz without anything other than the usual precautions. In this
area dedicated followers of fashion pay dearly for the privilege, as the cost
of the mechanical parts will be nearly doubled.
Microphony is an important factor in the sound of an amplifier, so any
attempt at vibration-damping is a good idea.
Audio Power Amplifier Design Handbook
Microphony is essentially something that happens in sensitive valve preamplifiers, If it happens in solid-state power amplifiers the level is so far
below the noise it is effectively non-existent.
Experiments on this sort of thing are rare (if not unheard of) and so I offer
the only scrap of evidence I have. Take a microphone pre-amp operating at
a gain of +70 dB, and tap the input capacitors (assumed electrolytic)
sharply with a screwdriver; the pre-amp output will be a dull thump, at low
level. The physical impact on the electrolytics (the only components that
show this effect) is hugely greater than that of any acoustic vibration; and
I think the effect in power amps, if any, must be so vanishingly small that
it could never be found under the inherent circuit noise.
Let us for a moment assume that some or all of the above hypotheses are
true, and explore the implications. The effects are not detectable by
conventional measurement, but are assumed to be audible. Firstly, it can
presumably be taken as axiomatic that for each audible defect some
change occurs in the pattern of pressure fluctuations reaching the ears, and
therefore a corresponding modification has occurred to the electrical signal
passing through the amplifier. Any other starting point supposes that there
is some other route conveying information apart from the electrical signals,
and we are faced with magic or forces-unknown-to-science. Mercifully no
commentator has (so far) suggested this. Hence there must be defects in the
audio signals, but they are not revealed by the usual test methods. How
could this situation exist? There seem two possible explanations for this
failure of detection: one is that the standard measurements are relevant, but
of insufficient resolution, and we should be measuring frequency response,
etc. to thousandths of a dB. There is no evidence whatsoever that such
micro-deviations are audible under any circumstances.
An alternative (and more popular) explanation is that standard sinewave
THD measurements miss the point by failing to excite subtle distortion
mechanisms that are triggered only by music, the spoken word, or
whatever. This assumes that these music-only distortions are also left
undisturbed by multi-tone intermodulation tests, and even the complex
pseudorandom signals used in the Belcher distortion test [16]. The Belcher
method effectively tests the audio path at all frequencies at once, and it is
hard to conceive of a real defect that could escape it.
The most positive proof that subjectivism is fallacious is given by
subtraction testing. This is the devastatingly simple technique of subtracting
before-and-after amplifier signals and demonstrating that nothing audibly
detectable remains.
It transpires that these alleged music-only mechanisms are not even
revealed by music, or indeed anything else, and it appears the subtraction
test has finally shown as non-existent these elusive degradation
Figure 1.3
Baxandall cancellation
Audio Power Amplifier Design Handbook
Figure 1.4
Hafler straight-wire
differential test
The subtraction technique was proposed by Baxandall in 1977 [17]. The
principle is shown in Figure 1.3; careful adjustment of the rolloff-balance
network prevents minor bandwidth variations from swamping the true
distortion residual. In the intervening years the Subjectivist camp has made
no effective reply.
A simplified version of the test was introduced by Hafler [18]. This method
is less sensitive, but has the advantage that there is less electronics in the
signal path for anyone to argue about. See Figure 1.4. A prominent
Subjectivist reviewer, on trying this demonstration, was reduced to
claiming that the passive switchbox used to implement the Hafler test was
causing so much sonic degradation that all amplifier performance was
swamped [19]. I do not feel that this is a tenable position. So far all
experiments such as these have been ignored or brushed aside by the
Subjectivist camp; no attempt has been made to answer the extremely
serious objections that this demonstration raises.
In the twenty or so years that have elapsed since the emergence of the
Subjectivist Tendency, no hitherto unsuspected parameters of audio quality
have emerged.
The length of the audio chain
An apparently insurmountable objection to the existence of non-measurable amplifier quirks is that recorded sound of almost any pedigree has
passed through a complex mixing console at least once; prominent parts
like vocals or lead guitar will almost certainly have passed through at least
twice, once for recording and once at mix-down. More significantly, it must
have passed through the potential quality-bottleneck of an analogue tape
machine or more likely the A–D converters of digital equipment. In its long
path from here to ear the audio passes through at least a hundred op-amps,
dozens of connectors and several hundred metres of ordinary screened
cable. If mystical degradations can occur, it defies reason to insist that those
introduced by the last 1% of the path are the critical ones.
Introduction and general survey
The implications
This confused state of amplifier criticism has negative consequences.
Firstly, if equipment is reviewed with results that appear arbitrary, and
which are in particular incapable of replication or confirmation, this can be
grossly unfair to manufacturers who lose out in the lottery. Since subjective
assessments cannot be replicated, the commercial success of a given make
can depend entirely on the vagaries of fashion. While this is fine in the
realm of clothing or soft furnishings, the hi-fi business is still claiming
accuracy of reproduction as its raison d’être, and therefore you would
expect the technical element to be dominant.
A second consequence of placing subjectivism above measurements is that
it places designers in a most unenviable position. No degree of ingenuity or
attention to technical detail can ensure a good review, and the pressure to
adopt fashionable and expensive expedients (such as linear-crystal internal
wiring) is great, even if the designer is certain that they have no audible
effect for good or evil. Designers are faced with a choice between
swallowing the Subjectivist credo whole or keeping very quiet and leaving
the talking to the marketing department.
If objective measurements are disregarded, it is inevitable that poor
amplifiers will be produced, some so bad that their defects are unquestionably audible. In recent reviews [20] it was easy to find a £795 pre-amplifier
(Counterpoint SA7) that boasted a feeble 12 dB disc overload margin,
(another pre-amp costing £2040 struggled up to 15 dB (Burmester 838/846)
and another, costing £1550 that could only manage a 1 kHz distortion
performance of 1%; a lack of linearity that would have caused consternation ten years ago (Quicksilver). However, by paying £5700 one could inch
this down to 0.3% (Audio Research M100–2 monoblocs). This does not of
course mean that it is impossible to buy an audiophile amplifier that does
measure well; another example would be the pre-amplifier/power amplifier
combination that provides a very respectable disc overload margin of 31 dB
and 1 kHz rated-power distortion below 0.003%; the total cost being £725
(Audiolab 8000C/8000P). I believe this to be a representative sample, and
we appear to be in the paradoxical situation that the most expensive
equipment provides the worst objective performance. Whatever the rights
and wrongs of subjective assessment, I think that most people would agree
that this is a strange state of affairs. Finally, it is surely a morally ambiguous
position to persuade non-technical people that to get a really good sound
they have to buy £2000 pre-amps and so on, when both technical
orthodoxy and common sense indicate that this is quite unnecessary.
The reasons why
Some tentative conclusions are possible as to why hi-fi engineering has
reached the pass that it has. I believe one basic reason is the difficulty of
defining the quality of an audio experience; you can’t draw a diagram to
Audio Power Amplifier Design Handbook
communicate what something sounded like. In the same way, acoustical
memory is more evanescent than visual memory. It is far easier to visualise
what a London bus looks like than to recall the details of a musical performance. Similarly, it is difficult to ‘look more closely’; turning up the volume is
more like turning up the brightness of a TV picture; once an optimal level is
reached, any further increase becomes annoying, then painful.
It has been universally recognised for many years in experimental
psychology, particularly in experiments about perception, that people tend
to perceive what they want to perceive. This is often called the
experimenter expectancy effect; it is more subtle and insidious than it
sounds, and the history of science is littered with the wrecked careers of
those who failed to guard against it. Such self-deception has most often
occurred in fields like biology, where although the raw data may be
numerical, there is no real mathematical theory to check it against. When
the only ‘results’ are vague subjective impressions, the danger is clearly
much greater, no matter how absolute the integrity of the experimenter.
Thus in psychological work great care is necessary in the use of impartial
observers, double-blind techniques, and rigorous statistical tests for
significance. The vast majority of Subjectivist writings wholly ignore these
precautions, with predictable results. In a few cases properly controlled
listening tests have been done, and at the time of writing all have resulted
in different amplifiers sounding indistinguishable. I believe the conclusion
is inescapable that experimenter expectancy has played a dominant role in
the growth of subjectivism.
It is notable that in Subjectivist audio the ‘correct’ answer is always the
more expensive or inconvenient one. Electronics is rarely as simple as that.
A major improvement is more likely to be linked with a new circuit
topology or new type of semiconductor, than with mindlessly specifying
more expensive components of the same type; cars do not go faster with
platinum pistons.
It might be difficult to produce a rigorous statistical analysis, but it is my
view that the reported subjective quality of a piece of equipment correlates
far more with the price than with anything else. There is perhaps here an
echo of the Protestant Work Ethnic; you must suffer now to enjoy yourself
later. Another reason for the relatively effortless rise of subjectivism is the
me-too effect; many people are reluctant to admit that they cannot detect
acoustic subtleties as nobody wants to be labelled as insensitive,
outmoded, or just plain deaf. It is also virtually impossible to absolutely
disprove any claims, as the claimant can always retreat a fraction and say
that there was something special about the combination of hardware in use
during the disputed tests, or complain that the phenomena are too delicate
for brutal logic to be used on them. In any case, most competent engineers
with a taste for rationality probably have better things to do than dispute
every controversial report.
Introduction and general survey
Under these conditions, vague claims tend, by a kind of intellectual
inflation, to gradually become regarded as facts. Manufacturers have some
incentive to support the Subjectivist camp as they can claim that only they
understand a particular non-measurable effect, but this is no guarantee that
the dice may not fall badly in a subjective review.
The outlook
It seems unlikely that subjectivism will disappear for some time, given the
momentum that it has gained, the entrenched positions that some people
have taken up, and the sadly uncritical way in which people accept an
unsupported assertion as the truth simply because it is asserted with
frequency and conviction. In an ideal world every such statement would be
greeted by loud demands for evidence. However, the history of the world
sometimes leads one to suppose pessimistically that people will believe
anything. By analogy, one might suppose that subjectivism would persist
for the same reason that parapsychology has; there will always be people
who will believe what they want to believe rather than what the hard facts
Technical errors
Misinformation also arises in the purely technical domain; I have also
found that some of the most enduring and widely held technical beliefs to
be unfounded. For example, if you take a Class-B amplifier and increase its
quiescent current so that it runs in Class-A at low levels, i.e. in Class AB,
most people will tell you that the distortion will be reduced as you have
moved nearer to the full Class-A condition. This is untrue. A correctly
configured amplifier gives more distortion in Class-AB, not less, because of
the abrupt gain changes inherent in switching from A to B every cycle.
Discoveries like this can only be made because it is now straightforward to
make testbed amplifiers with ultra-low distortion – lower than that which
used to be thought possible. The reduction of distortion to the basic or
inherent level that a circuit configuration is capable of is a fundamental
requirement for serious design work in this field; in Class-B at least this
gives a defined and repeatable standard of performance that in later
chapters I name a Blameless amplifier, so-called because it avoids error
rather than claiming new virtues.
It has proved possible to take the standard Class-B power amplifier
configuration, and by minor modifications, reduce the distortion to below
the noise floor at low frequencies. This represents approximately 0.0005 to
0.0008% THD, depending on the exact design of the circuitry, and the
actual distortion can be shown to be substantially below this if spectrumanalysis techniques are used to separate the harmonics from the noise.
Audio Power Amplifier Design Handbook
The performance requirements for amplifiers
This section is not a recapitulation of international standards, which are
intended to provide a minimum level of quality rather than extend the art.
It is rather my own view of what you should be worrying about at the start
of the design process, and the first items to consider are the brutally
pragmatic ones related to keeping you in business and out of prison.
In the drive to produce the finest amplifier ever made, do not forget that the
Prime Directive of audio design is – Thou Shalt Not Kill. Every other
consideration comes a poor second, not only for ethical reasons, but also
because one serious lawsuit will close down most audio companies
If you are in the business of manufacturing, you had better make sure that
your equipment keeps working, so that you too can keep working. It has to
be admitted that power amplifiers – especially the more powerful ones –
have a reputation for reliability that is poor compared with most branches
of electronics. The ‘high end’ in particular has gathered to itself a bad
reputation for dependability [21].
Power output
In commercial practice, this is decided for you by the marketing
department. Even if you can please yourself, the power output capability
needs careful thought as it has a powerful and non-linear effect on the
The last statement requires explanation. As the output power increases, a
point is reached when single output devices are incapable of sustaining the
thermal dissipation, parallel pairs are required, and the price jumps up.
Similarly, transformer laminations come in standard sizes, so the transformer size and cost will also increase in discrete steps.
Domestic hi-fi amplifiers usually range from 20 W to 150 W into 8 ,
though with a scattering of much higher powers. PA units will range from
50 W, for foldback purposes (i.e. the sound the musician actually hears, to
monitor his/her playing, as opposed to that thrown out forwards by the
main PA stacks; also called stage monitoring) to 1 kW or more. Amplifiers
of extreme high power are not popular, partly because the economies of
scale are small, but mainly because it means putting all your eggs in one
basket, and a failure becomes disastrous. This is accentuated by the
statistically unproven but almost universally-held opinion that high-power
solid-state amplifiers are inherently less reliable than others.
Introduction and general survey
If an amplifier gives a certain output into 8 , it will not give exactly twice
as much into 4 loads; in fact it will probably be much less than this, due
to the increased resistive losses in 4 operation, and the way that power
alters as the square of voltage. Typically, an amplifier giving 180 W into 8 might be expected to yield 260 W into 4 and 350 W into 2 , if it can
drive so low a load at all. These figures are approximate, depending very
much on power supply design.
Nominally 8 loudspeakers are the most common in hi-fi applications.
The nominal title accommodates the fact that all loudspeakers, especially
multi-element types, have marked changes in input impedance with
frequency, and are only resistive at a few spot frequencies. Nominal 8 loudspeakers may be expected to drop to at least 6 in some part of the
audio spectrum. To allow for this, almost all amplifiers are rated as capable
of 4 as well as 8 loads. This takes care of almost any nominal 8 speaker, but leaves no safety margin for nominal 4 designs, which are
likely to dip to 3 or less. Extending amplifier capability to deal with lower
load impedances for anything other than very short periods has serious cost
implications for the power-supply transformer and heatsinking; these
already represent the bulk of the cost.
The most important thing to remember in specifying output power is that
you have to increase it by an awful lot to make the amplifier significantly
louder. We do not perceive acoustic power as such – there is no way we
could possibly integrate the energy liberated in a room, and it would be a
singularly useless thing to perceive if we could. It is much nearer the truth
to say that we perceive pressure. It is well known that power in watts must
be quadrupled to double sound pressure level (SPL) but this is not the same
as doubling subjective loudness; this is measured in Sones rather than dB
above threshold, and some psychoacousticians have reported that doubling subjective loudness requires a 10 dB rather than 6 dB rise in SPL,
implying that amplifier power must be increased tenfold, rather than
merely quadrupled [22]. It is any rate clear that changing from a 25 W to a
30 W amplifier will not give an audible increase in level.
This does not mean that fractions of a watt are never of interest. They can
matter either in pursuit of maximum efficiency for its own sake, or because
a design is only just capable of meeting its output specification.
Some hi-fi reviewers set great value on very high peak current capability for
short periods. While it is possible to think up special test waveforms that
demand unusually large peak currents, any evidence that this effect is
important in use is so far lacking.
Frequency response
This can be dealt with crisply; the minimum is 20 Hz to 20 kHz, +/–0.5 dB,
though there should never be any plus about it when solid-state amplifiers
Audio Power Amplifier Design Handbook
are concerned. Any hint of a peak before the roll-off should be looked at
with extreme suspicion, as it probably means doubtful HF stability. This is
less true of valve amplifiers, where the bandwidth limits of the output
transformer mean that even modest NFB factors tend to cause peaking at
both high and low ends of the spectrum.
Having dealt with the issue crisply, there is no hope that everyone will
agree that this is adequate. CDs do not have the built-in LF limitations of
vinyl and could presumably encode the barometric pressure in the
recording studio if this was felt to be desirable, and so an extension to
–0.5 dB at 5 or 10 Hz is perfectly feasible. However, if infrabass information
does exist down at these frequencies, no domestic loudspeaker will
reproduce them.
There should be as little as possible without compromising other
parameters. The noise performance of a power amplifier is not an
irrelevance [23], especially in a domestic setting.
Once more, a sensible target might be: As little as possible without messing
up something else. This ignores the views of those who feel a power
amplifier is an appropriate device for adding distortion to a musical
performance. Such views are not considered in the body of this book; it is,
after all, not a treatise on fuzz-boxes or other guitar effects.
I hope that the techniques explained in this book have a relevance beyond
power amplifiers. Applications obviously include discrete-op-amp based
pre-amplifiers [24], and extend to any amplifier aiming at static or dynamic
My philosophy is the simple one that distortion is bad, and high-order
distortion is worse. The first part of this statement, is, I suggest, beyond
argument, and the second part has a good deal of evidence to back it. The
distortion of the nth harmonic should be weighted by n2/4 worse,
according to many authorities [25]. This leaves the second harmonic
unchanged, but scales up the third by 9/4, i.e. 2.25 times, the fourth by
16/4, i.e. 4 times, and so on. It is clear that even small amounts of highorder harmonics could be unpleasant, and this is one reason why even
modest crossover distortion is of such concern.
Digital audio now routinely delivers the signal with less than 0.002% THD,
and I can earnestly vouch for the fact that analogue console designers work
furiously to keep the distortion in long complex signal paths down to
similar levels. I think it an insult to allow the very last piece of electronics
in the chain to make nonsense of these efforts.
Introduction and general survey
I would like to make it clear that I do not believe that an amplifier yielding
0.001% THD is going to sound much better than its fellow giving 0.002%.
However, if there is ever a scintilla of doubt as to what level of distortion is
perceptible, then using the techniques I have presented it should be
possible to routinely reduce the THD below the level at which there can be
any rational argument.
I am painfully aware that there is a school of thought that regards low THD
as inherently immoral, but this is to confuse electronics with religion. The
implication is that very low THD can only be obtained by huge global NFB
factors that require heavy dominant-pole compensation that severely
degrades slew-rate; the obvious flaw in this argument is that once the
compensation is applied the amplifier no longer has a large global NFB
factor, and so its distortion performance presumably reverts to mediocrity,
further burdened with a slew-rate of four volts per fortnight.
To me low distortion has its own aesthetic and philosophical appeal; it is
satisfying to know that the amplifier you have just designed and built is so
linear that there simply is no realistic possibility of it distorting your
favourite material. Most of the linearity-enhancing strategies examined in
this book are of minimal cost (the notable exception being resort to Class-A)
compared with the essential heatsinks, transformer, etc. and so why not
have ultra-low distortion? Why put up with more than you must?
Damping factor
Audio amplifiers, with a few very special exceptions [26], approximate to
perfect voltage sources; i.e., they aspire to a zero output impedance across
the audio band. The result is that amplifier output is unaffected by loading,
so that the frequency-variable impedance of loudspeakers does not give an
equally variable frequency response, and there is some control of speaker
cone resonances.
While an actual zero impedance is impossible, a very close approximation
is possible if large negative-feedback factors are used. (Actually, a judicious
mixture of voltage and current feedback will make the output impedance
zero, or even negative – i.e., increasing the loading makes the output
voltage increase. This is clever, but usually pointless, as will be seen.) Solidstate amplifiers are quite happy with lots of feedback, but it is usually
impractical in valve designs.
Damping factor is defined as the ratio of the load impedance Rload to the
amplifier output resistance Rs:
Damping factor =
Equation 1.1
A solid-state amplifier typically has output resistance of the order of 0.05 ,
so if it drives an 8 speaker we get a damping factor of 160 times. This
Audio Power Amplifier Design Handbook
simple definition ignores the fact that amplifier output impedance usually
varies considerably across the audio band, increasing with frequency as the
negative feedback factor falls; this indicates that the output resistance is
actually more like an inductive reactance. The presence of an output
inductor to give stability with capacitative loads further complicates the
Mercifully, damping factor as such has very little effect on loudspeaker
performance. A damping factor of 160 times, as derived above, seems to
imply a truly radical effect on cone response – it implies that resonances
and such have been reduced by 160 times as the amplifier output takes an
iron grip on the cone movement. Nothing could be further from the
The resonance of a loudspeaker unit depends on the total resistance in the
circuit. Ignoring the complexities of crossover circuitry in multi-element
speakers, the total series resistance is the sum of the speaker coil resistance,
the speaker cabling, and, last of all, the amplifier output impedance. The
values will be typically 7 , 0.5 and 0.05 , so the amplifier only
contributes 0.67% to the total, and its contribution to speaker dynamics
must be negligible.
The highest output impedances are usually found in valve equipment,
where global feedback including the output transformer is low or nonexistent; values around 0.5 are usual. However, idiosyncratic semiconductor designs sometimes also have high output resistances; see
Olsher [27] for a design with Rout = 0.6 , which I feel is far too high.
This view of the matter was practically investigated and fully confirmed by
James Moir as far back as 1950 [28], though this has not prevented periodic
resurgences of controversy.
The only reason to strive for a high damping factor – which can, after all,
do no harm – is the usual numbers game of impressing potential customers
with spec. figures. It is as certain as anything can be that the subjective
difference between two amplifiers, one with a DF of 100, and the other
boasting 2000, is undetectable by human perception. Nonetheless, the
specifications look very different in the brochure, so means of maximising
the DF may be of some interest. This is examined further in Chapter 7.
Absolute phase
Concern for absolute phase has for a long time hovered ambiguously
between real audio concerns like noise and distortion, and the Subjective
realm where solid copper is allegedly audible. Absolute phase means the
preservation of signal phase all the way from microphone to loudspeaker,
so that a drum impact that sends an initial wave of positive pressure
towards the live audience is reproduced as a similar positive pressure wave
Introduction and general survey
from the loudspeaker. Since it is known that the neural impulses from the
ear retain the periodicity of the waveform at low frequencies, and
distinguish between compression and rarefaction, there is a prima facie
case for the audibility of absolute phase.
It is unclear how this applies to instruments less physical than a kickdrum.
For the drum the situation is simple – you kick it, the diaphragm moves
outwards and the start of the transient must be a wave of compression in the
air. (Followed almost at once by a wave of rarefaction.) But what about an
electric guitar? A similar line of reasoning – plucking the string moves it in
a given direction, which gives such-and-such a signal polarity, which leads
to whatever movement of the cone in the guitar amp speaker cabinet –
breaks down at every point in the chain. There is no way to know how the
pickups are wound, and indeed the guitar will almost certainly have a
switch for reversing the phase of one of them. I also suggest that the
preservation of absolute phase is not the prime concern of those who
design and build guitar amplifiers.
The situation is even less clear if more than one instrument is concerned,
which is of course almost all the time. It is very difficult to see how two
electric guitars played together could have a correct phase in which to
listen to them.
Recent work on the audibility of absolute phase [29],[30] shows it is
sometimes detectable. A single tone flipped back and forth in phase,
providing it has a spiky asymmetrical waveform and an associated harsh
sound, will show a change in perceived timbre and, according to some
experimenters, a perceived change in pitch. A monaural presentation has to
be used to yield a clear effect. A complex sound, however, such as that
produced by a musical ensemble, does not in general show a detectable
Proposed standards for the maintenance of absolute phase have just begun
to appear [31], and the implication for amplifier designers is clear; whether
absolute phase really matters or not, it is simple to maintain phase in a
power amplifier (compare a complex mixing console, where correct phase
is vital, and there are hundreds of inputs and outputs, all of which must be
in phase in every possible configuration of every control) and so it should
be done. In fact, it probably already has been done, even if the designer
hasn’t given absolute phase a thought, because almost all amplifiers use
series negative feedback, and this must be non-inverting. Care is however
required if there are stages such as balanced line input amplifiers before the
power amplifier itself.
I have kept the number of acronyms used to a minimum. However, those
few are used extensively, so a list is given in case they are not all blindingly
Audio Power Amplifier Design Handbook
Bipolar junction transistor
Complementary feedback pair
Equivalent input noise
Field-effect transistor
Amplifier behaviour above the dominant pole frequency,
where the open-loop gain is usually falling at 6 dB/octave
Relating to amplifier action below the dominant pole, where
the open-loop gain is assumed to be essentially flat with
Negative feedback
Open loop
The first o/l response pole, and its frequency in Hz (i.e. the
–3 dB point of a 6 dB/oct rolloff)
The second response pole, at a higher frequency
Power supply rejection ratio
Total harmonic distortion
Voltage-amplifier stage
1. Martin Gardner Fads & Fallacies in the Name of Science Ch. 12,
pp. 140–151. Pub. Dover.
2. David F Mark Investigating the Paranormal Nature, Vol. 320, 13 March
3. Randi, J Flim-Flam! Psychics, ESP Unicorns and Other Delusions
Prometheus Books, 1982. pp. 196–198.
4. Harris, J D Loudness discrimination J. Speech Hear. Dis. Monogr.
Suppl. 11, pp. 1–63.
5. Moore, B C J Relation between the critical bandwidth k the frequencydifference limen Journ. Acoust. Soc. Am. 55, p. 359.
6. Moir, J Just Detectable Distortion Levels Wireless World, February
1981, pp. 32–34.
7. Hawksford, M The Essex Echo Hi-fi News & RR, May 1986, p. 53.
8. Self, D Ultra-Low-Noise Amplifiers & Granularity Distortion Journ.
Audio Eng. Soc., November 1987, pp. 907–915.
9. Harwood & Shorter Stereophony and The effect of crosstalk between
left and right channels BBC Engineering Monograph No 52.
10. Lipshitz et al, On the audibility of midrange phase distortion in audio
systems JAES, September 1982, pp. 580–595.
11. Harwood, H Audibility of phase effects in loudspeakers Wireless
World, January 1976, pp. 30–32.
12. Shinners, S Modern control system theory and application publ.
Addison-Wesley, p. 310.
Introduction and general survey
13. King, G Hi-fi reviewing Hi-fi News & RR, May 1978, p. 77.
14. Harley, R Review of Cary CAD-300SEI Single-Ended Triode Amplifier
Stereophile Sept 1995, p. 141.
15. Baxandall, P Audio power amplifier design Wireless World, January
1978, p. 56.
16. Belcher, R A A new distortion measurement Wireless World, May
1978, pp. 36–41.
17. Baxandall, P Audible amplifier distortion is not a mystery Wireless
World, November 1977, pp. 63–66.
18. Hafler, D A Listening Test for Amplifier Distortion Hi-fi News & RR,
November 1986, pp. 25–29.
19. Colloms, M Hafler XL-280 Test Hi-Fi News & RR, June 1987, pp. 65–
20. Hi-fi Choice; The Selection Pub. Sportscene, 1986.
21. Lawry, R H High End Difficulties Stereophile, May 1995, p. 23.
22. Moore, B J An Introduction to the Psychology of Hearing Academic
Press, 1982, pp. 48–50.
23. Fielder, L Dynamic range issues in the Modern Digital Audio
Environment Journ. Audio Eng. Soc. Vol 43.
24. Self, D Advanced Preamplifier Design Wireless World, Nov 1976,
p. 41.
25. Moir, J Just Detectable Distortion Levels Wireless World, Feb 1981,
p. 34.
26. Mills & Hawksford Transconductance Power Amplifier Systems for
Current-Driven Loudspeakers Journ. Audio Eng. Soc. Vol 37.
27. Olsher, D Times One RFS400 Power Amplifier Review Stereophile,
Aug 1995, p. 187.
28. Moir, J Transients and Loudspeaker Damping Wireless World, May
1950, p. 166.
29. Greiner & Melton A Quest for the Audibility of Polarity Audio, Dec
1993, p. 40.
30. Greiner & Melton Observations on the Audibility of Acoustic Polarity
Journ. Audio Eng. Soc. Vol 42.
31. AES Draft AES recommended practice Standard for professional audio
– Conservation of the Polarity of Audio Signals Inserted in: Journ.
Audio Eng. Soc. Vol 42.
History, architecture and
negative feedback
A brief history of amplifiers
A full and detailed account of semiconductor amplifier design since its
beginnings would be a book in itself – and a most fascinating volume it
would be. This is not that book, but I still feel obliged to give a very brief
account of how amplifier design has evolved in the last three or four
Valve amplifiers, working in push-pull Class-A or AB1, and perforce
transformer-coupled to the load, were dominant until the early 1960s,
when truly dependable transistors could be made at a reasonable price.
Designs using germanium devices appeared first, but suffered severely from
the vulnerability of germanium to even moderately high temperatures; the
term thermal runaway was born. At first all silicon power transistors were
NPN, and for a time most transistor amplifiers relied on input and output
transformers for push-pull operation of the power output stage. These
transformers were as always heavy, bulky, expensive, and non-linear, and
added insult to injury as their LF and HF phase-shifts severely limited the
amount of negative feedback that could be safely applied.
The advent of the transformerless Lin configuration [1], with what became
known as a quasi-complementary output stage, disposed of a good many
problems. Since modestly capable PNP driver transistors were available,
the power output devices could both be NPN, and still work in push-pull.
It was realised that a transformer was not required for impedance matching
between power transistors and 8 loudspeakers.
Proper complementary power devices appeared in the late 1960s, and full
complementary output stages soon proved to give less distortion than their
quasi-complementary predecessors. At about the same time DC-coupled
History, architecture and negative feedback
amplifiers began to take over from capacitor-coupled designs, as the
transistor differential pair became a more familiar circuit element.
A much fuller and generally excellent history of power amplifier
technology is given in Sweeney and Mantz [2].
Amplifier architectures
This grandiose title simply refers to the large-scale structure of the amplifier;
i.e. the block diagram of the circuit one level below that representing it as
a single white block labelled Power Amplifier. Almost all solid-state
amplifiers have a three-stage architecture as described below, though they
vary in the detail of each stage.
The three-stage architecture
The vast majority of audio amplifiers use the conventional architecture,
shown in Figure 2.1. There are three stages, the first being a transconductance stage (differential voltage in, current out) the second a
transimpedance stage (current in, voltage out) and the third a unity-voltagegain output stage. The second stage clearly has to provide all the voltage gain
and I have therefore called it the voltage-amplifier stage or VAS. Other
authors have called it the pre-driver stage but I prefer to reserve this term for
the first transistors in output triples. This three-stage architecture has several
advantages, not least being that it is easy to arrange things so that interaction
between stages is negligible. For example, there is very little signal voltage
at the input to the second stage, due to its current-input (virtual-earth) nature,
and therefore very little on the first stage output; this minimises Miller phaseshift and possible Early effect in the input devices.
Figure 2.1
The three-stage
amplifier structure.
There is a
stage, a
transadmittance stage
(the VAS) and a unitygain buffer output
Audio Power Amplifier Design Handbook
Similarly, the compensation capacitor reduces the second stage output
impedance, so that the non-linear loading on it due to the input impedance
of the third stage generates less distortion than might be expected. The
conventional three-stage structure, familiar though it may be, holds several
elegant mechanisms such as this. They will be fully revealed in later
chapters. Since the amount of linearising global NFB available depends
upon amplifier open-loop gain, how the stages contribute to this is of great
interest. The three-stage architecture always has a unity-gain output stage –
unless you really want to make life difficult for yourself – and so the total
forward gain is simply the product of the transconductance of the input
stage and the transimpedance of the VAS, the latter being determined solely
by the Miller capacitor Cdom, except at very low frequencies. Typically, the
closed-loop gain will be between +20 and +30 dB. The NFB factor at
20 kHz will be 25 to 40 dB, increasing at 6 dB per octave with falling
frequency until it reaches the dominant pole frequency P1, when it flattens
out. What matters for the control of distortion is the amount of negative
feedback (NFB) available, rather than the open-loop bandwidth, to which
it has no direct relationship. In my Electronics World Class-B design, the
input stage gm is about 9 ma/V, and Cdom is 100 pF, giving an NFB factor
of 31 dB at 20 kHz. In other designs I have used as little as 26 dB (at 20 kHz)
with good results.
Compensating a three-stage amplifier is relatively simple; since the pole at
the VAS is already dominant, it can be easily increased to lower the HF
negative-feedback factor to a safe level. The local NFB working on the VAS
through Cdom has an extremely valuable linearising effect.
The conventional three-stage structure represents at least 99% of the solidstate amplifiers built, and I make no apology for devoting much of this book
to its behaviour. I doubt if I have exhausted its subtleties.
The two-stage amplifier architecture
In contrast, the architecture in Figure 2.2 is a two-stage amplifier, the first
stage being once more a transconductance stage, though now without a
guaranteed low impedance to accept its output current. The second stage
combines VAS and output stage in one block; it is inherent in this scheme
that the VAS must double as a phase splitter as well as a generator of raw
gain. There are then two quite dissimilar signal paths to the output, and it
is not at all clear that trying to break this block down further will assist a
linearity analysis. The use of a phase-splitting stage harks back to valve
amplifiers, where it was inescapable as a complementary valve technology
has so far eluded us.
Paradoxically, a two-stage amplifier is likely to be more complex in its gain
structure than a three-stage. The forward gain depends on the input stage
gm, the input stage collector load (because the input stage can no longer be
History, architecture and negative feedback
Figure 2.2
The two-stage amplifier
structure. A voltageamplifier output follows
the same
transconductance input
assumed to be feeding a virtual earth) and the gain of the output stage,
which will be found to vary in a most unsettling manner with bias and
loading. Choosing the compensation is also more complex for a two-stage
amplifier, as the VAS/phase-splitter has a significant signal voltage on its
input and so the usual pole-splitting mechanism that enhances Nyquist
stability by increasing the pole frequency associated with the input stage
collector will no longer work so well. (I have used the term Nyquist
stability, or Nyquist oscillation throughout this book to denote oscillation
due to the accumulation of phase-shift in a global NFB loop, as opposed to
local parasitics, etc.)
The LF feedback factor is likely to be about 6 dB less with a 4 load, due
to lower gain in the output stage. However, this variation is much reduced
above the dominant pole frequency, as there is then increasing local NFB
acting in the output stage.
Two-stage amplifiers are not popular; I can quote only two examples,
Randi [3] and Harris [4]. The two-stage amplifier offers little or no reduction
in parts cost, is harder to design and in my experience invariably gives a
poor distortion performance.
Power amplifier classes
For a long time the only amplifier classes relevant to high-quality audio
were Class-A and Class-AB. This is because valves were the only active
devices, and Class-B valve amplifiers generated so much distortion that
they were barely acceptable even for Public Address purposes. All
amplifiers with pretensions to high fidelity operated in push-pull Class-A.
Audio Power Amplifier Design Handbook
Solid-state gives much more freedom of design; all of the amplifier classes
below have been commercially exploited. Unfortunately, there will only be
space to deal in detail in this book with A, AB, and B, though this certainly
covers the vast majority of solid-state amplifiers. Plentiful references are
given so that the intrigued can pursue matters further.
In a Class-A amplifier current flows continuously in all the output devices,
which enables the non-linearities of turning them on and off to be avoided.
They come in two rather different kinds, although this is rarely explicitly
stated, which work in very different ways. The first kind is simply a Class-B
stage (i.e. two emitter-followers working back-to-back) with the bias
voltage increased so that sufficient current flows for neither device to cut off
under normal loading. The great advantage of this approach is that it
cannot abruptly run out of output current; if the load impedance becomes
lower than specified then the amplifier simply takes brief excursions into
Class AB, hopefully with a modest increase in distortion and no seriously
audible distress.
The other kind could be called the controlled-current-source (VCIS) type,
which is in essence a single emitter-follower with an active emitter load for
adequate current-sinking. If this latter element runs out of current capability
it makes the output stage clip much as if it had run out of output voltage.
This kind of output stage demands a very clear idea of how low an
impedance it will be asked to drive before design begins.
Valve textbooks will be found to contain enigmatic references to classes of
operation called AB1 and AB2; in the former grid current did not flow for
any part of the cycle, but in the latter it did. This distinction was important
because the flow of output-valve grid current in AB2 made the design of the
previous stage much more difficult.
AB1 or AB2 has no relevance to semiconductors, for in BJT’s base current
always flows when a device is conducting, while in power FET’s gate
current never does, apart from charging and discharging internal
This is not really a separate class of its own, but a combination of A and B.
If an amplifier is biased into Class-B, and then the bias further increased, it
will enter AB. For outputs below a certain level both output devices
conduct, and operation is Class-A. At higher levels, one device will be
turned completely off as the other provides more current, and the distortion
jumps upward at this point as AB action begins. Each device will conduct
between 50% and 100% of the time, depending on the degree of excess
bias and the output level.
History, architecture and negative feedback
Class AB is less linear than either A or B, and in my view its only legitimate
use is as a fallback mode to allow Class-A amplifiers to continue working
reasonably when faced with a low load impedance.
Class-B is by far the most popular mode of operation, and probably more
than 99% of the amplifiers currently made are of this type. Most of this
book is devoted to it, so no more is said here.
Class-C implies device conduction for significantly less than 50% of the
time, and is normally only usable in radio work, where an LC circuit can
smooth out the current pulses and filters harmonics. Current-dumping
amplifiers can be regarded as combining Class-A (the correcting amplifier)
with Class-C (the current-dumping devices); however it is hard to visualise
how an audio amplifier using devices in Class-C only could be built.
These amplifiers continuously switch the output from one rail to the other
at a supersonic frequency, controlling the mark/space ratio to give an
average representing the instantaneous level of the audio signal; this is
alternatively called Pulse Width Modulation (PWM). Great effort and
ingenuity has been devoted to this approach, for the efficiency is in theory
very high, but the practical difficulties are severe, especially so in a world
of tightening EMC legislation, where it is not at all clear that a 200 kHz
high-power square wave is a good place to start. Distortion is not inherently
low [5], and the amount of global negative feedback that can be applied is
severely limited by the pole due to the effective sampling frequency in the
forward path. A sharp cut-off low-pass filter is needed between amplifier
and speaker, to remove most of the RF; this will require at least four
inductors (for stereo) and will cost money, but its worst feature is that it will
only give a flat frequency response into one specific load impedance. The
technique deserves a book to itself, and cannot be dealt with properly here.
Other references to consult for further information are Goldberg and
Sandler [6] and Hancock [7].
An extremely ingenious way of operating a transistor so that it has either a
small voltage across it or a small current through it almost all the time; in
other words the power dissipation is kept very low [8]. Regrettably this is an
RF technique that seems to have no sane application to audio.
There is no Class-F, as far as I know. This seems like a gap that needs
filling . . .
Audio Power Amplifier Design Handbook
This concept was introduced by Hitachi in 1976 with the aim of reducing
amplifier power dissipation. Musical signals have a high peak/mean ratio,
spending most of the time at low levels, so internal dissipation is much
reduced by running from low-voltage rails for small outputs, switching to
higher rails current for larger excursions.
The basic series Class-G with two rail voltages (i.e. four supply rails, as both
voltages are +/–) is shown in Figure 2.3 [9],[11]. Current is drawn from the
lower +/–V1 supply rails whenever possible; should the signal exceed
+/–V1, TR6 conducts and D3 turns off, so the output current is now drawn
entirely from the higher +/–V2 rails, with power dissipation shared between
TR3 and TR6. The inner stage TR3, 4 is usually operated in Class-B,
although AB or A are equally feasible if the output stage bias is suitably
increased. The outer devices are effectively in Class-C as they conduct for
significantly less than 50% of the time.
In principle movements of the collector voltage on the inner device
collectors should not significantly affect the output voltage, but in practice
Class-G is often considered to have poorer linearity than Class-B because of
glitching due to charge storage in commutation diodes D3, D4. However, if
Figure 2.3
Class-G-Series output
stage. When the
output voltage exceeds
the transition level, D3
or D4 turn off and
power is drawn from
the higher rails through
the outer power
Inner driver
V in
History, architecture and negative feedback
glitches occur they do so at moderate power, well displaced from the
crossover region, and so appear relatively infrequently with real signals.
An obvious extension of the Class-G principle is to increase the number of
supply voltages. Typically the limit is three. Power dissipation is further
reduced and efficiency increased as the average voltage from which the
output current is drawn is kept closer to the minimum. The inner devices
operate in Class-B/AB as before, and the middle devices are in Class-C. The
outer devices are also in Class-C, but conduct for even less of the time.
To the best of my knowledge three-level Class-G amplifiers have only been
made in Shunt mode, as described below, probably because in Series mode
the cumulative voltage drops become too great and compromise the
efficiency gains. The extra complexity is significant, as there are now six
supply rails and at least six power devices all of which must carry the full
output current. It seems most unlikely that this further reduction in power
consumption could ever be worthwhile for domestic hi-fi.
A closely related type of amplifier is Class-G-Shunt [10]. Figure 2.4 shows
the principle; at low outputs only Q3, Q4 conduct, delivering power from
Low voltage
Figure 2.4
A Class-G-Shunt output stage, composed of two EF output stages with the usual drivers. Vbias3, 4 set the
output level at which power is drawn from the higher rails
Audio Power Amplifier Design Handbook
the low-voltage rails. Above a threshold set by Vbias3 and Vbias4, D1 or
D2 conduct and Q6, Q8 turn on, drawing current from the high-voltage
rails, with D3, 4 protecting Q3, 4 against reverse bias. The conduction
periods of the Q6, Q8 Class-C devices are variable, but inherently less than
50%. Normally the low-voltage section runs in Class-B to minimise
dissipation. Such shunt Class-G arrangements are often called ‘commutating amplifiers’.
Some of the more powerful Class-G-Shunt PA amplifiers have three sets of
supply rails to further reduce the average voltage drop between rail and
output. This is very useful in large PA amplifiers.
Class-H is once more basically Class-B, but with a method of dynamically
boosting the single supply rail (as opposed to switching to another one) in
order to increase efficiency [12]. The usual mechanism is a form of
bootstrapping. Class-H is occasionally used to describe Class-G as above;
this sort of confusion we can do without.
Class-S, so named by Doctor Sandman [13], uses a Class-A stage with very
limited current capability, backed up by a Class-B stage connected so as to
make the load appear as a higher resistance that is within the first
amplifier’s capability.
The method used by the Technics SE-A100 amplifier is extremely
similar [14].
I hope that this necessarily brief catalogue is comprehensive; if anyone
knows of other bona fide classes I would be glad to add them to the
collection. This classification does not allow a completely consistent
nomenclature; for example, Quad-style Current-Dumping can only be
specified as a mixture of Class A and C, which says nothing about the basic
principle of operation, which is error-correction.
Variations on Class-B
The solid-state Class-B three-stage amplifier has proved both successful and
flexible, so many attempts have been made to improve it further, usually by
trying to combine the efficiency of Class-B with the linearity of Class-A. It
would be impossible to give a comprehensive list of the changes and
improvements attempted, so I give only those that have been either
commercially successful or particularly thought-provoking to the amplifierdesign community:
History, architecture and negative feedback
Error-correcting amplifiers
This refers to error-cancellation strategies rather than the conventional use
of negative feedback. This is a complex field, for there are at least three
different forms of error-correction, of which the best known is errorfeedforward as exemplified by the ground-breaking Quad 405 [15]. Other
versions include error feedback and other even more confusingly-named
techniques, some at least of which turn out on analysis to be conventional
NFB in disguise. For a highly ingenious treatment of the feedforward
method by Giovanni Stochino [16].
Non-switching amplifiers
Most of the distortion in Class-B is crossover distortion, and results from
gain changes in the output stage as the power devices turn on and off.
Several researchers have attempted to avoid this by ensuring that each
device is clamped to pass a certain minimum current at all times [17]. This
approach has certainly been exploited commercially, but few technical
details have been published. It is not intuitively obvious (to me, anyway)
that stopping the diminishing device current in its tracks will give less
crossover distortion. See also Chapter 9.
Current-drive amplifiers
Almost all power amplifiers aspire to be voltage sources of zero output
impedance. This minimises frequency response variations caused by the
peaks and dips of the impedance curve, and gives a universal amplifier that
can drive any loudspeaker directly.
The opposite approach is an amplifier with a sufficiently high output
impedance to act as a constant-current source. This eliminates some
problems – such as rising voice-coil resistance with heat dissipation – but
introduces others such as control of the cone resonance. Current amplifiers
therefore appear to be only of use with active crossovers and velocity
feedback from the cone [18].
It is relatively simple to design an amplifier with any desired output
impedance (even a negative one) and so any compromise between voltage
and current drive is attainable. The snag is that loudspeakers are universally
designed to be driven by voltage sources, and higher amplifier impedances
demand tailoring to specific speaker types [19].
The Blomley principle
The goal of preventing output transistors from turning off completely was
introduced by Peter Blomley in 1971 [20]; here the positive/negative
splitting is done by circuitry ahead of the output stage, which can then be
Audio Power Amplifier Design Handbook
designed so that a minimum idling current can be separately set up in each
output device. However, to the best of my knowledge this approach has not
yet achieved commercial exploitation.
Geometric mean Class-AB
The classical explanations of Class-B operation assume that there is a fairly
sharp transfer of control of the output voltage between the two output
devices, stemming from an equally abrupt switch in conduction from one
to the other. In practical audio amplifier stages this is indeed the case, but
it is not an inescapable result of the basic principle. Figure 2.5 shows a
conventional output stage, with emitter resistors Re1, Re2 included to
increase quiescent-current stability and allow current-sensing for overload
protection; it is these emitter resistances that to a large extent make classical
Class-B what it is.
However, if the emitter resistors are omitted, and the stage biased with two
matched diode junctions, then the diode and transistor junctions form a
translinear loop [21] around which the junction voltages sum to zero. This
links the two output transistor currents Ip , In in the relationship In *Ip =
constant, which in op-amp practice is known as Geometric-Mean Class AB
operation. This gives smoother changes in device current at the crossover
point, but this does not necessarily mean lower THD. Such techniques are
not very practical for discrete power amplifiers; firstly, in the absence of the
very tight thermal coupling between the four junctions that exists in an IC,
the quiescent-current stability will be atrocious, with thermal runaway and
spontaneous combustion a near-certainty. Secondly, the output device bulk
emitter resistance will probably give enough voltage drop to turn the other
device off anyway, when current flows. The need for drivers, with their
extra junction-drops, also complicates things.
Figure 2.5
A conventional double
emitter-follower output
stage with emitter
resistors Re shown
History, architecture and negative feedback
A new extension of this technique is to redesign the translinear loop so that
1/In + 1/Ip = constant, this being known as Harmonic-Mean AB operation [22]. It is too early to say whether this technique (assuming it can be
made to work outside an IC) will be of use in reducing crossover distortion
and thus improving amplifier performance.
Nested differentiating feedback loops
This is a most ingenious, but conceptually complex technique for
significantly increasing the amount of NFB that can be applied to an
amplifier. See Cherry [23].
AC and DC coupled amplifiers
All power amplifiers are either AC-coupled or DC-coupled. The first kind
have a single supply rail, with the output biased to be halfway between this
rail and ground to give the maximum symmetrical voltage swing; a large
DC-blocking capacitor is therefore used in series with the output. The
second kind have positive and negative supply rails, and the output is
biased to be at zero volts, so no output DC-blocking is required in normal
The advantages of AC-coupling
1 The output DC offset is always zero (unless the output capacitor is
2 It is very simple to prevent turn-on thump by purely electronic means. The
amplifier output must rise up to half the supply voltage at turn-on, but
providing this occurs slowly there is no audible transient. Note that in
many designs, this is not simply a matter of making the input bias voltage
rise slowly, as it also takes time for the DC feedback to establish itself, and
it tends to do this with a snap-action when a threshold is reached.
3 No protection against DC faults is required, providing the output
capacitor is voltage-rated to withstand the full supply rail. A DC-coupled
amplifier requires an expensive and possibly unreliable output relay for
dependable speaker protection.
4 The amplifier should be more easy to make short-circuit proof, as the
output capacitor limits the amount of electric charge that can be
transferred each cycle, no matter how low the load impedance. This is
speculative; I have no data as to how much it really helps in practice.
5 AC-coupled amplifiers do not in general appear to require output
inductors for stability. Large electrolytics have significant equivalent
series resistance (ESR) and a little series inductance. For typical amplifier
output sizes the ESR will be of the order of 100 m; this resistance is
probably the reason why AC-coupled amplifiers rarely had output
inductors, as it is enough resistance to provide isolation from capacita-
Audio Power Amplifier Design Handbook
tive loading and so gives stability. Capacitor series inductance is very low
and probably irrelevant, being quoted by one manufacturer as ‘A few
tens of nanoHenrys’. The output capacitor was often condemned in the
past for reducing the low-frequency damping factor (DF), for its ESR
alone is usually enough to limit the DF to 80 or so. As explained above,
this is not a technical problem because ‘damping factor’ means virtually
The advantages of DC-coupling
1 No large and expensive DC-blocking capacitor is required. On the other
hand the dual supply will need at least one more equally expensive
reservoir capacitor, and a few extra components such as fuses.
2 In principle there should be no turn-on thump, as the symmetrical supply
rails mean the output voltage does not have to move through half the
supply voltage to reach its bias point – it can just stay where it is. In
practice the various filtering time-constants used to keep the bias
voltages free from ripple are likely to make various sections of the
amplifier turn on at different times, and the resulting thump can be
substantial. This can be dealt with almost for free, when a protection
relay is fitted, by delaying the relay pull-in until any transients are over.
The delay required is usually less than a second.
3 Audio is a field where almost any technical eccentricity is permissible, so
it is remarkable that AC-coupling appears to be the one technique that is
widely regarded as unfashionable and unacceptable. DC-coupling
avoids any marketing difficulties.
4 Some potential customers will be convinced that DC-coupled amplifiers
give better speaker damping due to the absence of the output capacitor
impedance. They will be wrong, as explained on page 25, but this
misconception has lasted at least forty years and shows no sign of fading
5 Distortion generated by an output capacitor is avoided. This is a serious
problem, as it is not confined to low frequencies, as is the case in smallsignal circuitry. See page 173. For a 6800 µF output capacitor driving
40 W into an 8 load, there is significant mid-band third harmonic
distortion at .0025%, as shown in Figure 2.6. This is at least five times
more than the amplifier generates in this part of the frequency range. In
addition, the THD rise at the LF end is much steeper than in the smallsignal case, for reasons that are not yet clear. There are two cures for
output capacitor distortion. The straightforward approach uses a huge
output capacitor, far larger in value than required for a good lowfrequency response. A 100,000 µF/40 V Aerovox from BHC eliminated
all distortion, as shown in Figure 2.7. An allegedly ‘audiophile’ capacitor
gives some interesting results; a Cerafine Supercap of only moderate size
(4700 µF/63 V) gave Figure 2.8, where the mid-band distortion is gone,
but the LF distortion rise remains. What special audio properties this
History, architecture and negative feedback
Figure 2.6
The extra distortion
generated by an
6800 µF electrolytic
delivering 40 W into
8 . Distortion rises
as frequency falls, as
for the small-signal
case, but at this
current level there is
also added distortion
in the mid-band
Figure 2.7
Distortion with and
without a very large
output capacitor, the
BHC Aerovox
100,000 µF/40 V
(40 watts/8).
Capacitor distortion is
component is supposed to have are unknown; as far as I know
electrolytics are never advertised as ‘low mid-band THD’, but that seems
to be the case here. The volume of the capacitor case is about twice as
great as conventional electrolytics of the same value, so it is possible the
crucial difference may be a thicker dielectric film than is usual for this
voltage rating.
Either of these special capacitors costs more than the rest of the amplifier
electronics put together. Their physical size is large. A DC-coupled
amplifier with protective output relay will be a more economical option.
Audio Power Amplifier Design Handbook
Figure 2.8
Distortion with and
without an
‘audiophile’ Cerafine
4700 uF/63 V
capacitor. Mid-band
distortion is eliminated
but LF rise is much the
same as the standard
A little-known complication with output capacitors is that their series
reactance increases the power dissipation in the output stage at low
frequencies. This is counter-intuitive as it would seem that any
impedance added in series must reduce the current drawn and hence the
power dissipation. In fact it is the load phase shift that increases the
amplifier dissipation.
6 The supply currents can be kept out of the ground system. A single-rail
AC amplifier has half-wave Class-B currents flowing in the 0 V rail, and
these can have a serious effect on distortion and crosstalk
Negative feedback in power amplifiers
It is not the role of this book to step through elementary theory which can
be easily found in any number of textbooks. However, correspondence in
audio and technical journals shows that considerable confusion exists on
negative feedback as applied to power amplifiers; perhaps there is
something inherently mysterious in a process that improves almost all
performance parameters simply by feeding part of the output back to the
input, but inflicts dire instability problems if used to excess. I therefore deal
with a few of the less obvious points here; much more information is
provided in Chapter 7.
The main use of NFB in amplifiers is the reduction of harmonic distortion,
the reduction of output impedance, and the enhancement of supply-rail
rejection. There are analogous improvements in frequency response and
gain stability, and reductions in DC drift, but these are usually less
important in audio applications.
History, architecture and negative feedback
By elementary feedback theory, the factor of improvement for all these
quantities is;
Improvement ratio = A.
Equation 2.1
where A is the open-loop gain, and the attenuation in the feedback
network, i.e. the reciprocal of the closed-loop gain. In most audio
applications the improvement factor can be regarded as simply open-loop
gain divided by closed-loop gain.
In simple circuits you just apply negative feedback and that is the end of the
matter. In a typical power amplifier, which cannot be operated without
NFB, if only because it would be saturated by its own DC offset voltages,
there are several stages which may accumulate phase-shift, and simply
closing the loop usually brings on severe Nyquist oscillation at HF. This is
a serious matter, as it will not only burn out any tweeters that are unlucky
enough to be connected, but can also destroy the output devices by
overheating, as they may be unable to turn off fast enough at ultrasonic
frequencies. (See page 153.)
The standard cure for this instability is compensation. A capacitor is added,
usually in Miller-Integrator format, to roll-off the open-loop gain at 6 dB per
octave, so it reaches unity loop-gain before enough phase-shift can build
up to allow oscillation. This means the NFB factor varies strongly with
frequency, an inconvenient fact that many audio commentators seem to
It is crucial to remember that a distortion harmonic, subjected to a
frequency-dependent NFB factor as above, will be reduced by the NFB
factor corresponding to its own frequency, not that of its fundamental. If
you have a choice, generate low-order rather than high-order distortion
harmonics, as the NFB deals with them much more effectively.
Negative-feedback can be applied either locally (i.e. to each stage, or each
active device) or globally, in other words right around the whole amplifier.
Global NFB is more efficient at distortion reduction than the same amount
distributed as local NFB, but places much stricter limits on the amount of
phase-shift that may be allowed to accumulate in the forward path.
Above the dominant pole frequency, the VAS acts as a Miller integrator, and
introduces a constant 90-degree phase lag into the forward path. In other
words, the output from the input stage must be in quadrature if the final
amplifier output is to be in phase with the input, which to a close
approximation it is. This raises the question of how the ninety-degree phase
shift is accommodated by the negative-feedback loop; the answer is that
the input and feedback signals applied to the input stage are there
subtracted, and the small difference between two relatively large signals
with a small phase shift between them has a much larger phase shift. This
is the signal that drives the VAS input of the amplifier.
Audio Power Amplifier Design Handbook
Solid-state power amplifiers, unlike many valve designs, are almost
invariably designed to work at a fixed closed-loop gain. If the circuit is
compensated by the usual dominant-pole method, the HF open-loop gain
is also fixed, and therefore so is the important negative feedback factor. This
is in contrast to valve amplifiers, where the amount of negative feedback
applied was regarded as a variable, and often user-selectable parameter; it
was presumably accepted that varying the negative feedback factor caused
significant changes in input sensitivity. A further complication was serious
peaking of the closed-loop frequency response at both LF and HF ends of
the spectrum as negative feedback was increased, due to the inevitable
bandwidth limitations in a transformer-coupled forward path. Solid-state
amplifier designers go cold at the thought of the customer tampering with
something as vital as the NFB factor, and such an approach is only
acceptable in cases like valve amplification where global NFB plays a
minor role.
Some common misconceptions about negative feedback
All of the comments quoted below have appeared many times in the hi-fi
literature. All are wrong.
Negative feedback is a bad thing. Some audio commentators hold that,
without qualification, negative feedback is a bad thing. This is of course
completely untrue and based on no objective reality. Negative feedback is
one of the fundamental concepts of electronics, and to avoid its use
altogether is virtually impossible; apart from anything else, a small amount
of local NFB exists in every common-emitter transistor because of the
internal emitter resistance. I detect here distrust of good fortune; the uneasy
feeling that if something apparently works brilliantly then there must be
something wrong with it.
A low negative-feedback factor is desirable. Untrue; global NFB makes
just about everything better, and the sole effect of too much is HF
oscillation, or poor transient behaviour on the brink of instability. These
effects are painfully obvious on testing and not hard to avoid unless there
is something badly wrong with the basic design.
In any case, just what does low mean? One indicator of imperfect
knowledge of negative feedback is that the amount enjoyed by an amplifier
is almost always baldly specified as so many dB on the very few occasions
it is specified at all – despite the fact that most amplifiers have a feedback
factor that varies considerably with frequency. A dB figure quoted alone is
meaningless, as it cannot be assumed that this is the figure at 1 kHz or any
other standard frequency.
My practice is to quote the NFB factor at 20 kHz, as this can normally be
assumed to be above the dominant pole frequency, and so in the region
History, architecture and negative feedback
where open-loop gain is set by only two or three components. Normally
the open-loop gain is falling at a constant 6 dB/octave at this frequency on
its way down to intersect the unity-loop-gain line and so its magnitude
allows some judgement as to Nyquist stability. Open-loop gain at LF
depends on many more variables such as transistor beta, and consequently
has wide tolerances and is a much less useful quantity to know. This is dealt
with in more detail on page 101.
Negative feedback is a powerful technique, and therefore dangerous when
misused. This bland truism usually implies an audio Rakes’s Progress that
goes something like this: an amplifier has too much distortion, and so the
open-loop gain is increased to augment the NFB factor. This causes HF
instability, which has to be cured by increasing the compensation
capacitance. This is turn reduces the slew-rate capability, and results in a
sluggish, indolent, and generally bad amplifier.
The obvious flaw in this argument is that the amplifier so condemned no
longer has a high NFB factor, because the increased compensation
capacitor has reduced the open-loop gain at HF; therefore feedback itself
can hardly be blamed. The real problem in this situation is probably unduly
low standing current in the input stage; this is the other parameter
determining slew-rate.
NFB may reduce low-order harmonics but increases the energy in the
discordant higher harmonics. A less common but recurring complaint is
that the application of global NFB is a shady business because it transfers
energy from low-order distortion harmonics – considered musically
consonant – to higher-order ones that are anything but. This objection
contains a grain of truth, but appears to be based on a misunderstanding of
one article in an important series by Peter Baxandall [24] in which he
showed that if you took an amplifier with only second-harmonic distortion,
and then introduced NFB around it, higher-order harmonics were indeed
generated as the second harmonic was fed back round the loop. For
example, the fundamental and the second-harmonic intermodulate to give
a component at third-harmonic frequency. Likewise, the second and third
intermodulate to give the fifth harmonic. If we accept that high-order
harmonics should be numerically weighted to reflect their greater
unpleasantness, there could conceivably be a rise rather than a fall in the
weighted THD when negative feedback is applied.
All active devices, in Class A or B (including FETs, which are often
erroneously thought to be purely square-law), generate small amounts of
high-order harmonics. Feedback could and would generate these from
nothing, but in practice they are already there.
The vital point is that if enough NFB is applied, all the harmonics can be
reduced to a lower level than without it. The extra harmonics generated,
Audio Power Amplifier Design Handbook
effectively by the distortion of a distortion, are at an extremely low level
providing a reasonable NFB factor is used. This is a powerful argument
against low feedback factors like 6 dB, which are most likely to increase the
weighted THD. For a full understanding of this topic, a careful reading of
the Baxandall series is absolutely indispensable.
A low open-loop bandwidth means a sluggish amplifier with a low slewrate. Great confusion exists in some quarters between open-loop bandwidth and slew-rate. In truth open-loop bandwidth and slew-rate are
nothing to do with each other, and may be altered independently. Openloop bandwidth is determined by compensation Cdom, VAS beta, and the
resistance at the VAS collector, while slew-rate is set by the input stage
standing current and Cdom. Cdom affects both, but all the other parameters
are independent. (See Chapter 3 for more details.)
In an amplifier, there is a maximum amount of NFB you can safely apply at
20 kHz; this does not mean that you are restricted to applying the same
amount at 1 kHz, or indeed 10 Hz. The obvious thing to do is to allow the
NFB to continue increasing at 6 dB/octave – or faster if possible – as
frequency falls, so that the amount of NFB applied doubles with each
octave as we move down in frequency, and we derive as much benefit as
we can. This obviously cannot continue indefinitely, for eventually openloop gain runs out, being limited by transistor beta and other factors. Hence
the NFB factor levels-out at a relatively low and ill-defined frequency; this
frequency is the open-loop bandwidth, and for an amplifier that can never
be used open-loop, has very little importance.
It is difficult to convince people that this frequency is of no relevance
whatever to the speed of amplifiers, and that it does not affect the slew-rate.
Nonetheless, it is so, and any First-year electronics textbook will confirm
this. High-gain op-amps with sub-1 Hz bandwidths and blindingly fast
slewing are as common as the grass (if somewhat less cheap) and if that
doesn’t demonstrate the point beyond doubt then I really don’t know what
Limited open-loop bandwidth prevents the feedback signal from immediately following the system input, so the utility of this delayed feedback is
limited. No linear circuit can introduce a pure time-delay; the output
must begin to respond at once, even if it takes a long time to complete its
response. In the typical amplifier the dominant-pole capacitor introduces a
90-degree phase shift between input-pair and output at all but the lowest
audio frequencies, but this is not a true time-delay. The phrase delayed
feedback is often used to describe this situation, and it is a wretchedly
inaccurate term; if you really delay the feedback to a power amplifier
(which can only be done by adding a time-constant to the feedback
network rather than the forward path) it will quickly turn into the proverbial
power oscillator as sure as night follows day.
History, architecture and negative feedback
Amplifier stability and negative feedback
In controlling amplifier distortion, there are two main weapons. The first is
to make the linearity of the circuitry as good as possible before closing the
feedback loop. This is unquestionably important, but it could be argued it
can only be taken so far before the complexity of the various amplifier
stages involved becomes awkward. The second is to apply as much
negative feedback as possible while maintaining amplifier stability. It is
well known that an amplifier with a single time-constant is always stable,
no matter how high the feedback factor. The linearisation of the VAS by
local Miller feedback is a good example. However, more complex circuitry,
such as the generic three-stage power amplifier, has more than one timeconstant, and these extra poles will cause poor transient response or
instability if a high feedback factor is maintained up to the higher
frequencies where they start to take effect. It is therefore clear that if these
higher poles can be eliminated or moved upward in frequency, more
feedback can be applied and distortion will be less for the same stability
margins. Before they can be altered – if indeed this is practical at all – they
must be found and their impact assessed.
The dominant pole frequency of an amplifier is, in principle, easy to
calculate; the mathematics is very simple (see page 62). In practice, two of
the most important factors, the effective beta of the VAS and the VAS
collector impedance, are only known approximately, so the dominant pole
frequency is a rather uncertain thing. Fortunately this parameter in itself has
no effect on amplifier stability. What matters is the amount of feedback at
high frequencies.
Things are different with the higher poles. To begin with, where are they?
They are caused by internal transistor capacitances and so on, so there
is no physical component to show where the roll-off is. It is generally
regarded as fact that the next poles occur in the output stage, which will
use power devices that are slow compared with small-signal transistors.
Taking the Class-B design on page 176, the TO-92 MPSA06 devices have
an Ft of 100 MHz, the MJE340 drivers about 15 MHz (for some reason
this parameter is missing from the data sheet) and the MJ802 output
devices an Ft of 2.0 MHz. Clearly the output stage is the prime suspect.
The next question is at what frequencies these poles exist. There is no
reason to suspect that each transistor can be modelled by one simple
There is a huge body of knowledge devoted to the art of keeping feedback
loops stable while optimising their accuracy; this is called Control Theory,
and any technical bookshop will yield some intimidatingly fat volumes
called things like ‘Control System Design’. Inside, system stability is tackled
by Laplace-domain analysis, eigenmatrix methods, and joys like the
Lyapunov stability criterion. I think that makes it clear that you need to be
pretty good at mathematics to appreciate this kind of approach.
Audio Power Amplifier Design Handbook
Even so, it is puzzling that there seems to have been so little application of
Control Theory to audio amplifier design. The reason may be that so much
Control Theory assumes that you know fairly accurately the characteristics
of what you are trying to control, especially in terms of poles and zeros.
One approach to appreciating negative feedback and its stability problems
is SPICE simulation. Some SPICE simulators have the ability to work in the
Laplace or s-domain, but my own experiences with this have been deeply
unhappy. Otherwise respectable simulator packages output complete
rubbish in this mode. Quite what the issues are here I do not know, but it
does seem that s-domain methods are best avoided. The approach
suggested here instead models poles directly as poles, using RC networks to
generate the time-constants. This requires minimal mathematics and is far
more robust. Almost any SPICE simulator – evaluation versions included –
should be able to handle the simple circuit used here.
Figure 2.9 shows the basic model, with SPICE node numbers. The scheme
is to idealise the situation enough to highlight the basic issues and exclude
distractions like non-linearities or clipping. The forward gain is simply the
transconductance of the input stage multiplied by the transadmittance of
the VAS integrator. An important point is that with correct parameter values,
the current from the input stage is realistic, and so are all the voltages.
The input differential amplifier is represented by G. This is a standard SPICE
element – the VCIS, or voltage-controlled current source. It is inherently
differential, as the output current from Node 4 is the scaled difference
between the voltages at Nodes 3 and 7. The scaling factor of 0.009 sets the
input stage transconductance (gm) to 9 mA/V, a typical figure for a bipolar
input with some local feedback. Stability in an amplifier depends on the
amount of negative feedback available at 20 kHz. This is set at the design
stage by choosing the input gm and Cdom, which are the only two factors
affecting the open-loop gain (see page 61). In simulation it would be equally
Figure 2.9
Block diagram of system for SPICE stability testing
History, architecture and negative feedback
valid to change gm instead; however, in real life it is easier to alter Cdom as
the only other parameter this affects is slew rate. Changing input stage
transconductance is likely to mean altering the standing current and the
amount of local feedback, which will in turn impact input stage linearity.
The VAS with its dominant pole is modelled by the integrator Evas, which
is given a high but finite open-loop gain, so there really is a dominant pole
P1 created when the gain demanded becomes equal to that available. With
Cdom = 100 pF this is below 1 Hz. With infinite (or as near-infinite as SPICE
allows) open-loop gain the stage would be a perfect integrator. A explained
elsewhere, the amount of open-loop gain available in real versions of this
stage is not a well-controlled quantity, and P1 is liable to wander about in
the 1–100 Hz region; fortunately this has no effect at all on HF stability.
Cdom is the Miller capacitor that defines the transadmittance, and since the
input stage has a realistic transconductance Cdom can be set to 100 pF, its
usual real-life value. Even with this simple model we have a nested
feedback loop. This apparent complication here has little effect, so long as
the open-loop gain of the VAS is kept high.
The output stage is modelled as a unity-gain buffer, to which we add extra
poles modelled by R1, C1 and R2, C2. Eout1 is a unity-gain buffer internal
to the output stage model, added so the second pole does not load the first.
The second buffer Eout2 is not strictly necessary as no real loads are being
driven, but it is convenient if extra complications are introduced later. Both
are shown here as a part of the output stage but the first pole could equally
well be due to input stage limitations instead; the order in which the poles
are connected makes no difference to the final output. Strictly speaking, it
would be more accurate to give the output stage a gain of 0.95, but this is
so small a factor that it can be ignored.
The component values here are of course completely unrealistic, and
chosen purely to make the maths simple. It is easy to appreciate that 1 and 1 microfarad make up a 1 microsecond time-constant. This is a pole at
159 kHz. Remember that the voltages in the latter half of the circuit are
realistic, but the currents most certainly are not.
The feedback network is represented simply by scaling the output as it is
fed back to the input stage. The closed-loop gain is set to 23 times, which
is representative of most power amplifiers.
Note that this is strictly a linear model, so the slew-rate limiting which is
associated with Miller compensation is not modelled here. It would be
done by placing limits on the amount of current that can flow in and out of
the input stage.
Figure 2.10 shows the response to a 1 volt step input, with the dominant
pole the only time element in the circuit. (The other poles are disabled by
making C1, C2 0.00001 pF, because this is quicker than changing the
actual circuit.) The output is an exponential rise to an asymptote of 23 V,
Audio Power Amplifier Design Handbook
Figure 2.10
SPICE results in the
time domain. As
Cdom increases, the
response V(7)
becomes slower, and
the error g(i) declines
more slowly. The input
is the step-function
V(3) at the bottom
which is exactly what elementary theory predicts. The exponential shape
comes from the way that the error signal which drives the integrator
becomes less as the output approaches the desired level. The error, in the
shape of the output current from G, is the smaller signal shown; it has been
multiplied by 1000 to get mA onto the same scale as volts. The speed of
response is inversely proportional to the size of Cdom, and is shown here
for values of 50 pF and 220 pF as well as the standard 100 pF. This
simulation technique works well in the frequency domain, as well as the
time domain. Simply tell SPICE to run an AC simulation instead of a TRANS
(transient) simulation. The frequency response in Figure 2.11 exploits this to
Figure 2.11
SPICE simulation in
the frequency domain.
As the compensation
capacitor is
increased, the closedloop bandwidth
History, architecture and negative feedback
Figure 2.12
Adding a second
pole P2 causes
overshoot with smaller
values Cdom, but
cannot bring about
sustained oscillation
show how the closed-loop gain in a negative-feedback amplifier depends
on the open-loop gain available. Once more elementary feedback theory is
brought to life. The value of Cdom controls the bandwidth, and it can be
seen that the values used in the simulation do not give a very extended
response compared with a 20 kHz audio bandwidth.
In Figure 2.12, one extra pole P2 at 1.59 MHz (a time-constant of only
100 ns) is added to the output stage, and Cdom stepped through 50, 100
and 200 pF as before. 100 pF shows a slight overshoot that was not there
before; with 50 pF there is a serious overshoot that does not bode well for
the frequency response. Actually, it’s not that bad; Figure 2.13 returns to the
frequency-response domain to show that an apparently vicious overshoot is
actually associated with a very mild peaking in the frequency domain.
From here on Cdom is left set to 100 pF, its real value in most cases. In
Figure 2.14 P2 is stepped instead, increasing from 100 ns to 5 µs, and while
the response gets slower and shows more overshoot, the system does not
become unstable. The reason is simple: sustained oscillation (as opposed to
transient ringing) in a feedback loop requires positive feedback, which
means that a total phase shift of 180 degrees must have accumulated in the
forward path, and reversed the phase of the feedback connection. With
only two poles in a system the phase shift cannot reach 180 degrees. The
VAS integrator gives a dependable 90 degrees phase shift above P1, being
an integrator, but P2 is instead a simple lag and can only give 90 degrees
phase lag at infinite frequency. So, even this very simple model gives some
Audio Power Amplifier Design Handbook
Figure 2.13
The frequency
responses that go with
the transient plots of
Fig 2.12. The
response peaking for
Cdom = 50 pF is very
small compared with
the transient overshoot
Figure 2.14
Manipulating the P2
frequency can make
ringing more
prolonged but it is still
not possible to
provoke sustained
History, architecture and negative feedback
insight. Real amplifiers do oscillate if Cdom is too small, so we know that
the frequency response of the output stage cannot be meaningfully
modelled with one simple lag.
A certain president of the United States is alleged to have said: ‘Two wrongs
don’t make a right – so let’s see if three will do it.’ Adding in a third pole
P3 in the shape of another simple lag gives the possibility of sustained
Stepping the value of P2 from 0.1 to 5 µsec with P3 = 500 nsec shows
sustained oscillation starting to occur at P2 = 0.45 µsec. For values such as
P2 = 0.2 µsec the system is stable and shows only damped oscillation.
Figure 2.15 shows over 50 µsec what happens when the amplifier is made
very unstable (there are degrees of this) by setting P2 = 5 µsec and P3 =
500 nsec. It still takes time for the oscillation to develop, but exponentially
diverging oscillation like this is a sure sign of disaster. Even in the short time
examined here the amplitude has exceeded a rather theoretical half a
kilovolt. In reality oscillation cannot increase indefinitely, if only because
the supply rail voltages would limit the amplitude. In practice slew-rate
limiting is probably the major controlling factor in the amplitude of highfrequency oscillation.
We have now modelled a system that will show instability. But does it do
it right? Sadly, no. The oscillation is about 200 kHz, which is a rather lower
frequency than is usually seen when a amplifier misbehaves. This low
Figure 2.15
Adding a third pole
makes possible true
instability with
increasing amplitude
of oscillation. Note
the unrealistic voltage
scale on this plot
Audio Power Amplifier Design Handbook
frequency stems from the low P2 frequency we have to use to provoke
oscillation; apart from anything else this seems out of line with the known
Ft of power transistors. Practical amplifiers are likely to take off at around
500 kHz to 1 MHz when Cdom is reduced, and this seems to suggest that
phase shift is accumulating quickly at this sort of frequency. One possible
explanation is that there are a large number of poles close together at a
relatively high frequency.
A fourth pole can be simply added to Figure 2.9 by inserting another RCbuffer combination into the system. With P2 = 0.5 µsec and P3 = P4 =
0.2 µsec, instability occurs at 345 kHz, which is a step towards a realistic
frequency of oscillation. This is case B in Table 2.1.
When a fifth output stage pole is grafted on, so that P3 = P4 = P5 = 0.2 µsec
the system just oscillates at 500 kHz with P2 set to 0.01 usec. This takes us
close to a realistic frequency of oscillation. Rearranging the order of poles
so P2 = P3 = P4 = 0.2 µsec, while P5 = 0.01 µsec, is tidier, and the stability
results are of course the same; this is a linear system so the order does not
matter. This is case C in Table 2.1.
Table 2.1
Instability onset.
P2 is increased
until sustained
oscillation occurs
200 kHz
345 kHz
500 kHz
400 kHz
370 kHz
475 kHz
Having P2, P3 and P4 all at the same frequency does not seem very
plausible in physical terms, so case D shows what happens when the five
poles are staggered in frequency. P2 needs to be increased to 0.3 µsec to
start the oscillation, which is now at 400 kHz. Case E is another version
with five poles, showing that if P5 is reduced P2 needs to be doubled to
0.4 µsec for instability to begin.
In the final case F, a sixth pole is added to see if this permitted sustained
oscillation is above 500 kHz. This seems not to be the case; the highest
frequency that could be obtained after a lot of pole-twiddling was 475 kHz.
This makes it clear that this model is of limited accuracy (as indeed are all
models – it is a matter of degree) at high frequencies, and that further
refinement is required to gain further insight.
History, architecture and negative feedback
Maximising the negative feedback factor
Having freed ourselves from Fear of Feedback, and appreciating the
dangers of using only a little of it, the next step is to see how much can be
used. It is my view that the amount of negative feedback applied should be
maximised at all audio frequencies to maximise linearity, and the only limit
is the requirement for reliable HF stability. In fact, global or Nyquist
oscillation is not normally a difficult design problem in power amplifiers;
the HF feedback factor can be calculated simply and accurately, and set to
whatever figure is considered safe. (Local oscillations and parasitics are
beyond the reach of design calculations and simulations, and cause much
more trouble in practice.)
In classical Control Theory, the stability of a servomechanism is specified
by its Phase Margin, the amount of extra phase-shift that would be required
to induce sustained oscillation, and its Gain Margin, the amount by which
the open-loop gain would need to be increased for the same result. These
concepts are not very useful in amplifier work, where many of the
significant time-constants are only vaguely known. However it is worth
remembering that the phase margin will never be better than 90 degrees,
because of the phase-lag caused by the VAS Miller capacitor; fortunately
this is more than adequate.
In practice the designer must use his judgement and experience to
determine an NFB factor that will give reliable stability in production. My
own experience leads me to believe that when the conventional three-stage
architecture is used, 30 dB of global feedback at 20 kHz is safe, providing
an output inductor is used to prevent capacitive loads from eroding the
stability margins. I would say that 40 dB was distinctly risky, and I would
not care to pin it down any more closely than that.
The 30 dB figure assumes simple dominant-pole compensation with a 6 dB/
octave roll-off for the open-loop gain. The phase and gain margins are
determined by the angle at which this slope cuts the horizontal unity-loopgain line. (I am deliberately terse here; almost all textbooks give a very full
treatment of this stability criterion.) An intersection of 12 dB/octave is
definitely unstable. Working within this, there are two basic ways in which
to maximise the NFB factor:
1 while a 12 dB/octave gain slope is unstable, intermediate slopes greater
than 6 dB/octave can be made to work. The maximum usable is normally
considered to be 10 dB/octave, which gives a phase margin of 30
degrees. This may be acceptable in some cases, but I think it cuts it a
little fine. The steeper fall in gain means that more NFB is applied at
lower frequencies, and so less distortion is produced. Electronic circuitry
only provides slopes in multiples of 6 dB/octave, so 10 dB/octave
requires multiple overlapping time-constants to approximate a straight
line at an intermediate slope. This gets complicated, and this method of
maximising NFB is not popular,
Audio Power Amplifier Design Handbook
2 the gain slope varies with frequency, so that maximum open-loop gain
and hence NFB factor is sustained as long as possible as frequency
increases; the gain then drops quickly, at 12 dB/octave or more, but
flattens out to 6 dB/octave before it reaches the critical unity loop-gain
intersection. In this case the stability margins should be relatively
unchanged compared with the conventional situation. This approach is
dealt with in Chapter 7.
Maximising linearity before feedback
Make your amplifier as linear as possible before applying NFB has long
been a cliché. It blithely ignores the difficulty of running a typical solidstate amplifier without any feedback, to determine its basic linearity.
Virtually no dependable advice on how to perform this desirable
linearisation has been published. The two factors are the basic linearity of
the forward path, and the amount of negative feedback applied to further
straighten it out. The latter cannot be increased beyond certain limits or
high-frequency stability is put in peril, whereas there seems no reason why
open-loop linearity could not be improved without limit, leading us to what
in some senses must be the ultimate goal – a distortionless amplifier. This
book therefore takes as one of its main aims the understanding and
improvement of open-loop linearity; as it proceeds we will develop circuit
blocks culminating in some practical amplifier designs that exploit the
techniques presented here.
1. Lin, H C Transistor Audio Amplifier Electronics, Sept 1956, p. 173.
2. Sweeney & Mantz An Informal History of Amplifiers Audio, June 1988,
p. 46.
3. Linsley-Hood Simple Class-A Amplifier Wireless World, April 1969,
p. 148.
4. Olsson, B Better Audio from Non-Complements? Electronics World,
Dec 1994, p. 988.
5. Attwood, B Design Parameters Important for the Optimisation of PWM
(Class-D) Amplifiers Journ. Audio Eng. Soc. Vol 31 Nov 1983,
p. 842.
6. Goldberg & Sandler Noise Shaping and Pulse-Width Modulation for
All-Digital Audio Power Amplifier Journ. Audio Eng. Soc. Vol 39 Feb
1991, p. 449.
7. Hancock, J A Class-D Amplifier Using MOSFETS with Reduced
Minority Carrier Lifetime Journ. Audio Eng. Soc. Vol 39 Sept 1991,
p. 650.
8. Peters, A Class E RF Amplifiers IEEE Journ of Solid-State Circuits, June
1975, p. 168.
9. Feldman, L Class-G High-Efficiency Hi-Fi Amplifier Radio-Electronics
Aug 1976, p. 47.
History, architecture and negative feedback
10. Raab, F Average Efficiency of Class-G Power Amplifiers IEEE Transactions on Consumer Electronics, Vol CE-22 May 1986, p. 145.
11. Sampei et al Highest Efficiency & Super Quality Audio Amplifier Using
MOS-Power FETs in Class-G IEEE Transactions on Consumer Electronics, Vol CE-24 Aug 1978, p. 300.
12. Buitendijk, P A 40 W Integrated Car Radio Audio Amplifier IEEE
Conf on Consumer Electronics, 1991 Session THAM 12.4, p. 174.
13. Sandman, A Class S: A Novel Approach to Amplifier Distortion
Wireless World, Sept 1982, p. 38.
14. Sinclair (ed) Audio and Hi-Fi Handbook pub Newnes 1993, p. 541.
15. Walker, P J Current Dumping Audio Amplifier Wireless World, Dec
1975, p. 560.
16. Stochino, G Audio Design Leaps Forward? Electronics World, Oct
1994, p. 818.
17. Tanaka, S A New Biasing Circuit for Class-B Operation Journ. Audio
Eng. Soc. Jan/Feb 1981, p. 27.
18. Mills & Hawksford Transconductance Power Amplifier Systems for
Current-Driven Loudspeakers Journ. Audio Eng. Soc. Vol 37 March
1989, p. 809.
19. Evenson, R Audio Amplifiers with Tailored Output Impedances
Preprint for Nov 1988 AES convention (Los Angeles).
20. Blomley, P A New Approach to Class-B Wireless World, Feb 1971,
p. 57.
21. Gilbert, B Current Mode Circuits from a Translinear Viewpoint Ch 2,
Analogue IC Design: The Current-Mode Approach Ed Toumazou,
Lidgey & Haigh, IEE 1990.
22. Thus Compact Bipolar Class AB Output Stage IEEE Journal of SolidState Circuits, Dec 1992 p. 1718.
23. Cherry, E Nested Differentiating Feedback Loops in Simple Audio
Power Amplifiers Journ. Audio Eng. Soc. Vol 30 #5, May 1982,
p. 295.
24. Baxandall, P Audio Power Amplifier Design: Part 5 Wireless World,
Dec 1978, p. 53. (This superb series of articles had 6 parts and ran on
roughly alternate months, starting in Jan 1978.)
The general principles of
power amplifiers
How a generic amplifier works
Figure 3.1 shows a very conventional power amplifier circuit; it is as
standard as possible. A great deal has been written about this configuration,
though the subtlety and quiet effectiveness of the topology are usually
overlooked, and the explanation below therefore touches on several
aspects that seem to be almost unknown. The circuit has the merit of being
docile enough to be made into a functioning amplifier by someone who
has only the sketchiest of notions as to how it works.
The input differential pair implements one of the few forms of distortion
cancellation that can be relied upon to work reliably without adjustment –
this is because the transconductance of the input pair is determined by the
physics of transistor action rather than matching of ill-defined parameters
such as beta; the logarithmic relation between Ic and Vbe is proverbially
accurate over some eight or nine decades of current variation.
The voltage signal at the Voltage Amplifier Stage (hereafter VAS) transistor
base is typically a couple of millivolts, looking rather like a distorted
triangle wave. Fortunately the voltage here is of little more than academic
interest, as the circuit topology essentially consists of a transconductance
amp (voltage-difference input to current output) driving into a transresistance (current-to-voltage converter) stage. In the first case the
exponential Vbe/Ic law is straightened out by the differential-pair action,
and in the second the global (overall) feedback factor at LF is sufficient to
linearise the VAS, while at HF shunt Negative Feedback (hereafter NFB)
through Cdom conveniently takes over VAS-linearisation while the overall
feedback factor is falling.
The behaviour of Miller dominant-pole compensation in this stage is
actually exceedingly elegant, and not at all a case of finding the most
The general principles of power amplifiers
Figure 3.1
a A conventional
Class-B power amp
circuit. b With smallsignal Class-A output
replacing Class-B
output to make a
model amplifier
vulnerable transistor and slugging it. As frequency rises and Cdom begins to
take effect, negative feedback is no longer applied globally around the
whole amplifier, which would include the higher poles, but instead is
seamlessly transferred to a purely local role in linearising the VAS. Since
this stage effectively contains a single gain transistor, any amount of NFB
can be applied to it without stability problems.
The amplifier operates in two regions; the LF, where open-loop (o/I) gain is
substantially constant, and HF, above the dominant-pole breakpoint, where
the gain is decreasing steadily at 6 dB/octave. Assuming the output stage is
unity-gain, three simple relationships define the gain in these two regions:
LF gain = gm × beta × Rc
Equation 3.1
At least one of the factors that set this (beta) is not well-controlled and so
the LF gain of the amplifier is to a certain extent a matter of pot-luck;
Audio Power Amplifier Design Handbook
fortunately this doesn’t matter, so long as it is high enough to give a suitable
level of NFB to eliminate LF distortion. The use of the word eliminate is
deliberate, as will be seen later. Usually the LF gain, or HF local feedbackfactor, is made high by increasing the effective value of the VAS collector
impedance Rc, either by the use of current-source collector-load, or by
some form of bootstrapping.
The other important relations are:
HF gain = gm/ (w × Cdom )
Equation 3.2
Dominant pole freq P1 = 1/(w × Cdom × beta × Rc )
Equation 3.3
(where w = 2 × pi × freq).
In the HF region, things are distinctly more difficult as regards distortion, for
while the VAS is locally linearised, the global feedback-factor available to
linearise the input and output stages is falling steadily at 6 dB/octave. For
the time being we will assume that it is possible to define an HF gain (say
N dB at 20 kHz) which will assure stability with practical loads and
component variations. Note that the HF gain, and therefore both HF
distortion and stability margin, are set by the simple combination of the
input stage transconductance and one capacitor, and most components
have no effect on it at all.
It is often said that the use of a high VAS collector impedance provides a
current drive to the output devices, often with the implication that this
somehow allows the stage to skip quickly and lightly over the dreaded
crossover region. This is a misconception – the collector impedance falls to
a few kilohms at HF, due to increasing local feedback through Cdom, and
in any case it is very doubtful if true current drive would be a good thing
– calculation shows that a low-impedance voltage drive minimises
distortion due to beta-unmatched output halves [1], and it certainly
eliminates the effect of Distortion 4, described below.
The advantages of convention
It is probably not an accident that the generic configuration is by a long
way the most popular, though in the uncertain world of audio technology
it is unwise to be too dogmatic about this sort of thing. The generic
configuration has several advantages over other approaches:
The input pair not only provides the simplest way of making a DCcoupled amplifier with a dependably small output offset voltage, but can
also (given half a chance) completely cancel the 2nd-harmonic
distortion which would be generated by a single-transistor input stage.
One vital condition for this must be met; the pair must be accurately
balanced by choosing the associated components so that the two
collector currents are equal. (The typical component values shown in
Figure 3.1 do not bring about this most desirable state of affairs.)
The general principles of power amplifiers
The input devices work at a constant and near-equal Vce, giving good
thermal balance.
The input pair has virtually no voltage gain so no low-frequency pole
can be generated by Miller effect in the TR2 collector-base capacitance. All the voltage gain is provided by the VAS stage, which makes
for easy compensation. Feedback through Cdom lowers VAS input and
output impedances, minimising the effect of input-stage capacitance,
and the output stage capacitance. This is often known as polesplitting [2]; the pole of the VAS is moved downwards in frequency to
become the dominant pole, while the input-stage pole is pushed up in
The VAS Miller compensation capacitance smoothly transfers NFB from
a global loop that may be unstable, to the VAS local loop that cannot be.
It is quite wrong to state that all the benefits of feedback are lost as the
frequency increases above the dominant pole, as the VAS is still being
linearised. This position of Cdom also swamps the rather variable Ccb of
the VAS transistor.
The eight distortions
My original series of articles on amplifier distortion listed seven important
distortion mechanisms, all of which are applicable to any Class-B amplifier,
and do not depend on particular circuit arrangements. As a result of further
experimentation, I have now increased this to eight.
In the typical amplifier THD is often thought to be simply due to the Class-B
nature of the output stage, which is linearised less effectively as the
feedback factor falls with increasing frequency. This is, however, only true
when all the removable sources of distortion have been eliminated. In the
vast majority of amplifiers in production, the true situation is more
complex, as the small-signal stages can generate significant distortion of
their own, in at least two different ways; this distortion can easily exceed
output stage distortion at high frequencies. It is particularly inelegant to
allow this to occur given the freedom of design possible in the small-signal
If the ills that a class-B stage is heir to are included then there are eight
major distortion mechanisms. Note that this assumes that the amplifier is
not overloaded, and has proper global or Nyquist stability and does not
suffer from any parasitic oscillations; the latter, if of high enough frequency,
tend to manifest themselves only as unexpected increases in distortion,
sometimes at very specific power outputs and frequencies.
In Figure 3.2 an attempt has been made to show the distortion situation
diagrammatically, indicating the location of each mechanism within the
amplifier. Distortion 8 is not shown.
Audio Power Amplifier Design Handbook
Figure 3.2
The location of the first
seven major distortion
mechanisms. The
eighth (capacitor
distortion) is omitted for
Distortion one: input stage distortion
Non-linearity in the input stage. If this is a carefully-balanced differential
pair then the distortion is typically only measurable at HF, rises at 18 dB/
octave, and is almost pure third harmonic. If the input pair is unbalanced
(which from published circuitry it usually is) then the HF distortion emerges
from the noise floor earlier, as frequency increases, and rises at 12 dB/
octave as it is mostly second harmonic.
Distortion two: vas distortion
Non-linearity in the voltage-amplifier stage (which I call the VAS for
concision) surprisingly does not always figure in the total distortion. If it
does, it remains constant until the dominant-pole freq P1 is reached, and
then rises at 6 dB/octave. With the configurations discussed here it is always
second harmonic.
Usually the level is very low due to linearising negative feedback through
the dominant-pole capacitor. Hence if you crank up the local VAS openloop gain, for example by cascoding or putting more current-gain in the
local VAS-Cdom loop, and attend to Distortion 4) below, you can usually
ignore VAS distortion.
Distortion three: output stage distortion
Non-linearity in the output stage, which is naturally the obvious source.
This in a Class-B amplifier will be a complex mix of large-signal distortion
and crossover effects, the latter generating a spray of high-order harmonics,
and in general rising at 6 dB/octave as the amount of negative feedback
The general principles of power amplifiers
decreases. Large-signal THD worsens with 4 loads and worsens again at
2 . The picture is complicated by dilatory switch-off in the relatively slow
output devices, ominously signalled by supply current increasing in the top
audio octaves.
Distortion four: VAS loading distortion
Loading of the VAS by the non-linear input impedance of the output stage.
When all other distortion sources have been attended to, this is the limiting
distortion factor at LF (say below 2 kHz); it is simply cured by buffering the
VAS from the output stage. Magnitude is essentially constant with
frequency, though overall effect in a complete amplifier becomes less as
frequency rises and feedback through Cdom starts to linearise the VAS.
Distortion five: rail decoupling distortion
Non-linearity caused by large rail-decoupling capacitors feeding the
distorted signals on the supply lines into the signal ground. This seems to be
the reason that many amplifiers have rising THD at low frequencies.
Examining one commercial amplifier kit, I found that rerouting the
decoupler ground-return reduced the THD at 20 Hz by a factor of three.
Distortion six: induction distortion
Non-linearity caused by induction of Class-B supply currents into the
output, ground, or negative-feedback lines. This was highlighted by
Cherry [3] but seems to remain largely unknown; it is an insidious distortion
that is hard to remove, though when you know what to look for on the THD
residual it is fairly easy to identify. I suspect that a large number of
commercial amplifiers suffer from this to some extent.
Distortion seven: NFB takeoff distortion
Non-linearity resulting from taking the NFB feed from slightly the wrong
place near where the power-transistor Class-B currents sum to form the
output. This may well be another very prevalent defect.
Distortion eight: capacitor distortion
Distortion, rising as frequency falls, caused by non-linearity in the input
DC-blocking capacitor or the feedback network capacitor. The latter is
more likely.
Non-existent distortions
Having set down what might be called The Eight Great Distortions, we
must pause to put to flight a few Paper Tigers . . . The first is common-mode
Audio Power Amplifier Design Handbook
distortion in the input stage, a spectre that haunts the correspondence
columns. Since it is fairly easy to make an amplifier with less than
<0.00065% THD (1 kHz) without paying any special attention to this it
cannot be too serious a problem.
Giovani Stochino and I have investigated this a little, and we have
independently found that if the common-mode voltage on the input pair is
greatly increased, then a previously negligible distortion mechanism is
indeed provoked. This CM increase is achieved by reducing the C/L gain to
between 1 and 2x; the input signal is much larger for the same output, and
the feedback signal must match it, so the input stage experiences a
proportional increase in CM voltage.
At present it appears that the distortion produced by this mechanism
increases as the square of the CM voltage. It therefore appears that the only
precautions required against common-mode distortion are to ensure that
the closed-loop gain is at least 5 times (which is no hardship, as it almost
certainly is anyway) and to use a tail current-source for the input pair.
The second distortion conspicuous by its absence in the list is the injection
of distorted supply-rail signals directly into the amplifier circuitry. Although
this putative mechanism has received a lot of attention [4], dealing with
Distortion 5 above by proper grounding seems to be all that is required;
once more, if triple-zero THD can be attained using simple unregulated
supplies and without paying any attention to the Power Supply Rejection
Ratio beyond keeping the amplifier free from hum (which it reliably can be)
then there seems to be no problem. There is certainly no need for regulated
supply rails to get a good performance. PSRR does need careful attention if
the hum/noise performance is to be of the first order, but a little RC filtering
is usually all that is needed. This is dealt with in Chapter 8.
A third mechanism of very doubtful validity is thermal distortion,
allegedly induced by parameter changes in semiconductor devices whose
instantaneous power dissipation varies over a cycle. This would surely
manifest itself as a distortion rise at very low frequencies, but it simply
does not happen. There are several distortion mechanisms that can give a
THD rise at LF, but when these are eliminated the typical distortion trace
remains flat down to at least 10 Hz. The worst thermal effects would be
expected in Class-B output stages where dissipation varies wildly over a
cycle; however drivers and output devices have relatively large junctions
with high thermal inertia. Low frequencies are of course also where the
NFB factor is at its maximum. This contentious issue is dealt with at
greater length in Chapter 5.
To return to our list of the unmagnificent eight, note that only Distortion 3
is directly due to O/P stage non-linearity, though numbers 4–7 all result
from the Class-B nature of the typical output stage. Distortion 8 can happen
in any amplifier stage.
The general principles of power amplifiers
The performance of a standard amplifier
The THD curve for the standard amplifier is shown in Figure 3.3. As usual,
distortion increases with frequency, and as we shall see later, would give
grounds for suspicion if it did not. The flat part of the curve below 500 Hz
represents non-frequency-sensitive distortion rather than the noise floor,
which for this case is at the 0.0005% level. Above 500 Hz the distortion
rises at an increasing rate, rather than a constant number of dB/octave,
due to the combination of Distortions 1, 2, 3 and 4. (In this case
Distortions 5, 6 and 7 have been carefully eliminated to keep things
simple; this is why the distortion performance looks good already, and the
significance of this should not be overlooked.) It is often written that
having distortion constant across the audio band is a Good Thing; a most
unhappy conclusion, as the only practical way to achieve this with a
Class-B amplifier is to increase the distortion at LF, for example by
allowing the VAS to distort significantly.
It should now be clear why it is hard to wring linearity out of such a snakepit of contending distortions. A circuit-value change is likely to alter at least
2 of the distortion mechanisms, and probably change the o/l gain as well;
in the coming chapters I shall demonstrate how each distortion mechanism
can be measured and manipulated in isolation.
Open-loop linearity and how to determine it
Improving something demands measuring it, and thus it is essential to
examine the open-loop linearity of power-amp circuitry. This cannot be
done directly, so it is necessary to measure the NFB factor and calculate
open-loop distortion from closed-loop measurements. The closed-loop
gain is normally set by input sensitivity requirements.
Figure 3.3
The distortion
performance of the
Class-B amplifier in
Figure 3.1
Audio Power Amplifier Design Handbook
Figure 3.4
Test circuit for
measuring open-loop
gain directly. The
accuracy with which
high o/l gains can be
measured depends on
the testgear CMRR
Measuring the feedback-factor is at first sight difficult, as it means
determining the open-loop gain. Standard methods for measuring op-amp
open-loop gain involve breaking feedback-loops and manipulating closedloop (c/l) gains, procedures that are likely to send the average poweramplifier into fits. Nonetheless the need to measure this parameter is
inescapable, as a typical circuit modification – e.g. changing the value of
R2 – changes the open-loop gain as well as the linearity, and to prevent
total confusion it is essential to keep a very clear idea of whether an
observed change is due to an improvement in o/l linearity or merely
because the o/l gain has risen. It is wise to keep a running check on this as
work proceeds, so the direct method of open-loop gain measurement
shown in Figure 3.4 was evolved.
Direct o/l gain measurement
The amplifier shown in Figure 3.1 is a differential amplifier, so its openloop gain is simply the output divided by the voltage difference between
the inputs. If output voltage is kept constant by providing a constant
swept-frequency voltage at the +ve input, then a plot of open-loop gain
versus frequency is obtained by measuring the error-voltage between the
inputs, and referring this to the output level. This gives an upside-down
plot that rises at HF rather than falling, as the differential amplifier
requires more input for the same output as frequency increases, but the
method is so quick and convenient that this can be lived with. Gain is
plotted in dB with respect to the chosen output level (+16 dBu in this
case) and the actual gain at any frequency can be read off simply by
dropping the minus sign. Figure 3.5 shows the plot for the amplifier in
Figure 3.1.
The general principles of power amplifiers
Figure 3.5
Open-loop gain
versus freq plot for
Figure 3.1. Note that
the curve rises as gain
falls, because the
amplifier error is the
actual quantity
The HF-region gain slope is always 6 dB/octave unless you are using
something special in the way of compensation, and by the Nyquist rules
must continue at this slope until it intersects the horizontal line
representing the feedback factor, if the amplifier is stable. In other words,
the slope is not being accelerated by other poles until the loop gain has
fallen to unity, and this provides a simple way of putting a lower bound
on the next pole P2; the important P2 frequency (which is usually
somewhat mysterious) must be above the intersection frequency if the
amplifier is seen to be stable.
Given test-gear with a sufficiently high Common-Mode-Rejection-Ratio
balanced input, the method of Figure 3.4 is simple; just buffer the
differential inputs from the cable capacitance with TL072 buffers, which
place negligible loading on the circuit if normal component values are
used. In particular be wary of adding stray capacitance to ground to the –ve
input, as this directly imperils amplifier stability by adding an extra
feedback pole. Short wires from power amplifier to buffer IC can usually be
unscreened as they are driven from low impedances.
The testgear input CMRR defines the maximum open-loop gain measurable; I used an Audio Precision System-1 without any special alignment of
CMRR. A calibration plot can be produced by feeding the two buffer inputs
from the same signal; this will probably be found to rise at 6 dB/octave,
being set by the inevitable input assymmetries. This must be low enough for
amplifier error signals to be above it by at least 10 dB for reasonable
accuracy. The calibration plot will flatten out at low frequencies, and may
even show an LF rise due to imbalance of the test-gear input-blocking
capacitors; this can make determination of the lowest pole P1 difficult, but
this is not usually a vital parameter in itself.
Audio Power Amplifier Design Handbook
Using model amplifiers
Distortions 1 and 2 can dominate amplifier performance and need to be
studied without the manifold complications introduced by a Class-B output
stage. This can be done by reducing the circuit to a model amplifier that
consists of the small-signal stages alone, with a very linear Class-A emitterfollower attached to the output to allow driving the feedback network; here
small-signal refers to current rather than voltage, as the model amplifier
should be capable of giving a full power-amp voltage swing, given
sufficiently high rail voltages. From Figure 3.2 it is clear that this will allow
study of Distortions 1 and 2 in isolation, and using this approach it will
prove relatively easy to design a small-signal amplifier with negligible
distortion across the audio band, and this is the only sure foundation on
which to build a good power amplifier.
A typical plot combining Distortions 1 and 2 from a model amp is shown
in Figure 3.6, where it can be seen that the distortion rises with an
accelerating slope, as the initial rise at 6 dB/octave from the VAS is
contributed to and then dominated by the 12 dB/octave rise in distortion
from an unbalanced input stage.
The model can be powered from a regulated current-limited PSU to cut
down the number of variables, and a standard output level chosen for
comparison of different amplifier configurations; the rails and output level
used for the results in this work were +/–15 V and +16 dBu. The rail
voltages can be made comfortably lower than the average amplifier HT rail,
so that radical bits of circuitry can be tried out without the creation of a
silicon cemetery around your feet. It must be remembered that some
phenomena such as input-pair distortion depend on absolute output level,
Figure 3.6
The distortion from a
model amplifier,
produced by the input
pair and the VoltageAmplifier Stage – note
increasing slope as
input pair distortion
begins to add to VAS
The general principles of power amplifiers
rather than the proportion of the rail voltage used in the output swing, and
will be increased by a mathematically predictable amount when the real
voltage swings are used.
The use of such model amplifiers requires some caution, and gives no
insight into BJT output stages, whose behaviour is heavily influenced by the
sloth and low current gain of the power devices. As a general rule, it should
be possible to replace the small-signal output with a real output stage and
get a stable and workable power amplifier; if not, then the model is
probably dangerously unrealistic.
The concept of the Blameless amplifier
Here I introduce the concept of what I have chosen to call a Blameless
audio power amplifier. This is an amplifier designed so that all the easilydefeated distortion mechanisms have been rendered negligible. (Note that
the word Blameless has been carefully chosen to not imply Perfection, but
merely the avoidance of known errors.) Such an amplifier gives about
0.0005% THD at 1 kHz and approximately 0.003% at 10 kHz when driving
8 . This is much less THD than a Class-B amplifier is normally expected
to produce, but the performance is repeatable, predictable, and definitely
does not require large global feedback factors.
Distortion 1 cannot be totally eradicated, but its onset can be pushed
well above 20 kHz by the use of local feedback. Distortion 2 (VAS
distortion) can be similarly suppressed by cascoding or beta-enhancement, and Distortions 4 to 7 can be made negligible by simple
topological methods. All these measures will be detailed later. This leaves
Distortion 3, which includes the intractable Class-B problems, i.e.
crossover distortion (Distortion 3b) and HF switch-off difficulties (Distortion 3c). Minimising 3b requires a Blameless amplifier to use a BJT output
rather than FETs.
A Blameless Class-B amplifier essentially shows crossover distortion only,
so long as the load is no heavier than 8 ; this distortion increases with
frequency as the amount of global NFB falls. At 4 loading an extra
distortion mechanism (3a) generates significant third harmonic.
The importance of the Blameless concept is that it represents the best
distortion performance obtainable from straightforward Class-B. This
performance is stable and repeatable, and varies little with transistor type as
it is not sensitive to variable quantities such as beta.
Blamelessness is a condition that can be defined with precision, and is
therefore a standard other amplifiers can be judged against. A Blameless
design represents a stable point of departure for more radical designs, such
as the Trimodal concept in Chapter 9. This may be the most important use
of the idea.
Audio Power Amplifier Design Handbook
1. Oliver Distortion In Complementary-Pair Class-B Amplifiers HewlettPackard Journal Feb 1971, p. 11.
2. Feucht Handbook of Analog Circuit Design Academic Press 1990,
p. 256 (Pole-splitting).
3. Cherry, E A New Distortion Mechanism in Class-B Amplifiers Journ.
Audio Eng. Soc. May 1981, p. 327.
4. Ball, G Distorting Power Supplies Electronics World+WW, Dec 1990,
p. 1084.
The small signal stages
‘A beginning is the time for taking the most delicate care that the
balances are correct.’ Frank Herbert, Dune.
The role of the input stage
The input stage of an amplifier performs the critical duty of subtracting the
feedback signal from the input, to generate the error signal that drives the
output. It is almost invariably a differential transconductance stage; a
voltage-difference input results in a current output that is essentially
insensitive to the voltage at the output port. Its design is also frequently
neglected, as it is assumed that the signals involved must be small, and that
its linearity can therefore be taken lightly compared with that of the VAS or
the output stage. This is quite wrong, for a misconceived or even mildly
wayward input stage can easily dominate the HF distortion performance.
The input transconductance is one of the two parameters setting HF openloop (o/l) gain, and therefore has a powerful influence on stability and
transient behaviour as well as distortion. Ideally the designer should set out
with some notion of how much o/l gain at 20 kHz will be safe when driving
worst-case reactive loads (this information should be easier to gather now
there is a way to measure o/l gain directly) and from this a suitable
combination of input transconductance and dominant-pole Miller capacitance can be chosen.
Many of the performance graphs shown here are taken from a model
(small-signal stages only) amplifier with a Class-A emitter-follower output,
at +16 dBu on +/–15 V rails; however, since the output from the input pair
is in current form, the rail voltage in itself has no significant effect on the
linearity of the input stage; it is the current swing at its output that is the
crucial factor.
Audio Power Amplifier Design Handbook
Distortion from the input stage
The motivation for using a differential pair as the input stage of an amplifier
is usually its low DC offset. Apart from its inherently lower offset due to the
cancellation of the Vbe voltages, it has the important added advantage that
its standing current does not have to flow through the feedback network.
However a second powerful reason, which seems less well-known, is that
linearity is far superior to single-transistor input stages. Figure 4.1 shows
three versions, in increasing order of sophistication. The resistor-tail version
at 1a has poor CMRR and PSRR and is generally a false economy of the
shabbiest kind; it will not be further considered here. The mirrored version
at 1c has the best balance, as well as twice the transconductance of 1b.
Figure 4.1
Three versions of an
input pair. a Simple
tail resistor. b Tail
current-source. c With
collector current-mirror
to give inherently
good lc balance
At first sight, the input stage should generate a minimal proportion of the
overall distortion because the voltage signals it handles are very small,
appearing as they do upstream of the VAS that provides almost all the
voltage gain. However, above the first pole frequency P1, the current
required to drive Cdom dominates the proceedings, and this remorselessly
doubles with each octave, thus:
ipk = w × Cdom × Vpk
Equation 4.1
where W = 2 × pi × freq
For example the current required at 100 W (8 ) and 20 kHz, with a 100 pF
Cdom is 0.5 mA peak, which may be a large proportion of the input
standing current, and so the linearity of transconductance for large current
excursions will be of the first importance if we want low distortion at high
Curve A in Figure 4.2 shows the distortion plot for a model amplifier (at
+16 dBu output) designed so the distortion from all other sources is
negligible compared with that from the carefully balanced input stage; with
a small-signal class A stage this reduces to making sure that the VAS is
The small signal stages
Figure 4.2
Distortion performance
of model amplifierdifferential pair at A
compared with
singleton input at B.
The singleton
generates copious
properly linearised. Plots are shown for both 80 kHz and 500 kHz
measurement bandwidths, in an attempt to show both HF behaviour and
the vanishingly low LF distortion. It can be seen that the distortion is below
the noise floor until 10 kHz, when it emerges and heaves upwards at a
precipitous 18 dB/octave. This rapid increase is due to the input stage signal
current doubling with every octave, to feed Cdom; this means that the
associated third harmonic distortion will quadruple with every octave
increase. Simultaneously the overall NFB available to linearise this
distortion is falling at 6 dB/octave since we are almost certainly above the
dominant-pole frequency P1, and so the combined effect is an octuple or
18 dB/octave rise. If the VAS or the output stage were generating distortion
this would be rising at only 6 dB/octave, and so would look quite different
on the plot.
This non-linearity, which depends on the rate-of-change of the output
voltage, is the nearest thing that exists to the late unlamented TID (Transient
Intermodulation Distortion), an acronym that now seems to be falling out of
fashion. SID (Slew-Induced-Distortion) is a better description of the effect,
but implies that slew-limiting is responsible, which is not the case.
If the input pair is not accurately balanced, then the situation is more
complex. Second as well as third harmonic distortion is now generated,
and by the same reasoning this has a slope nearer to 12 dB/octave; this vital
point is examined more closely below.
BJTs vs FETs for the input stage
At every stage in the design of an amplifier, it is perhaps wise to consider
whether BJTs or FETs are the best devices for the job. I may as well say
Audio Power Amplifier Design Handbook
at once that the predictable Vbe/Ic relationship and much higher
transconductance of the bipolar transistor make it, in my opinion, the best
choice for all three stages of a generic power amplifier. To quickly
summarise the position:
Advantages of the FET input stage
There is no base current with FETs, so this is eliminated as a source of DC
offset errors. However, it is wise to bear in mind that FET gate leakage
currents increase very rapidly with temperature, and under some circumstances may need to be allowed for.
Disadvantages of FET input stage
1 The undegenerated transconductance is low compared with BJTs. There
is much less scope for linearising the input stage by adding degeneration
in the form of source resistors, and so an FET input stage will be very nonlinear compared with a BJT version degenerated to give the same low
2 the Vgs offset spreads will be high. Having examined many different
amplifier designs, it seems that in practice it is essential to use dual FETs,
which are relatively very expensive and not always easy to obtain. Even
then, the Vgs mismatch will probably be greater than Vbe mismatch in
a pair of cheap discrete BJTs; for example the 2N5912 N-channel dual
FET has a specified maximum Vgs mismatch of 15 mV. In contrast the
Vbe mismatches of BJTs, especially those taken from the same batch
(which is the norm in production) will be much lower, at about 2–3 mV,
and usually negligible compared with DC offset caused by unbalanced
base currents,
3 the noise performance will be inferior if the amplifier is being driven
from a low-impedance source, say 5 k or less. This is almost always the
Singleton input stage versus differential pair
Using a single input transistor (Figure 4.3a) may seem attractive, where the
amplifier is capacitor-coupled or has a separate DC servo; it at least
promises strict economy. However, the snag is that this singleton
configuration has no way to cancel the second-harmonics generated in
copious quantities by its strongly-curved exponential Vin/lout characteristic [1]. The result is shown in Figure 4.2 curve-B, where the distortion is
much higher, though rising at the slower rate of 12 dB/octave.
The input stage distortion in isolation
Examining the slope of the distortion plot for the whole amplifier
is instructive, but for serious research we need to measure input-stage
The small signal stages
Figure 4.3
Singleton and
differential pair input
stages, showing
typical DC
conditions. The large
DC offset of the
singleton is mainly
due to all the stage
current flowing
through the feedback
resistor RF1
non-linearity in isolation. This can be done with the test circuit of Figure
4.4. The op-amp uses shunt feedback to generate an appropriate AC virtualearth at the input-pair output. Note that this current-to-voltage conversion
op-amp requires a third –30 V rail to allow the i/p pair collectors to work
at a realistic DC voltage – i.e. about one diode’s-worth above the –15 V rail.
Rf can be scaled as convenient, to stop op-amp clipping, without the input
stage knowing anything has changed. The DC balance of the pair can be
manipulated by VR1, and it is instructive to see the THD residual diminish
as balance is approached, until at its minimum amplitude it is almost pure
third harmonic.
Figure 4.4
Test circuit for
examining input stage
distortion in isolation.
The shunt-feedback
op-amp is biased to
provide the right DC
conditions for TR2
Audio Power Amplifier Design Handbook
The differential pair has the great advantage that its transfer characteristic is
mathematically highly predictable [2]. The output current is related to the
differential input voltage Vin by:
Iout = Ie .tanh(–Vin /2Vt )
Equation 4.2
(where Vt is the usual thermal voltage of about 26 mV at 25°C, and le the
tail current).
Two vital facts derived from this equation are that the transconductance
(gm) is maximal at Vin = 0, when the two collector currents are equal, and
that the value of this maximum is proportional to the tail current le. Device
beta does not figure in the equation, and the performance of the input pair
is not significantly affected by transistor type.
Figure 4.5a shows the linearising effect of local feedback or degeneration
on the voltage-in/current-out law; Figure 4.5b plots transconductance
Figure 4.5
Effect of
degeneration on
input pair V/I law,
showing how
transconductance is
sacrificed in favour
of linearity. (SPICE
The small signal stages
against input voltage and shows clearly how the peak transconductance
value is reduced, but the curve made flatter and linear over a wider
operating range. Simply adding emitter degeneration markedly improves
the linearity of the input stage, but the noise performance is slightly
worsened, and of course the overall amplifier feedback factor has been
reduced, for as previously shown, the vitally-important HF closed-loop
gain is determined solely by the input transconductance and the value of
the dominant-pole capacitor.
Input stage balance
Exact DC balance of the input differential pair is essential in power
amplifiers. It still seems almost unknown that minor deviations from equal
Ic in the pair seriously upset the second-harmonic cancellation, by moving
the operating point from A in Figure 4.5a to B. The average slope of the
characteristic is greatest at A, so imbalance also reduces the open-loop gain
if serious enough. The effect of small amounts of imbalance is shown in
Figure 4.6 and Table 4.1; for an input of –45 dBu a collector-current
imbalance of only 2% gives a startling worsening of linearity, with THD
Figure 4.6
Effect of collectorcurrent imbalance on
an isolated input pair;
the second harmonic
rises well above the
level of the third if the
pair moves away from
balance by as little as
Table 4.1
(Key to Figure 4.6) Curve No.
Ic Imbalance
Curve No.
Ic Imbalance
Audio Power Amplifier Design Handbook
Figure 4.7
Improvements to the
input pair. a Poorly
designed version.
b Better; partial
balance by correct
choice of R2. c Best;
near-perfect Ic
balance enforced by
increasing from 0.10% to 0.16%; for 10% imbalance this deteriorates badly
to 0.55%. Unsurprisingly, imbalance in the other direction (Ic1>Ic2) gives
similar results.
Imbalance defined as deviation of Ic (per device) from that value which
gives equal currents in the pair.
This explains the complex distortion changes that accompany the
apparently simple experiment of altering the value of R2 [3]. We might
design an input stage like Figure 4.7a, where R1 has been selected as 1k
by uninspired guesswork and R2 made highish at 10k in a plausible but
misguided attempt to maximise o/l gain by minimising loading on Q1
collector. R3 is also 10k to give the stage a notional balance, though
unhappily this is a visual rather than electrical balance. The asymmetry is
shown in the resulting collector currents; the design generates a lot of
avoidable second harmonic distortion, displayed in the 10k curve of
Figure 4.8.
Recognising the crucial importance of DC balance, the circuit can be
rethought as Figure 4.7b. If the collector currents are to be roughly equal,
then R2 must be about 2 × R1, as both have about 0.6 V across them. The
dramatic effect of this simple change is shown in the 2k2 curve of Figure
4.8; the improvement is accentuated as the o/l gain has also increased by
some 7 dB, though this has only a minor effect on the closed-loop linearity
compared with the improved balance of the input pair. R3 has been excised
as it contributes very little to input stage balance.
The joy of current-mirrors
Although the input pair can be approximately balanced by the correct
values for R1 and R2, we remain at the mercy of several circuit tolerances.
Figure 4.6 shows that balance is critical, needing an accuracy of 1% or
The small signal stages
Figure 4.8
Distortion of model
a Unbalanced with
R2 = 10k. b Partially
balanced with R =
2k2. c Accurately
balanced by currentmirror
better for optimal linearity and hence low distortion at HF, where the input
pair works hardest. The standard current-mirror configuration in Figure
4.7c forces the two collector currents very close to equality, giving correct
cancellation of the second harmonic; the great improvement that results is
seen in the current-mirror curve of Figure 4.8. There is also less DC offset
due to unequal base-currents flowing through input and feedback
resistances; I often find that a power-amplifier improvement gives at
least two separate benefits. This simple mirror has well-known residual
base-current errors but they are not large enough to affect the distortion
The hyperbolic-tangent law also holds for the mirrored pair [4], though the
output current swing is twice as great for the same input voltage as the
resistor-loaded version. This doubled output is given at the same distortion
as for the unmirrored version, as linearity depends on the input voltage,
which has not changed. Alternatively, we can halve the input and get the
same output, which with a properly balanced pair generating third
harmonic only will give one-quarter the distortion. A pleasing result.
The input mirror is made from discrete transistors, regretfully foregoing the
Vbe-matching available to IC designers, and it needs its own emitterdegeneration for good current-matching. A voltage-drop across the currentmirror emitter-resistors in the range 30–60 mV will be enough to make the
effect of Vbe tolerances on distortion negligible; if degeneration is omitted
then there is significant variation in HF distortion performance with
different specimens of the same transistor type.
Putting a current-mirror in a well-balanced input stage increases the total
o/l gain by at least 6 dB, and by up to 15 dB if the stage was previously
poorly balanced; this needs to be taken into account in setting the
Audio Power Amplifier Design Handbook
compensation. Another happy consequence is that the slew-rate is roughly
doubled, as the input stage can now source and sink current into Cdom
without wasting it in a collector load. If Cdom is 100 pF, the slew-rate of
Figure 4.7b is about 2.8 V/µsec up and down, while 4.7c gives 5.6 V/µsec.
The unbalanced pair at 4.7a displays further vices by giving 0.7 V/µsec
positive-going and 5 V/µsec negative-going.
Improving input-stage linearity
Even if the input pair has a current-mirror, we may still feel that the HF
distortion needs further reduction; after all, once it emerges from the noise
floor it octuples with each doubling of frequency, and so it is well worth
postponing the evil day until as far as possible up the frequency range. The
input pair shown has a conventional value of tail-current. We have seen
that the stage transconductance increases with Ic, and so it is possible to
increase the gm by increasing the tail-current, and then return it to its
previous value (otherwise Cdom would have to be increased proportionately to maintain stability margins) by applying local NFB in the form of
emitter-degeneration resistors. This ruse powerfully improves input linearity, despite its rather unsettling flavour of something-for-nothing. The
transistor non-linearity can here be regarded as an internal non-linear
emitter resistance re, and what we have done is to reduce the value of this
(by increasing Ic) and replaced the missing part of it with a linear external
resistor Re.
For a single device, the value of re can be approximated by:
re = 25/Ic ohms (for Ic in mA)
Equation 4.3
Our original stage at Figure 4.9a has a per-device Ic of 600 µA, giving a
differential (i.e. mirrored) gm of 23 mA/V and re = 41.6 . The improved
version at Figure 4.9b has Ic = 1.35 mA and so re = 18.6 ; therefore
emitter degeneration resistors of 22 are required to reduce the gm back
to its original value, as 18.6 + 22 = 41.6 . The distortion measured by the
circuit of Figure 4.4 for a –40 dBu input voltage is reduced from 0.32% to
0.032%, which is an extremely valuable linearisation, and will translate
into a distortion reduction at HF of about 5 times for a complete amplifier;
for reasons that will emerge later the full advantage is rarely gained. The
distortion remains a visually pure third-harmonic, so long as the input pair
remains balanced. Clearly this sort of thing can only be pushed so far, as the
reciprocal-law reduction of re is limited by practical values of tail current.
A name for this technique seems to be lacking; constant-gm degeneration
is descriptive but rather a mouthful.
The standing current is roughly doubled so we have also gained a higher
slew-rate; it has theoretically increased from 10 V/µsec to 20 V/µsec, and
once again we get two benefits for the price of one inexpensive
The small signal stages
Figure 4.9
Input pairs before and
after constant-gm
degeneration, showing
how to double stage
current while keeping
constant; distortion is
reduced by about ten
Radical methods of improving input linearity
If we are seeking still better linearity, various techniques exist. Whenever it
is needful to increase the linearity of a circuit, it is often a good approach
to increase the local feedback factor, because if this operates in a tight local
NFB loop there is often little effect on the overall global-loop stability. A
reliable method is to replace the input transistors with complementaryfeedback (CFP or Sziklai) pairs, as shown in the stage of Figure 4.10a. If an
isolated input stage is measured using the test circuit of Figure 4.4, the
constant-gm degenerated version shown in Figure 4.9b yields 0.35% thirdharmonic distortion for a –30 dBu input voltage, while the CFP version
Figure 4.10
Some enhanced
differential pairs: a The
Feedback Pair. b The
Cross-quad. c The
Audio Power Amplifier Design Handbook
gives 0.045%. (Note that the input level here is 10 dB up on the previous
example, to get well clear of the noise floor.) When this stage is put to work
in a model amplifier, the third-harmonic distortion at a given frequency is
roughly halved, assuming all other distortion sources have been appropriately minimised. However, given the high-slope of input-stage distortion,
this only extends the low-distortion regime up in frequency by less than an
octave. See Figure 4.11.
A compromise is required in the CFP circuit on the value of Rc, which sets
the proportion of the standing current that goes through the NPN and PNP
devices on each side of the stage. A higher value of Rc gives better linearity,
but more noise, due to the lower Ic in the NPN devices that are the inputs
of the input stage, as it were, causing them to match less well the relatively
low source resistances. 2k2 is a good compromise.
Several other elaborations of the basic input pair are possible, although
almost unknown in the audio community. We are lucky in power-amp
design as we can tolerate a restricted input common-mode range that
would be unusable in an op-amp, giving the designer great scope.
Complexity in itself is not a serious disadvantage as the small-signal stages
of the typical amplifier are of almost negligible cost compared with mains
transformers, heatsinks, etc.
Two established methods to produce a linear input transconductance stage
(referred to in op-amp literature simply as a transconductor) are the crossquad [5] and the cascomp [6] configurations. The cross-quad (Figure 4.10b)
gives a useful reduction in input distortion when operated in isolation but
is hard to incorporate in a practical amplifier because it relies on very low
source-resistances to tame the negative conductances inherent in its
operation. The cross-quad works by imposing the input voltage to each half
Figure 4.11
Whole-amplifier THD
with normal and CFP
input stages; input
stage distortion only
shows above noise
floor at 20 kHz, so
improvement occurs
above this frequency.
The noise floor
appears high as the
bandwidth is 500 kHz
The small signal stages
across two base-emitter junctions in series, one in each arm of the circuit.
In theory the errors due to non-linear re of the transistors is divided by beta,
but in practice the reduction in distortion is modest.
The cascomp (Figure 4.10c) does not have problems with negative
impedances, but it is significantly more complex to design. Q2, Q3 are the
main input pair as before, delivering current through cascode transistors
Q4, Q5 (this does not in itself affect linearity), which, since they carry
almost the same current as Q2, Q3 duplicate the input Vbe errors at their
emitters. This is sensed by error diff-amp Q6, Q7, whose output currents
are summed with the main output in the correct phase for error-correction.
By careful optimisation of the (many) circuit variables, distortion at –30 dBu
input can be reduced to about 0.016% with the circuit values shown. Sadly,
this effort provides very little further improvement in whole-amplifier HF
distortion over the simpler CFP input, as other distortion mechanisms are
coming into play, one of which is the finite ability of the VAS to source
current into the other end of Cdom.
Input stage cascode configurations
Power amplifiers with pretensions to sophistication sometimes add
cascoding to the standard input differential amplifier. This does nothing
whatever to improve input-stage linearity, as there is no appreciable voltage
swing on the input collectors; its main advantage is reduction of the high
Vce that the input devices work at. This allows cooler running, and
therefore possibly improved thermal balance; a Vce of 5 V usually works
well. Isolating the input collector capacitance from the VAS input
sometimes allows Cdom to be slightly reduced for the same stability
margins, but the improvement is marginal.
Input noise and how to reduce it
The noise performance of a power amplifier is defined by its input stage,
and so the issue is examined here. Power-amp noise is not an irrelevance;
a powerful amplifier will have a high voltage gain, and this can easily result
in a faint but irritating hiss from efficient loudspeakers even when all
volume controls are fully retarded [3]. In the design considered here the EIN
has been measured at –120 dBu, which is only 7 or 8 dB worse than a firstclass microphone preamplifier; the inferiority is largely due to the source
resistances seen by the input devices being higher than the usual 150 microphone impedance. By way of demonstration, halving the impedance
of the usual feedback network (22k and 1k) reduces the EIN further by
about 2 dB.
Amplifier noise is defined by a combination of the active devices at the
input and the surrounding resistances. The operating conditions of the
Audio Power Amplifier Design Handbook
input transistors themselves are set by the demands of linearity and slewrate, so there is little freedom of design here; however the collector currents
are already high enough to give near-optimal noise figures with the low
source impedances (a few hundred ohms) that we have here, so this is not
too great a problem. Noise figure is a weak function of Ic, so minor
tweakings of the tail-current make no detectable difference. We certainly
have the choice of input device type; there are many more possibles if we
have relatively low rail voltages. Noise performance is, however, closely
bound up with source impedance, and we need to define this before device
Looking therefore to the passives, there are several resistances generating
Johnson Noise in the input, and the only way to reduce this noise is to
reduce them in value. The obvious candidates are R2, R3 see Figure 4.12
(input stage degeneration resistors) and R9, which determines the output
Figure 4.12
Stable input
bootstrapping from the
feedback point. Riso is
essential for HF
stability; with 100 ,
as shown, the input
impedance is 13 k
The small signal stages
impedance of the negative-feedback network. There is also another unseen
component; the source resistance of the preamplifier or whatever upstream.
Even if this equipment were miraculously noise-free, its output resistance
would still generate Johnson noise. If the preamplifier had, say, a 20k
volume pot at its output (not a good idea, as this gives a poor gain structure
and cable dependent HF losses, but that is another story [5] ) then the source
resistance could be a maximum of 5k, which would almost certainly
generate enough Johnson Noise to dominate the power-amplifier’s noise
behaviour. However, there is nothing that power-amp designers can do
about this, so we must content ourselves with minimising the noisegenerating resistances we do have control over.
Noise from the input degeneration resistors R2, R3 is the price we pay for
linearising the input stage by running it at a high current, and then bringing
its transconductance down to a useable value by adding linearising local
negative feedback. These resistors cannot be reduced if the HF NFB factor
is then to remain constant, for Cdom will have to be proportionally
increased, reducing slew-rate. With the original 22k–1k NFB network,
these resistors degrade the noise performance by 1.7 dB. (This figure, like
all other noise measurements given here, assumes a 50 external source
If we cannot alter the input degeneration resistors, then the only course left
is the reduction of the NFB network impedance, and this sets off a whole
train of consequences. If R8 is reduced to 2k2, then R9 becomes 110 , and
this reduces noise output from –93.5 dBu to –95.4 dBu. (Note that if R2, R3
were not present, the respective figures would be –95.2 and –98.2 dBu.)
However, R1 must also be reduced to 2k2 to maintain DC balance, and this
is too low an input impedance for direct connection to the outside world.
If we accept that the basic amplifier will have a low input impedance, there
are two ways to deal with it. The simplest is to decide that a balanced line
input is essential; this puts an op-amp stage before the amplifier proper,
buffers the low input impedance, and can provide a fixed source
impedance to allow the HF and LF bandwidths to be properly defined by
an RC network using non-electrolytic capacitors. The usual practice of
slapping an RC network on an unbuffered amplifier input must be roundly
condemned as the source impedance is unknown, and so therefore is the
roll-off point. A major stumbling block for subjectivist reviewing, one
would have thought.
Another approach is to have a low resistance DC path at the input but a
high AC impedance; in other words to use the fine old practice of input
bootstrapping. Now this requires a low-impedance unity-gain-withrespect-to-input point to drive the bootstrap capacitor, and the only one
available is at the amplifier inverting input, i.e. the base of TR3. While this
node has historically been used for the purpose of input bootstrapping [6], it
has only been done with simple circuitry employing very low feedback
Audio Power Amplifier Design Handbook
factors. There is very real reason to fear that any monkey business with the
feedback point (TR3 base) will add shunt capacitance, creating a feedback
pole that will degrade HF stability. There is also the awkward question of
what will happen if the input is left open-circuit . . .
The input can be safely bootstrapped; Figure 4.12 shows how. The total DC
resistance of R1 and Rboot equals R8, and their central point is driven by
Cboot. Connecting Cboot directly to the feedback point did not produce
gross instability, but it did seem to increase susceptibility to odd bits of
parasitic oscillation. Riso was then added to isolate the feedback point from
stray capacitance, and this seemed to effect a complete cure. The input
could be left open-circuit without any apparent ill-effects, though this is not
good practice if loudspeakers are connected. A value for Riso of 220 increases the input impedance to 7.5k, and 100 raises it to 13.3k, safely
above the 10k standard value for a bridging impedance. Despite successful
tests, I must admit to a few lingering doubts about the HF stability of this
approach, and it might be as well to consider it as experimental until more
experience is gained.
One more consequence of a low-impedance NFB network is the need for
feedback capacitor C2 to be proportionally increased to maintain LF
response, and prevent capacitor distortion from causing a rise in THD at
low frequencies; it is the latter requirement that determines the value. (This
is a separate distortion mechanism from the seven originally identified, and
is given the title Distortion 8.) This demands a value of 1000 µF,
necessitating a low rated voltage such as 6V3 if the component is to be of
reasonable size. This means that C2 needs protective shunt diodes in both
directions, because if the amplifier fails it may saturate in either direction.
Examination of the distortion residual shows that the onset of conduction of
back-to-back diodes will cause a minor increase in THD at 10 Hz, from less
than 0.001% to 0.002%, even at the low power of 20 W/8 . It is not my
practice to tolerate such gross non-linearity, and therefore four diodes are
used in the final circuit, and this eliminates the distortion effect. It could be
argued that a possible reverse-bias of 1.2 V does not protect C2 very well,
but at least there will be no explosion.
We can now consider alternative input devices to the MPSA56, which was
never intended as a low-noise device. Several high-beta low-noise types
such as 2SA970 give an improvement of about 1.8 dB with the lowimpedance NFB network. Specialised low-Rb devices like 2SB737 give
little further advantage (possibly 0.1 dB) and it is probably better to go for
one of the high-beta types; the reason why will soon emerge.
It could be argued that the above complications are a high price to pay for
a noise reduction of some 2 dB; however, with the problems comes a
definite advantage, for the above NFB network modification also significantly improves the output DC offset performance.
The small signal stages
Offset and match: the DC precision issue
The same components that dominate amplifier noise performance also
determine the output DC offset; if R9 is reduced to minimise the source
resistance seen by TR3, then the value of R8 is scaled to preserve the same
closed-loop gain, and this reduces the voltage drops caused by input
transistor base currents.
Most of my amplifier designs have assumed that a +/–50 mV output DC
offset is acceptable. This allows DC trimpots, offset servos, etc. to be
gratefully dispensed with. However, it is not in my nature to leave well
enough alone, and it could be argued that +/–50 mV is on the high side for
a top-flight amplifier. I have therefore reduced this range as much as
possible without resorting to a servo; the required changes have already
been made when the NFB network was reduced in impedance to minimise
Johnson noise. (See page 85.)
With the usual range of component values, the DC offset is determined not
so much by input transistor Vbe mismatch, which tends to be only 5 mV or
so, but more by a second mechanism – imbalance in beta. This causes
imbalance of the base currents (Ib) drawn thorough input bias resistor R1
and feedback resistor R8, and the cancellation of the voltage-drops across
these components is therefore compromised.
A third source of DC offset is non-ideal matching of input degeneration
resistors R2, R3. Here they are 100 , with 300 mV dropped across each, so
two 1% components at opposite ends of their tolerance bands could give
a maximum offset of 6 mV. In practice this is most unlikely, and the error
from this source will probably not exceed 2 mV.
There are several ways to reduce DC offset. Firstly, low-power amplifiers
with a single output pair must be run from modest HT rails and so the
requirement for high-Vce input transistors can be relaxed. This allows
higher beta devices to be used, directly reducing Ib. The 2SA970 devices
used in this design have a beta range of 350–700, compared with 100 or
less for MPSA06/56. Note the pinout is not the same.
On page 85, we reduced the impedance of the feedback network by a
factor of 4.5, and the offset component due to Ib imbalance is reduced by
the same ratio. We might therefore hope to keep the DC output offset for
the improved amplifier to within +/–15 mV without trimming or servos.
Using high-beta input devices, the Ib errors did not exceed +/–15 mV for
ten sample pairs (not all from the same batch) and only three pairs
exceeded +/–10 mV. Ib errors are now reduced to the same order of
magnitude as Vbe mismatches, and so no great improvement can be
expected from further reduction of circuit resistances. Drift over time was
measured at less than 1 mV, and this seems to be entirely a function of
temperature equality in the input pair.
Audio Power Amplifier Design Handbook
Figure 4.13
The measured DC
conditions in a real input
stage. Ideal voltages and
currents for perfectly
matched components are
shown in brackets
Figure 4.13 shows the ideal DC conditions in a perfectly-balanced input
stage, assuming ß = 400, compared with a set of real voltages and currents
from the prototype amplifier. In the latter case, there is a typical partial
cancellation of offsets from the three different mechanisms, resulting in a
creditable output offset of –2.6 mV.
The input stage and the slew-rate
This is another parameter which is usually assumed to be set by the input
stage, and has a close association with HF distortion. A brief summary is
therefore given here, but the subject is dealt with in much greater depth in
Chapter 7.
An amplifier’s slew-rate is proportional to the input stage’s maximumcurrent capability, most circuit configurations being limited to switching
the whole of the tail current to one side or the other. The usual differential
pair can only manage half of this, as with the output slewing negatively half
the tail-current is wasted in the input collector load R2. The addition of an
The small signal stages
input current-mirror, as advocated above, will double the slew rate in both
directions as this inefficiency is abolished. With a tail current of 1.2 mA a
mirror improves the slew-rate from about 5 V/µsec to 10 V/µsec (for Cdom
= 100 pF). The constant-gm degeneration method of linearity enhancement
in Figure 4.9 further increases it to 20 V/µsec.
In practice slew rates are not exactly identical for positive and negativegoing directions, especially in the conventional amplifier architecture
which is the main focus of this book.
The voltage-amplifier stage
The Voltage-Amplifier Stage (or VAS) has often been regarded as the most
critical part of a power-amplifier, since it not only provides all the voltage
gain but also must give the full output voltage swing. (The input stage may
give substantial transconductance gain, but the output is in the form of a
current.) However, as is not uncommon in audio, all is not quite as it
appears. A well-designed VAS stage will contribute relatively little to the
overall distortion total of an amplifier, and if even the simplest steps are
taken to linearise it further, its contribution sinks out of sight.
As a starting point, Figure 4.14 shows the distortion plot of a model
amplifier with a Class-A output (+/–15 V rails, +16 dBu out) as per Chapter
3, where no special precautions have been taken to linearise the input stage
or the VAS; output stage distortion is negligible. It can be seen that the
distortion is below the noise floor at LF; however, the distortion slowly
rising from about 1 kHz is coming from the VAS. At higher frequencies,
where the VAS 6 dB/octave rise becomes combined with the 12 or 18 dB/
Figure 4.14
THD plot for model
amp showing very
low distortion (below
noise floor) at LF, and
increasing slope from
2 kHz to 20 kHz. The
ultimate flattening is
due to the 80 kHz
Audio Power Amplifier Design Handbook
octave rise of input-stage distortion, we can see the distortion slope of
accelerating steepness that is typical of many amplifier designs.
As previously explained, the main reason why the VAS generates
relatively little distortion is because at LF, global feedback linearises the
whole amplifier, while at HF the VAS is linearised by local NFB through
Measuring VAS distortion in isolation
Isolating the VAS distortion for study requires the input pair to be specially
linearised, or else its steeply-rising distortion characteristic will swamp the
VAS contribution. This is most easily done by degenerating the input stage;
this also reduces the open-loop gain, and the reduced feedback factor
mercilessly exposes the non-linearity of the VAS. This is shown in Figure
4.15, where the 6 dB/octave slope suggests that this must originate in the
VAS, and increases with frequency solely because the compensation is
rolling-off the global feedback factor. To confirm that this distortion is due
solely to the VAS, it is necessary to find a method for experimentally
varying VAS linearity while leaving all other circuit parameters unchanged.
Figure 4.16 shows my arrangement for doing this by varying the VAS V–
voltage; this varies the proportion of its characteristic over which the VAS
swings, and thus only alters the effective VAS linearity, as the important
input stage conditions remain unchanged. The current-mirror must go up
and down with the VAS emitter for correct operation, and so the Vce of the
input devices also varies, but this has no significant effect, as can be proved
by the unchanged behaviour on inserting cascode stages in the input
transistor collectors.
Figure 4.15
The change in HF
distortion resulting
from varying V– in the
VAS test circuit. The
VAS distortion is only
revealed by
degenerating the input
stage with 100 resistors
The small signal stages
Figure 4.16
VAS distortion test
circuit. Although the
input pair mirror moves
up and down with the
VAS emitter, the only
significant parameter
being varied is the
available voltageswing at the VAS
VAS operation
The typical VAS topology as shown in Figure 4.17a is a classical commonemitter voltage-amplifier stage, with a current-drive input into the base. The
small-signal characteristics, which set open-loop gain and so on, can be
usefully simulated by the Spice model shown in Figure 4.18, of a VAS
reduced to its conceptual essentials. G is a current-source whose value is
controlled by the voltage-difference between Rin and Rf2, and represents
the differential transconductance input stage. F represents the VAS
transistor, and is a current-source yielding a current of beta times that
sensed flowing through ammeter V which by Spice convention is a voltagesource set to 0 V; the value of beta, representing current-gain as usual,
models the relationship between VAS collector current and base current.
Rc represents the total VAS collector impedance, a typical real value being
22k. With suitable parameter values, this simple model provides a good
demonstration of the relationships between gain, dominant-pole frequency,
and input stage current that were introduced in Chapter 3. Injecting a small
signal current into the output node from an extra current-source also allows
the fall of impedance with frequency to be examined.
The overall voltage-gain clearly depends linearly on beta, which in real
transistors may vary widely. Working on the trusty engineering principle
that what cannot be controlled must be made irrelevant, local shunt NFB
through Cdom sets the crucial HF gain that controls Nyquist stability. The
LF gain below the dominant-pole frequency P1 remains variable (and
therefore so does P1) but is ultimately of little importance; if there is an
adequate NFB factor for overall linearisation at HF then there are unlikely
to be problems at LF, where the gain is highest. As for the input stage, the
linearity of the VAS is not greatly affected by transistor type, given a
reasonably high beta.
a Conventional VAS with
current-source load
b Conventional VAS with
bootstrapped load
c Increase in local NFB by
adding beta-enhancing
d Increase in local NFB by
cascoding VAS
e Buffering the VAS collector
from the output stage
f Alternative buffering,
bootstrapping VAS load R
Six variations on a VAS:
Figure 4.17
The small signal stages
Figure 4.18
Conceptual SPICE
model of differential
input stage (G) and
VAS (F). The current in F
is Beta times the current
in VA
VAS distortion
VAS distortion arises from the fact that the transfer characteristic of a
common-emitter amplifier is curved, being a small portion of an
exponential [7]. This characteristic generates predominantly second-harmonic distortion, which in a closed-loop amplifier will increase at 6 dB/
octave with frequency.
VAS distortion does not get worse for more powerful amplifiers as the stage
traverses a constant proportion of its characteristic as the supply-rails are
increased. This is not true of the input stage; increasing output swing
increases the demands on the transconductance amp as the current to drive
Cdom increases. The increased Vce of the input devices does not
measurably affect their linearity.
It is ironic that VAS distortion only becomes clearly visible when the input
pair is excessively degenerated – a pious intention to linearise before
applying feedback can in fact make the closed-loop distortion worse by
reducing the open-loop gain and hence the NFB factor available to
linearise the VAS. In a real (non-model) amplifier with a distortive output
stage the deterioration will be worse.
Linearising the VAS: active load techniques
As described in Chapter 3, it is important that the local open-loop gain of
the VAS (that existing inside the local feedback loop closed by Cdom) be
high, so that the VAS can be linearised, and therefore a simple resistive load
is unusable.
Increasing the value of Rc will decrease the collector current of the VAS
transistor, reducing its transconductance and getting you back where you
started in terms of voltage gain.
One way to ensure enough local loop gain is to use an active load to
increase the effective collector impedance at TR4 and thus increase the raw
voltage gain; either bootstrapping or a current-source will do this
Audio Power Amplifier Design Handbook
effectively, though the current source is perhaps more dependable, and is
the usual choice for hi-fi or professional amplifiers. The Bootstrap promises
more o/p swing, as the collector of TR4 can in theory soar like a lark above
the V+ rail; under some circumstances this can be the overriding concern,
and bootstrapping is alive and well in applications such as automotive
power-amps that must make the best possible use of a restricted supply
voltage [8].
Both active-load techniques have another important role; ensuring that the
VAS stage can source enough current to properly drive the upper half of the
output stage in a positive direction, right up to the rail. If the VAS collector
load was a simple resistor to +V, then this capability would certainly be
It may not be immediately obvious how to check that impedanceenhancing measures are working properly, but it is actually fairly simple.
The VAS collector impedance can be determined by the simple expedient
of shunting the VAS collector to ground with decreasing resistance until the
open-loop gain reading falls by 6 dB, indicating that the collector
impedance is equal to the current value of the test resistor.
The popular current source version is shown in Figure 4.17a. This works
well, though the collector impedance is limited by the effective output
resistance Ro of the VAS and the current source transistors [9], which is
another way of saying that the improvement is limited by Early effect.
It is often stated that this topology provides current-drive to the output
stage; this is only partly true. It is important to realise that once the local
NFB loop has been closed by adding Cdom the impedance at the VAS
output falls at 6 dB/octave for frequencies above P1. With typical values the
impedance is only a few k – at 10 kHz, and this hardly qualifies as
current-drive at all.
Collector-load bootstrapping (Figure 4.17b) works in most respects as well
as a current source load, for all its old-fashioned look. Conventional
capacitor bootstrapping has been criticised for prolonging recovery from
clipping; I have no evidence to offer on this myself, but one subtle
drawback definitely does exist – with bootstrapping the LF open-loop gain
is dependent on amplifier output loading. The effectiveness of bootstrapping depends crucially on the output stage gain being unity or very
close to it; however the presence of the output-transistor emitter resistors
means that there will be a load-dependant gain loss in the output stage,
which in turn significantly alters the amount by which the VAS collector
impedance is increased; hence the LF feedback factor is dynamically
altered by the impedance characteristics of the loudspeaker load and the
spectral distribution of the source material. This has a special significance
if the load is an audiophile speaker that may have impedance dips down
to 2 , in which case the gain loss is serious. If anyone needs a new
The small signal stages
audio-impairment mechanism to fret about, then I humbly offer this one in
the confident belief that its effects, while measurable, are not of audible
significance. Possibly this is a more convincing reason for avoiding
bootstrapping than alleged difficulties with recovery from clipping.
Another drawback of bootstrapping is that the standing DC current through
the VAS, and hence the bias generator, varies with rail voltage. Setting and
maintaining the quiescent conditions is quite difficult enough already, so an
extra source of possible variation is decidedly unwelcome.
A less well-known but more dependable form of bootstrapping is available
if the amplifier incorporates a unity-gain buffer between the VAS collector
and the output stage; this is shown in Figure 4.17f, where Rc is the collector
load, defining the VAS collector current by establishing the Vbe of the
buffer transistor across itself. This is constant, and Rc is therefore
bootstrapped and appears to the VAS collector as a constant-current source.
In this sort of topology a VAS current of 3 mA is quite sufficient, compared
with the 6 mA standing current in the buffer stage. The VAS would in fact
work well with lower collector currents down to 1 mA, but this tends to
compromise linearity at the high-frequency, high-voltage corner of the
operating envelope, as the VAS collector current is the only source for
driving current into Cdom.
VAS enhancements
Figure 4.15 shows VAS distortion only, clearly indicating the need for
further improvement over that given inherently by Cdom if our amplifier is
to be as good as possible. The virtuous approach might be to try to
straighten out the curved VAS characteristic, but in practice the simplest
method is to increase the amount of local negative feedback through
Cdom. Equation 1 in Chapter 3 shows that the LF gain (i.e. the gain before
Cdom is connected) is the product of input stage transconductance, TR4
beta and the collector impedance Rc. The last two factors represent the VAS
gain and therefore the amount of local NFB can be augmented by
increasing either. Note that so long as the value of Cdom remains the same,
the global feedback factor at HF is unchanged and so stability is not
The effective beta of the VAS can be substantially increased by replacing
the VAS transistor with a Darlington, or in other words putting an emitterfollower before it (Figure 4.17c). Adding an extra stage to a feedback
amplifier always requires thought, because if significant additional phaseshift is introduced, the global loop stability can suffer. In this case the new
stage is inside the Cdom Miller-loop and so there is little likelihood of
trouble from this. The function of such an emitter-follower is sometimes
described as buffering the input stage from the VAS but its true function is
linearisation by enhancement of local NFB through Cdom.
Audio Power Amplifier Design Handbook
Alternatively the VAS collector impedance can be increased to get more
local gain. This is straightforwardly done with a cascode configuration –
(see Figure 4.17d) but it should be said at once that the technique is only
really useful when the VAS is not directly driving a markedly non-linear
impedance . . . such as that at the input of a Class-B output stage.
Otherwise this non-linear loading renders it largely a cosmetic feature.
Assuming for the moment that this problem is dealt with, either by use of
a Class-A output or by VAS-buffering, the drop in distortion is dramatic, as
for the beta-enhancement method. The gain increase is ultimately limited
by Early effect in the cascode and current-source transistors, and more
seriously by the loading effect of the next stage, but it is of the order of 10
times and gives a useful effect. This is shown by curves A, B in Figure 4.19,
where once more the input stage of a model amplifier has been overdegenerated with 100 emitter resistors to bring out the VAS distortion
more clearly. Note that in both cases the slope of the distortion increase is
6 dB/octave. Curve C shows the result when a standard undegenerated
input pair is combined with the cascoded VAS; the distortion is submerged
in the noise floor for most of the audio band, being well below 0.001%. I
think this justifies my contention that input-stage and VAS distortions need
not be problems; we have all but eliminated Distortions 1 and 2 from the
list of eight in Chapter 3.
Using a cascode transistor also allows the use of a high-beta transistor for
the VAS; these typically have a limited Vceo that cannot withstand the high
rail voltages of a high-power amplifier. There is a small loss of available
voltage swing, but only about 300 mV, which is usually tolerable.
Experiment shows that there is nothing to be gained by cascoding the
current-source collector load.
A cascode topology is often used to improve frequency response, by
isolating the upper collector from the Cbc of the lower transistor. In this
case the frequency response is deliberately defined by Cdom, so this
appears irrelevant, but in fact it is advantageous that Cbc – which carries
Figure 4.19
Showing the reduction
of VAS distortion
possible by
cascoding. The results
from adding an
emitter-follower to the
VAS, as an alternative
method of increasing
local VAS feedback,
are very similar
The small signal stages
the double demerit of being unpredictable and signal-dependent – is
rendered harmless. Thus compensation is determined only by a welldefined passive component.
It is hard to say which technique is preferable; the beta-enhancing emitterfollower circuit is slightly simpler than the cascode version, which requires
extra bias components, but the cost difference is tiny. When wrestling with
these kind of financial decisions it is as well to remember that the cost of
a small-signal transistor is often less than a fiftieth of that of an output
device, and the entire small-signal section of an amplifier usually
represents less than 1% of the total cost, when heavy metal such as the
mains transformer and heatsinks are included.
Note that although the two VAS-linearising approaches look very different,
the basic strategy of increased local feedback is the same. Either method,
properly applied, will linearise a VAS into invisibility.
The importance of voltage drive
As explained above, it is fundamental to linear VAS operation that the
collector impedance is high, and not subject to external perturbations. Thus
a Class-B output stage, with large input impedance variations around the
crossover point, is about the worst thing you could connect to it, and it is
a tribute to the general robustness of the standard amplifier configuration
that it can handle this internal unpleasantness gracefully, 100 W/8 distortion typically degrading only from 0.0008% to 0.0017% at 1 kHz,
assuming that the avoidable distortions have been eliminated. Note
however that the effect becomes greater as the global feedback-factor is
reduced. There is little deterioration at HF, where other distortions
dominate. To the best of my knowledge I first demonstrated this in reference
10; if I am wrong then I have no doubt I shall soon hear about it.
The VAS buffer is most useful when LF distortion is already low, as it
removes Distortion 4, which is (or should be) only visible when grosser
non-linearities have been seen to. Two equally effective ways of buffering
are shown in Figure 4.17e and f.
There are other potential benefits to VAS buffering. The effect of beta
mismatches in the output stage halves is minimised [11]. Voltage drive also
promises the highest fT from the output devices, and therefore potentially
greater stability, though I have no data of my own to offer on this point. It
is right and proper to feel trepidation about inserting another stage in an
amplifier with global feedback, but since this is an emitter-follower its
phase-shift is minimal and it works well in practice.
If we have a VAS buffer then, providing we put it the right way up we can
implement a form of DC-coupled bootstrapping that is electrically very
similar to providing the VAS with a separate current-source. (See Figure
Audio Power Amplifier Design Handbook
Figure 4.20
The beneficial effect
of using a VAS-buffer
in a full-scale Class-B
amplifier. Note that
the distortion needs to
be low already for the
benefit to be
The use of a buffer is essential if a VAS cascode is to do some good. Figure
4.20 shows before/after distortion for a full-scale power amplifier with
cascode VAS driving 100 W into 8 .
The balanced VAS
When we are exhorted to make the amplifier linear before adding negative
feedback one of the few specific recommendations made is usually the use
of a balanced VAS – sometimes combined with a double input stage
consisting of two differential amplifiers, one complementary to the other.
The latter seems to have little to recommend it, as you cannot balance a
stage that is already balanced, but a balanced (and, by implication, more
linear) VAS has its attractions. However, as explained above, the distortion
contribution from a properly-designed VAS is negligible under most
circumstances, and therefore there seems to be little to be gained.
Two possible versions are shown in Figure 4.21; Type 1 gives approximately 10 dB more o/l gain than the standard, but this naturally requires an
increase in Cdom if the same stability margins are to be maintained. In a
model amplifier, any improvement in linearity can be wholly explained by
this o/l gain increase, so this seems (not unexpectedly) an unpromising
approach. Also, as Linsley-Hood has pointed out [12], the standing current
through the bias generator is ill-defined compared with the usual currentsource VAS; similarly the balance of the input pair is likely to be poor
compared with the current-mirror version. A further difficulty is that there
are now two signal paths from the input stage to the VAS output, and it is
difficult to ensure that these have the same bandwidth; if they do not then
a pole-zero doublet is generated in the open-loop gain characteristic that
will markedly increase settling-time after a transient. This seems likely to
apply to all balanced VAS configurations.
The small signal stages
Figure 4.21
Two kinds of balanced
VAS: Type 1 gives
more open-loop gain,
but no better open-loop
linearity. Type 2 – the
circuit originated by
Type 2 is attributed by Borbely to Lender [13]. Figure 4.21 shows one
version, with a quasi-balanced drive to the VAS transistor, via both base and
emitter. This configuration does not give good balance of the input pair, as
this is at the mercy of the tolerances of R2, R3, the Vbe of the VAS, and so
on. Borbely has advocated using two complementary versions of this,
giving Type 3, but it is not clear that this in any way overcomes the
objections above, and the increase in complexity is significant.
This can be only a brief examination of balanced VAS stages; many configurations are possible, and a comprehensive study of them all would be a
major undertaking. All seem to be open to the objection that the vital balance
of the input pair is not guaranteed, and that the current through the bias
generator is not well-defined. However one advantage would seem to be the
potential for sourcing and sinking large currents into Cdom, which might
improve the ultimate slew-rate and HF linearity of a very fast amplifier.
The VAS and manipulating open-loop bandwidth
Acute marketing men will by now have realised that reducing the LF o/l
gain, leaving HF gain unchanged, must move the P1 frequency upwards, as
shown in Figure 4.22 Open-loop gain is held constant up to 2 kHz sounds
Audio Power Amplifier Design Handbook
Figure 4.22
Showing how
frequency P1 can be
altered by changing
the LF open-loop gain;
the gain at HF, which
determines Nyquist
stability and HF
distortion, is unaffected
so much better than the open-loop bandwidth is restricted to 20 Hz
although these two statements could describe near-identical amplifiers,
except that the first has plenty of open-loop gain at LF while the second has
even more than that. Both amplifiers have the same feedback factor at HF,
where the amount available has a direct effect on distortion performance,
and could easily have the same slew-rate. Nonetheless the second
amplifier somehow reads as sluggish and indolent, even when the truth of
the matter is known.
It therefore follows that reducing the LF o/l gain may be of interest to
commercial practitioners. Low values of open-loop gain also have their
place in the dogma of the subjectivist, and the best way to bring about this
state of affairs is worth examining, always bearing in mind that:
1 there is no engineering justification for it,
2 reducing the NFB factor will reveal more of the output stage distortion;
since in general NFB is the only weapon we have to deal with this,
blunting its edge seems ill-advised.
It is of course simple to reduce o/l gain by degenerating the input pair, but this
diminishes it at HF as well as LF. To alter it at LF only it is necessary to tackle
the VAS instead, and Figure 4.23 shows two ways to reduce its gain. Figure
4.23a reduces gain by reducing the value of the collector impedance, having
previously raised it with the use of a current-source collector load. This ain’t
no way to treat a gain stage; loading resistors low enough to have a
significant effect cause unwanted current variations in the VAS as well as
shunting its high collector impedance, and serious LF distortion appears.
While this sort of practice has been advocated in the past [14], it seems to have
nothing to recommend it as it degrades VAS linearity at the same time as
syphoning off the feedback that would try to minimise the harm. Figure
4.23b also reduces overall o/l gain, but by adding a frequency-insensitive
component to the local shunt feedback around the VAS. The value of RNFB is
too high to load the collector significantly and therefore the full gain is
available for local feedback at LF, even before Cdom comes into action.
The small signal stages
Figure 4.23
Two ways to reduce
o/l gain:
a by simply loading
down the collector.
This is a cruel way
to treat a VAS;
current variations
cause extra
b local NFB with a
resistor in parallel
with Cdom. This
looks crude, but
actually works very
Figure 4.24 shows the effect on the open-loop gain of a model amplifier for
several values of RNFB ; this plot is in the format described in Chapter 3, where
error-voltage is plotted rather than gain directly, and so the curve once more
appears upside down compared with the usual presentation. Note that the
dominant-pole frequency is increased from 800 Hz to above 20 kHz by
using a 220k value for RNFB; however the gain at higher frequencies is
Figure 4.24
The result of VAS
gain-reduction by
local feedback; the
dominant pole
frequency is
increased from about
800 Hz to about
20 kHz, with highfrequency gain hardly
Audio Power Amplifier Design Handbook
unaffected and so is the stability. Although the amount of feedback available
at 1 kHz has been decreased by nearly 20 dB, the distortion at +16 dBu
output is only increased from less than 0.001 to 0.0013%; most of this
reading is due to noise.
In contrast, reducing the open-loop gain even by 10 dB by loading the VAS
collector to ground requires a load of 4k7, which under the same
conditions yields distortion of more than 0.01%.
Manipulating open-loop bandwidth
If the value of RNFB required falls below about 100K, then the standing
current flowing through it can become large enough to upset the amplifier
operating conditions (Figure 4.23b). This is revealed by a rise in distortion
above that expected from reducing the feedback factor, as the input stage
becomes unbalanced as a result of the global feedback straightening things
up. This effect can be simply prevented by putting a suitably large capacitor
in series with RNFB. A 2µ2 non-electrolytic works well, and does not cause
any strange response effects at low frequencies.
An unwelcome consequence of reducing the global negative feedback is
that power-supply rejection is impaired (see page 252). To prevent negative
supply-rail ripple reaching the output it is necessary to increase the filtering
of the V-rail that powers the input stage and the VAS. Since the voltage drop
in an RC filter so used detracts directly from the output voltage swing, there
are severe restrictions on the highest resistor value that can be tolerated.
The only direction left to go is increasing C, but this is also subject to
limitations as it must withstand the full supply voltage and rapidly becomes
a bulky and expensive item.
That describes the ‘brawn’ approach to improving PSRR. The ‘brains’
method is to use the input cascode compensation scheme described on
page 248. This solves the problem by eliminating the change of reference
at the VAS, and works extremely well with no compromise on HF stability.
No filtering at all is now required for the V-supply rail – it can feed the input
stage and VAS directly.
Hopefully the first half of this chapter has shown that input stage design is
not something to be taken lightly if low noise, low distortion, and low offset
are desired. A good design choice even for very high quality requirements
is a constant-gm-degenerated input pair with a degenerated current-mirror;
the extra cost of the mirror will be trivial.
The latter half of this chapter showed how the strenuous efforts of the input
circuitry can be best exploited by the voltage-amplifier stage following it. At
first it appears axiomatic that the stage providing all the voltage gain of an
The small signal stages
amplifier, at the full voltage swing, is the prime suspect for generating a
major part of its non-linearity. In actual fact, this is unlikely to be true, and
if we select for an amplifier a cascode VAS with current-source collectorload and buffer it from the output stage, or use a beta-enhancer in the VAS,
the second of our eight distortions is usually negligible.
1. Gray and Meyer Analysis and Design of Analog Integrated Circuits
Wiley 1984, p. 172 (exponential law of singleton).
2. Gray and Meyer ibid, p. 194 (tanh law of simple pair).
3. Self Sound Mosfet Design Electronics and Wireless World, Sept 1990,
p. 760 (varying input balance with R2).
4. Gray and Meyer ibid, p. 256 (tanh law of current-mirror pair).
5. Feucht Handbook of Analog Circuit Design Academic Press 1990,
p. 432 (Cross-quad).
6. Quinn IEEE International Solid-State Circuits Conference, THPM 14.5,
p. 188 (Cascomp).
7. Gray and Meyer Analysis and Design of Analog Integrated Circuits
Wiley 1984, p. 251 (VAS transfer characteristic).
8. Antognetti (Ed) Power Integrated Circuits McGraw-Hill 1986 (see page
9. Gray and Meyer Analysis and Design of Analog Integrated Circuits
Wiley 1984, p. 252 (Rco limit on VAS gain).
10. Self Sound Mosfet Design Electronics and Wireless World Sept 1990,
p. 760.
11. Oliver Distortion In Complementary-Pair Class-B Amplifiers HewlettPackard Journal, Feb 1971, p. 11.
12. Linsley-Hood, J Solid State Audio Power – 3 Electronics and Wireless
World, Jan 1990, p. 16.
13. Borbely A 60 W MOSFET Power Amplifier The Audio Amateur, Issue 2,
1982, p. 9.
14. Hefley High Fidelity, Low Feedback, 200 W Electronics and Wireless
World, June 92 p. 454.
The output stage I
Classes and devices
The almost universal choice in semiconductor power amplifiers is for a
unity-gain output stage, and specifically a voltage-follower. Output stages
with gain are not unknown – see Mann [1] for a design with ten times gain
in the output section – but they have significantly failed to win popularity.
Most people feel that controlling distortion while handling large currents is
quite hard enough without trying to generate gain at the same time.
In examining the small-signal stages, we have so far only needed to deal
with one kind of distortion at a time, due to the monotonic transfer
characteristics of such stages, which usually (but not invariably [2] ) work in
Class A. Economic and thermal realities mean that most output stages are
Class B, and so we must now also consider crossover distortion, (which
remains the thorniest problem in power amplifier design) and HF switchoff
We must also decide what kind of active device is to be used; JFETs offer
few if any advantages in the small-current stages, but power FETS in the
output appear to be a real possibility, providing that the extra cost proves to
bring with it some tangible benefits.
The most fundamental factor in determining output-stage distortion is the
Class of operation. Apart from its inherent inefficiency, Class-A is the ideal
operating mode, because there can be no crossover or switchoff distortion.
However, of those designs which have been published or reviewed, it is
notable that the large-signal distortion produced is still significant. This
looks like an opportunity lost, as of the distortions enumerated in Chapter
3, we now only have to deal with Distortion 1 (input-stage), Distortion 2
(VAS), and distortion 3 (output-stage large-signal non-linearity). Distortions
4, 5, 6 and 7, as mentioned earlier, are direct results of Class-B operation
The output stage I
and therefore can be thankfully disregarded in a Class-A design. However,
Class-B is overwhelmingly of the greater importance, and is therefore dealt
with in detail below.
Class B is subject to much misunderstanding. It is often said that a pair of
output transistors operated without any bias are working in Class-B, and
therefore generate severe crossover distortion. In fact, with no bias each
output device is operating for slightly less than half the time, and the
question arises as to whether it would not be more accurate to call this
Class-C and reserve Class-B for that condition of quiescent current which
eliminates, or rather minimises, the crossover artefacts.
There is a further complication; it is not generally appreciated that moving
into what is usually called Class-AB, by increasing the quiescent current,
does not make things better. In fact, if the output power is above the level
at which Class-A operation can be sustained, the THD reading will
certainly increase as the bias control is advanced. This is due to what is
usually called gm-doubling (i.e. the voltage-gain increase caused by both
devices conducting simultaneously in the centre of the output-voltage
range, that is, in the Class-A region) putting edges into the distortion
residual that generate high-order harmonics much as under-biasing does.
This vital fact seems almost unknown, presumably because the gmdoubling distortion is at a relatively low level and is completely obscured
in most amplifiers by other distortions.
This phenomenon is demonstrated in Figure 5.1a, b and c, which shows
spectrum analysis of the distortion residuals for under-biasing, optimal, and
over-biasing of a 150 W/8 amplifier at 1 kHz. As before, all nonlinearities except the unavoidable Distortion 3 (output stage) have been
effectively eliminated. The over-biased case had its quiescent current
increased until the gm-doubling edges in the residual had an approximately
50:50 mark/space ratio, and so was in Class-A about half the time, which
represents a rather generous amount of quiescent current for Class-AB.
Nonetheless, the higher-order odd harmonics in Figure 5.1c are at least
10 dB greater in amplitude than those for the optimal Class-B case, and the
third harmonic is actually higher than for the under-biased case as well.
However the under-biased amplifier, generating the familiar sharp spikes
on the residual, has a generally greater level of high-order odd harmonics
above the fifth; about 8 dB higher than the AB case.
Since high-order odd harmonics are generally considered to be the most
unpleasant, there seems to be a clear case for avoiding Class-AB altogether,
as it will always be less efficient and generate more high-order distortion
than the equivalent Class-B circuit as soon as it leaves Class-A. Class
distinction seems to resolve itself into a binary choice between A or B.
It must be emphasised that these effects are only visible in an amplifier
where the other forms of distortion have been properly minimised. The
Audio Power Amplifier Design Handbook
Figure 5.1
Spectrum analysis of
Class-B and AB
distortion residual
The output stage I
RMS THD reading for Figure 5.1a was 0.00151%, for Figure 5.1b
0.00103%, and for Figure 5.1c 0.00153%. The tests were repeated at the
40 W power level with very similar results. The spike just below 16 kHz is
interference from the testgear VDU.
This is complex enough, but there are other and deeper subtleties in ClassB, which are dealt with below.
The distortions of the output
I have called the distortion produced directly by the output stage Distortion
3 (see page 64) and this can now be subdivided into 3 categories.
Distortion 3a describes the large-signal distortion that is produced by both
Class-A and B, ultimately because of the large current swings in the active
devices; in bipolars, but not FETs, large collector currents reduce the beta,
leading to drooping gain at large output excursions. I shall use the term LSN
for Large-Signal Non-linearity, as opposed to crossover and switchoff
phenomena that cause trouble at all output levels.
These other two contributions to Distortion 3 are associated with Class-B
and AB only; Distortion 3b is classic crossover distortion, resulting from the
non-conjugate nature of the output characteristics, and is essentially nonfrequency dependent. In contrast, Distortion 3c is switchoff distortion,
generated by the output devices failing to turn off quickly and cleanly at
high frequencies, and is very strongly frequency-dependent. It is sometimes
called switching distortion, but this allows room for confusion, as some
writers use switching distortion to cover crossover distortion as well; hence
I have used the term switchoff distortion to refer specifically to chargestorage turn-off troubles. Since Class-B is almost universal, and introduces
all three kinds of non-linearity, we will concentrate on this.
Harmonic generation by crossover distortion
The usual non-linear distortions generate most of their unwanted energy in
low-order harmonics that NFB can deal with effectively. However,
crossover and switching distortions that warp only a small part of the output
swing tend to push energy into high-order harmonics, and this important
process is demonstrated here, by Fourier analysis of a SPICE waveform.
Taking a sinewave fundamental, and treating the distortion as an added
error signal E, let the ratio WR describe the proportion of the cycle where
E is non-zero. If this error is a triangle-wave extending over the whole cycle
(WR = 1) this would represent large-signal nonlinearity, and Figure 5.2
shows that most of the harmonic energy goes into the third and fifth
harmonics; the even harmonics are all zero due to the symmetry of the
Audio Power Amplifier Design Handbook
Figure 5.2
The amplitude of each
harmonic changes with
WR; as the error
waveform gets
narrower, energy is
transferred to the
higher harmonics
Figure 5.3
Diagram of the error
waveform E for some
values of WR
Figure 5.3 shows how the situation is made more like crossover or
switching distortion by squeezing the triangular error into the centre of the
cycle so that its value is zero elsewhere; now E is non-zero for only half the
cycle (denoted by WR = 0.5) and Figure 5.2 shows that the even harmonics
are no longer absent. As WR is further decreased, the energy is pushed into
higher-order harmonics, the amplitude of the lower falling.
The high harmonics have roughly equal amplitude, spectrum analysis (see
Figure 5.1, page 108) confirming that even in a Blameless amplifier driven
at 1 kHz, harmonics are freely generated from the seventh to the nineteenth
at an equal level to a dB or so. The nineteenth harmonic is only 10 dB
below the third.
Thus, in an amplifier with crossover distortion, the order of the harmonics
will decrease as signal amplitude reduces, and WR increases; their lower
The output stage I
frequencies allow them to be better corrected by the frequency-dependant
NFB. This effect seems to work against the commonly assumed rise of
percentage crossover distortion as level is reduced.
Comparing output stages
One of my aims in this book is to show how to isolate each source of
distortion so that it can be studied, (and hopefully reduced) with a
minimum of confusion and perplexity. When investigating output behaviour, it is perfectly practical to drive output stages open-loop, providing the
driving source-impedance is properly specified; this is difficult with a
conventional amplifier, as it means the output must be driven from a
frequency-dependant impedance simulating that at the VAS collector, with
some sort of feedback mechanism incorporated to keep the drive voltage
However, if the VAS is buffered from the output stage by some form of
emitter-follower, as advocated on page 99, it makes things much simpler, a
straightforward low-impedance source (e.g. 50 ) providing a good
approximation of conditions in a VAS-buffered closed-loop amplifier. The
VAS-buffer makes the system more designable by eliminating two variables
– the VAS collector impedance at LF, and the frequency at which it starts to
decrease due to local feedback through Cdom. This markedly simplifies the
study of output stage behaviour.
The large-signal linearity of various kinds of open-loop output stage with
typical values are shown in Figures 5.6–5.16. These diagrams were all
generated by SPICE simulation, and are plotted as incremental output gain
against output voltage, with the load resistance stepped from 16 to 2 ,
which I hope is the lowest impedance that feckless loudspeaker designers
will throw at us. They have come to be known as wingspread diagrams,
from their vaguely birdlike appearance. The power devices are MJ802 and
MJ4502, which are more complementary than many so-called pairs, and
minimise distracting large-signal asymmetry. The quiescent conditions are
in each case set to minimise the peak deviations of gain around the
crossover point for 8 loading; for the moment it is assumed that you can
set this accurately and keep it where you want it. The difficulties in actually
doing this will be examined later.
If we confine ourselves to the most straightforward output stages, there are
at least 16 distinct configurations, without including error-correcting [3],
current-dumping [4], or Blomley [5] types. These are:
Complementary Feedback Pair
Output Triples
Power FET
3 types
1 type
2 types
At least 7 types
3 types
Figure 5.4
Figure 5.5
Figure 5.5
Figure 5.6
Chapter 11
Audio Power Amplifier Design Handbook
The emitter-follower output
Three versions of the most common type of output stage are shown in
Figure 5.4; this is the double-emitter-follower, where the first follower acts
as driver to the second (output) device. I have deliberately called this an
Emitter-Follower (EF) rather than a Darlington configuration, as this latter
implies an integrated device that includes driver, output, and assorted
emitter resistors in one ill-conceived package. As for all the circuitry here,
the component values are representative of real practice. Important
attributes of this topology are:
1 the input is transferred to the output via two base-emitter junctions in
series, with no local feedback around the stage (apart from the very local
100% voltage feedback that makes an emitter-follower what it is),
2 there are two dissimilar base-emitter junctions between the bias voltage
and the emitter resistor Re, carrying different currents and at different
temperatures. The bias generator must attempt to compensate for both at
once, though it can only be thermally-coupled to one. The output
devices have substantial thermal inertia, and so any thermal compensation can only be a time-average of the preceding conditions. Figure 5.4a
shows the most prevalent version (Type I) which has its driver emitter
resistors connected to the output rail.
The Type II configuration in Figure 5.4b is at first sight merely a pointless
variation on Type I, but in fact it has a valuable extra property. The shared
driver emitter-resistor Rd, with no output-rail connection, allows the drivers
to reverse-bias the base-emitter junction of the output device being turned
off. Assume that the output voltage is heading downwards through the
crossover region; the current through Re1 has dropped to zero, but that
through Re2 is increasing, giving a voltage-drop across it, so TR4 base is
caused to go more negative to get the output to the right voltage. This
negative excursion is coupled to TR3 base through Rd, and with the values
shown can reverse bias it by up to –0.5 V, increasing to –1.6 V with a 4 load. The speed-up capacitor Cs markedly improves this action, preventing
the charge-suckout rate being limited by the resistance of Rd. While the
Type I circuit has a similar voltage drop across Re2, the connection of the
mid-point of R1, R2 to the output rail prevents this from reaching TR3 base;
instead TR1 base is reverse-biased as the output moves negative, and since
charge-storage in the drivers is usually not a problem, this does little good.
In Type II the drivers are never reverse-biased, though they do turn off. The
important issue of output turn-off and switching distortion is further
examined on page 153.
The Type III topology shown in Figure 5.4c maintains the drivers in Class-A
by connecting the driver Re’s to the opposite supply rail, rather than the
output rail. It is a common misconception [6] that Class-A drivers somehow
maintain better low-frequency control over the output devices, but I have
yet to locate any advantage myself. The driver dissipation is of course
Figure 5.4
Three types of
output stages
Audio Power Amplifier Design Handbook
substantially increased, and nothing seems to be gained at LF as far as the
output transistors are concerned, for in both Type I and Type II the drivers
are still conducting at the moment the outputs turn off, and are back in
conduction before the outputs turn on, which would seem to be all that
matters. Type III is equally good as Type II at reverse-biasing the output
bases, and may give even cleaner HF turn-off as the carriers are being
swept from the bases by a higher resistance terminated in a higher voltage,
approximating constant-current drive; this remains to be determined by
The large-signal linearity of these three versions is virtually identical – all
have the same feature of two base-emitter junctions in series between input
and load. The gain/output voltage plot is shown at Figure 5.7; with BJTs the
gain reduction with increasing loading is largely due to the Re’s. Note that
the crossover region appears as a relatively smooth wobble rather than a
jagged shape. Another major feature is the gain-droop at high output
voltages and low loads, and this gives us a clue that high collector currents
are the fundamental cause of this. A close-up of the crossover region gain
for 8 loading only is shown in Figure 5.8; note that no Vbias setting can
be found to give a constant or even monotonic gain; the double-dip and
central gain peak are characteristic of optimal adjustment. The region
extends over an output range of about +/–5 V, independent of load
The CFP output
The other major type of bipolar complementary output is the Complementary Feedback Pair (hereinafter CFP) sometimes called the SziklaiPair, seen in Figure 5.5a. There seems to be only one popular configuration,
though versions with gain are possible. The drivers are now placed so that
they compare the output voltage with that at the input. Thus wrapping the
outputs in a local NFB loop promises better linearity than emitter-follower
versions with 100% feedback applied separately to driver and output
The CFP topology is generally considered to show better thermal stability
than the EF, because the Vbe of the output devices is inside the local NFB
loop, and only the driver Vbe affects the quiescent conditions. The true
situation is rather more complex, and is explored in Chapter 12.
In the CFP output, like the EF, the drivers are conducting whenever the
outputs are, so special arrangements to keep them in Class-A seem
pointless. The CFP stage, like EF Type I, can only reverse-bias the driver
bases, and not the output bases, unless extra voltage rails outside the main
ones are provided.
The output gain plot is shown in Figure 5.9; Fourier analysis of this shows
that the CFP generates less than half the LSN of an emitter-follower stage.
Figure 5.5
CFP circuit and Quasicomplementary stages
Figure 5.6
Three of the possible
The output stage I
Table 5.1 Summary of output distortion
Type 1
Table 5.1 summarises the SPICE curves for 4 and 8 loadings; FET results from Ch.11 are included for
comparison. Each gain plot was subjected to Fourier analysis to calculate THD % results for a +/–40 V input.
(See Table 5.1.) Given also the greater quiescent stability, it is hard to see
why this topology is not more popular.
The crossover region is much narrower, at about +/–0.3 V (Figure 5.10).
When under-biased, this shows up on the distortion residual as narrower
spikes than an emitter-follower output gives. The bad effects of gmdoubling as Vbias increases above optimal (here 1.296 V) can be seen in
the slopes moving outwards from the centre.
Figure 5.7
Emitter-Follower largesignal gain vs output
Audio Power Amplifier Design Handbook
Figure 5.8
EF crossover region
gain deviations,
+/–5 V range
Figure 5.9
ComplementaryFeedback-Pair gain
vs output
The output stage I
Figure 5.10
CFP crossover region
+/–2 V, Vbias as a
Quasi-complementary outputs
Originally, the quasi-complementary configuration [7] was virtually mandatory, as it was a long time before PNP silicon power transistors were
available in anything approaching complements of the NPN versions. The
standard version shown at Figure 5.5b is well known for poor symmetry
around the crossover region, as shown in Figure 5.11. Figure 5.12 zooms in
to show that the crossover region is a kind of unhappy hybrid of the EF and
CFP, as might be expected, and that no setting of Vbias can remove the
sharp edge in the gain plot.
A major improvement to symmetry can be made by using a Baxandall
diode [8], as shown in Figure 5.5c. This stratagem yields gain plots very
similar to those for the true complementary EF at Figures 5.7, 5.8, though
in practice the crossover distortion seems rather higher. When this QuasiBaxandall stage is used closed-loop in an amplifier in which Distortions 1
and 2, and 4 to 7 have been properly eliminated, it is capable of much
better performance than is commonly believed; for example, 0.0015%
(1 kHz) and 0.015% (10 kHz) at 100 W is straightforward to obtain from an
amplifier with a moderate NFB factor of about 34 dB at 20 kHz.
The best reason to use the quasi-Baxandall approach today is to save
money on output devices, as PNP power BJTs remain somewhat pricier
than NPNs. Given the tiny cost of a Baxandall diode, and the absolutely
dependable improvement it gives, there seems no reason why anyone
should ever use the standard quasi circuit. My experiments show that the
Audio Power Amplifier Design Handbook
Figure 5.11
large-signal gain vs
Figure 5.12
Quasi crossover region
+/–20 V, Vbias as
The output stage I
value of R1 in Figure 5.5c is not critical; making it about the same as Rc
seems to work well.
Triple-based output configurations
If we allow the use of three rather than two bipolar transistors in each half
of an output stage, the number of circuit permutations possible leaps
upwards, and I cannot provide even a rapid overview in the space
available. There are two possible advantages if output triples are used
1 better linearity at high output voltages and currents,
2 more stable quiescent setting as the pre-drivers can be arranged to
handle very little power indeed, and to remain almost cold in use.
However, triples do not abolish crossover distortion, and they are, as
usually configured, incapable of reverse-biasing the output bases to
improve switchoff. Figure 5.6 shows three of the more useful ways to make
a triple output stage – all of those shown (with the possible exception of
Figure 5.6c, which I have just made up) have been used in commercial
designs, and Figure 5.6a will be recognised as the Quad-303 quasicomplementary triple. The design of triples demands care, as the possibility
of local HF instability in each output half is very real.
Triple EF output stages
Sometimes it is necessary to use a triple output stage simply because the
currents flowing in the output stage are too big to be handled by two
transistors in cascade. If you are driving 2 or 1 loads, then typically
there will be multiple output devices in parallel. Providing the base current
for five or more output transistors, with their relatively low beta, will
usually be beyond the normal driver types, and it is common to use another
output device as the driver. This will hopefully have the power-handling
capability, but with this comes low beta once again. This means that the
driver base currents in turn become too large for a normal VAS stage to
source. There are two solutions – make the VAS capable of sourcing
hundreds of mA, or insert another stage of current – gain between VAS and
drivers. The latter is much easier, and the usual choice. These extra
transistors are usually called the pre-drivers (see Figure 5.13).
In this circuit the pre-drivers dissipate relatively little power, and providing
they are medium-power devices such as those in a TO220 package it is
unlikely that they will need heatsinking to cope with the demands made on
them. There is, however, another reason to fit pre-drive heatsinks – or at
least make room at the layout stage so you have the option.
In Figure 5.13 there is about 1.2 V across R2, so Q3, 4 have to supply a
standing current of about 7 mA. This has no effect on the drivers as they are
Audio Power Amplifier Design Handbook
Figure 5.13
A triple-EF output stage. Both pre-drivers and drivers have emitter-resistors
likely to be well cooled to deal with normal load demands. However, the
voltage across R1 is two Vbe’s higher, at 2.4 V, so the standing current
through it is actually higher at 7.3 mA. (The exact figures naturally depend
on the values for R1, R2 that are chosen, but it is difficult to make them
much higher than shown here without compromising the speed of highfrequency turn-off.) The pre-drivers are usually small devices, and so they
are likely to get warm, and this leads to drift in the bias conditions after
switch-on. Adding heatsinks cannot eliminate this effect, but does usefully
reduce it.
In a triple-EF output stage like this the Vbias generator must produce
enough voltage to turn on six base-emitter junctions, plus the small
standing voltage Vq across the emitter resistors, totalling about 3.9 V in
practice. The Vbe of the bias transistor is therefore being multiplied by a
larger factor, and Vbias will drop more for the same temperature rise. This
should be taken into account, as it is easy with this kind of output stage to
come up with a bias generator that is overcompensated for temperature.
Distortion and its mechanisms
Subdividing Distortion 3 into Large-Signal Non-linearity, crossover, and
switchoff distortion provides a basis for judging which output stage is best.
The LSN is determined by both circuit topology and device characteristics,
The output stage I
crossover distortion is critically related to quiescent-conditions stability,
and switchoff distortion depends strongly on the output stage’s ability to
remove carriers from power BJT bases. I now look at how these
shortcomings can be improved, and the effect they have when an output
stage is used closed-loop.
In Chapter 4 it was demonstrated that the distortion from the small-signal
stages can be kept to very low levels that will prove to be negligible
compared with closed-loop output-stage distortion, by the adroit use of
relatively conventional circuitry. Likewise, Chapter 6 will reveal that
Distortions 4 to 8 can be effectively eliminated by lesser-known but
straightforward methods. This leaves Distortion 3, in its three components,
as the only distortion that is in any sense unavoidable, as Class-B stages
completely free from crossover artefacts are so far beyond us.
This is therefore a good place to review the concept of a Blameless
amplifier, introduced in Chapter 3; one designed so that all the easilydefeated distortion mechanisms have been rendered negligible. (Note that
the word Blameless has been carefully chosen to not imply Perfection.)
Distortion 1 cannot be totally eradicated, but its onset can be pushed well
above 20 kHz. Distortion 2 can be effectively eliminated by cascoding, and
Distortion 4–Distortion 7 can be made negligible by simple measures to be
described later. This leaves Distortion 3, which includes the knottiest ClassB problems, i.e. crossover distortion (Distortion 3b) and HF switchoff
difficulties (Distortion 3c).
The design rules presented here will allow the routine design of Blameless
Amplifiers. However, this still leaves the most difficult problem of Class-B
unsolved, so it is too early to conclude that as far as amplifier linearity is
concerned, history is over . . .
Large-signal distortion (Distortion 3a)
Amplifiers always distort more with heavier loading. This is true without
exception so far as I am aware. Why? Is there anything we can do about it?
A Blameless Class-B amplifier typically gives an 8 distortion performance
that depends very little on variable transistor characteristics such as beta. At
this load impedance output stage non-linearity is almost entirely crossover
distortion, which is a voltage-domain effect.
As the load impedance of the amplifier is decreased from infinity to 4 ,
distortion increases in an intriguing manner. The unloaded THD is not
much greater than that from the AP System-1 test oscillator, but as loading
increases crossover distortion rises steadily: see Figure 7.25. When the load
impedance falls below about 8 , a new distortion begins to appear,
overlaying the existing crossover non-linearities. It is essentially third
harmonic. In Figure 5.14 the upper trace shows the 4 THD is consistently
twice that for 8 , once it appears above the noise floor.
Audio Power Amplifier Design Handbook
Figure 5.14
Upper trace shows
distortion increase
due to LSN as load
goes from 8 to 4 .
Blameless amplifier at
25 W/8 I label this Distortion 3a, or Large Signal Non-linearity (LSN), where ‘Large’
refers to currents rather than voltages. Unlike crossover Distortion 3b, the
amount of LSN generated is highly dependent on device characteristics.
The distortion residual is basically third order because of the symmetric and
compressive nature of the output stage gain characteristic, with some
second harmonic because the beta loss is component dependent and not
perfectly symmetrical in the upper and lower output stage halves. Figure
5.15 shows a typical THD residual for Large Signal Non-linearity, driving
50 W into 4 . The residual is averaged 64 times to reduce noise.
LSN occurs in both emitter-follower (EF) and Complementary Feedback
Pair (CFP) output configurations; this section concentrates on the CFP
version, as shown in Figure 5.5a. Figure 5.16 shows the incremental gain
Figure 5.15
Large Signal Nonlinearity, driving
50 W into 4 and
averaged 64 times
The output stage I
Figure 5.16
The incremental gain
of a standard CFP
output stage. The
4 trace droops
much more as the
gain falls off at
higher currents.
PSpice simulation
of a simulated CFP output stage for 8 and 4 ; the lower 4 trace has
greater downward curvature, i.e. a greater falloff of gain with increasing
current. Note that this falloff is steeper in the negative half, so the THD
generated will contain even as well as odd harmonics. The simulated EF
behaviour is very similar.
As it happens, an 8 nominal impedance is a reasonably good match for
standard power BJTs, though 16 might be better for minimising LSN if
loudspeaker technology permits. It is coincidental that an 8 nominal
impedance corresponds approximately with the heaviest load that can be
driven without LSN appearing, as this value is a legacy from valve
technology. LSN is an extra distortion component laid on top of others, and
usually dominating them in amplitude, so it is obviously simplest to
minimise the 8 distortion first. 4 effects can then be seen more or less
in isolation when load impedance is reduced.
The typical result of 4 loading was shown in Figure 5.14, for the modern
MJ15024/25 complementary pair from Motorola. Figure 5.17 shows the
same diagram for one of the oldest silicon complementary pairs, the
2N3055/2955. The 8 distortion is similar for the different devices, but the
4 THD is 3.0 times worse for the venerable 2N3055/2955. Such is
Such experiments with different output devices throw useful light on the
Blameless concept – from the various types tried so far it can be said that
Audio Power Amplifier Design Handbook
Figure 5.17
4 distortion is 3×
greater than 8 for
output devices.
Compare Figure
Blameless performance, whatever the output device type, should not
exceed 0.001% at 1 kHz and 0.006% at 10 kHz, when driving 8 . The
components existed to build sub-0.001% THD amplifiers in mid-1969, but
not the knowledge.
Low-impedance loads have other implications beyond worse THD. The
requirements for sustained long-term 4 operation are severe, demanding
more heatsinking and greater power supply capacity. For economic reasons
the peak/average ratio of music is usually fully exploited, though this can
cause real problems on extended sinewave tests, such as the FTC
40%-power-for-an-hour preconditioning procedure.
The focus of this section is the extra distortion generated in the output stage
itself by increased loading, but there are other ways in which linearity may
be degraded by the higher currents flowing. Of the amplifier distortion
mechanisms (see page 63), Distortions 1, 2, and 8 are unaffected by output
stage current magnitudes. Distortion 4 might be expected to increase, as
increased loading on the output stage is reflected in increased loading on
the VAS. However, both the beta-enhanced EF and buffered-cascode
methods of VAS linearisation deal effectively with sub-8 loads, and this
does not seem to be a problem.
When a 4 load is driven, the current taken from the power supply is
greater, potentially increasing the rail ripple, which could worsen
Distortion 5. However, if the supply reservoir capacitances have been sized
to permit greater power delivery, their increased capacitance reduces ripple
again, so this effect tends to cancel out. Even if rail ripple doubles, the usual
RC filtering of bias supplies should keep it out of the amplifier, preventing
intrusion via the input pair tail, and so on.
Distortion 6 could worsen as the half-wave currents flowing in the output
circuitry are twice as large, with no counteracting mechanism. Distortion 7,
The output stage I
if present, will be worse due to the increased load currents flowing in the
output stage wiring resistances.
Of those mechanisms above, Distortion 4 is inherent in the circuit
configuration (though easily reducible below the threshold of measurement) while 5, 6, and 7 are topological, in that they depend on the spatial
and geometrical relationships of components and wiring. The latter three
distortions can therefore be completely eliminated in both theory and
practice. This leaves only the LSN component, otherwise known as
Distortion 3a, to deal with.
The load-invariant concept
In an ideal amplifier the extra LSN distortion component would not exist.
Such an amplifier would give no more distortion into 4 than 8, and could
be called ‘Load-Invariant to 4 ’. The minimum load qualification is
required because it will be seen that the lower the impedance, the greater
the difficulties in aspiring to Load-Invariance. I assume that we start out
with an amplifier that is Blameless at 8 ; it would be logical but quite
pointless to apply the term ‘Load-Invariant’ to an ill-conceived amplifier
delivering 1% THD into both 8 and 4 .
The LSN mechanism
When the load impedance is reduced, the voltage conditions are
essentially unchanged. LSN is therefore clearly a current-domain effect, a
function of the magnitude of the signal currents flowing in drivers and
output devices.
A 4 load doubles the output device currents, but this does not in itself
generate significant extra distortion. The crucial factor appears to be that
the current drawn from the drivers by the output device bases more than
doubles, due to beta falloff in the output devices as collector current
increases. It is this extra increase of current that causes almost all the
additional distortion. The exact details of this have not been completely
clarified, but it seems that this ‘extra current’ due to beta falloff varies very
non-linearly with output voltage, and combines with driver non-linearity to
reinforce it rather than cancel. Beta-droop is ultimately due to high-level
injection effects, which are in the province of semiconductor physics rather
than amplifier design. Such effects vary greatly with device type, so when
output transistors are selected, the likely performance with loads below 8 must be considered.
There is good simulator evidence that LSN is entirely due to beta-droop
causing extra current to be drawn from the drivers. To summarise:
Simulated output stages with output devices modified to have no betadroop (by increasing SPICE model parameter IKF) do not show LSN. It
Audio Power Amplifier Design Handbook
appears to be specifically that extra current taken due to beta-droop
causes the extra non-linearity.
Simulated output devices driven with zero-impedance voltage sources
instead of the usual transistor drivers exhibit no LSN. This shows that
LSN does not occur in the outputs themselves, and so it must be
happening in the driver transistors.
Output stage distortion can be treated as an error voltage between
input and output. The double emitter-follower (EF) stage error is
therefore: driver Vbe + output Vbe + Re drop. A simulated EF output
stage with the usual drivers shows that it is primarily non-linearity
increases in the driver Vbe rather than in the output Vbe, as load
resistance is reduced. The voltage drop across the emitter resistors Re
is essentially linear.
The knowledge that beta-droop caused by increased output device Ic is at
the root of the problem leads to some solutions. Firstly, the per-device Ic
can be reduced by using parallel output devices. Alternatively Ic can be left
unchanged and output device types selected for those with the least betadroop.
Doubled output devices
LSN can be effectively reduced by doubling the output devices, when this
is quite unnecessary for handling the rated power output. The falloff of beta
depends on collector current, and if two output devices are connected in
parallel, the collector current divides in two between them. Beta-droop is
much reduced.
From the above evidence, I predicted that this doubling ought to reduce
LSN – and when measured, indeed it does. Such reality checks must never
be omitted when using circuit simulators. Figure 5.18 compares the 4 THD at 60 W for single and double output devices, showing that doubling
Figure 5.18
4 distortion is
reduced by 1.9×
upon doubling
output transistors.
30 W/8 128
The output stage I
reduces distortion by about 1.9 times, which is a worthwhile improvement.
The output transistors used for this test were modern devices, the Motorola
MJ15024/15025. The much older 2N3055/2955 complementary pair give
a similar halving of LSN when their number is doubled, though the initial
distortion is three times higher into 4 . 2N3055 specimens with an H
suffix show markedly worse linearity than those without.
No explicit current-sharing components were added when doubling the
devices, and this lack seemed to have no effect on LSN reduction. There
was no evidence of current hogging, and it appears that the circuit cabling
resistances alone were sufficent to prevent this.
Doubling the number of power devices naturally increases the power
output capability, though if this is exploited LSN will tend to rise again, and
you are back where you started. Opting for increased power output will
also make it necessary to uprate the power supply, heatsinks, and so on.
The essence of this technique is to use parallel devices to reduce distortion
long before power handling alone compels you to do so.
Better output devices
The 2SC3281 2SA1302 complementary pair are plastic TO3P devices with
a reputation in the hi-fi industry for being ‘more linear’ than the general run
of transistors. Vague claims of this sort arouse the deepest of suspicions;
compare the many assertions of superior linearity for power FETs, which is
the exact opposite of reality. However, in this case the core of truth is that
2SC3281 and 2SA1302 show much less beta-droop than average power
transistors. These devices were introduced by Toshiba; Motorola versions
are MJL3281A, MJL1302A, also in TO3P package. Figure 5.19 shows betadroop, for the various devices discussed here, and it is clear that more
droop means more LSN.
The 3281/1302 pair are clearly in a different class from conventional
transistors, as they maintain beta much more effectively when collector
current increases. There seems to be no special name for this class of BJTs,
so I have called them ‘sustained-beta’ devices here.
The THD into 4 and 8 for single 3281/1302 devices is shown in Figure
5.20. Distortion is reduced by about 1.4 times compared with the standard
devices of Figure 5.14, over the range 2–8 kHz. Several pairs of 3281/1302
were tested and the 4 improvement is consistent and repeatable.
The obvious next step is to combine these two techniques by using doubled
sustained-beta devices. The doubled-device results are shown in Figure
5.21 where the distortion at 80 W/4 (15 kHz) is reduced from 0.009% in
Figure 5.20 to 0.0045%; in other words, halved. The 8 and 4 traces are
now very close together, the 4 THD being only 1.2 times higher than in
the 8 case.
Audio Power Amplifier Design Handbook
Figure 5.19
Power transistor beta falls as collector current increases. Beta is normalised to 100 at 0.5 A (from
manufacturers’ data sheets)
Figure 5.20
THD at 40 W/8 and 80 W/4 with
single 3281/1302
The output stage I
Figure 5.21
THD at 40 W/8 and 80 W/4 with
3281/1302 output
transistors. 4 THD
has been halved
compared with
Figure 5.12
There are other devices showing less beta-droop than standard. In a very
quick survey I unearthed the MJ21193, MJ21194 pair (TO3 package) and
the MJL21193, MJL21194 pair (TO3P package), both from Motorola. These
devices show beta-maintenance intermediate between the ‘super’
3281/1302 and ‘ordinary’ MJ15024/25, so it seemed likely that they would
give less LSN than ordinary power devices, but more than the 3281/1302.
This prediction was tested and duly fulfilled.
It could be argued that multiplying output transistors is an expensive way to
solve a linearity problem. To give this perspective, in a typical stereo power
amplifier the total cost including heatsink, metal work and mains
transformer will only increase by about 5% when the output devices are
Feedforward diodes
The first technique I tried to reduce LSN was the addition of power diodes
across OR22 output emitter resistors. The improvement was only significant for high power into sub-3 loading, and was of rather doubtful
utility for hi-fi. Feedforward diodes treat the symptoms (by attempting
distortion cancellation) rather than the root cause, so it is not surprising this
method is of limited effectiveness; see Figure 5.25.
It is my current practice to set the output emitter resistors Re at 0.1 , rather
than the more common OR22. This change both improves voltage-swing
efficiency and reduces the extra distortion generated if the amplifier is
erroneously biased into Class AB. As a result even low-impedance loads
give a relatively small voltage drop across Re, which is insufficient to turn
on a silicon power diode at realistic output levels.
Schottky diodes have a lower forward voltage drop and might be useful
here. Tests with 50 A diodes have been made but have so far not been
Audio Power Amplifier Design Handbook
encouraging in the distortion reduction achieved. Suitable Schottky diodes
cost at least as much as an output transistor, and two will be needed.
Trouble with triples
In electronics, as in many fields, there is often a choice between applying
brawn (in this case multiple power devices) or brains to solve a given
problem. The ‘brains’ option here would be a clever circuit configuration
that reduced LSN without replication of expensive power silicon, and the
obvious place to look is the output-triple approach. Note ‘output triples’ here
refers to pre-driver, driver, and output device all in one local NFB loop, rather
than three identical output devices in parallel, which I would call ‘tripled
outputs’. Getting the nomenclature right is a bit of a problem.
In simulation, output-triple configurations do reduce the gain-droop that
causes LSN. There are many different ways to configure output triples, and
they vary in their linearity and immunity to LSN. The true difficulty with this
approach is that three transistors in a tight local loop are very prone to
parasitic and local oscillations. This tendency is exacerbated by reducing
the load impedances, presumably because the higher collector currents
lead to increased device transconductance. This sort of instability can be
very hard to deal with, and in some configurations appears almost
insoluble. At present this approach has not been studied further.
Loads below 4 So far I have concentrated on 4 loads; loudspeaker impedances often
sink lower than this, so further tests were done at 3 . One pair of
3281/1302 devices will give 50 W into 3 for THD of 0.006% (10 kHz),
see Figure 5.22. Two pairs of 3281/1302 reduce the distortion to 0.003%
(10 kHz) as in Figure 5.23. This is an excellent result for such simple
circuitry, and may well be a record for 3 linearity.
Figure 5.22
Distortion for 3, 4 and
8 loads, single
3281/1302 devices.
20 W/8 ,
40 W/4 and
60 W/3 132
The output stage I
Figure 5.23
Distortion for 3, 4 and
8 load, double
3281/1302 devices.
Power as Figure 5.22
It appears that whatever the device type, doubling the outputs halves the
THD percentage for 4 loading. This principle can be extended to 2 operation, but tripled devices are required for sustained operation at
significant powers. The resistive losses will be serious, so 2 power output
may be little greater than that into 4 .
Better 8 performance
It was not expected that the sustained-beta devices would also show lower
crossover distortion at 8 , but they do, and the effect is once more
repeatable. It may be that whatever improves the beta characteristic also
somewhat alters the turn-on law so that crossover distortion is reduced;
alternatively traces of LSN, not visible in the THD residual, may have been
eliminated. The latter is probably the more likely explanation.
The plot in Figure 5.23 shows the improvement over the MJ15024/25
pair; compare the 8 line in Figure 5.14. The 8 THD at 10 kHz is
reduced from 0.003% to 0.002%, and with correct bias adjustment, the
crossover artefacts are invisible on the 1 kHz THD residual. Crossover
artefacts are only just visible in the 4 case, and to get a feel for the
distortion being produced, and to set the bias optimally, it is necessary
to test at 5 kHz into 4 .
A practical load-invariant design
Figure 5.24 is the circuit of a practical Load-Invariant amplifier designed for
8 nominal loads with 4 impedance dips; not for speakers that start out
at 4 nominal and plummet from there. The distortion performance is
shown in Figures 5.21 and 5.22 for various fitments of output device. The
supply voltage can be from +/–20 to +/–40 V; checking power capability
for a given output device fit must be left to the constructor.
Circuit diagram of
the Load-Invariant
power amplifier
Figure 5.24
10R Q1
Q101 Q102
1 2SB737 2SB737
Drawn by:
Q10 0VA
P6 Output
2SC3281 Clip-TSC506
Drawing No.
3 MJE350
Power Output
ground ground
The Signal Transfer Co. owns the
copyright of this drawing, which may
not be copied, reproduced or
disclosed, in part or in whole, to a
third party without written permission.
PR1 3
1k +
2 –
Fit either
MPSA56 or 2SB737
Q8 & Q14 mounted
on top of each other
The output stage I
Figure 5.25
Simple diode
feedforward reduces
distortion with sub-8 loads. Measured at
210 W into 2.7 Apart from Load-Invariance, the design also incorporates two new
techniques from the Thermal Dynamics section of this book.
The first technique greatly reduces time lag in the thermal compensation.
With a CFP output stage, the bias generator aims to shadow driver junction
temperature rather than the output junctions. A much faster response to
power dissipation changes is obtained by mounting bias generator
transistor TR8 on top of driver TR14, rather than on the other side of the
heatsink. The driver heatsink mass is largely decoupled from the thermal
compensation system, and the response is speeded up by at least two
orders of magnitude.
The second innovation is a bias generator with an increased temperature
coefficient, to reduce the static errors introduced by thermal losses between
driver and sensor. The bias generator tempco is increased to –4.0 mV/°C. D5
also compensates for the effect of ambient temperature changes.
This design is not described in detail because it closely resembles the
Blameless Class-B amp described on page 176. The low-noise feedback
network is taken from the Trimodal amplifier on page 270; note the
requirement for input bootstrapping if a 10k input impedance is required.
Single-slope VI limiting is incorporated for overload protection, implemented
by TR12, 13. The global NFB factor is once more a modest 30 dB at 20 kHz.
The latest findings
I have recently done further experiments with multiple devices, using three,
four, five and six in parallel. The 2SC2922/2SA1612 complementary pair
were used. In this case the circuit used was somewhat different (see Figure
5.26). With a greater number of devices I was now more concerned about
proper current sharing, and so each device has its own emitter resistor. This
makes it look much more like a conventional paralleled output stage,
Audio Power Amplifier Design Handbook
Figure 5.26
The triple-EF output stage used for the measurements described below. ‘Triple’ refers to the fact that there are three
transistors from input to output, rather than the fact that there happen to be three output devices in parallel
which essentially it is. This time I tried both double and the triple-EF output
configurations, as I wished to prove:
(a) that LSN theory worked for both of the common configurations EF and
CFP – it does;
(b) that LSN theory worked for both double and triple versions of the EF
output stage – it does.
For reasons of space only the triple-EF results are discussed here.
Figure 5.27 shows the measured THD results for one complementary pair
of output devices in the triple-EF circuit of Fig 5.25. Distortion is slightly
higher, and the noise floor relatively lower, than in the standard result (Fig
2 in Part 1) because of the higher output power of 50 W/8 . Figure 5.28
shows the same except there are now two pairs of output devices. Note that
THD has halved at both 8 and 4 loads; this is probably due to the larger
currents taken by 8 loads at this higher power. Figure 5.29 shows the
result for six devices; 8 distortion has almost been abolished, and the 4 result is almost as good. It is necessary to go down to a 2 load to get the
THD clear of the noise so it can be measured accurately. With six outputs,
driving a substantial amount of power into this load is not a problem.
On a practical note, the more output devices you have, the harder the
amplifier may be to purge of parasitic oscillations in the output stage. This
is presumably due to the extra raw transconductance available, and can be
The output stage I
Figure 5.27
THD for one pair
(N=1) of output
devices, at 50W/8R
and 100W/4R
a problem even with the triple-EF circuit, which has no local NFB loops. I
don’t pretend to be able to give a detailed explanation of this effect at the
Having demonstrated that sustained-beta output devices not only reduce
LSN but also unexpectedly reduce crossover distortion, it seemed worth
checking if using multiple output devices would give a similar reduction at
light loading. I was rather surprised to find they did.
Figure 5.28
THD for two pairs
(N=2) of output
devices, at 50W/8R
and 100W/4R. A
definite improvement
Audio Power Amplifier Design Handbook
Figure 5.29
THD for six pairs
(N=6) of output
devices, at 50W/8R,
200W/2R. Note
very low distortion at
8 ohms
Adding more output devices in parallel, while driving an 8- load, results
in a steady reduction in distortion. Figures 5.27–5.29 show how this works
in reality. The SPICE simulations in Figure 5.30 reveal that increasing the
number N of output devices not only flattens the crossover gain wobble,
but spreads it out over a greater width. This spreading effect is an extra
Figure 5.30
SPICE simulation of
triple-EF output with
N=1, 2 and 3. As N
increases the
crossover gain
wobble becomes
flatter and more
spread out laterally
The output stage I
bonus because it means that lower-order harmonics are generated, and at
lower frequencies there will be more negative feedback to linearise them.
(Bear in mind also that a triple-EF output has an inherently wider gain
wobble than the double-EF.) Taking the gain wobble width as the voltage
between the bottoms of the two dips, this appears to be proportional to N.
The amount of gain wobble, as measured from top of the peak to bottom of
the dips, appears to be proportional to 1/N.
This makes sense. We know that crossover distortion increases with heavier
loading, i.e. with greater currents flowing in the output devices, but under
the same voltage conditions. It is therefore not surprising that reducing the
device currents by using multiple devices has the same effect as reducing
loading. If there are two output devices in parallel, each sees half the
current variations, and crossover non-linearity is reduced. The voltage
conditions are the same in each half and so are unchanged. This offers us
the interesting possibility that crossover distortion – which has hitherto
appeared inescapable – can be reduced to an arbitrary level simply by
paralleling enough output transistors. To the best of my knowledge this is a
new insight.
In conventional amplifiers, reducing the 8 load to 4 increases the THD
by 2 to 3 times. The figure attained by this amplifier is 1.2 times, and the
ratio could be made even closer to unity by tripling the output devices.
Crossover distortion (Distortion 3b)
In a field like Audio where consensus of any sort is rare, it is a truth
universally acknowledged that crossover distortion is the worst problem
that can afflict Class-B power amplifiers. The problem is the crossover
region, where control of the output voltage must be handed over from one
device to another. Crossover distortion is rightly feared as it generates
unpleasant high-order harmonics, with at least the potential to increase in
percentage as signal level falls.
The pernicious nature of crossover distortion is partly because it occurs
over a small part of the signal swing, and so generates high-order
harmonics. Worse still, this small range over which it does occur is at the
zero-crossing point, so not only is it present at all levels and all but the
lightest loads, but is generally believed to increase as output level falls,
threatening very poor linearity at the modest listening powers that most
people use.
There is a consensus that crossover caused the transistor sound of the
1960s, though to the best of my knowledge this has never actually been
confirmed by the double-blind testing of vintage equipment.
Audio Power Amplifier Design Handbook
The Vbe-Ic characteristic of a bipolar transistor is initially exponential,
blending into linear as the internal emitter resistance re comes to dominate
the transconductance. The usual Class-B stage puts two of these curves
back-to-back, and Peter Blomley has shown [12] that these curves are nonconjugate, i.e. there is no way they can be shuffled about so they will sum
to a completely linear transfer characteristic, whatever the offset between
them imposed by the bias voltage. This can be demonstrated quickly and
easily by SPICE simulation; see Figure 5.31. There is at first sight not much
you can do except maintain the bias voltage, and hence quiescent current,
at some optimal level for minimum gain deviation at crossover; quiescentcurrent control is a complex subject that could fill a big book in itself, and
is considered in Chapter 12.
It should be said that the crossover distortion levels generated in a
Blameless amplifier can be very low up to around 1 kHz, being barely
visible in residual noise and only measurable with a spectrum-analyser. As
an instructive example, if a Blameless closed-loop Class-B amplifier is
driven through a TL072 unity-gain buffer the added noise from this op-amp
will usually submerge the 1 kHz crossover artefacts into the noise floor, at
least as judged by the eye on the oscilloscope. (It is most important to note
that Distortions 4, 5, 6 and 7 create disturbances of the THD residual at the
zero-crossing point that can be easily mistaken for crossover distortion, but
the actual mechanisms are quite different). However, the crossover
distortion becomes obvious as the frequency increases, and the high-order
harmonics benefit less from NFB.
Figure 5.31
Gain/output voltage
plot for an EF output
shows how nonconjugate transistor
characteristics at the
crossover region
cannot be blended into
a flat line at any bias
voltage setting. Bias
varies 2.75 to 2.95 V
in 25 mV steps, from
too little to too much
The output stage I
It will be seen later that in a Blameless amplifier driving 8 the overall
linearity is dominated by crossover distortion, even with a well-designed
and optimally biased output stage. There is an obvious incentive to
minimise this distortion mechanism, but there seems no obvious way to
reduce crossover gain deviations by tinkering with any of the relatively
conventional stages considered so far.
Figure 5.32 shows the signal waveform and THD residual from a Blameless
power amplifier with optimal Class-B bias. Output power was 25 W into
8 , or 50 W into 4 (i.e. the same output voltage) as appropriate, for all
the residuals shown here. The figure is a record of a single sweep so the
residual appears to be almost totally random noise; without the visual
averaging that occurs when we look at an oscilloscope the crossover
artefacts are much less visible than in real time.
In Figure 5.33 64 times averaging is applied, and the disturbances around
crossover become very clear. There is also revealed a low-order component at roughly 0.0004%, which is probably due to very small amounts
of Distortion 6 that were not visible when the amplifier layout was
Figure 5.34 shows Class-B slightly underbiased to generate crossover
distortion. The crossover spikes are very sharp, so their height in the
residual depends strongly on measurement bandwidth. Their presence
warns immediately of underbiasing and avoidable crossover distortion.
In Figure 5.35 an optimally biased amplifier is tested at 10 kHz. The THD
increases to approx. 0.004%, as the amount of global negative feedback
is 20 dB less than at 1 kHz. The timebase is faster so crossover events
Figure 5.32
The THD residual
from an optimally
biased Blameless
power amplifier at
1 kHz, 25 W/8 is
essentially white
noise. There is some
evidence of artefacts
at the crossover
point, but they are
not measurable. THD
0.00097%, 80 kHz
Audio Power Amplifier Design Handbook
Figure 5.33
Averaging Figure 5.2
residual 64 times
reduces the noise by
18 dB, and crossover
discontinuities are
now obvious. The
residual has been
scaled up by 2.5
times from Figure 5.2
for greater clarity
appear wider than in Figure 5.34. The THD level is now higher and
above the noise so the residual is averaged 8 times only. The measurement bandwidth is still 80 kHz, so harmonics above the eighth are now
lost. This is illustrated in Figure 5.36, which is Figure 5.35 rerun with a
500 kHz bandwidth. The distortion products now look much more
Figure 5.37 shows the gain-step distortion introduced by Class-AB. The
undesirable edges in the residual are no longer in close pairs that partially
Figure 5.34
The results of mild
underbias in Class-B
The output stage I
Figure 5.35
An optimally biased
Blameless power
amplifier at 10 kHz.
THD approx.
0.004%, bandwidth
80 kHz. Averaged 8
cancel, but are spread apart on either side of the zero crossing. No
averaging is used here as the THD is higher. See page 275 for more on
Class-AB distortion.
It is commonplace in Audio to discover that a problem like crossover
distortion has been written about and agonised over for decades, but the
amount of technical investigation that has been done (or at any rate
published) is disappointingly small. I had to do some basic investigations
Figure 5.36
As Figure 5.6, but in
500 kHz bandwidth.
The distortion
products look quite
Audio Power Amplifier Design Handbook
Figure 5.37
The gm-doubling
distortion introduced
by Class-AB. The
edges in the residual
are larger and no
longer at the zero
crossing, but
displaced either side
of it
1 10.0V
2 20.0 mv
200 s /
I first looked to see if crossover distortion really did increase with
decreasing output level in a Blameless amplifier; to attempt its study with
an amplifier contaminated with any of the avoidable distortion mechanisms is completely pointless. One problem is that a Blameless amplifier
has such a low level of distortion at 1 kHz (0.001% or less) that the
crossover artefacts are barely visible in circuit noise, even if low-noise
techniques are used. The measured percentage level of the noise-plusdistortion residual is bound to rise with falling output, because the noise
voltage remains constant; this is the lowest line in Figure 5.38. To
circumvent this, the amplifier was deliberately underbiased by varying
amounts to generate ample crossover spikes, on the assumption that any
correctly adjusted amplifier should be less barbarous than this.
The answer from Figure 5.38 is that the THD percentage does increase as
level falls, but relatively slowly. Both EF and CFP output stages give similar
diagrams to Figure 5.38, and whatever the degree of underbias, THD
increases by about 1.6 times as the output voltage is halved. In other words,
reducing the output power from 25 W to 250 mW, which is pretty drastic,
only increases THD % by six times, and so it is clear that the absolute (as
opposed to percentage) THD level in fact falls slowly with amplitude, and
therefore probably remains imperceptible. This is something of a relief; but
crossover distortion remains a bad thing to have.
Distortion versus level was also investigated at high frequencies, i.e. above
1 kHz where there is more THD to measure, and optimal biasing can be
used. Figure 5.39 shows the variation of THD with level for the EF stage at
a selection of frequencies; Figure 5.40 shows the same for the CFP. Neither
shows a significant rise in percentage THD with falling level, though it is
The output stage I
Figure 5.38
Showing how
crossover distortion
rises slowly as output
power is reduced
from 25 W to
250 mW (8 ) for
optimal bias and
increasingly severe
underbias (upper
lines). This is an EF
type output stage.
bandwidth 22 kHz
noticeable that the EF gives a good deal less distortion at lower power
levels around 1 W. This is an unexpected observation, and possibly a new
To further get the measure of the problem, Figure 5.41 shows how HF
distortion is greatly reduced by increasing the load resistance, providing
further confirmation that almost all the 8 distortion originates as
crossover in the output stage.
Crossover distortion, unlike some more benign kinds of signal-warping, is
unanimously agreed to be something any amplifier could well do
without. The amount of crossover distortion produced depends strongly
on optimal quiescent adjustment, so the thermal compensation used to
stabilise this against changes in temperature and power dissipation must
be accurate. This section deals with the crossover region and its
Figure 5.39
Variation of crossover
distortion with output
level for higher
Optimally biased EF
output stage.
Bandwidth 80 kHz
Audio Power Amplifier Design Handbook
Figure 5.40
Variation of distortion
with level for higher
Optimally biased
CFP output stage.
Bandwidth 80 kHz
Figure 5.41
How crossover
distortion is reduced
with increasing load
resistance. 20 W into
8 , 80 kHz
quiescent conditions, and the specific issues of the effectiveness of the
thermal compensation for temperature effects is dealt with in detail in
Chapter 12.
Output stage quiescent conditions
Figure 5.42 shows the two most common types of output stage: the
Emitter-Follower (EF) and the Complementary-Feedback-Pair (CFP) configurations. The manifold types of output stage based on triples will have to
be set aside for the moment. The two circuits shown have few
components, and there are equally few variables to explore in attempting
to reduce crossover distortion.
The two most
popular kinds of
output stage: the
(EF) and
Feedback Pair
(CFP) Vbias and
Vq are identified
Figure 5.42
Audio Power Amplifier Design Handbook
Table 5.2
Pq (per o/p device)
Average gain
Peak gain deviation from average
Crossover width*
2.930 V
50 mV
114 mA
4.6 W
+/–12 V
1.297 V
5 mV
11 mA
0.44 W
+/–0.6 V
(For Re = 0R22, 8 load, and +/–40 V supply rails)
* Crossover-width is the central region of the output voltage range over which crossover
effects are significant; I have rather arbitrarily defined it as the +/– output range over
which the incremental gain curves diverge by more than 0.0005 when Vbias is altered
around the optimum value. This is evaluated here for an 8 load only.
To get the terminology straight: here, as in my previous writings, Vbias
refers to the voltage set up across the driver bases by the Vbe-multiplier bias
generator, and is in the range 1–3 V for Class-B operation. Vq is the
quiescent voltage across the two emitter resistors (hereafter Re) alone, and
is between 5 and 50 mV, depending on the configuration chosen.
Quiescent current lq refers only to that flowing in the output devices, and
does not include driver standing currents.
I have already shown that the two most common output configurations are
quite different in behaviour, with the CFP being superior on most criteria.
Table 5.2 shows that crossover gain variation for the EF stage is smoother,
(being some 20 times wider) but of four times higher amplitude than for the
CFP version. It is not immediately obvious from this which stage will
generate the least HF THD, bearing in mind that the NFB factor falls with
Table 5.2 also emphasises that a little-known drawback of the EF version is
that its quiescent dissipation may be far from negligible.
An experiment on crossover distortion
Looking hard at the two output stage circuit diagrams, intuition suggests
that the value of emitter resistor Re is worth experimenting with. Since
these two resistors are placed between the output devices, and alternately
pass the full load current, it seems possible that their value could be critical
in mediating the handover of output control from one device to the other.
Re was therefore stepped from 0.1 to 0.47 , which covers the practical
range. Vbias was reoptimised at each step, though the changes were very
small, especially for the CFP version.
The output stage I
Figure 5.43
Output linearity of the
EF output stage for
emitter-resistance Re
between 0.1 and
0.47 Figure 5.43 shows the resulting gain variations in the crossover region for
the EF stage, while Figure 5.44 shows the same for the CFP configuration.
Table 5.3 summarises some numerical results for the EF stage, and Table 5.4
for the CFP.
There are some obvious features; firstly Re is clearly not critical in value as
the gain changes in the crossover region are relatively minor. Reducing the
Figure 5.44
Output linearity of the
CFP output stage for
emitter-resistance Re
between 0.1 and
0.47 149
Audio Power Amplifier Design Handbook
Table 5.3
output (Type-1).
Data for 8 load
and EF o/p stage
Optimal Vbias
Optimal Vq
Average Gain
As Re is varied, Vq varies by only 29%, while lq varies by 365%
Table 5.4
CFP output. Data
for 8 load and
CFP o/p stage
Optimal Vbias
Optimal Vq
Average Gain
Re value allows the average gain to approach unity more closely, with a
consequent advantage in output power capability. See page 272. Similarly,
reducing Re widens the crossover region for a constant load resistance,
because more current must pass through one Re to generate enough
voltage-drop to turn off the other output device. This implies that as Re is
reduced, the crossover products become lower-order and so of lower
frequency. They should be better linearised by the frequency-dependent
global NFB, and so overall closed-loop HF THD should be lower.
The simulated crossover distortion experiment described on page 110
showed that as the crossover region was made narrower, the distortion
energy became more evenly spread over higher harmonics. A wider
crossover region implies energy more concentrated in the lower harmonics,
which will receive the benefit of more negative feedback. However, if the
region is made wider, but retains the same amount of gain deviation, it
seems likely that the total harmonic energy is greater, and so there are two
opposing effects to be considered.
This is partly confirmed by Figure 5.41, where measurements show that
the THD reaches a very shallow minimum for Re = OR22, at any rate
for that particular configuration, level, and load; this is consistent with
two opposing effects. While the variation of THD with Re appears to be
The output stage I
real, it is small, and I conclude that selecting Re = OR1 for maximum
efficiency is probably the over-riding consideration. This has the additional benefit that if the stage is erroneously over-biased into Class AB,
the resulting gm-doubling distortion will only be half as bad as if the
more usual OR22 values had been used for Re.
It would be easy to assume that higher values of Re must be more linear,
because of a vague feeling that there is more local feedback but this
cannot be true as an emitter-follower already has 100% voltage feedback
to its emitter, by definition. Changing the value of Re alters slightly the
total resistive load seen by the emitter itself, and this does seem to have
a small but measurable effect on linearity.
As Re is varied, Vq varies by 230% while Iq varies by 85%. However
the absolute Vq change is only 4 mV, while the sum of Vbe’s varies by
only 0.23%. This makes it pretty plain that the voltage domain is what
counts, rather than the absolute value of Iq.
The first surprise from this experiment is that in the typical Class-B
output stage, quiescent current as such does not matter a great deal. This
may be hard to believe, particularly after my repeated statements that
quiescent conditions are critical in Class-B, but both assertions are true.
The data for both the EF and CFP output stages show that changing Re
alters the Iq considerably, but the optimal value of Vbias and Vq barely
change. The voltage across the transistor base-emitter junctions and Re’s
seems to be what counts, and the actual value of current flowing as a
result is not in itself of much interest. However, the Vbias setting remains
critical for minimum distortion; once the Re value is settled at the design
stage, the adjustment procedure for optimal crossover is just as before.
The irrelevance of quiescent current was confirmed by the Trimodal
amplifier, which was designed after the work described here was done,
and where I found that changing the output emitter resistor value Re
over a 5:1 range required no alteration in Vbias to maintain optimal
crossover conditions.
The critical factor is therefore the voltages across the various components in the output stage. Output stages get hot, and when the
junction temperatures change, both experiment and simulation show that
if Vbias is altered to maintain optimal crossover, Vq remains virtually
constant. This confirms the task of thermal compensation is solely to
cancel out the Vbe changes in the transistors; this may appear to be a
blinding glimpse of the obvious, but it was worth checking as there is no
inherent reason why the optimal Vq should not be a function of device
temperature. Fortunately it isn’t, for thermal compensation that also dealt
with a need for Vq to change with temperature might be a good deal
more complex.
Audio Power Amplifier Design Handbook
Vq as the critical quiescent parameter
The recognition that Vq is the critical parameter has some interesting
implications. Can we immediately start setting up amplifiers for optimal
crossover with a cheap DVM rather than an expensive THD analyser?
Setting up quiescent current with a milliammeter has often been advocated,
but the direct measurement of this current is not easy. It requires breaking
the output circuit so a meter can be inserted, and not all amplifiers react
favourably to so rude an intrusion. (The amplifier must also have near-zero
DC offset voltage to get any accuracy.) Measuring the total amplifier
consumption is not acceptable because the standing-current taken by the
small-signal and driver sections will, in the CFP case at least, swamp the
quiescent current. It is possible to determine quiescent current indirectly
from the Vq drop across the Re’s (still assuming zero DC offset) but this can
never give a very accurate current reading as the tolerance of low-value
Re’s is unlikely to be better than +/–10%.
However, if Vq is the real quantity we need to get at, then Re tolerances can
be blissfully ignored. This does not make THD analysers obsolete
overnight. It would be first necessary to show that Vq was always a reliable
indicator of crossover setting, no matter what variations occurred in driver
or output transistor parameters. This would be a sizeable undertaking.
There is also the difficulty that real-life DC offsets are not zero, though this
could possibly be side-stepped by measuring Vq with the load disconnected. A final objection is that without THD analysis and visual
examination of the residual, you can never be sure an amplifier is free from
parasitic oscillations and working properly.
I have previously demonstrated that the distortion behaviour of a typical
amplifier is quite different when driving 4 rather than 8 loads. This is
because with the heavier load, the output stage gain-behaviour tends to be
dominated by beta-loss in the output devices at higher currents, and
consequent extra loading on the drivers, giving third-harmonic distortion. If
this is to be reduced, which may be well worthwhile as many loudspeaker
loads have serious impedance dips, then it will need to be tackled in a
completely different way from crossover distortion.
It is disappointing to find that no manipulation of output-stage component
values appears to significantly improve crossover distortion, but apart from
this one small piece of (negative) information gained, we have in addition
determined that:
1 quiescent current as such does not matter; Vq is the vital quantity,
2 a perfect thermal compensation scheme, that was able to maintain Vq at
exactly the correct value, requires no more information than the junction
temperatures of the driver and output devices. Regrettably none of these
temperatures are actually accessible, but at least we know what to aim
The output stage I
Switching distortion (Distortion 3c)
This depends on several variables, notably the speed characteristics of the
output devices and the output topology. Leaving aside the semiconductor
physics and concentrating on the topology, the critical factor is whether or
not the output stage can reverse-bias the output device base-emitter
junctions to maximise the speed at which carriers are sucked out, so the
device is turned off quickly. The only conventional configuration that can
reverse-bias the output base-emitter junctions is the EF Type II, described
on page 112.
A second influence is the value of the driver emitter or collector resistors;
the lower they are the faster the stored charge can be removed. Applying
these criteria can reduce HF distortion markedly, but of equal importance
is that it minimises overlap of output conduction at high frequencies, which
if unchecked results in an inefficient and potentially destructive increase in
supply current [13]. To illustrate this, Figure 5.45 shows a graph of current
consumption vs frequency for varying driver collector resistance, for a CFP
type output.
Figure 5.45
Power supply current
versus freq, for a CFP
output with the driver
collector resistors
varied. There is little
to be gained from
reducing Rc below
50 Figure 5.46 shows the reduction of HF THD by adding a speedup capacitor
across the common driver resistor of an EF Type II. At LF the difference is
small, but at 40 kHz THD is halved, indicating much cleaner switchoff.
There is also a small benefit over the range 300 Hz–8 kHz.
Thermal distortion
Thermal distortion is that caused by cyclic temperature changes at signal
frequency, causing corresponding modulation of device parameters. While
it is certainly a real problem in IC op-amps, which have input and output
Audio Power Amplifier Design Handbook
Figure 5.46
HF THD reduction by
adding speedup
capacitance across
the common driver
resistance of a
Type II EF output
devices in very close thermal proximity, the situation in a normal discretecomponent power amplifier is quite different, and thermal distortion
cannot be detected. Having studied in detail distortion mechanisms that are
all too real, it comes as some relief to find that one prospective distortion
is illusory. Some writers appear to take it as given that such a distortion
mechanism exists in power amplifiers, but having studied the subject in
some depth I have yet to see the effect, and quite frankly I don’t think it
While now and again there have been odd mentions of thermal distortion
in power amps in some of the hi-fi press, you will never find:
1 any explanation of how it might work,
2 any estimate of the magnitude of the effect,
3 a circuit that will demonstrate its production.
In the usual absence of specific theories, one can only assume that the
alleged mechanism induces parameter changes in semiconductors whose
power dissipation varies over a cycle. If this were to happen, it would
presumably manifest itself as a rise in second or third harmonic distortion
at very low frequencies, but this simply does not happen. The largest effects
would be expected in Class-B output stages where dissipation varies wildly
over a cycle; the effect is still wholly absent.
One reason for this may be that drivers and output devices have relatively
large junctions with high thermal inertia – a few seconds with a hammer
and chisel revealed that an MJE340 driver has a chip with four times the
total area of a TL072. Given this thermal mass, parameters presumably
cannot change much even at 10 Hz. Low frequencies are also where the
global NFB factor is at its maximum; it is perfectly possible to design an
amplifier with 100 dB of feedback at 10 Hz, though much more modest
figures are sufficient to make distortion unmeasurably low up to 1 kHz or
The output stage I
so. Using my design methodology a Blameless amplifier can be straightforwardly designed to produce less than 0.0006% THD at 10 Hz (150 W/8 )
without even considering thermal distortion; this suggests that we have
here a non-problem.
I accept that it is not uncommon to see amplifier THD plots that rise at low
frequencies; but whenever I have been able to investigate this, the LF rise
could be eliminated by attending to either defective decoupling or
feedback-capacitor distortion. Any thermal distortion must be at a very low
level as it is invisible at 0.0006%; remember that this is the level of a THD
reading that is visually pure noise, though there are real amplifier distortion
products buried in it.
I have therefore done some deeper investigation by spectrum analysis of
the residual, which enables the harmonics to be extracted from the noise.
The test amplifier was an optimally-biased Class-B machine very similar to
that on Figure 6.16, except with a CFP output. The Audio Precision
oscillator is very, very clean but this amplifier tests it to its limits, and so
Table 5.5 below shows harmonics in a before-and-after-amplifier comparison. The spectrum analyser bandwidth was 1 Hz for 10 Hz tests, and
4.5 Hz for 1 kHz, to discriminate against wideband noise.
This further peeling of the distortion onion shows several things; that the AP is
a brilliant piece of machinery, and that the amplifier is really quite linear too.
However there is nothing resembling evidence for thermal distortion effects.
As a final argument, consider the distortion residual of a slightly
underbiased power-amp, using a CFP output configuration so that output
Table 5.5 Relative amplitute of distortion harmonics
AP THD reading
(80 kHz bandwidth)
10 Hz AP out · · · · Amp out
1 kHz AP out · · · · Amp out
NB: The rejection of the fundamental is not perfect, and this is shown as it contributes to the THD figure.
Audio Power Amplifier Design Handbook
device junction temperatures do not affect the quiescent current; it
therefore depends only on the driver temperatures. When the amplifier is
switched on and begins to apply sinewave power to a load, the crossover
spikes (generated by the deliberate underbiasing) will be seen to slowly
shrink in height over a couple of minutes as the drivers warm up. This
occurs even with the usual temperature compensation system, because of
the delays and losses in heating up the Vbe-multiplier transistor.
The size of these crossover spikes gives in effect a continuous readout of
driver temperature, and the slow variations that are seen imply timeconstants measured in tens of seconds or more; this must mean a negligible
response at 10 Hz.
There is no doubt that long-term thermal effects can alter Class-B amplifier
distortion, because as I have written elsewhere, the quiescent current
setting is critical for the lowest possible high-frequency THD. However this
is strictly a slow (several minutes) phenomenon, whereas enthusiasts for
thermal distortion are thinking of the usual sort of per-cycle distortion.
The above arguments lead me to conclude that thermal distortion as usually
described does not exist at a detectable level.
Thermal distortion in a power amp IC
Audio writers sometimes speculate about ‘thermal distortion’. This is
assumed to be caused by cyclic temperature changes at signal frequency,
causing modulation of transistor parameters. It is undoubtedly a real
problem in power ICs, which have input and output devices in close
thermal proximity on the same piece of sillcon, but in a discretecomponent power amplifier there is no such thermal coupling, and no such
Thermal non-linearities would presumably appear as second or third
harmonic distortion rising at low frequencies, and the largest effects should
be in Class-B output stages where dissipation varies greatly over a cycle.
There is absolutely no such effect to be seen in discrete-component power
But thermal distortion certainly does exist in IC power amplifiers. Figure
5.47 is a distortion plot for the Philips TDA 1522Q power amp IC, which
I believe shows the effect. The power level was 4.4 W into 8 , 8 W into
4 . As is usual for such amplifiers, the distortion is generally high, but
drops into a notch at 40 Hz; the only feasible explanation for this is
cancellation of distortion products from two separate distortion sources. At
frequencies below this notch there is second-harmonic distortion rising at
12 dB/octave as frequency falls. The LF residual looks quite different from
the midband distortion, which was a mixture of second and third harmonic
plus crossover spikes.
The output stage I
Figure 5.47
Distortion plot for the
Phllips TDA1522Q
IC. Power out was
4.4 W rms into 8 ,
8 W rms into 4 . The
dotted line shows a
12 dB/octave slope
The THD figure falls above 10 kHz because of the 80 kHz bandwidth
limitation on the residual, and the high-order nature of the harmonics that
make up crossover distortion.
All other possible sources of an LF distortion rise, such as inadequate
decoupling, were excluded. There was no output capacitor to introduce
It seems pretty clear that the steep rise here is due to thermal distortion, in
the form of feedback from the power output stage to earlier parts of the
amplifier – probably the input stage. As would be expected, the effect is
greater with a heavier load which causes more heating; in fact halving the
load doubles the THD reading below the 40 Hz notch.
Selecting an output stage
Even if we stick to the most conventional of output stages, there are still an
embarrassingly large number to choose form. The cost of a complementary
pair of power FETs is currently at least twice that of roughly equivalent BJTs,
and taken with the poor linearity and low efficiency of these devices, the
use of them may require a marketing rather than a technical motivation.
Turning to BJTs, I conclude that there are the following candidates for Best
Output Stage:
1 the Emitter-Follower Type II output stage is the best at coping with
switchoff distortion but the quiescent-current stability may be
2 the CFP topology has good quiescent stability and low LSN; its worst
drawback is that reverse-biasing the output bases for fast switchoff is
impossible without additional HT rails,
3 the quasi-complementary-with-Baxandall-diode stage comes close to
mimicking the EF-type stages in linearity, with a potential for cost-saving
on output devices. Quiescent stability is not as good as the CFP.
Audio Power Amplifier Design Handbook
Closing the loop: distortion in complete amplifiers
In Chapter 4 it was shown how relatively simple design rules could ensure
that the THD of the small-signal stages alone could be reduced to less than
0.001% across the audio band, in a thoroughly repeatable fashion, and
without using frightening amounts of negative feedback. Combining this
sub-system with one of the more linear output stages described in Chapter
4, such as the CFP version which gives 0.014% THD open-loop, and
bearing in mind that ample NFB is available, it seems we have all the
ingredients for a virtually distortionless power amplifier. However, life is
rarely so simple . . .
(Note – the AP plots in Figures 5.5–5.7 were taken at 100 W rms into 8 ,
from an amplifier with an input error of –70 dB at 10 kHz and a c/l gain of
27 dB, giving a feedback factor of 43 dB at this frequency. This is well above
the dominant-pole frequency and so the NFB factor is dropping at 6 dB/
octave and will be down to 37 dB at 20 kHz. My experience suggests that
this is about as much feedback as is safe for general hi-fi usage, assuming
an output inductor to improve stability with capacitative loads. Sadly,
published data on this touchy topic seems to be non-existent).
Figure 5.48 shows the distortion performance of such a closed-loop
amplifier with an EF output stage, Figure 5.49 showing the same with a CFP
output stage. Figure 5.50 shows the THD of a quasi-complementary stage
with Baxandall diode [14]. In each case Distortion 1, Distortion 2 and
Distortion 4–Distortion 7 have been eliminated, by methods described in
past and future chapters, to make the amplifier Blameless.
It will be seen at once that these amplifiers are not distortionless, though
the performance is markedly superior to the usual run of hardware. THD
in the LF region is very low, well below a noise floor of 0.0007%, and the
usual rise below 100 Hz is very small indeed. However, above 2 kHz,
Figure 5.48
Closed-loop amplifier
performance with
Emitter-Follower output
stage. 100 W into
The output stage I
Figure 5.49
Closed-loop amplifier
performance with
CFP output. 100 W
into 8 THD rises with frequency at between 6 and 12 dB/octave, and the
distortion residual in this region is clearly time-aligned with the crossover
region, and consists of high-order harmonics rather than second or third.
It is intriguing to note that the quasi-Bax output gives about the same HF
THD as the EF topology, which confirms the statement on page 119 that
the addition of a Baxandall diode essentially turns a conventional quasicomplementary stage with serious crossover asymmetry into a reasonable
emulation of a complementary EF stage. There is less HF THD with a
CFP output; this cannot be due to large-signal non-linearity as this is
negligible with an 8 load for all three stages, and so it must be due to
high-order crossover products.
The distortion figures given in this book are rather lower than usual. I would
like to emphasise that these are not freakish or unrepeatable figures; they
Figure 5.50
Closed-loop amplifier
performance; quasicomplementary
output stage with
Baxandall diode.
100 W into 8 159
Audio Power Amplifier Design Handbook
Table 5.6
Summary of
closed-loop amp
Quasi Bax
1 kHz
10 kHz
are the result of attending to all of the major sources of distortion, rather
than just one or two. I have at the time of writing personally built 12 models
of the CFP version, and performance showed little variation.
Here the closed-loop distortion is much greater than that produced by the
small-signal stages alone; however if the input pair is badly designed its HF
distortion can easily exceed that caused by the output stage.
Our feedback-factor here is a minimum of 70× across the band (being
much higher at LF) and the output stages examined above are mostly
capable of less than 0.1% THD open-loop. It seems a combination of these
should yield a closed loop distortion at least 70 times better, i.e. below
0.001% from 10 Hz to 20 kHz. This happy outcome fails to materialise, and
we had better find out why . . .
Firstly, when an amplifier with a frequency-dependent NFB factor generates
distortion, the reduction is not that due to the NFB factor at the fundamental
frequency, but the amount available at the frequency of the harmonic in
question. A typical amplifier with o/l gain rolling-off at 6 dB/octave will be
half as effective at reducing fourth-harmonic distortion as it is at reducing
the second harmonic. LSN is largely third (and possibly second) harmonic,
and so NFB will deal with this effectively. However, both crossover and
switchoff distortions generate high-order harmonics significant up to at
least the nineteenth and these receive much less linearisation. As the
fundamental moves up in frequency the harmonics do too, and benefit
from even less feedback. This is the reason for the differentiated look to
many distortion residuals; higher harmonics are emphasised at the rate of
6 db/octave.
Here is a real example of the inability of NFB to cure all possible amplifier
ills. To reduce this HF distortion we must reduce the crossover gaindeviations of the output stage before closing the loop. There seems no
obvious way to do this by minor modifications to any of the conventional
output stages; we can only optimise the quiescent current.
As I stated on page 33, Class AB is generally not a Good Thing, as it gives
more distortion than Class B, rather than less, and so will not help us. Figure
5.51 makes this very clear for the closed-loop case; Class-AB clearly gives
the worst performance. (As before, the AB quiescent was set for 50:50 m/s
ratio of the gm-doubling artefacts on the residual.)
The output stage I
Figure 5.51
Closed-loop CFP
amp. Setting
quiescent for Class
AB gives more HF
THD than either
Class A or B
To summarise:
1 Class-AB is best avoided. Use pure Class-A or B, as AB will always have
more distortion than either,
2 FET outputs offer freedom from some BJT problems, but in general have
poorer linearity and cost more,
3 the distortion generated by a Blameless amplifier driving an 8 load is
almost wholly due to the effects of crossover and switching distortion.
This does not hold for 4 or lower loads, where third-harmonic on the
residual shows the presence of large-signal non-linearity, caused by betaloss at high output currents.
1. Mann The Texan 20+20 Watt Stereo Amplifier Practical Wireless, May
1972, p. 48 (Output stage with gain).
2. Takahashi Design and Construction of High Slew Rate Amplifiers
Preprint No. 1348 (A-4) for 60th AES Convention 1978 (Class-B smallsignal stages).
3. Hawksford Distortion Correction in Audio Power Amplifiers Journ.
Audio Eng. Soc. Jan/Feb 1981, p. 27 (Error-correction).
4. Walker, P Current-Dumping Audio Amplifier Wireless World 1975,
pp. 560–562.
5. Blomley New Approach To Class-B Wireless World, Feb 1971, p. 57
and Mar 1971, pp. 127–131.
6. Otala An Audio Power Amplifier for Ultimate Quality Requirements
IEEE Trans on Audio and Electroacoustics, Dec 1973, p. 548.
7. Lin, H Electronics, Sept 1956, pp. 173–175 (Quasi-comp).
Audio Power Amplifier Design Handbook
8. Baxandall, P Symmetry in Class B Letters, Wireless World Sept 1969,
p. 416 (Baxandall diode).
9. Gray and Meyer Analysis and Design of Analog Integrated Circuits
Wiley 1984, p. 172.
10. Crecraft et al Electronics pub Chapman and Hall 1993, p. 538.
11. Oliver Distortion In Complementary-Pair Class-B Amps HewlettPackard Journal, Feb 1971, p. 11.
12. Blomley, P New Approach To Class-B Wireless World, Feb 1971,
p. 57.
13. Alves, J Power Bandwidth Limitations in Audio Amplifiers IEEE Trans
on Broadcast and TV, March 1973, p. 79.
14. Baxandall, P Symmetry in Class B Letters, Wireless World Sept 1969,
p. 416 (Baxandall diode).
The output stage II
Distortion number 4: VAS loading distortion
Distortion 4 is that which results from the loading of the Voltage Amplifier
Stage (VAS) by the non-linear input impedance of a Class-B output stage.
This was looked at in Chapter 4 from the point of view of the VAS, where
it was shown that since the VAS provides all the voltage gain, its collector
impedance tends to be high. This renders it vulnerable to non-linear
loading unless it is buffered or otherwise protected.
The VAS is routinely (though usually unknowingly) linearised by applying
local negative-feedback via the dominant-pole Miller capacitor Cdom, and
this is a powerful argument against any other form of compensation. If VAS
distortion still adds significantly to the amplifier total, then the local openloop gain of the VAS stage can be raised to increase the local feedback
factor. The obvious method is to raise the impedance at the VAS collector,
and so the gain, by cascoding. However, if this is done without buffering
the output stage loading will render the cascoding almost completely
ineffective. Using a VAS-buffer eliminates this problem.
As explained in Chapter 4, the VAS collector impedance, while high at LF
compared with other circuit nodes, falls with frequency as soon as Cdom
takes effect, and so Distortion 4 is usually only visible at LF. It is also often
masked by the increase in output stage distortion above dominant-pole
frequency P1 as the amount of global NFB reduces.
The fall in VAS impedance with frequency is demonstrated in Figure 6.1,
obtained from the Spice conceptual model in Chapter 4, with values
appropriate to real life. The LF impedance is basically that of the VAS
collector resistance, but halves with each octave once P1 is reached. By
3 kHz the impedance is down to 1 k, and still falling. Nevertheless, it
usually remains high enough for the input impedance of a Class-B output
Audio Power Amplifier Design Handbook
Figure 6.1
Distortion 4; the
impedance at the VAS
collector falls at 6 dB/
octave with frequency
Figure 6.2
Distortion 4 in action;
the lower trace shows
the result of its
elimination by the use
of a VAS-buffer
stage to significantly degrade linearity, the actual effect being shown in
Figure 6.2.
In Chapter 4 it was shown that as an alternative to cascoding, an effective
means of linearising the VAS is to add an emitter-follower within the VAS
local feedback loop, increasing the local NFB factor by raising effective
beta rather than the collector impedance. As well as good VAS linearity, this
establishes a much lower VAS collector impedance across the audio band,
and is much more resistant to Distortion 4 than the cascode version. VAS
The output stage II
Figure 6.3
Distortion 4 and its
root cause; the nonlinear input impedance
of an EF Class-B output
buffering is not required, so this method has a lower component count. The
only drawback is a greater tendency to parasitic oscillation near negative
clipping, when used with a CFP output stage.
Figure 6.3 confirms that the input impedance of a conventional EF Type I
output stage is highly non-linear; the data is derived from a SPICE output
stage simulation with optimal Iq. Even with an undemanding 8 load, the
impedance varies by 10:1 over the output voltage swing. The Type II EF
output (using a shared drive emitter resistance) has a 50% higher
impedance around crossover, but the variation ratio is rather greater. CFP
output stages have a more complex variation that includes a precipitous
drop to less than 20 k around the crossover point. With all types underbiasing produces additional sharp impedance changes at crossover.
Distortion number 5: rail decoupling distortion
Almost all amplifiers have some form of rail decoupling apart from the
main reservoir capacitors; this is usually required to guarantee HF stability.
Standard decoupling arrangements include small to medium-size electrolytics (say 10–470 µF) connected between each rail and ground, and an
inevitable consequence is that rail-voltage variations cause current to flow
into the ground connection chosen. This is just one mechanism that defines
the Power Supply Rejection Ratio (PSRR) of an amplifier, but it is one that
can seriously damage linearity.
Audio Power Amplifier Design Handbook
If we use an unregulated power supply (and there are almost overwhelming
reasons for using such a supply, detailed in Chapter 8) comprising
transformer, bridge rectifier, and reservoir capacitors, then these rails have
a non-zero AC impedance and their voltage variations will be due to
amplifier load currents as well as 100 Hz ripple. In Class-B, the supply-rail
currents are halfwave-rectified sine pulses with strong harmonic content,
and if they contaminate the signal then distortion is badly degraded; a
common route for interaction is via decoupling grounds shared with input
or feedback networks, and a separate decoupler ground is usually a
complete cure. This point is easy to overlook, and attempts to improve
amplifier linearity by labouring on the input pair, VAS, etc. are doomed to
failure unless this distortion mechanism is eliminated first. As a rule it is
simply necessary to take the decoupling ground separately back to the
ground star point, as shown in Figure 6.4. (Note that the star-point A is
Figure 6.4
Distortion 5; The
correct way to route
decouple grounding to
the star-point
defined on a short spur from the heavy connection joining the reservoirs;
trying to use B as the star point will introduce ripple due to the large
reservoir-charging current pulses passing through it.)
Figure 6.5 shows the effect on an otherwise Blameless amplifier handling
60 W/8 , with 220 µF rail decoupling capacitors; at 1 kHz distortion has
increased by more than ten times, which is quite bad enough. However, at
20 Hz the THD has increased at least 100-fold, turning a very good
amplifier into a profoundly mediocre one with one misconceived
When the waveform on the supply rails is examined, the 100 Hz ripple
amplitude will usually be found to exceed the pulses due to Class-B signal
current, and so some of the distortion on the upper curve of the plot is
actually due to ripple injection. This is hinted at by the phase-crevasse at
100 Hz, where the ripple happened to partly cancel the signal at the instant
of measurement. Below 100 Hz the curve rises as greater demands are
made on the reservoirs, the signal voltage on the rails increases, and more
distorted current is forced into the ground system.
The output stage II
Figure 6.5
Distortion 5 in action;
The upper trace was
produced simply by
taking the decoupler
ground from the starpoint and connecting it
via the input ground
line instead
Figure 6.6 shows a typical Distortion 5 residual, produced by deliberately
connecting the negative supply-rail decoupling capacitor to the input
ground instead of properly giving it its own return to the far side of the starpoint. THD increased from 0.00097% to 0.008%, appearing mostly as
second harmonic. Distortion 5 is usually easy to identify as it is
accompanied by 100 Hz power-supply ripple; Distortions 6 and 7
introduce no extra ripple. The ripple contamination here – the the two
humps at the bottom – is significant and contributes to the THD reading.
As a general rule, if an amplifier is made free from ripple injection under
drive conditions, demonstrated by a THD residual without ripple
Figure 6.6
Distortion 5 revealed.
Connecting the rail
decoupler to input
ground increases
THD eight-fold from
0.00097% to
0.008%, mostly as
second harmonic.
100 Hz ripple is also
visible. No
1 10.0V
2 200 mv
2.00 mv /
Audio Power Amplifier Design Handbook
components, there will be no distortion from the power-supply rails, and
the complications and inefficiencies of high-current rail regulators are
quite unnecessary.
There has been much discussion of PSRR-induced distortion in the
literature recently, e.g. Greg Ball [1]. I part company with some writers at the
point where they assume a power amplifier is likely to have 25 dB PSRR,
making an expensive set of HT regulators the only answer. Greg Ball also
initially assumes that a power amp has the same PSRR characteristics as an
op-amp, i.e. falling steadily at 6 dB/octave. There is absolutely no need for
this to be so, given a little RC decoupling, and Ball states at the end of his
article that a more elegant solution . . . is to depend on a high PSRR in the
amplifier proper. This issue is dealt with in detail in Chapter 8.
Distortion number 6: induction distortion
The existence of this distortion mechanism, like Distortion 5, stems directly
from the Class-B nature of the output stage. With a sine input, the output
hopefully carries a good sinewave, but the supply-rail currents are
halfwave-rectified sine pulses, which will readily crosstalk into sensitive
parts of the circuit by induction. This is very damaging to the distortion
performance, as Figure 6.7 shows.
The distortion signal may intrude into the input circuitry, the feedback path,
or even the cables to the output terminals. The result is a kind of sawtooth
on the distortion residual that is very distinctive, and a large extra distortion
component that rises at 6 dB/octave with frequency.
A Distortion 6 residual is displayed in Figure 6.8. The V-supply rail was
routed parallel to the negative-feedback line to produce this diagram. THD
is more than doubled, but is still relatively low at 0.0021%. 64-times
Figure 6.7
Distortion 6 exposed.
The upper trace shows
the effects of Class-B
rail induction into
signal circuitry
The output stage II
Figure 6.8
Distortion 6.
Induction of halfwave signal from the
negative supply rail
into the NFB line
increases THD to
0.0021%. Averaged
64 times
1 20.0V
2 20.0 mv
200 ms /
averaging is used. Distortion 6 is easily identified if the DC supply cables
are movable, for altering their run will strongly affect the quantity
This inductive effect appears to have been first publicised by Cherry [2], in
a paper that deserves more attention. The effect has however been
recognised and avoided by some practitioners for many years [3]. However,
having examined many power amplifiers with varying degrees of virtue, I
feel that this effect, being apparently unknown to most designers, is
probably the most widespread cause of unnecessary distortion.
The contribution of Distortion 6 can be reduced below the measurement
threshold by taking sufficient care over the layout of supply-rail cabling
relative to signal leads, and avoiding loops that will induce or pick up
magnetic fields. I wish I could give precise rules for layout that would
guarantee freedom from the problem, but each amplifier has its own
physical layout, and the cabling topology has to take this into account.
However, here are some guidelines:
Firstly, implement rigorous minimisation of loop area in the input and
feedback circuitry; keeping each signal line as close to its ground return as
possible. Secondly, minimise the ability of the supply wiring to establish
magnetic fields in the first place; thirdly, put as much distance between
these two areas as you can. Fresh air beats shielding on price every
Figure 6.9 shows one straightforward approach to solving the problem; the
supply and ground wires are tightly twisted together to reduce radiation. In
practice this doesn’t seem too effective, for reasons that are not wholly
Audio Power Amplifier Design Handbook
Figure 6.9
Distortion 6;
against the induction of
distortion from the
supply rails. 6.7b is
usually more effective
clear, but seem to involve the difficulty of ensuring exactly equal coupling
between three twisted conductors. In Figure 6.9, the supply rails are twisted
together but kept well away from the ground return; this will allow field
generation, but if the currents in the two rails butt together to make a nice
sinewave at the output, then they should do the same when the magnetic
fields from each rail sum. There is an obvious risk of interchannel crosstalk
if this approach is used in a stereo amplifier, but it does deal effectively with
the induced-distortion problem in some layouts.
Distortion number 7: NFB takeoff point distortion
It has become a tired old truism that negative feedback is a powerful
technique, and like all such, must be used with care if you are to avoid
tweeter-frying HF instability.
However, there is another and much more subtle trap in applying global
NFB. Class-B output stages are a maelstrom of high-amplitude halfwaverectified currents, and if the feedback takeoff point is in slightly the wrong
place, these currents contaminate the feedback signal, making it an
inaccurate representation of the output voltage, and hence introducing
distortion; Figure 6.10 shows the problem. At the current levels in question,
all wires and PCB tracks must be treated as resistances, and it follows that
point C is not at the same potential as point D whenever TR1 conducts. If
feedback is taken from D, then a clean signal will be established here, but
the signal at output point C will have a half-wave rectified sinewave added
to it, due to the resistance C–D. The actual output will be distorted but the
feedback loop will do nothing about it as it does not know about the error.
The output stage II
Figure 6.10
Distortion 7; Wrong
and Right ways of
arranging the critical
takeoff point
Figure 6.11 shows the practical result for an amplifier driving 100 W into
8 , with the extra distortion interestingly shadowing the original curve as
it rises with frequency. The resistive path C–D that did the damage was a
mere 6 mm length of heavy-gauge wirewound resistor lead.
Figure 6.12 shows a THD residual for Distortion 7, introduced by
deliberately taking the NFB from the wrong point. The THD rose from
0.00097% to 0.0027%, simply because the NFB feed was taken from the
wrong end of the leg of one of the output emitter resistors Re. Note this is
not the wrong side of the resistor, or the distortion would have been gross,
but a mere 10 mm along a very thick resistor leg from the actual output
junction point.
Figure 6.11
Distortion 7 at work;
the upper (WRONG)
trace shows the result
of a mere 6 mm of
heavy-gauge wire
between the output
and the feedback
Audio Power Amplifier Design Handbook
Figure 6.12
1 20.0V
2 50.0 mv
Distortion 7, caused
by choosing an NFB
takeoff point inside
the Class-B output
stage rather than on
the output line itself.
THD is increased
from 0.00097% to
0.0027%, by taking
the NFB from the
wrong end of 10 mm
of very thick resistor
leg. Averaged 64
200 ms /
Of the distortions that afflict generic Class-B power amplifiers, 5, 6 and 7
all look rather similar when they appear in the THD residual, which is
perhaps not surprising since all result from adding half-wave disturbances
to the signal.
To eliminate this distortion is easy, once you are alert to the danger. Taking
the NFB feed from D is not advisable as D is not a mathematical point, but
has a physical extent, inside which the current distribution is unknown.
Point E on the output line is much better, as the half-wave currents do not
flow through this arm of the circuit.
Distortion number 8: capacitor distortion
When I wrote the original series on amplifier distortion [4], I listed seven
types of distortion that defined an amplifier’s linearity. The number has
grown to eight, with the addition of electrolytic capacitor distortion. This
has nothing to do with Subjectivist hypotheses about mysterious nonmeasurable effects; this phenomenon is all too real, though for some reason
it seems to be almost unknown amongst audio designers.
Standard aluminium electrolytics generate distortion whenever they are
used so a significant AC voltage develops across them; this is usually when
they are used for coupling and DC blocking, whilst driving a significant
resistive load. Figure 6.13 is the test circuit; Figure 6.14 shows the resulting
distortion for a 47 µF 25 V capacitor driving +20 dBm (7.75 Vrms) into a
680 load, while Figure 6.15 shows how the associated LF roll-off has
barely begun. The distortion is a mixture of second and third harmonic, and
rises rapidly as frequency falls, at something between 12 and 18 dB/octave.
The output stage II
Figure 6.13
A very simple circuit to
demonstrate electrolytic
capacitor distortion.
Measurable distortion
begins at 100 Hz
Figure 6.14
Capacitor distortion vs
frequency, showing the
rapid rise in THD once
the distortion threshold
is reached
The great danger of this mechanism is that serious distortion begins while
the response roll-off is barely detectable; here the THD reaches 0.01%
when the response has only fallen by 0.2 dB. The voltage across the
capacitor is 2.6 V peak, and this voltage is a better warning of danger than
the degree of roll-off.
Further tests showed that the distortion roughly triples as the applied
voltage doubles; this factor seems to vary somewhat between different
capacitor rated voltages.
The mechanism by which capacitors generate this distortion is unclear.
Dielectric absorption appears to be ruled out as this is invariably (and
therefore presumably successfully) modelled by adding linear components,
in the shape of resistors and capacitors, to the basic capacitor model.
Reverse biasing is not the problem, for capacitors DC biased by up to +15 V
show slightly increased, not reduced distortion. Non-polarised electrolytics
Audio Power Amplifier Design Handbook
Figure 6.15
The small amount of
LF roll-off associated
with the distortion rise
in Figure 6.11
show the same effect but at a much greater AC voltage, typically giving the
same distortion at one-tenth the frequency of a conventional capacitor with
the same time-constant; the cost and size of these components generally
rules out their use to combat this effect. Usually the best solution is simply
to keep increasing the capacitor value until the LF distortion rise disappears
off the left of the THD graph. Negligible roll-off in the audio band is not a
sufficient criterion.
Electrolytics are therefore best reserved for DC filtering, and for signal
coupling where the AC voltage across them will be negligible. If a coupling
capacitor does have AC voltage across it, and drives the usual resistive
load, then it must be acting as a high-pass filter. This is never good design
practice, because electrolytics have large tolerances and make inaccurate
filters; it is now clear they generate distortion as well.
It is therefore most undesirable to define the lower bandwidth limit simply
by relying on the high-pass action of electrolytics and circuit resistances; it
should be done with a non-electrolytic capacitor, made as large as is
economical in order to reduce the value of the associated resistance and so
keep down circuit impedances, thus minimising the danger of noise and
Capacitor distortion in power amplifiers is most likely to occur in the
feedback network blocking capacitor (assuming a DC-coupled amplifier).
The input blocking capacitor usually feeds a high impedance, but the
feedback arm must have the lowest possible resistances to minimise both
noise and DC offset. The feedback capacitor therefore tends to be relatively
large, and if it is not quite large enough the THD plot of the amplifier will
show the characteristic kick up at the LF end. An example of this is dealt
with in detail on page 88.
The output stage II
It is common for amplifiers to show a rise in distortion at the LF end, but
there is no reason why this should ever occur. Capacitor distortion is
usually the reason, but Distortion 5 (Rail Decoupling Distortion) can also
contribute. They can be distinguished because Distortion 5 typically rises
by only 6 dB/octave as frequency decreases, rather than 12–18 dB/
Amplifiers with AC-coupled outputs are now fairly rare, possibly because
distortion in the output capacitor is a major problem, occurring in the midband as well as at LF. See page 42 for details.
Design example: a 50 W Class-B amplifier
Figure 6.16 shows a design example of a Class-B amplifier, intended for
domestic hi-fi applications. Despite its relatively conventional appearance,
the circuit parameters selected give much better than a conventional
distortion performance; this is potentially a Blameless design, but only if
due care is given to wiring topology and physical layout will this be
With the supply voltages and values shown it gives 50 W into 8 , for
1 Vrms input. In earlier chapters I have used the word Blameless to describe
amplifiers in which all distortion mechanisms, except the apparently
unavoidable ones due to Class-B, have been rendered negligible. This
circuit has the potential to be Blameless, (as do we all) but achieving this
depends on care in cabling and layout. It does not aim to be a cookbook
project; for example, overcurrent and DC-offset protection are omitted.
In Chapter 11, output topologies are examined, and the conclusion drawn
that power-FETs were disappointingly expensive, inefficient, and nonlinear. Bipolars it is, therefore. The best BJT configurations were the
Emitter-Follower Type II, with least output switchoff distortion, and the
Complementary Feedback Pair (CFP), giving the best basic linearity.
The output configuration chosen is the Emitter-Follower Type II, which has
the advantage of reducing switchoff non-linearities (Distortion 3c) due to
the action of R15 in reverse-biasing the output base-emitter junctions as
they turn off. A possible disadvantage is that quiescent stability might be
worse than for the CFP output topology, as there is no local feedback loop
to servo out Vbe variations in the hot output devices. Domestic ambient
temperature changes will be small, so that adequate quiescent stability can
be attained by suitable heatsinking and thermal compensation.
A global NFB factor of 30 dB at 20 kHz was chosen, which should give
generous HF stability margins. The input stage (current-source TR1 and
differential pair TR2, 3) is heavily degenerated by R2, 3 to delay the onset
of third-harmonic Distortion 1, and to assist this the contribution of
transistor internal re variation is minimised by using the unusually high tail
50 W Class-B amplifier
circuit diagram.
Transistor numbers
correspond with the
generic amplifier in
Chapter 3
Figure 6.16
Audio Power Amplifier Design Handbook
The output stage II
current of 4 ma. TR11, 12 form a degenerated current-mirror that enforces
accurate balance of the TR2, 3 collector currents, preventing the generation
of second-harmonic distortion. Tail source TR1, 14 has a basic PSRR 10 dB
better than the usual two-diode version, though this is academic when C11
is fitted.
Input resistor R1 and feedback arm R8 are made equal and kept as low as
possible consistent with a reasonably high input impedance, so that base
current mismatch caused by beta variations will give a minimal DC offset;
this does not affect TR2–TR3 Vbe mismatches, which appear directly at the
output, but these are much smaller than the effects of lb. Even if TR2, 3 are
high voltage types with low beta, the output offset should be within
+/–50 mV, which should be quite adequate, and eliminates balance presets
and DC servos. A low value for R8 also gives a low value for R9, which
improves the noise performance.
The value of C2 shown (220 µF) gives an LF roll-off with R9 that is –3 dB at
1.4 Hz. The aim is not an unreasonably extended sub-bass response, but to
prevent an LF rise in distortion due to capacitor non-linearity; 100 µF
degraded the THD at 10 Hz from less than 0.0006% to 0.0011%, and I
judge this unacceptable aesthetically if not audibly. Band-limiting should
be done earlier, with non-electrolytic capacitors. Protection diode D1
prevents damage to C2 if the amplifier suffers a fault that makes it saturate
negatively; it looks unlikely but causes no measurable distortion [5]. C7
provides some stabilising phase-advance and limits the closed-loop
bandwidth; R20 prevents it upsetting TR3.
The VAS stage is enhanced by an emitter-follower inside the Millercompensation loop, so that the local NFB that linearises the VAS is
increased by augmenting total VAS beta, rather than by increasing the
collector impedance by cascoding. This extra local NFB effectively
eliminates Distortion 2 (VAS non-linearity). Further study has shown that
thus increasing VAS beta gives a much lower collector impedance than a
cascode stage, due to the greater local feedback, and so a VAS-buffer to
eliminate Distortion 4 (loading of VAS collector by the non-linear input
impedance of the output stage) appears unnecessary. Cdom is relatively
high at 100 pF, to swamp transistor internal capacitances and circuit strays,
and make the design predictable. The slew-rate calculates as 40 V/µsec.
The VAS collector-load is a standard current source, to avoid the
uncertainties of bootstrapping.
Since almost all the THD from a blameless amplifier is crossover, keeping
the quiescent conditions optimal is essential. Quiescent stability requires
the bias generator to cancel out the Vbe variations of four junctions in
series; those of two drivers and two output devices. Bias generator TR8 is
the standard Vbe-multiplier, modified to make its voltage more stable
against variations in the current through it. These occur because the biasing
of TR5 does not completely reject rail variations; its output current also
Audio Power Amplifier Design Handbook
Figure 6.17
SPICE plot of the
behaviour of a currentcompensated bias
drifts initially due to heating and changes in TR5 Vbe. Keeping Class-B
quiescent stable is hard enough at the best of times, and so it makes sense
to keep these extra factors out of the equation. The basic Vbe-multiplier has
an incremental resistance of about 20 ; in other words its voltage changes
by 1 mV for a 50 µA drift in standing current. Adding R14 converts this to
a gently-peaking characteristic that can be made perfectly flat at one
chosen current; see Figure 6.17. Setting R14 to 22 makes the voltage
peak at 6 mA, and standing current now must deviate from this value by
more than 500 µA for a 1 mV bias change. The R14 value needs to be
altered if TR15 is run at a different current; for example, 16 makes the
voltage peak at 8 mA instead. If TO3 outputs are used the bias generator
should be in contact with the top or can of one of the output devices, rather
than the heatsink, as this is the fastest and least attenuated source for
thermal feedback.
The output stage is a standard double emitter-follower apart from the
connection of R15 between the driver emitters without connection to the
output rail. This gives quicker and cleaner switchoff of the outputs at high
frequencies; switchoff distortion may significantly degrade THD from
10 kHz upwards, dependent on transistor type. Speedup capacitor C4
noticeable improves the switchoff action. C6, R18 form the Zobel network,
(sometimes confusingly called a Boucherot cell) while L1, damped by R19,
isolates the amplifier from load capacitance.
Figure 6.18 shows the 50 W/8 distortion performance; about 0.001% at
1 kHz, and 0.006% at 10 kHz. The measurement bandwidth makes a big
The output stage II
Figure 6.18
Class-B amplifier: THD
performance at
50 W/8 ;
bandwidths 30 kHz
and 80 kHz
difference to the appearance, because what little distortion is present is
crossover-derived, and so high-order. It rises at 6 dB/octave, at the rate the
feedback factor falls, and it is instructive to watch the crossover glitches
emerging from the noise, like Grendel from the marsh, as the test frequency
increases above 1 kHz. There is no precipitous THD rise in the ultrasonic
The zigzags on the LF end of the plot are measurement artefacts, apparently
caused by the Audio Precision system trying to winkle out distortion from
visually pure white noise. Below 700 Hz the residual was pure noise with a
level equivalent to approx. 0.0006% (yes, three zeros) at 30 kHz bandwidth;
the actual THD here must be microscopic. This performance can only be
Figure 6.19
The dramatic THD
improvement obtained
by converting the
Class-B amplifier to
2-pole compensation
Audio Power Amplifier Design Handbook
obtained if all seven of the distortion mechanisms are properly addressed;
Distortions 1–4 are determined by the circuit design, but the remaining three
depend critically on physical layout and grounding topology.
It is hard to beat a well-gilded lily, and so Figure 6.19 shows the startling
results of applying 2-pole compensation to the basic amplifier; C3 remains
100 pF, while CP2 was 220 pF and Rp 1k (see Figure 7.1d, page 185). The
Figure 6.20
Class-B amplifier with
simple quasicomplementary output.
Lower trace is for twopole compensation
Figure 6.21
Class-B amplifier with
quasi-comp plus
Baxandall diode
output. Lower trace is
the two-pole case
The output stage II
extra global NFB does its work extremely well, the 10 kHz THD dropping
to 0.0015%, while the 1 kHz figure can only be guessed at. There were no
unusual signs of instability, but as always unusual compensation schemes
require careful testing. It does appear that a Blameless amplifier with 2-pole
compensation takes us close to the long-sought goal of the Distortionless
The basic Blameless EF amplifier was experimentally rebuilt with three
alternative output stages; the simple quasi-complementary, the quasiBaxandall, and the CFP. The results for both single and two-pole
compensation are shown in Figures 6.20, 6.21, and 6.22. The simple quasicomplementary generates more crossover distortion, as expected, and the
Figure 6.22
Class-B amplifier with
feedback pair (CFP)
output stage. Normal
compensation only
Table 6.1
Class-B amplifier
Power output:
Freq Response:
50 W rms into 8 Below 0.0006% at 1 kHz and 50 W/8 Below 0.006% at 10 kHz
Approx. 35 V/µsec
91 dBu at the output
117 dBu (referred to input)
+0, –0.5 dB over 20 Hz–20 kHz
(Most of the AP plots in this book were obtained from an amplifier similar to Figure
6.16, though with higher supply rails and so greater power capability. The main
differences were the use of a cascode-VAS with a buffer, and a CFP output to
minimise distracting quiescent variations. Measurements at powers above
100 W/8 used a version with two paralleled output devices.)
Audio Power Amplifier Design Handbook
quasi-Baxandall version is not a lot better, probably due to remaining
asymmetries around the crossover region. The CFP gives even lower
distortion than the original EF-II output, with Figure 6.19 showing only the
result for single-pole compensation; in this case the improvement with twopole was marginal and the trace is omitted for clarity.
1. Ball, G Distorting Power Supplies Electronics & Wireless World, Dec
1990, p. 1084.
2. Cherry, A New Distortion Mechanism in Class-B Amplifiers Journ. Audio
Eng. Soc. May 1981, p. 327.
3. Baxandall, P Private communication, 1995.
4. Self, D Distortion In Power Amplifiers Series in Electronics & Wireless
World, Aug 93 to March 94.
5. Self, D An Advanced Preamplifier Wireless World, Nov 1976, p. 43.
Compensation, slew-rate,
and stability
Frequency compensation in general
The compensation of an amplifier is the tailoring of its open-loop gain and
phase characteristics so that is dependably stable when the global feedback
loop is closed.
It must be said straight away that compensation is a thoroughly misleading
word to describe the subject of this chapter. It implies that one problematic
influence is being balanced out by another opposing force, when in fact it
means the process of tailoring the open-loop gain and phase of an amplifier
so that it is satisfactorily stable when the global feedback loop is closed.
The derivation of the word is historical, going back to the days when all
servomechanisms were mechanical, and usually included an impressive
Watt governor pirouetting on top of the machinery.
An amplifier requires compensation because its basic open-loop gain is still
high at frequencies where the internal phase-shifts are reaching 180
degrees. This turns negative feedback into positive at high frequencies, and
causes oscillation, which in audio amplifiers can be very destructive. The
way to prevent this is to ensure that the loop gain falls to below unity before
the phase-shift reaches 180 degrees; oscillation therefore cannot develop.
Compensation is therefore vital simply because it makes the amplifier
stable; there are other considerations, however, because the way in which
the compensation is applied has a major effect on the closed-loop
distortion behaviour.
The distortion performance of an amplifier is determined not only by openloop linearity, but also the negative feedback factor applied when the loop
is closed; in most practical circumstances doubling the NFB factor halves
the distortion. So far I have assumed that open-loop gain falls at 6 dB/octave
due to a single dominant pole, with the amount of NFB permissible at HF
Audio Power Amplifier Design Handbook
being set by the demands of HF stability. We have seen that this results in
the distortion from a Blameless amplifier consisting almost entirely of
crossover artefacts, because of their high-order and hence high frequency.
Audio amplifiers using more advanced compensation are rather rare.
However, certain techniques do exist, and are described later.
This book sticks closely to conventional topologies, because even
apparently commonplace circuitry has proven to have little-known aspects,
and to be capable of remarkable linearity. This means the classical threestage architecture circuit with transconductance input, transimpedance
VAS, and unity-gain output stage. Negative feedback is applied globally,
but is smoothly transferred by Cdom to be local solely to the VAS as
frequency increases. Other configurations are possible; a two-stage
amplifier with transconductance input and unity-gain output is an
intriguing possibility – this is common in CMOS op-amps – but is probably
ill-suited to power-amp impedances. Another architecture with a voltagegain input stage is described in Chapter 11, and see Otala [1] for an
eccentric four-stage amplifier with a low open-loop gain of 52 dB (due to
the dogged use of local feedback) and only 20 dB of global feedback. Most
of this chapter relates only to the conventional three-stage structure.
Dominant-pole compensation
Dominant-pole compensation is the simplest kind, though its action is
subtle. Simply take the lowest pole to hand (P1), and make it dominant, i.e.
so much lower in frequency than the next pole P2 that the total loop-gain
(i.e. the open-loop gain as reduced by the attenuation in the feedback
network) falls below unity before enough phase-shift accumulates to cause
HF oscillation. With a single pole, the gain must fall at 6 dB/octave,
corresponding to a constant 90-degree phase shift. Thus the phase margin
will be 90 degrees, giving good stability.
Figure 7.1a shows the traditional Miller method of creating a dominant
pole. The collector pole of TR4 is lowered by adding the external Millercapacitance Cdom to that which unavoidably exists as the internal Cbc of
the VAS transistor. However, there are some other beneficial effects; Cdom
causes pole-splitting, in which the pole at TR2 collector is pushed up in
frequency as P1 is moved down – most desirable for stability. Simultaneously the local NFB through Cdom linearises the VAS.
Assuming that input-stage transconductance is set to a plausible 5 mA/V,
and stability considerations set the maximal 20 kHz open-loop gain to
50 dB, then from Equations 3.1–3.3 on pages 61 and 62, Cdom must be
125 pF. This is more than enough to swamp the internal capacitances of the
VAS transistor, and is a practical real-life value.
The peak current that flows in and out of this capacitor for an output of 20 V
rms at 20 kHz, is 447 µA. Since the input stage must sink Cdom current
Compensation, slew-rate, and stability
Figure 7.1
(a) The traditional
Miller method of
making a dominant
pole. (b) Shunt
compensation shows a
much less satisfactory
method – the addition
of capacitance to
ground from the VAS
collector. (c) Inclusive
Miller compensation.
(d) Two-pole
while the VAS collector-load sources it, and likewise the input stage must
source it while the VAS sinks it, there are four possible ways in which slewrate may be limited by inadequate current capacity; if the input stage is
properly designed then the usual limiting factor is VAS current-sourcing. In
this example a peak current of less than 0.5 ma should be easy to deal with,
and the maximum frequency for unslewed output will be comfortably
above 20 kHz.
Lag compensation
Figure 7.1b shows a much less satisfactory method of compensation – the
addition of capacitance to ground from the VAS collector. This is usually
called shunt or lag compensation, and as Peter Baxandall [2] aptly put it,
‘The technique is in all respects sub-optimal.’ We have already seen on
page 101 that loading the VAS collector resistively to ground is a very poor
option for reducing LF open-loop gain, and a similar argument shows that
capacitative loading to ground for compensation purposes is an even worse
Audio Power Amplifier Design Handbook
idea. To reduce open-loop gain at 20 kHz to 50 dB as before, the shunt
capacitor Clag must be 43.6 nF, which is a whole different order of things
from 125 pF. The current in and out of Clag at 20 V rms, 20 kHz, is 155 mA
peak, which is going to require some serious electronics to provide it. This
important result is yielded by simple calculation, confirmed by Spice
simulation. The input stage no longer constrains the slew-rate limits, which
now depend entirely on the VAS.
A VAS working under these conditions will have poor linearity. The lc
variations in the VAS, caused by the heavy extra loading, produce more
distortion and there is no local NFB through a Miller capacitor to correct it.
To make matters worse, the dominant pole P1 will probably need to be set
to a lower frequency than for the Miller case, to maintain the same stability
margins, as there is now no pole-splitting action to increase the frequency
of the pole at the input-stage collector. Hence Clag may have to be even
larger than 43 nF, requiring even higher peak currents.
Takahashi [3] has produced a fascinating paper on this approach, showing
one way of generating the enormous compensation currents required for
good slew-rates. The only thing missing is an explanation of why shunt
compensation was chosen in the first place.
Including the output stage: inclusive Miller compensation
Miller-capacitor compensation elegantly solves several problems at once,
and the decision to adopt it is simple. However the question of whether to
include the output stage in the Miller feedback loop is less easy. Such
inclusion (see Figure 7.1c) presents the alluring possibility that local
feedback could linearise both the VAS and the output stage, with just the
input stage left out in the cold as frequency rises and global NFB falls. This
idea is most attractive as it would greatly increase the total feedback
available to linearise a distortive Class-B output stage.
There is certainly some truth in this, as I have shown [4], where applying
Cdom around the output as well as the VAS reduced the peak (not rms)
1 kHz THD from 0.05% to 0.02%. However I must say that the output stage
was deliberately under-biased to induce crossover spikes, because with
optimal bias the improvement, although real, was too small to be either
convincing or worthwhile. A vital point is that this demonstration used a
model amplifier with TO-92 output transistors, because in my experience
the technique just does not work well with real power bipolars, tending to
intractable HF oscillation. There is evidence that inclusive compensation,
when it can be made stable, is much less effective at dealing with ordinary
crossover distortion than with the spikes produced by deliberate underbiasing.
The use of local NFB to linearise the VAS demands a tight loop with
minimal extra phase-shift beyond that inherent in the Cdom dominant pole.
Compensation, slew-rate, and stability
It is permissible to insert a cascode or a small-signal emitter-follower into this
local loop, but a sluggish output stage seems to be pushing luck too far; the
output stage poles are now included in the loop, which loses its dependable
HF stability. Bob Widlar [5] stated that output stage behaviour must be wellcontrolled up to 100 MHz for the technique to be reliable; this would appear
to be virtually impossible for discrete power stages with varying loads.
While I have so far not found Inclusive Miller-compensation to be useful
myself, others may know different; if anyone can shed further light I would
be most interested.
Nested feedback loops
Nested feedback is a way to apply more NFB around the output stage
without increasing the global feedback factor. The output has an extra
voltage gain stage bolted on, and a local feedback loop is closed around
these two stages. This NFB around the composite output bloc reduces
output stage distortion and increase frequency response, to make it safe to
include in the global NFB loop.
Suppose that bloc A1 (Figure 7.2a) is a Distortionless small-signal amplifier
providing all the open-loop gain and so including the dominant pole. A3 is
a unity-gain output stage with its own main pole at 1 MHz and distortion of
1% under given conditions; this 1 MHz pole puts a firm limit on the amount
of global NFB that can be safely applied. Figure 7.2b shows a nested-
Figure 7.2a
Normal single-loop
global negative
Figure 7.2b
Nested feedback
Audio Power Amplifier Design Handbook
feedback version; an extra gain-bloc A2 has been added, with local
feedback around the output stage. A2 has the modest gain of 20 dB so there
is a good chance of stability when this loop is closed to bring the gain of A3
+ A2 back to unity. A2 now experiences 20 dB of NFB, bringing the
distortion down to 0.1%, and raising the main pole to 10 MHz, which
should allow the application of 20 dB more global NFB around the overall
loop that includes A1. We have thus decreased the distortion that exists
before global NFB is applied, and simultaneously increased the amount of
NFB that can be safely used, promising that the final linearity could be very
good indeed. For another theoretical example see Pernici et al [6].
Real-life examples of this technique in power amps are not easy to find, but it
is widely used in op-amps. Many of us were long puzzled by the way that the
much-loved 5534 maintained such low THD up to high frequencies.
Contemplation of its enigmatic entrails appears to reveal a three-gain-stage
design with an inner Miller loop around the third stage, and an outer Miller
loop around the second and third stages; global NFB is then applied
externally around the whole lot. Nested Miller compensation has reached its
apotheosis in CMOS opamps – the present record appears [7] to be three
nested Miller loops plus the global NFB; don’t try this one at home. More
details on the theory of nested feedback can be found in Scott and Spears [8].
Two-pole compensation
Two-pole compensation is well-known as a technique for squeezing the
best performance from an op-amp [9], [10], but it has rarely been applied to
power amplifiers; the only example I know is found in Widlar [5]. An extra
HF time constant is inserted in the Cdom path, giving an open-loop gain
curve that initially falls at almost 12 dB/octave, but which gradually reverts
to 6 dB/octave as frequency continues to increase. This reversion is
arranged to happen well before the unity loop-gain line is reached, and so
stability should be the same as for the conventional dominant-pole scheme,
but with increased negative feedback over part of the operational
frequency range. The faster gain roll-off means that the maximum amount
of feedback can be maintained up to a higher frequency. There is no
measurable mid-band peak in the closed-loop response.
It is right to feel nervous about any manoeuvre that increases the NFB
factor; power amplifiers face varying conditions and it is difficult to be sure
that a design will always be stable under all circumstances. This makes
designers rather conservative about compensation, and I approached this
technique with some trepidation. However, results were excellent with no
obvious reduction in stability. See Figure 7.4 for the happy result of
applying this technique to the Class-B amplifier seen in Figure 7.5.
The simplest way to implement two-pole compensation is shown in Figure
7.1d, with typical values. Cp1 should have the same value as it would for
Compensation, slew-rate, and stability
stable single-pole compensation, and Cp2 should be at least twice as big;
Rp is usually in the region 1k–10k. At intermediate frequencies Cp2 has an
impedance comparable with Rp, and the resulting extra time-constant
causes the local feedback around the VAS to increase more rapidly with
frequency, reducing the open-loop gain at almost 12 dB/octave. At HF the
impedance of Rp is high compared with Cp2, the gain slope asymptotes
back to 6 dB/octave, and then operation is the same as conventional
dominant-pole, with Cdom equal to the series capacitance combination.
So long as the slope returns to 6 dB/octave before the unity loop-gain
crossing occurs, there seems no obvious reason why the Nyquist stability
should be impaired. Figure 7.3 shows a simulated two-pole open-loop gain
plot for realistic component values; Cp2 should be at least twice Cp1 so the
gain falls back to the 6 dB/octave line before the unity loop-gain line is
crossed. The potential feedback factor has been increased by more than
20 dB from 3 kHz to 30 kHz, a region where THD tends to increase due to
falling NFB. The open-loop gain peak at 8 kHz looks extremely dubious,
but I have so far failed to detect any resulting ill-effects in the closed-loop
There is however a snag to the approach shown here, which reduces the
linearity improvement. Two-pole compensation may decrease open-loop
linearity at the same time as it raises the feedback factor that strives to
correct it. At HF, Cp2 has low impedance and allows Rp to directly load the
VAS collector to ground; as we have seen, this worsens VAS linearity.
Figure 7.3
The open-loop gain
plot for two-pole
compensation with
realistic component
Audio Power Amplifier Design Handbook
Figure 7.4
Distortion reduction
with two-pole
However, if Cp2 and Rp are correctly proportioned the overall reduction in
distortion is dramatic and extremely valuable. When two-pole compensation was added to the amplifier circuit shown in Figure 7.5, the crossover
glitches on the THD residual almost disappeared, being partially replaced
by low-level second harmonic which almost certainly results from VAS
loading. The positive slew-rate will also be slightly reduced.
This looks like an attractive technique, as it can be simply applied to an
existing design by adding two inexpensive components. If Cp2 is much
larger than Cp1, then adding/removing Rp allows instant comparison
between the two kinds of compensation. Be warned that if an amplifier is
prone to HF parasitics then this kind of compensation may worsen them.
Output networks
The usual output networks for a power amplifier are shown in Figure 7.6,
with typical values. They comprise a shunt Zobel network, for stability into
inductive loads, and a series output inductor/damping resistor for stability
into capacitive loads.
Amplifier output impedance
The main effect of output impedance is usually thought to be its effect on
Damping Factor. This is wrong, as explained in Chapter 1. Despite this
demonstration of its irrelevance, I will refer to Damping Factor here, to
show how an apparently impressive figure dwindles as more parts of the
speaker-cable system are included.
Figure 7.5
The Class-B amplifier
from Chapter 6. At the
simplest level the
maximum slew-rate is
defined by the current
source TR1 and the
value of Cdom
Audio Power Amplifier Design Handbook
Figure 7.6
The amplifier-cable-speaker system. Simplified amplifier with Zobel network and damped output inductor, and
a resistive load. Cable resistance and inductance values are typical for a 5 metre length
Figure 7.6 shows a simplified amplifier with Zobel network and series
output inductor, plus simple models of the connecting cable and speaker
load. The output impedance of a solid-state amplifier is very low if even a
modest amount of global NFB is used. I measured a Blameless Class-B
amplifier similar to Figure 7.5 with the usual NFB factor of 29 dB at 20 kHz,
increasing at 6 dB/octave as frequency falls. Figure 7.7 shows the output
impedance at point B before the output inductor, measured by injecting a
10 mA signal current into the output via a 600 resistance.
Figure 7.7
Output impedance of
a Blameless amplifier,
with and without
6 µH output inductor.
Adding the inductor
(upper trace)
increases both the
flat LF output
impedance, due to
its series resistance,
and the rising HF
Compensation, slew-rate, and stability
The low-frequency output impedance is approx 9 m (an 8 Damping
Factor of 890). To put this into perspective, one metre of thick 32/02
equipment cable (32 strands of 0.2 mm diameter) has a resistance of
16.9 m. The internal cabling resistance in an amplifier can equal or
exceed the output impedance of the amplifier itself at LF.
Output impedance rises at 6 dB/octave above 3 kHz, as global NFB falls off,
reaching 36 m at 20 kHz. The 3 kHz break frequency does not correspond
with the amplifier dominant pole frequency, which is much lower at
around 10 Hz.
The closed-loop output impedance of any amplifier is set by the open-loop
output impedance and the negative feedback factor. The output impedance
is not simply the output impedance of the output stage alone, because the
latter is driven from the VAS, so there is a significant and frequency-varying
source impedance at point A in Figure 7.6.
When the standard EF and CFP stages are driven from a zero-impedance
source, in both cases the raw output impedance is in the region of
150–180 m. This assumes the emitter resistors Re are 0.1 . Increasing Re
to 0.22 increases output impedance to the range 230–280 m, showing
that these resistors in fact make up most of the output impedance. The
output devices and drivers have little influence.
If the average open-loop output impedance is 200 m, and the NFB factor
at 20 kHz is 29 dB, or 28 times, we would expect a closed-loop output
impedance of approximately 200/28, which is 7 m. Since it is actually
about 33 m at this frequency, there is clearly more going on than simple
theory implies. In a real amplifier the output stage is not driven from a zero
impedance, but a fairly high one that falls proportionally with frequency;
for my Blameless Class-B design it falls from 3 k at 1 kHz to about 220 at 20 kHz. A 220 source impedance produces an open-loop output
impedance of about 1 , which when reduced by a factor of 28 when
global feedback is applied, gives 35 m. This is close to the value
measured at 20 kHz at point B in Figure 7.6.
All of these measured closed-loop output impedances are very low
compared with the other impedances in the amp-cable-speaker system. It
would appear they can in most cases be ignored.
The Blameless amplifier design shown on page 176 has an output inductor
of approx. 6 µH; the aim is absolutely guaranteed stability into all
capacitative loads, and the inductance is therefore at the high end of the
permissible range. This is limited by the HF roll-off into the lowest load
resistance to be driven. This substantial component comprises 20 turns of
1.5 mm diam. copper wire, wound to 1 inch diameter, and has a DC
resistance of 19 m. This small extra resistance raises the flat section of the
impedance plot to 24 m, and in fact dominates the LF output impedance
Audio Power Amplifier Design Handbook
as measured at the amplifier terminals (point C). It also sharply reduces the
notional Damping Factor from 890 to 330.
Naturally the inductance of the coil pushes the rising portion of the
impedance curve higher. The output impedance now starts to rise from
700 Hz, still at 6 dB per octave, reaching 0.6 at 20 kHz. See Figure 7.7.
Minimising amplifier output impedance
This issue is worth considering, not because it optimises speaker dynamics,
which it doesn’t, but because it minimises frequency response variations due
to varying speaker impedance. There is also, of course, specmanship to be
It is clear from Figure 7.7 that the output impedance of a generic amplifier
will very probably be less than the inductor resistance, so the latter should be
attended to first. Determine the minimum output inductance for stability
with capacitive loads, because lower inductance means fewer turns of wire
and less resistance. Some guidance on this is given in the next section. Note,
however, that the inductance of the usual single-layer coil varies with the
square of the number of turns, so halving the inductance only reduces the
turns, and hence the series resistance, by root-two. The coil wire must be as
thick as the cost/quality tradeoffs allow.
It is also desirable to minimise the resistance of the amplifier internal wiring,
and to carefully consider any extra resistance introduced by output relays,
speaker switching, etc. When these factors have been reduced as far as cost
and practicality allow, it is likely that the output impedance of the actual
amplifier will still be the smallest component of the total.
Zobel networks
All power amplifiers except for the most rudimentary kinds include a Zobel
network in their arrangements for stability. This simple but somewhat
enigmatic network comprises a resistor and capacitor in series from the
amplifier output rail to ground. It is always fitted on the inside (i.e. upstream)
of the output inductor, though a few designs have a second Zobel network
after the output inductor; the thinking behind this latter approach is obscure.
The resistor approximates to the expected load impedance, and is usually
between 4.7 and 10 . The capacitor is almost invariably 100 nF, and these
convenient values and their constancy in the face of changing amplifier
design might lead one to suppose that they are not critical; in fact experiment
suggests that the real reason is that the traditional values are just about right.
The function of the Zobel network (sometimes also called a Boucherot cell)
is rarely discussed, but is usually said to prevent too inductive a reactance
being presented to the amplifier output by a loudspeaker voice-coil, the
implication being that this could cause HF instability. It is intuitively easy to
Compensation, slew-rate, and stability
see why a capacitative load on an amplifier with a finite output resistance
could cause HF instability by introducing extra lagging phase-shift into the
global NFB loop, but it is less clear why an inductive load should be a
problem; if a capacitive load reduces stability margins, then it seems
reasonable that an inductive one would increase them.
At this point I felt some experiments were called for, and so I removed the
standard 10 /0.1 µF Zobel from a Blameless Class-B amplifier with CFP
output and the usual NFB factor of 32 dB at 20 kHz. With an 8 resistive
load the THD performance and stability were unchanged. However, when
a 0.47 mH inductor was added in series, to roughly simulate a single-unit
loudspeaker, there was evidence of local VHF instability in the output
stage; there was certainly no Nyquist instability of the global NFB loop.
I also attempted to reduce the loading placed on the output by the Zobel
network. However, increasing the series resistance to 22 still gave some
evidence of stability problems, and I was forced to the depressing
conclusion that the standard values are just about right. In fact, with the
standard 10 /0.1 µF network the extra loading placed on the amplifier at
HF is not great; for a 1 V output at 10 kHz the Zobel network draws 6.3 mA,
rising to 12.4 mA at 20 kHz, compared with 125 mA drawn at all
frequencies by an 8 resistor. These currents can be simply scaled up for
realistic output levels, and this allows the Zobel resistor power rating to be
determined. Thus an amplifier capable of 20 Vrms output must have a
Zobel resistor capable of sustaining 248 mA rms at 20 kHz, dissipating
0.62 W; a 1 W component could be chosen.
In fact, the greatest stress is placed on the Zobel resistor by HF instability, as
amplifier oscillation is often in the range 50–500 kHz. It should therefore be
chosen to withstand this for at least a short time, as otherwise faultfinding
becomes rather fraught; ratings in the range 3 to 5 W are usual.
To conclude this section, there seems no doubt that a Zobel network is
required with any load that is even mildly inductive. The resistor can be of
an ordinary wire-wound type, rated to 5 W or more; this should prevent its
burn-out under HF instability. A wire-wound resistor may reduce the
effectiveness of the Zobel at VHF, but seems to work well in practice; the
Zobel still gives effective stabilisation with inductive loads.
Output inductors
Only in the simplest kinds of power amplifier is it usual for the output stage
to be connected directly to the external load. Direct connection is generally
only feasible for amplifiers with low feedback factors, which have large
safety margins against Nyquist instability caused by reactive loads.
For many years designers have been wary of what may happen when a
capacitive load is connected to their amplifiers; a fear that dates back to the
Audio Power Amplifier Design Handbook
introduction of the first practical electrostatic loudspeaker from Quad
Acoustics, which was crudely emulated by adding a 2 µF capacitor in
parallel to the usual 8 resistive test load. The real load impedance
presented by an electrostatic speaker is far more complex than this, largely
as a result of the step-up transformer required to develop the appropriate
drive voltages, but a 2 µF capacitor alone can cause instability in an
amplifier unless precautions are taken.
When a shunt capacitor is placed across a resistive load in this way, and no
output inductor is fitted, it is usually found that the value with the most
destabilising effect is nearer 100 nF than 2 µF.
The most effective precaution against this form of instability is a small aircored inductor in series with the amplifier output. This isolates the amplifier
from the shunt capacitance, without causing significant losses at audio
frequencies. The value is normally in the region 1–7 µH, the upper limit
being set by the need to avoid significant HF roll-off into a 4 load. If 2 loads are contemplated then this limit must be halved.
It is usual to test amplifier transient response with a square-wave while the
output is loaded with 8 and 2 µF in parallel to simulate an electrostatic
loudspeaker, as this is often regarded as the most demanding condition.
However, there is an inductor in the amplifier output, and when there is
significant capacitance in the load they resonate together, giving a peak in
the frequency response at the HF end, and overshoot and ringing on fast
This test therefore does not actually examine amplifier response at all, for
the damped ringing that is almost universally seen during these capacitive
loading tests is due to the output inductor resonating with the test load
capacitance, and has nothing whatever to do with amplifier stability. The
ringing is usually around 40 kHz or so, and this is much too slow to be
blamed on any normally compensated amplifier. The output network adds
ringing to the transient response even if the amplifier itself is perfect.
It is good practice to put a low-value damping resistor across the inductor;
this reduces the Q of the output LC combination on capacitive loading, and
thus reduces overshoot and ringing.
If a power amplifier is deliberately provoked by shorting out the output
inductor and applying a capacitive load, then the oscillation is usually
around 100–500 kHz, and can be destructive of the output transistors if
allowed to persist. It is nothing like the neat ringing seen in typical
capacitive load tests. In this case there is no such thing as nicely damped
ringing because damped oscillation at 500 kHz probably means you are
one bare step away from oscillatory disaster.
Attempts to test this on the circuit of Figure 7.5 were frustrated because it
is actually rather resistant to capacitance-induced oscillation, probably
Compensation, slew-rate, and stability
because the level of global feedback is fairly modest. 100 nF directly across
the output induced damped ringing at 420 kHz, while 470 nF gave ringing
at 300 kHz, and 2 µF at 125 kHz.
While the 8 /2 µF test described above actually reveals nothing about
amplifier transient response, it is embedded in tradition, and it is too
optimistic to expect its doubtful nature to be universally recognised.
Minimising output ringing is of some commercial importance; several
factors affect it, and can be manipulated to tidy up the overshoot and avoid
deterring potential customers:
The output inductance value. Increasing the inductance with all other
components held constant reduces the overshoot and the amount of
response peaking, but the peak moves downward in frequency so the
rising response begins to invade the audio band. See Figures 7.8, 7.9.
The value of the damping resistor across the output coil. Reducing its
value reduces the Q of the output LC tuned circuit, and so reduces
overshoot and ringing. The resistor is usually 10 , and can be a
conventional wirewound type without problems due to self-inductance;
10 reduces the overshoot from 58% without damping to 48%, and
much reduces ringing. Response peaking is reduced with only a slight
effect on frequency. See Figures 7.10, 7.11. The damping resistor can in
fact be reduced as to low as 1 , providing the amplifier stability into
capacitance remains dependable, and this reduces the transient overshoot further from 48% to 19%, and eliminates ringing altogether; there
Figure 7.8
Transient response
with varying output
increasing L reduces
ringing frequency,
without much effect
on overshoot. Input
risetime 1 µsec
Audio Power Amplifier Design Handbook
Figure 7.9
Increasing the output
inductance reduces
frequency response
peaking and lowers
its frequency
Figure 7.10
The effect of varying
the damping
resistance on
transient response.
1 almost eliminates
Compensation, slew-rate, and stability
Figure 7.11
The effect of varying
damping resistance
on frequency
response. Lower
values reduce the
peaking around
40 kHz
is just a single overshoot. Whether this is more visually appealing to the
potential customer is an interesting point.
The load capacitance value. Increasing this with the shunt resistor held
at 8 gives more overshoot and lower frequency ringing that decays
more slowly. The response peaking is both sharper and lower in
frequency, which is not a good combination. However, this component
is part of the standard test load and is outside the designer’s control. See
Figures 7.12, 7.13.
In actual fact, by far the most important factor affecting overshoot and
ringing is the rise-time of the applied square wave. This is yet another
rather important audio fact that seems to be almost unknown. Figure
7.14 shows how the overshoot given by the circuit in Figure 7.6 is 51%
for a 1 µsec rise-time, but only 12% for a 20 µsec rise-time. It is clear that
the transient response measured in this test may depend critically on the
details of the testgear and the amplifier slew-rate, and can be
manipulated to give the result you want.
An output inductor should be air-cored to eliminate the possibility of extra
distortion due to the saturation of magnetic materials. Ferrite-based VHF
chokes give stable operation, but their linearity must be considered
dubious. In the 1970s there was a fashion for using one of the big powersupply electrolytics as a coil-former, but this is not a good idea. The
magnetic characteristics of the capacitor are unknown, and its lifetime may
be reduced by the heat dissipated in the coil winding resistance.
Audio Power Amplifier Design Handbook
Figure 7.12
Increasing the load
increases the
transient overshoot,
while lowering its
Figure 7.13
Increasing the load
increases frequency
response peaking
and lowers its
Compensation, slew-rate, and stability
Figure 7.14
The most important
factor in transient
response is actually
the rise-time of the
square-wave input,
especially for
percentage. The
ringing frequency is
The resistance of an air-cored 7 µH coil made from 20 turns of 1.5 mm
diameter wire (this is quite a substantial component 3 cm in diameter and
6 cm long) is enough to cause a measurable power loss into a 4 load, and
to dominate the output impedance as measured at the amplifier terminals.
The coil wire should therefore be as thick as your cost/quality tradeoffs
The power rating for the damping resistor is assessed as follows. For a
resistive 8 load the voltage across the output inductor increases slowly
with frequency, and the damping resistor dissipation only reaches 1.2 mW
at 20 kHz for 1 Vrms output. This assumes a normal 10 damping resistor;
if the value is reduced to 1 to eliminate ringing into capacitive loads, as
described above, then the dissipation is ten times as great at 12 mW.
A much greater potential dissipation occurs when the load is the traditional
8 /2 µF combination. The voltage across the output inductor peaks as it
resonates with the load capacitance, and the power dissipated in a 10 damping resistor at resonance is 0.6 W for 1 Vrms. This is however at an
ultrasonic frequency (around 50 kHz with a 7 µH inductor) and is a fairly
sharp peak, so there is little chance of musical signals causing high
dissipation in the resistor in normal use. However, as for the Zobel network,
some allowance must be made for sinewave testing and oscillatory faults,
so the damping resistor is commonly rated at between 1 and 5 W. An
ordinary wirewound component works well with no apparent problems
due to self-inductance.
Audio Power Amplifier Design Handbook
The output inductor value
As mentioned above, the output inductor for all my designs started out at
20 turns and approx. 6 µH. In later tests the inductor was cut in half, now
measuring 2.3 µH inductance and 10.1 m DC resistance; this component
was stable for all capacitor values, but has not had rigorous testing with real
loudspeakers. It does now look more like an ‘average’ amplifier inductor,
rather than an oversized one.
An alternative method of stabilisation is a series resistor instead of the
inductor. Even with 100 nF loading, a OR1 wirewound output resistor
completely removed ringing on the amplifier output. This is cheaper, but
obviously less efficient than an inductor, as 100 m of extra resistance has
been introduced instead of 10 m with the new 2.3 µH inductor. The
Damping Factor with OR1 cannot exceed 80. A more important objection
is that the 4 output power appears to be significantly reduced – a
200 W/4 amplifier is reduced to a 190 W unit, which doesn’t look so
good in the specs, even though the reduction in perceived loudness is
Cable effects
Looking at the amplifier-cable-load system as a whole, the amplifier and
cable impedances have the following effects with an 8 resistive load:
A constant amplitude loss due to the cable resistance forming a potential
divider with the 8 load. The resistive component from the amplifier
output is usually negligible.
A high-frequency roll-off due to the cable inductance forming an LR
lowpass filter with the 8 load. The amplifier’s output inductor (to give
stability with capacitative loads) adds directly to this to make up the total
series inductance. The shunt capacitance of any normal speaker cable is
trivially small, and can have no significant effect on frequency response
or anything else.
The main factors in speaker cable selection are therefore series resistance
and inductance. If these parameters are below 100 m and 3 µH, any
effects will be imperceptible. This can be met by 13 amp mains cable,
especially if all three conductors are used.
If the amplifier is connected to a typical loudspeaker rather than a pure
resistance the further effects are:
The frequency response of the voltage at the loudspeaker terminals
shows small humps and dips as the uneven speaker impedance loads
the series combination of amplifier output impedance and cable
The variable loading affects the amplifier distortion performance. HF
crossover distortion reduces as load resistance increases above 8 ; even
Compensation, slew-rate, and stability
68 loading increases HF distortion above the unloaded condition. For
heavier loading than 8 , crossover may continue to increase, but this is
usually masked by the onset of Large Signal Non-linearity [16].
Severe dips in impedance may activate the overload protection circuitry
unexpectedly. Signal amplitudes are higher at LF so impedance dips here
are potentially more likely to draw enough current to trigger protection.
Crosstalk in amplifier output inductors
When designing a stereo power amplifier, the issue of interchannel
crosstalk is always a concern. Now that amplifiers with up to seven
channels for home theatre are becoming more common, the crosstalk issue
is that much more important, if only because the channels are likely to be
more closely packed. Here I deal with one aspect of it. Almost all power
amplifiers have output coils to stabilise them against capacitative reactances, and a question often raised is whether inductive coupling between
the two is likely to degrade crosstalk. It is sometimes suggested that the
coils – which are usually in solenoid form, with length and diameter of the
same order – should be mounted with their axes at right angles rather than
parallel, to minimise coupling. But does this really work?
I think I’m pretty safe in saying there is no published work on this, so it was
time to make some. The coil coupling could no doubt be calculated
(though not by me) but as often in the glorious pursuit of electronics, it was
quicker to measure it.
The coils I used were both of 14 turn of 1 mm diameter copper wire, overall
length 22 mm and diameter 20 mm. This has an inductance of about 2 µH,
and is pretty much an ‘average’ output coil, suitable for stabilising
amplifiers up to about 150 W/8 . Different coils will give somewhat
different results, but extrapolation to whatever component you are using
should be straightforward; for example, twice the turns on both coils means
four times the coupling.
Figure 7.15 shows the situation in a stereo power amplifier. The field
radiated due to the current in Coil A is picked up by Coil B and a crosstalk
voltage added to the output signal at B.
Figure 7.16 shows the experimental setup. Coil A is driven from a signal
generator with a source impedance of 50 , set to 5 V rms. Virtually all of
this is dropped across the source resistance, so Coil A is effectively driven
with a constant current of 100 mA rms.
Figure 7.17 shows the first result, taken with the coils coaxial and the ends
touching. (This proved, as expected, to be the worst case for coupling.) The
crosstalk rises at 6 dB/octave, because the voltage induced in Coil B is
proportional to the rate of change of flux, and the magnitude of peak flux
is fixed. This is clearly not the same as conventional transformer action,
Audio Power Amplifier Design Handbook
Figure 7.15
(a) The coupling of
output coils in a stereo
power amplifier.
(b) The experimental
circuit. The
‘transmitting’ Coil A is
driven with an
effectively constant
current, and the
voltage across the
‘receiving’ Coil B
Figure 7.16
The physical coil
configuration for the
measurement of
coaxial coils
Figure 7.17
Crosstalk vs spacing
for coaxial coils
Compensation, slew-rate, and stability
where the frequency response is flat. In a transformer the primary
inductance is much greater than the circuit series impedance, so the
magnetic flux that couples with the secondary halves when the input
frequency doubles, and the voltage induced in the secondary is constant.
The crosstalk at 20 kHz was taken as the 0 dB reference. This represented
2.4 mV rms across Coil B. 100 mA rms in Coil A corresponds to 800 mV rms
across an 8 load, so this gives a final crosstalk figure from channel to
channel of –54 dB at 20 kHz. It carries on deteriorating above 20 kHz but
no one can hear it. All crosstalk figures given below are at 20 kHz.
The coils were then separated 10 mm at a time, and with each increment the
crosstalk dropped by 10 dB, as seen in Figure 7.17. At 110 mm spacing,
which is quite practical for most designs, the crosstalk had fallen by 47 dB
from the reference case, giving an overall crosstalk of 54 + 47 = 101 dB total.
This is a very low level, and at the very top of the audio band. At 1 kHz, where
the ear is much more sensitive, the crosstalk will be some 25 dB less, which
brings it down to –126 dB total which I can say with some confidence is not
going to be a problem. This is obtained with what looks like the least
favourable orientation of coils. Coil–coil coupling is –32 dB at 50 mm, and
the figure at this spacing will be used to compare the configurations.
The next configuration tested was that of Figure 7.18, where the coils have
parallel axes but are displaced to the side. The results are in Figure 7.19; the
crosstalk is now –38 dB at 50 mm. With each 10 mm spacing increment the
crosstalk dropped by 7 dB. This setup is worse than the crossed-axis version
but better than the coaxial one.
The final configurations had the axes of the coils at 90 degrees; the crossedaxis condition. The base position is with the corners of the coils touching;
see Figure 7.20 When the coil is in the position X, still touching, crosstalk
almost vanishes as there is a cancellation null. With the coils so close, this
is a very sharp null and exploiting it in quantity production is quite
Figure 7.18
The coil configuration
for non-coaxial
parallel-axis coils
Audio Power Amplifier Design Handbook
Figure 7.19
Crosstalk vs spacing
for parallel-axis coils
impractical. The slightest deformation of either coil ruins the effect. Moving
the Coil A away from B again gives the results in Figure 7.21. The crosstalk
is now –43 dB at 50 mm, only an improvement of 11 dB over the coaxial
case; turning coils around is clearly not as effective as might be supposed.
This time, with each 10 mm spacing increment the crosstalk dropped by
8 dB rather than 10 dB.
The obvious next step is to try combining distance with cancellation as in
Figure 7.22. This can give a good performance even if a large spacing is not
possible. Figure 7.23 shows that careful coil positioning can give crosstalk
better than –60 dB (–114 dB total) across the audio band, although the
spacing is only 20 mm. The other curves show the degradation of
performance when the coil is misaligned by moving it bodily sideways by
1, 2, 3 and 4 mm; just a 2 mm error has worsened crosstalk by 20 dB at
20 kHz. Obviously in practice the coil PCB hole won’t move – but it is very
possible that coils will be bent slightly sideways in production.
Figure 7.20
The coil configuration
for crossed-axis
Compensation, slew-rate, and stability
Figure 7.21
Crosstalk vs spacing
for crossed-axis coils
Figure 7.24 gives the same results for a 50 mm spacing, which can usually
be managed in a stereo design. The null position once more just gives the
noise floor across the band, and a 2 mm misalignment now only worsens
things by about 5 dB. This is definitely the best arrangement if the spacing
is limited.
Coil orientation can help. Simply turning one coil through 90 degrees gives
an improvement of only 11 dB, but if it is aligned to cancel out the
coupling, there is a big improvement. See how –38 dB in Figure 7.19
becomes –61 dB in Figure 7.24 at 20 kHz. On a typical stereo amplifier
Figure 7.22
The coil configuration
for crossed-axis with
Audio Power Amplifier Design Handbook
Figure 7.23
Crosstalk vs alignment
for crossed-axis coils
spaced at 20 mm,
using cancellation
PCB, the coils are likely to be parallel – probably just for the sake of
appearance – but their spacing is unlikely to be less than 50 mm unless the
output components have been deliberately grouped together. As with
capacitative crosstalk, physical distance is cheaper than anything else, and
if the results are not good enough, use more of it. In this case the overall
crosstalk at 20 kHz will be 54 + 38 = –92 dB total, which is probably
Figure 7.24
Crosstalk vs alignment
for crossed-axis coils
spaced at 50 mm,
using cancellation
Compensation, slew-rate, and stability
already well below other forms of interchannel crosstalk. A quick quarterturn of the coil improves this to at least –114 dB. It should do.
Reactive loads and speaker simulation
Amplifiers are almost universally designed and tested running into a purely
resistive load, although they actually spend their working lives driving
loudspeakers, which contain both important reactive components and also
electromechanical resonances. At first sight this is a nonsensical situation;
however, testing into resistive loads is neither naive nor an attempt to avoid
the issue of real loads; there is in fact little alternative.
Loudspeakers vary greatly in their design and construction, and this is
reflected in variations in the impedance they present to the amplifier on
test. It would be necessary to specify a standard speaker for the results from
different amplifiers to be comparable. Secondly, loudspeakers have a
notable tendency to turn electricity into sound, and the sinewave testing of
a 200 W amplifier would be a demanding experience for all those in
earshot; soundproof chambers are not easy or cheap to construct. Thirdly,
such a standard test speaker would have to be capable of enormous powerhandling if it were to be able to sustain long-term testing at high power;
loudspeakers are always rated with the peak/average ratio of speech and
music firmly in mind, and the lower signal levels at high frequencies are
also exploited when choosing tweeter power ratings. A final objection is
that loudspeakers are not noted for perfect linearity, especially at the LF
end, and if the amplifier does not have a very low output impedance this
speaker non-linearity may confuse the measurement of distortion. Amplifier
testing would demand a completely different sort of loudspeaker from that
used for actually listening to music; the market for it would be very, very
small, so it would be expensive.
Resistive loads
Amplifiers are normally developed through 8 and 4 testing, though
intermediate values such as 5.66 (the geometric mean of 8 and 4) are
rarely explored considering how often they occur in real use. This is
probably legitimate in that if an amplifier works well at 8 and 4 it is most
unlikely to give trouble at intermediate loadings. In practice few nominal
8 speakers have impedance dips that go below 5 , and design to 4 gives a safety margin, if not a large one.
The most common elaboration on a simple resistive load is the addition of
2 µF in parallel with 8 to roughly simulate an electrostatic loudspeaker;
this is in fact not a particularly reactive load, for the impedance of a 2 µF
capacitor only becomes equal to the resistance at 9.95 kHz, so most of the
audio band is left undisturbed by phase shift. This load is in fact a worse
approximation to a moving-coil speaker than is a pure resistance.
Audio Power Amplifier Design Handbook
Modelling real loudspeaker loading
The impedance curve of a real loudspeaker may be complex, with multiple
humps and dips representing various features of the speaker. The resonance
in the bass driver unit will give a significant hump in LF impedance, with
associated phase changes. Reflex (ported enclosure) designs have a
characteristic double-hump in the LF, with the middle dip corresponding to
the port tuning. The HF region is highly variable, and depends in a
complicated fashion on the number of drive units, and their interactions
with the crossover components.
Connection of an amplifier to a typical speaker impedance rather than a
resistance has several consequences:
The frequency response, measured in terms of the voltage across the
loudspeaker terminals, shows small humps and bumps due to the
uneven impedance loading the series combination of amplifier output
impedance and connecting cable resistance.
Severe dips in impedance may activate the overload protection circuitry
prematurely. This has to be looked at in terms of probability, because a
high amplitude in a narrow frequency band may not occur very often,
and if it does it may be so brief that the distortion generated is not
perceptible. Amplitudes are higher at LF and so impedance dips here are
potentially more serious.
The variable loading affects the distortion performance.
Figure 7.25 shows how the HF crossover distortion varies with load
resistance for loads lighter than those usually considered. Even 68 loading increases HF distortion.
Figure 7.25
The reduction of HF
THD as resistive
amplifier loading is
made lighter than 8 210
Compensation, slew-rate, and stability
Figure 7.26
Electrical model of a
single speaker unit in a
sealed enclosure
Figure 7.26 shows an electrical model of a single full-range loudspeaker
unit. While a single-driver design is unlikely to be encountered in hi-fi
applications, many PA, disco and sound reinforcement applications use
full-range drive units, for which this is a good model. Rc and Lc represent
the resistance and inductance of the voicecoil. Lr and Cr model the
electromechanical resonance of the cone mass with the suspension
compliance and air-spring of the enclosure, with Rr setting the damping;
these last three components have no physical existence, but give the same
impedance characteristics as the real resonance.
The input impedance magnitude this network presents to an amplifier is
shown in Figure 7.27. The peak at 70 Hz is due to the cone resonance;
without the sealed enclosure, the restoring force on the cone would be less
Figure 7.27
Input impedance of
single speaker unit
Audio Power Amplifier Design Handbook
and the free-air resonance would be at a lower frequency. The rising
impedance above 1 kHz is due to the voicecoil inductance Lc.
When the electrical model of a single-unit load replaces the standard 8 resistive load, something remarkable happens; HF distortion virtually
disappears, as shown in Figure 7.28. This is because a Blameless amplifier
driving 8 only exhibits crossover distortion, increasing with frequency as
the NFB factor falls, and the magnitude of this depends on the current
drawn from the output stage; with an inductive load this current falls at high
Most hi-fi amplifiers will be driving two-way or three-way loudspeaker
systems, and four-way designs are not unknown. This complicates the
impedance characteristic, which in a typical two-way speaker looks
something like Figure 7.29, though the rise above 10 kHz is often absent.
The bass resonance remains at 70 Hz as before, but there are two drive
units, and hence two resonances. There is also the considerable complication of a crossover network to direct the HF to the tweeter and the LF to the
low-frequency unit, and this adds several extra variables to the situation. In
a bass reflex design the bass resonance hump may be supplemented by
another LF resonant peak due to the port tuning. An attempt at a
representative load simulator for a two-way infinite-baffle loudspeaker
system is shown in Figure 7.30. This assumes a simple crossover network
without compensation for rising tweeter coil impedance, and is partially
based on a network proposed by Ken Kantnor in Atkinson [11].
Some loudspeaker crossover designs include their own Zobel networks,
typically placed across the tweeter unit, to compensate for the HF rise in
impedance due to the voicecoil inductance. If these Zobels are placed
there to terminate the crossover circuitry in a roughly resistive load, then
the loudspeaker designer has every right to do it; electroacoustic design is
Figure 7.28
The reduction of HF
THD with an inductive
load; adding 330 µH
in series with the 8 reduces the 20 kHz
THD by more than four
Compensation, slew-rate, and stability
Figure 7.29
The circuit of the 2-way
speaker model
quite difficult enough without adding extra restrictions. However, if they
are incorporated simply to make the impedance curve look tidier, and
allow a claim that the load has been made easier for the amplifier to drive,
then this seems misguided. The actual effect is the opposite; a typical
amplifier has no difficulty driving an inductive reactance, and the HF
crossover distortion can be greatly reduced when driving a load with an
impedance that rises above the nominal value at HF.
This is only an introduction to the huge subject of real amplifier loads.
More detailed information is given in Benjamin [12].
Figure 7.30
The circuit of the 2-way
speaker model
Audio Power Amplifier Design Handbook
Loudspeaker loads and output stages
There is a common assumption that any reactive load is more difficult for
an amplifier to drive than a purely resistive one; however, it is devoutly to
be wished that people would say what they mean by ‘difficult’. It could
mean that stability margins are reduced, or that the stresses on the output
devices are increased. Both problems can exist, but I suspect that this belief
is rooted in anthropomorphic thinking. It is easy to assume that if a signal
is more complex to contemplate, it is harder for an amplifier to handle. This
is not, however, true; it is not necessary to understand the laws of physics
to obey them. Everything does anyway.
When solid-state amplifiers show instability it is always at ultrasonic
frequencies, assuming we are not grappling with some historical curiosity
that has AC coupling in the forward signal path. It never occurs in the
middle of the audio band although many loudspeakers have major
convulsions in their impedance curves in this region. Reactive loading can
and does imperil stability at high frequencies unless precautions are taken,
usually in the form of an output inductor. It does not cause oscillation or
ringing mid-band.
Reactive loads do increase output device stresses. In particular peak power
dissipation is increased by the altered voltage/current phase relationships in
a reactive load.
Single-speaker load
Considering a single speaker unit with the equivalent circuit of Figure 7.26,
the impedance magnitude never falls below the 8 nominal value, and is
much greater in some regions; this suggests the overall amplifier power
dissipation would be less than for an 8 resistive load.
Unfortunately this is not so; the voltage/current phase relationship brought
about by the reactive load is a critical factor. When a pure resistance is
driven, the voltage across the output device falls as the current through it
rises, and they never reach a maximum at the same time. See Figure 7.31,
for Class-B with an 8 resistive load. The instantaneous power is the
product of instantaneous current and voltage drop, and in Class-B has a
characteristic two-horned shape, peaking twice at 77 W during its
conducting half-cycle.
When the single-speaker load is driven at 50 Hz, the impedance is a mix of
resistive and inductive, at 8.12 + 3.9 j. Therefore the current phase-lags
the voltage, altering the instantaneous product of voltage and power to that
shown in Figure 7.32. The average dissipation over the Class-B half-cycle
is slightly reduced, but the peak instantaneous power increases by 30% due
to the voltage/current phase shift. This could have serious results on
amplifier reliability if not considered at the design stage. Note that this
Compensation, slew-rate, and stability
Figure 7.31
Instantaneous Vce, Ic,
and Pdiss in an output
transistor driving 8 to
40 V peak at 50 Hz,
from +/–50 V rails.
Device dissipation
peaks twice at 77
watts in each half-cycle
Figure 7.32
As Figure 7.31, but
driving 50 Hz into the
single-speaker load. At
this frequency the load
is partly inductive so
current lags voltage
and the instantaneous
power curve is
asymmetrical, peaking
higher at 110 watts
towards the end of the
Audio Power Amplifier Design Handbook
impedance is equivalent at 50 Hz only to 8.5 in series with 10.8 mH.
Trying to drive this replacement load at any other frequency, or with a nonsine waveform, would give completely wrong results. Not every writer on
this topic appears to appreciate this.
Similarly, if the single-speaker load is driven at 200 Hz, on the other side of
the resonance peak, the impedance is a combination of resistive and
capacitative at 8.4 – 3.4 j and the current leads the voltage. This gives
much the same result as Figure 7.32, except that the peak power now
occurs in the first part of the half-cycle. The equivalent load at 200 Hz only
is 10.8 in parallel with 35 µF.
When designing output stages, there are four electrical quantities to
accommodate within the output device ratings; peak current, average
current, peak power and average power. (Junction temperatures must of
course also be considered at some point.) The critical quantities for
semiconductor safety in amplifiers are usually the peak instantaneous
values; for heatsink design average power is what counts, while for the
power supply average current is the significant quantity.
To determine the effect of real speaker loads on device stress I simulated an
EF output stage driving a single-speaker load with a 40 V peak sinewave,
powered from +/–50 V rails. The load was as Figure 7.26 except for a
reduction in the voicecoil inductance to 0.1 mH; the resulting impedance
curve is shown in Figure 7.33. Transient simulations over many cycles were
done for 42 spot frequencies from 20 Hz to 20 kHz, and the peak and
average quantities recorded and plotted. Many cycles must be simulated as
the bass resonance in the impedance model takes time to reach steady state
when a sinewave is abruptly applied; not everyone writing on this topic
appears to have appreciated this point.
Figure 7.33
Impedance curve of
the single-speaker
model. The dotted
line is 8 resistive
Compensation, slew-rate, and stability
Steady sinewave excitation was used as a practical approach to simulation
and testing, and does not claim to be a good approximation to music or
speech. Arbitrary non-cyclic transients could be investigated by the same
method, but the number of waveform possibilities is infinite. It would also
be necessary to be careful about the initial conditions.
Figures 7.33, 7.34 and 7.35 are the distilled results of a very large number
of simulations. Figure 7.34 shows that the gentle foothills of the impedance
peak at bass resonance actually increase the peak instantaneous power
stress on the output devices by 30%, despite the reduced current drawn.
Figure 7.34
Peak and average
output device power
dissipation driving
the single-unit
speaker impedance
as Figure 7.33. The
dotted line is peak
power for 8 resistive
Figure 7.35
Peak and average
output device current
driving the single-unit
speaker impedance.
Dotted lines are peak
and average current
into 8 217
Audio Power Amplifier Design Handbook
The most dangerous regions for the amplifier are the sides of a resonance
hump where the phase shift is the greatest. Peak dissipation only falls below
that for an 8 resistor (shown dotted) around the actual resonance peak,
where it drops quickly to a quarter of the resistive case.
Likewise, the increase in impedance at the HF end of the spectrum, where
voicecoil inductance is significant, causes a more serious rise in peak
dissipation to 50% more than the resistive case. The conclusion is that for peak
power, the phase angle is far more important than the impedance magnitude.
The effects on the average power dissipation, and on the peak and average
device current in Figure 7.35, are more benign. With this type of load
network, all three quantities are reduced when the speaker impedance
increases, the voltage/current phase shifts having no effect on the current.
Two-way speaker loads
The impedance plot for the simulated two-way speaker load of Figure 7.29
is shown in Figure 7.36 at 59 spot frequencies. The curve is more complex
and shows a dip below the nominal impedance as well as peaks above; this
is typical of multi-speaker designs. An impedance dip causes the maximum
output device stress as it combines increased current demand with phase
shifts that increase peak instantaneous dissipation.
In Figure 7.37 the impedance rise at bass resonance again causes increased
peak power dissipation due to phase shifts; the other three quantities are
reduced. In the HF region there is an impedance dip at 6 kHz which nearly
Figure 7.36
Impedance curve of
model of the two-unit
speaker model in
Figure 7.30. Dotted
line is 8 resistive
Compensation, slew-rate, and stability
Figure 7.37
Peak and average
output device power
dissipation driving the
two-way speaker
model. Dotted lines are
peak and average for
doubles peak power dissipation on its lower slopes, the effect being greater
because both phase-shift and increased current demand are acting. The
actual bottom of the dip sharply reduces peak power where the phase angle
passes through zero, giving the notch effect at the top of the peak.
Average power (Figure 7.37) and peak and average current (Figure 7.38) are
all increased by the impedance dip, but to a more modest extent. Peak
Figure 7.38
Peak and average
output device current
driving two-way
speaker impedance as
Figure 7.13. Dotted
lines are peak and
average for 8 219
Audio Power Amplifier Design Handbook
power would appear to be the critical quantity. Power device ratings often
allow the power and second-breakdown limits (and sometimes the bondwire current limit also) to be exceeded for brief periods. If you attempt to
exploit these areas in an audio application, you are living very dangerously,
as the longest excursion specified is usually 5 msec, and a half-cycle at
20 Hz lasts for 25 msec.
From this it can be concluded that a truly ‘difficult’ load impedance is one
with lots of small humps and dips giving significant phase shifts and
increased peak dissipation across most of the audio band. Impedance dips
cause more stress than peaks, as might be expected. Low impedances at the
high-frequency end (above 5 kHz) are particularly undesirable as they will
increase amplifier crossover distortion.
Enhanced loudspeaker currents
When amplifier current capability and loudspeaker loading are discussed it
is often said that it is possible to devise special waveforms that cause a
loudspeaker to draw more transient current than would at first appear to be
possible. This is perfectly true. The issue was raised by Otala et al [13], and
expanded on in Otala and Huttunen [14]. The effect was also demonstrated
by Cordell [15].
The effect may be demonstrated with the electrical analogue of a single
speaker unit as shown in Figure 7.26. Rc is the resistance of the voicecoil
and Lc its inductance. Lr and Cr model the cone resonance, with Rr
controlling its damping. These three components simulate the impedance
characteristics of the real electromechanical resonance. The voicecoil
inductance is 0.29 mH, and its resistance 6.8 , typical for a 10 inch bass
unit of 8 nominal impedance. Measurements on this circuit cannot show
an impedance below 6.8 at any frequency, and it is easy to assume that
the current demands can therefore never exceed those of a 6.8 resistance. This is not so.
The secret of getting unexpectedly high currents flowing is to make use of
the energy stored in the circuit reactances. This is done by applying an
asymmetrical waveform with transitions carefully timed to match the
speaker resonance. Figure 7.39 shows PSpice simulation of the currents
drawn by the circuit of Figure 7.26. The rectangular waveform is the current
in a reference 8 resistance driven with the same waveform. A +/–10 V
output limit is used here for simplicity but this could obviously be much
higher, depending on the amplifier rail voltages.
At the start of the waveform at A, current flows freely into Cr, reducing to
B as the capacitance charges. Current is also slowly building up in Lr,
causing the total current drawn to increase again to C. A positive transition
to the opposite output voltage then takes the system to point D; this is not
the same state as at A because energy has been stored in Lr during the long
negative period.
Compensation, slew-rate, and stability
Figure 7.39
An asymmetrical
waveform to generate
enhanced speaker
currents. The sequence
ABCDE generates a
negative current spike;
to the right, the inverse
sequence produces a
positive spike. The
rectangular waveform
is the current through
an 8 resistive load
A carefully timed transition is then made at E, at the lowest point in this part
of the curve. The current change is the same amplitude as at D, but it starts
off from a point where the current is already negative, so the final peak goes
much lower to 2.96 amps, 2.4 times greater than that drawn by the 8 resistor. I call this the Current Timing Factor, or CTF.
Otala and Huttunen [14] show that the use of multi-way loudspeakers, and
more complex electrical models, allows many more degrees of freedom in
maximising the peak current. They quote a worst case CTF of 6.6 times. An
amplifier driving 50 W into 8 must supply a peak current into an 8 resistance of 3.53 amps; amplifiers are usually designed to drive 4 or
lower to allow for impedance dips and this means the peak current
capability must be at least 7.1 amps. However, a CTF of implies that the
peak capability should be at least 23 amps. This peak current need only be
delivered for less than a millisecond, but it could complicate the design of
protection circuitry.
The vital features of the provocative waveform are the fast transitions and
their asymmetrical timing. The optimal transition timing for high currents
varies with the speaker parameters. The waveform in Figure 7.39 uses
ramped transitions lasting 10 µsec; if these transitions are made longer the
peak currents are reduced. There is little change up to 100 µsec, but with
transitions lengthened to 500 µsec the CTF is reduced from 2.4 to 2.1.
Without doing an exhaustive survey, it is impossible to know how many
power amplifiers can supply six times the nominal peak current required.
Audio Power Amplifier Design Handbook
I suspect there are not many. Is this therefore a neglected cause of real
audible impairment? I think not, because:
1 Music signals do not contain high-level rectangular waveforms, nor
trapezoidal approximations to them. A useful investigation would be a
statistical evaluation of how often (if ever) waveforms giving significant
peak current enhancement occur. As an informal test, I spent some time
staring at a digital scope connected to general-purpose rock music, and
saw nothing resembling the test waveform. Whether the asymmetrical
timings were present is not easy to say; however, the large-amplitude
vertical edges were definitely not.
2 If an amplifier does not have a huge current-peak capability, then the
overload protection circuitry will hopefully operate. If this is of a nonlatching type that works cleanly, the only result will be rare and very brief
periods of clipping distortion when the loudspeaker encounters a
particularly unlucky waveform. Such infrequent transient distortion is
known to be inaudible and this may explain why the current
enhancement effect has attracted relatively little attention so far.
Amplifier instability
Amplifier instability refers to unwanted oscillations at either HF or LF. The
latter is very rare in solid-state amplifiers, though still very much an issue for
valve designers. Instability has to be taken very seriously, because it may not
only destroy the amplifier that hosts it, but also damage the loudspeakers.
Instability at middle frequencies such as 1 kHz is virtually impossible unless
you have a very eccentric design with roll-offs and phase-shifts in the
middle of the audio band.
HF instability
HF instability is probably the most difficult problem that may confront the
amplifier designer, and there are several reasons for this:
1 the most daunting feature of HF oscillation is that under some
circumstances it can cause the destruction of the amplifier in relatively
short order. It is often most inadvisable to let the amplifier sit there
oscillating while you ponder its shortcomings.
BJT amplifiers will suffer overheating because of conduction overlap in the
output devices; it takes time to clear the charge carriers out of the device
junctions. Some designs deal with this better than others, but it is still true
that subjecting a BJT design to prolonged sinewave testing above 20 kHz
should be done with great caution. Internal oscillations may of course have
much higher frequencies than this, and in some cases the output devices
may be heated to destruction in a few seconds. The resistor in the Zobel
network will probably also catch fire.
Compensation, slew-rate, and stability
FET amplifiers are less vulnerable to this overlap effect, due to their
different conduction mechanism, but show a much greater tendency to
parasitic oscillation at high frequencies, which can be equally destructive.
Under high-amplitude oscillation plastic-package FETs may fail explosively; this is usually a prompt failure within a second or so and leaves very
little time to hit the off switch.
2 various sub-sections of the amplifier may go into oscillation on their own
account, even if the global feedback loop is stable against Nyquist
oscillation. Even a single device may go into parasitic oscillation (e.g.
emitter-followers fed from inappropriate source impedances) and this is
usually at a sufficiently high frequency that it either does not fight its way
through to the amplifier output, or does not register on a 20 MHz scope.
The presence of this last kind of parasitic is usually revealed by excessive
and unexpected non-linearity,
3 another problem with HF oscillation is that it cannot in general be
modelled theoretically. The exception to this is global Nyquist oscillation,
(i.e. oscillation around the main feedback loop because the phase-shift has
become too great before the loop gain has dropped below unity) which can
be avoided by calculation, simulation, and design. The forward-path gain
and the dominant pole frequency are both easy to calculate, though the
higher pole frequencies that cause phase-shift to accumulate are usually
completely mysterious; to the best of my knowledge virtually no work has
been done on the frequency response of audio amplifier output stages.
Design for Nyquist stability therefore reduces to deciding what feedback
factor at 20 kHz will give reliable stability with various resistive and
reactive loads, and then apportioning the open-loop gain between the
transconductance of the input stage and the transresistance of the VAS.
The other HF oscillations, however, such as parasitics and other more
obscure oscillatory misbehaviour, seem to depend on various unknown or
partly-known second-order effects that are difficult or impossible to deal
with quantitatively and are quite reasonably left out of simulator device
models. This means we are reduced to something not much better than
trial-and-error when faced with a tricky problem.
The CFP output stage has two transistors connected together in a very tight
100% local feedback loop, and there is a clear possibility of oscillation
inside this loop. When it happens, this tends to be benign, at a relatively
high frequency (say 2–10 MHz) with a clear association with one polarity
of half-cycle.
LF instability
Amplifier instability at LF (motorboating) is largely a thing of the past now
that amplifiers are almost invariably designed with DC-coupling throughout the forward and feedback paths. The theoretical basis for it is exactly as
for HF Nyquist oscillation; when enough phase-shift accumulates at a given
Audio Power Amplifier Design Handbook
frequency, there will be oscillation, and it doesn’t matter if that frequency
is 1 Hz or 1 MHz.
At LF things are actually easier, because all the relevant time-constants are
known, or can at least be pinned down to a range of values based on
electrolytic capacitor tolerances, and so the system is designable. The
techniques for dealing with almost any number of LF poles and zeros were
well-known in the valve era, when AC coupling between stages was
usually unavoidable, because of the large DC voltage difference between
the anode of one stage and the grid of the next.
Oscillation at LF is unlikely to be provoked by awkward load impedances.
This is not true at HF, where a capacitative load can cause serious
instability. However, this problem at least is easily handled by adding an
output inductor.
Speed and slew-rate in audio amplifiers
It seems self-evident that a fast amplifier is a better thing to have than a slow
one, but – what is a fast amplifier? Closed-loop bandwidth is not a promising
yardstick; it is virtually certain that any power amplifier employing negative
feedback will have a basic closed-loop frequency response handsomely in
excess of any possible aural requirements, even if the overall system
bandwidth is defined at a lower value by earlier filtering.
There is always a lot of loose talk about the importance of an amplifier’s
open-loop bandwidth, much of it depressingly ill-informed. I demonstrated [16] that the frequency of the dominant pole P1 that sets the open-loop
bandwidth is a variable and rather shifty quantity that depends on transistor
beta and other ill-defined parameters. (I also showed how it can be cynically
manipulated to make it higher by reducing open-loop gain below P1.) While
P1 may vary, the actual gain at HF (say 20 kHz) is thankfully a much more
dependable figure that is set only by frequency, input stage transconductance, and the value of Cdom [17]. It is this which is the meaningful
figure in describing the amount of NFB that an amplifier enjoys.
The most meaningful definition of an amplifier’s speed is its maximal slewrate. The minimum slew-rate for a 100 W/8 amplifier to cleanly
reproduce a 20 kHz sinewave is easily calculated as 5.0 V/µsec; so
10 V/µsec is adequate for 400 W/8 , a power level that takes us somewhat
out of the realms of domestic hi-fi. A safety-margin is desirable, and if we
make this a bare factor of two then it could be logically argued that
20 V/µsec is enough for any hi-fi application; there is in fact a less obvious
but substantial safety-margin already built in, as 20 kHz signals at
maximum level are mercifully rare in music; the amplitude distribution falls
off rapidly at higher frequencies.
Firm recommendations on slew-rate are not common; Peter Baxandall
made measurements of the slew-rate produced by vinyl disc signals, and
Compensation, slew-rate, and stability
concluded that they could be reproduced by an amplifier with a slew limit
corresponding to maximum output at 2.2 kHz. For the 100 W amplifier this
corresponds to 0.55 V/µsec [18].
Nelson Pass made similar tests, with a moving-magnet (MM) cartridge, and
quoted a not dissimilar maximum of 1 V/µsec at 100 W. A moving-coil (MC)
cartridge doubled this to 2 V/µsec, and Pass reported [19] that the absolute
maximum possible with a combination of direct-cut discs and MC
cartridges was 5 V/µsec at 100 W. This is comfortably below the 20 V/µsec
figure arrived at theoretically above; Pass concluded that even if a generous
10:1 factor of safety was adopted, 50 V/µsec would be the highest speed
ever required from a 100 W amplifier.
However, in the real world we must also consider The Numbers Game; if
all else is equal then the faster amplifier is the more saleable. As an example
of this, it has been recently reported in the hi-fi press that a particular
50 W/8 amplifier has been upgraded from 20 V/µsec to 40 V/µsec [20] and
this is clearly expected to elicit a positive response from intending
purchasers. This report is exceptional, for equipment reviews in the hi-fi
press do not usually include slew-rate measurements. It is therefore difficult
to get a handle on the state of the art, but a trawl through the accumulated
data of years shows that the most highly specified equipment usually
plumps for 50 V/µsec – slew-rates always being quoted in suspiciously
round numbers. There was one isolated claim of 200 V/µsec, but I must
admit to doubts about the reality of this.
The Class-B amplifier shown in Figure 7.5 is that already described in
Chapter 6; the same component numbers have been preserved. This
generic circuit has many advantages, though an inherently good slew
performance is not necessarily one of them; however, it remains the basis
for the overwhelming majority of amplifiers so it seems the obvious place
to start. I have glibly stated that its slew-rate calculated at 40 V/usec, which
by the above arguments is more than adequate. However, let us assume
that a major improvement in slew-rate is required to counter the
propaganda of the Other Amplifier Company down the road, and examine
how it might be done. As in so many areas of life, things will prove much
more complicated than expected.
The basics of amplifier slew-limiting
At the simplest level, slew-rate in a conventional amplifier configuration
like Figure 7.5 depends on getting current in and out of Cdom, (C3) with the
convenient relation:
Slew-rate = I/Cdom V/µsec, for I in µA, Cdom in pF
Equation 7.1
The maximum output frequency for a given slew-rate and voltage is:
Freq max = SR/(2 × pi × Vpk) = SR/(2 × pi × root2 × Vrms) Equation 7.2
Audio Power Amplifier Design Handbook
So, for example, with a slew-rate of 20 V/µsec the maximum freq at
which 35 Vrms can be sustained is 64 kHz, and if Cdom is 100 pF then
the input stage must be able to source and sink 2 mA peak. Likewise, a
sinewave of given amplitude and frequency has a maximum slew-rate (at
zero-crossing) of:
SR of sinewave = dV/dt = max Vpk = 2 × pi × freq × Vpk
Equation 7.3
For Figure 7.5, our slew-rate equation yields 4000/100, or about 40 V/µsec,
as quoted above, if we assume (as all textbooks do) that the only currentlimitation is the tail-source of the input pair. If this differential pair has a
current-mirror collector load – and there are pressing reasons why it should
– then almost the full tail-current is available to service Cdom. This seems
very simple – to increase slew-rate increase the tail-current. But . . .
The tail-current is not the only limit on the slew current in Cdom. (This
point was touched on by Self [21].) Figure 7.40 shows the current paths for
Figure 7.40a
The current path for
positive slewing. At the
limit all of the slewing
current has to pass
through the currentmirror, TR2 being cut
Figure 7.40b
The current path at
negative slew limit.
TR2 is saturated and
the current-mirror is cut
Compensation, slew-rate, and stability
positive and negative slew-limit, and it can be seen at once that the positive
current can only be supplied by the VAS current-source load. This will
reduce the maximum positive rate, causing slew asymmetry, if the VAS
current-source cannot supply as much current as the tail source. In contrast,
for negative slewing TR4 can turn on as much as required to sink the Cdom
current, and the VAS collector load is not involved.
In most designs the VAS current-source value does not appear to be an
issue, as the VAS is run at a higher current than the input stage to ensure
enough pull-up current for the top half of the output stage; however it will
transpire that the VAS source can still cause problems.
Slew-rate measurement techniques
Directly measuring the edge-slopes of fast square waves from a scope
screen is not easy, and without a delayed timebase it is virtually impossible.
A much easier (and far more accurate) method is to pass the amplifier
output through a suitably-scaled differentiator circuit; slew-rate then
becomes simple amplitude, which is much easier to read from a graticule.
The circuit in Figure 7.41 gives a handy 100 mV output for each V/µsec of
slew; the RC time-constant must be very short for reasonable accuracy. The
differentiator was driven directly by the amplifier, and not via an output
inductor. Be aware that this circuit needs to be coupled to the scope by a
proper × 10 probe; the capacitance of plain screened cable gives serious
under-readings. We are dealing here with sub-microsecond pulse techniques, so bear in mind that waveform artefacts such as ringing are as likely
to be due to test cabling as to the amplifier.
Applying a fast-edged square wave to an amplifier does not guarantee that
it will show its slew-rate limits. If the error voltage so generated is not
enough to saturate the input stage then the output will be an exponential
response, without non-linear effects. For most of the tests described here,
the amplifier had to be driven hard to ensure that the true slew-limits were
revealed; this is due to the heavy degeneration that reduces the
transconductance of the input pair. Degeneration increases the error
voltage required for saturation, but does not directly alter slew limits.
Running a slew test on the circuit of Figure 7.5, with an 8 load, sharply
highlights the inadequacies of simple theory. The differentiator revealed
asymmetrical slew-rates of +21 V/µsec up and –48 V/µsec down, which is
Figure 7.41
A simple (but very
useful) differentiator. A
local probe ground is
essential for accuracy
to exceed +/–10%
Audio Power Amplifier Design Handbook
both a letdown and a puzzle considering that the simple theory promises
40 V/µsec. To get results worse than theory predicts is merely the common
lot of the engineer; to simultaneously get results that are better is grounds
for the gravest suspicions.
Improving the slew-rate
Looking again at Figure 7.5, the VAS current-source value is apparently
already bigger than required to source the current Cdom requires when the
input stage is sinking hard, so we confidently decrease R4 to 100 R (to
match R13) in a plausible attempt to accelerate slewing. With considerable
disappointment we discover that the slew-rate only changes to +21 V/µsec,
–62 V/µsec; the negative rate still exceeds the new theoretical value of
60 V/µsec. Just what is wrong here? Honesty compels us to use the lower of
the two figures in our ads, (doesn’t it?) and so the priority is to find out why
the positive slewing is so feeble.
At first it seems unlikely that the VAS current source is the culprit, as with
equal-value R4 and R13, the source should be able to supply all the input
stage can sink. Nonetheless, we can test this cherished belief by increasing
the VAS source current while leaving the tail-current at its original value.
We find that R4 = 150 R, R13 = 68 R gives +23 V/µsec, –48 V/µsec, and this
small but definite increase in positive rate shows clearly there is something
non-obvious going on in the VAS source.
(This straightforward method of slew acceleration by increasing standing
currents means a significant increase in dissipation for the VAS and its
current source. We are in danger of exceeding the capabilities of the TO92
package, leading to a cost increase. The problem is less in the input stage,
as dissipation is split between at least three devices.)
Simulating slew-limiting
When circuits turn truculent, it’s time to simplify and simulate. The circuit
was reduced to a model amplifier by replacing the Class-B output stage
with a small-signal Class-A emitter follower; this was then subjected to
some brutally thorough PSPICE simulation, which revealed the various
mechanisms described below.
Figure 7.42 shows the positive-going slew of this model amplifier, with both
the actual output voltage and its differential, the latter suitably scaled by
dividing by 106 so it can be read directly in V/µsec from the same plot. Figure
7.43 shows the same for the negative-going slew. The plots are done for a
series of changes to the resistors R4, 23 that set the standing currents.
Several points need to be made about these plots; firstly the slew-rates
shown for the lower R4, 23 values are not obtainable in the real amplifier
with output stage, for reasons that will emerge. Note that almost
Compensation, slew-rate, and stability
Figure 7.42
Positive slewing of
simulated model
amplifier. The lower
traces show the
amplifier output
slewing from –30 to
+30 V while the
upper traces are the
scaled differentiation
imperceptible wobbles in the output voltage put large spikes on the plot of
the slew-rate, and it is unlikely that these are being simulated accurately, if
only because circuit strays are neglected. To get valid slew-rates, read the
flat portions of the differential plots.
Using this method, the first insight into slew-rate asymmetry was obtained.
At audio frequencies, a constant current-source provides a fairly constant
current and that is the end of the matter, making it the usual choice for the
Figure 7.43
Negative slewing of
simulated model
amplifier. Increasing
the slew-rate limit
causes a larger part
of the output transient
to become
exponential, as the
input pair spends less
time saturated. Thus
the differential trace
has a shorter flat
Audio Power Amplifier Design Handbook
VAS collector load; as a result its collector is exposed to the full output
swing and the full slew-rate. When an amplifier slews rapidly, there is a
transient feedthrough from the collector to the base (see Figure 7.44) via the
collector-base capacitance. If the base voltage is not tightly fixed then fast
positive slewing drives the base voltage upwards, reducing the voltage on
the emitter and hence the output current. Conversely, for negative slew the
current-source output briefly increases; see Erdi [22]. In other words, fast
positive slewing itself reduces the current available to implement it.
Figure 7.44
One reason why
simple theory fails. Fast
positive edges on the
collector of the VAS
source TR6 couple
through the internal
Cbc to momentarily
reduce standing current
Having discovered this hidden constraint, the role of isolation resistor R23
immediately looks suspect. Simulation confirms that its presence worsens
the feedthrough effect by increasing the impedance of the reference voltage
fed to TR5 base. As is usual, the input-stage tail-source TR1 is biased from
the same voltage as TR5; this minor economy complicates things
significantly, as the tail current also varies during fast transients, reducing
for positive slew, and increasing for negative.
Slewing limitations in real life
Bias isolation resistors are not unique to the amplifier of Figure 7.5; they are
very commonly used. For an example taken at random, see Meyer [23]. My
own purpose in adding R23 was not to isolate the two current sources from
each other at AC (something it utterly fails to do) but to aid fault-finding.
Without this resistor, if the current in either source drops to zero (e.g. if TR1
fails open-circuit) then the reference voltage collapses, turning off both
sources, and it can be time-consuming to determine which has died and
which has merely come out in sympathy. Accepting this, we return to the
original Figure 7.5 values and replace R23 with a link; the measured slewrates at once improve from +21, –48 to +24, –48 (from here on the V/µsec is
omitted). This is already slightly faster than our first attempt at acceleration,
without the thermal penalties of increasing the VAS standing current.
The original amplifier used an active tail-source, with feedback control by
TR14; this was a mere whim, and a pair of diodes gave identical THD
Compensation, slew-rate, and stability
Figure 7.45
A modified biasing
system that makes TR6
current the controlled
variable, and reduces
the feedthrough effect
figures. It seems likely that reconfiguring the two current-sources so that
the VAS source is the active one would make it more resistant to
feedthrough, as the current-control loop is now around TR5 rather than
TR1, with feedback applied directly to the quantity showing unwanted
variations (see Figure 7.45). There is indeed some improvement, from
+24, –48 to +28, –48.
This change seems to work best when the VAS current is increased, and R4
= 100 R, R13 = 68 R now gives us +37, –52, which is definite progress on
the positive slewing. The negative rate has also slightly increased,
indicating that the tail-current is still being increased by feedthrough effect.
It seems desirable to minimise this transient feedthrough, as it works against
us just at the wrong time. One possibility would be a cascode transistor to
shield TR5 collector from rapid voltage changes; this would require more
biasing components and would reduce the positive output swing, albeit
only slightly.
Since it is the VAS current-source feedthrough capacitance that causes so
much grief, can we turn it against itself, so that an abrupt voltage transition
increases the current available to sustain it, rather than reducing it? Oh yes
we can, for if a small capacitance Cs is added between TR5 collector
(carrying the full voltage swing) and the sensing point A of the active tail
source, then as the VAS collector swings upward, the base of TR14 is also
driven positive, tending to turn it off and hence increasing the bias applied
to VAS source TR5 via R21. This technique is highly effective, but it smacks
of positive feedback and should be used with caution; Cs must be kept
small. I found 7.5 pF to be the highest value usable without degrading the
amplifier’s HF stability.
With R4 = 100, R13 = 68 adding Cs = 6 pF takes us from +37, –52 to +42,
–43; and the slew asymmetry that has dogged this circuit from the start has
been corrected. Fine adjustment of this capacitance is needful if good slew
symmetry is demanded.
Audio Power Amplifier Design Handbook
Some additional complications
Some other unsuspected effects were uncovered in the pursuit of speed; it is
not widely known that slew-rate is affected both by output loading and the
output stage operating class. For example, above we have noted that R4 =
100, R13 = 68 yields +37, –52 for Class-B and an 8 load. With 4 loading
this changes to +34, –58, and again the loss in positive speed is the most
significant. If the output stage is biased into Class-A (for an 8 load) then we
get +35, –50. The explanation is that the output stage, despite the cascading
of drivers and output devices, draws significant current from the VAS stage.
The drivers draw enough base current in the 4 case to divert extra current
from Cdom, and current is in shortest supply during positive slew. The effect
in Class-A is more severe because the output device currents are always high,
the drivers requiring more base current even when quiescent, and again this
will be syphoned off from the VAS collector.
Speeding-up this amplifier would be easier if the Miller capacitor Cdom
was smaller. Does it really need to be that big? Well yes, because if we want
the NFB factor to be reasonably low for dependable HF stability, the HF
loop gain must be limited. Open-loop gain above the dominant pole
frequency P1 is the product of input stage gm with the value of Cdom, and
the gm is already as low as it can reasonably be made by emitter
degeneration. Emitter resistors R2, 3 at 100 are large enough to mildly
compromise the input offset voltage, because the tail current splits in two
through a pair of resistors that are unlikely to be matched to better than 1%,
and noise performance is also impaired by this extra resistance in the input
pair emitters. Thus for a given NFB factor at 20 kHz, Cdom is fixed.
Despite these objections, the approach was tested by changing the
distribution of open-loop gain between the input stage and the VAS. R2, 3
were increased from 100 R to 220 R, and Cdom reduced to 66 pF; this does
not give exactly the same NFB factor, but in essence we have halved the
transconductance of the input stage, while doubling the gain of the VAS.
This gain-doubling allows Cdom to be reduced to 66 pF without reduction
of stability margins.
With R4 = 100, R13 = 68 as before, the slew-rate is increased to +50, –50
with Cs = 6 pF to maintain slewing symmetry. This is a 25% increase in
speed rather than the 50% that might be expected from simple theory, and
indicates that other restrictions on speed still exist; in fact PSPICE showed
there are several.
One of these restrictions is as follows; when slewing positively, TR4 and
TR12 must be turned off as fast as possible, by pulling current out of Cdom.
The input pair therefore causes TR10 to be turned on by an increasing
voltage across TR11 and R7. As TR10 turns on, its emitter voltage rises due
to R6, while at the same time the collector voltage must be pulled down to
near the –ve rail to turn off Q4. In the limit TR10 runs out of Vce, and is
Compensation, slew-rate, and stability
unable to pull current out of Cdom fast enough. The simplest way to reduce
this problem is to reduce the resistors R6, 7 that degenerate the currentmirror. This risks HF distortion variations due to input-pair lc imbalance,
but values down to 12 have given acceptable results. Once more it is the
positive rate that suffers.
Another way to reduce the value needed for Cdom is to lower the loop-gain
by increasing the feedback network attenuation, or in other words, to run
the amplifier at a higher closed-loop gain. This might be no bad thing; the
current standard of 1 V for full output is (I suspect) due to a desire for low
closed-loop gain in order to maximise the NFB factor, so reducing
distortion. I recall JLH advocating this strategy back in 1974. However, we
must take the world as we find it, and so I have left closed-loop gain alone.
We could of course attenuate the input signal so it can be amplified more,
though I have an uneasy feeling about this sort of thing; amplifying in a preamp then attenuating in the power amp implies a headroom bottleneck, if
such a curdled metaphor is permissible. It might be worth exploring this
approach; this amplifier has good open-loop linearity and I don’t think
excessive THD would be a problem.
Having previously spent some effort on minimising distortion, we do not
wish to compromise the THD of a Blameless amplifier. Mercifully, none of
the modifications set out here have any significant effect on overall THD,
though there may be minor variations around 10–20 kHz.
Further improvements and other configurations
The results I have obtained in my attempts to improve slewing are not at
first sight exactly stunning; however they do have the merit of being as
grittily realistic as I can make them. I set out in the belief that enhancing
slew-rate would be fairly simple; the very reverse has proved to be the case.
It may well be that other VAS configurations, such as the push-pull VAS
examined in Self [16], will prove more amenable to design for rapid slewrates; however such topologies have other disadvantages to overcome.
Stochino in a fascinating paper [24] has presented a topology, which,
although a good deal more complex than the conventional arrangement,
claims to make slew-rates up to 400 V/µsec achievable.
Otala, M An Audio Power Amplifier for Ultimate Quality Requirements IEEE Trans on Audio and Electroacoustics, Vol AU-21, No. 6,
Dec 1973.
Baxandall Audio Power Amplifier Design: Part 4 Wireless World,
July 1978, p. 76.
Takahashi et al Design and Construction of High Slew-Rate
Amplifiers AES 60th Convention, Preprint No. 1348 (A-4) 1978.
Audio Power Amplifier Design Handbook
Self Crossover Distortion and Compensation Letters, Electronics and
Wireless World, Aug 1992, p. 657.
Widlar, A Monolithic Power Op-Amp IEEE Journal of Solid-State
Circuits, Vol 23, No 2, April 1988.
Bonello Advanced Negative Feedback Design for High Performance
Amplifiers AES 67th Convention, Preprint No. 1706 (D-5) 1980.
Pernici et al A CMOS Low-Distortion Amplifier with Double-Nested
Miller Compensation IEEE J. Solid-State Circuits, July 1993, p. 758.
Scott and Spears On The Advantages of Nested Feedback Loops J.
Audio Eng Soc, Vol 39, March 1991, p. 115.
National Semi Fast Compensation Extends Power Bandwidth Linear
Brief 4, NatSem Linear Apps Handbook, 1991.
Feucht Handbook of Analog Circuit Design Academic Press 1990,
p. 264.
Atkinson, J Review of Krell KSA-50S Power Amplifier Stereophile
Aug 1995, p. 168.
Benjamin, E Audio Power Amplifiers for Loudspeaker Loads Journ.
Audio Eng. Soc. Vol 42, Sept 1994, p. 670.
Otala et al Input Current Requirements of High-Quality Loudspeaker
Systems AES preprint #1987 (D7) for 73rd Convention, March
Otala and Huttunen Peak Current Requirement of Commercial
Loudspeaker Systems JAES, June 1987, p. 455. See Ch. 12, p. 294.
Cordell, R Interface Intermodulation in Amplifiers Wireless World,
Feb 1983, p. 32.
Self, D Distortion In Power Amplifiers, Part 3 Electronics
World+WW, Oct 1993, p. 824.
Self, D Ibid Part 1 Electronics World+WW, Aug 1993, p. 631.
Baxandall, P Audio Power Amplifier Design Wireless World, Jan
1978, p. 56.
Pass, N Linearity, Slew rates, Damping, Stasis and . . . Hi-Fi News
and RR, Sept 1983, p. 36.
Hughes, J Arcam Alpha5/Alpha6 Amplifier Review Audiophile, Jan
1994, p. 37.
Self, D Distortion In Power Amplifiers, Part 7 Electronics
World+WW, Feb 1994 p. 138.
Erdi, G A 300 v/uS Monolithic Voltage Follower IEEE J. of Solid-State
Circuits, Dec 1979, p. 1062.
Meyer, D Assembling a Universal Tiger Popular Electronics, Oct
Stochino, G Ultra-Fast Amplifier Electronics World+WW, Oct 1995,
p. 835.
Power supplies and PSRR
Power supply technologies
There are three principal ways to power an amplifier:
1 a simple unregulated power supply consisting of transformer, rectifiers,
and reservoir capacitors,
2 a linear regulated power supply,
3 a switch-mode power supply.
It is immediately obvious that the first and simplest option will be the most
cost-effective, but at a first glance it seems likely to compromise noise and
ripple performance, and possibly interchannel crosstalk. It is therefore
worthwhile to examine the pros and cons of each technology in a little
more detail:
Simple unregulated power supplies
Simple, reliable, and cheap. (Relatively speaking – the traditional copper
and iron mains transformer will probably be the most expensive
component in the amplifier.)
No possibility of instability or HF interference from switching
The amplifier can deliver higher power on transient peaks, which is just
what is required.
Significant ripple is present on the DC output and the PSRR of the
amplifier will need careful attention.
The mains transformer will be relatively heavy and bulky.
Audio Power Amplifier Design Handbook
Transformer primary tappings must be changed for different countries
and mains voltages.
The absence of switch-mode technology does not mean total silence as
regards RF emissions. The bridge rectifier will generate bursts of RF at a
100 Hz repetition rate as the diodes turn off. This worsens with
increasing current drawn.
Linear regulated power supplies
Can be designed so that virtually no ripple is present on the DC output (in
other words the ripple is below the white noise the regulator generates)
allowing relaxation of amplifier supply-rail rejection requirements.
However, you can only afford to be careless with the PSRR of the power
amp if the regulators can maintain completely clean supply-rails in the
face of sudden current demands. If not, there will be interchannel
crosstalk unless there is a separate regulator for each channel. This means
four for a stereo amplifier, making the overall system very expensive.
A regulated output voltage gives absolutely consistent audio power
output in the face of mains voltage variation.
The possibility exists of electronic shutdown in the event of an amplifier
DC fault, so that an output relay can be dispensed with. However, this
adds significant circuitry, and there is no guarantee that a failed output
device will not cause a collateral failure in the regulators which leaves
the speakers still in jeopardy.
Complex and therefore potentially less reliable. The overall amplifier
system is at least twice as complicated. The much higher componentcount must reduce overall reliability, and getting it working in the first
place will take longer and be more difficult. For an example circuit see
Sinclair [1]. If the power amplifier fails, due to an output device failure,
then the regulator devices will probably also be destroyed, as protecting
semiconductors with fuses is a very doubtful business; in fact it is
virtually impossible. The old joke about the transistors protecting the
fuse is not at all funny to power-amplifier designers, because this is
precisely what happens. Electronic overload protection for the regulator
sections is therefore essential to avert the possibility of a domino-effect
failure, and this adds further complications, as it will probably need to
be some sort of foldback protection characteristic if the regulator
transistors are to have a realistic prospect of survival.
Comparatively expensive, requiring at least two more power semiconductors, with associated control circuitry and over-current protection. These power devices in turn need heatsinks and mounting
hardware, checking for shorts in production, etc.
Power supplies and PSRR
Transformer tappings must still be changed for different mains
IC voltage regulators are usually ruled out by the voltage and current
requirements, so it must be a discrete design, and these are not simple to
make bulletproof. Cannot usually be bought in as an OEM item, except
at uneconomically high cost.
May show serious HF instability problems, either alone or in combination with the amplifiers powered. The regulator output impedance is
likely to rise with frequency, and this can give rise to some really
unpleasant sorts of HF instability. Some of my worst amplifier experiences have involved (very) conditional stability in such amplifiers.
The amplifier can no longer deliver higher power on transient peaks.
The overall power dissipation for a given output is considerably
increased, due to the minimum voltage-drop though the regulator
The response to transient current demands is likely to be slow, affecting
slewing behaviour.
Switch-mode power supplies
Ripple can be considerably lower than for unregulated power supplies,
though never as low as a good linear regulator design. 20 mV pk–pk is
There is no heavy mains transformer, giving a considerable saving in
overall equipment weight. This can be important in PA equipment.
Can be bought in as an OEM item; in fact this is virtually compulsory as
switch-mode design is a specialised job for experts.
Can be arranged to shutdown if amplifier develops a dangerous DC
Can be specified to operate properly, and give the same audio output
without adjustment, over the entire possible worldwide mains-voltage
range, which is normally taken as 90–260 V.
A prolific source of high-frequency interference. This can be extremely
difficult to eradicate entirely from the audio output.
The 100 Hz ripple output is significant, as noted above, and will require
the usual PSRR precautions in the amplifiers.
Much more complex and therefore less reliable than unregulated
supplies. Dangerous if not properly cased, as high DC voltage is
The response to transient current demands is likely to be relatively
Audio Power Amplifier Design Handbook
On perusing the above list, it seems clear that regulated supplies for power
amplifiers are a Bad Thing. Not everyone agrees with me; see for example
Linsley-Hood [2]. Unfortunately he does not adduce any evidence to
support his case.
The usual claim is that linear regulated supplies give tighter bass; advocates
of this position are always careful not to define tighter bass too closely, so
no-one can disprove the notion. If the phrase means anything, it
presumably refers to changes in the low-frequency transient response;
however since no such changes can be detected, this appears to be simply
untrue. If properly designed, all three approaches can give excellent sound,
so it makes sense to go for the easiest solution; with the unregulated supply
the main challenge is to keep the ripple out of the audio, which will be seen
to be straightforward if tackled logically. The linear regulated approach
presents instead the challenge of designing not one but two complex
negative-feedback systems, close-coupled in what can easily become a
deadly embrace if one of the partners shows any HF instability. As for
switchmode supplies, their design is very much a matter for specialists.
The generic amplifier designs examined in this book have excellent supplyrail rejection, and so a simple unregulated supply is perfectly adequate. The
use of regulated supplies is definitely unnecessary, and I would recommend
strongly against their use. At best, you have doubled the amount of highpower circuitry to be bought, built, and tested. At worst, you could have
intractable HF stability problems, peculiar slew-limiting, and some
expensive device failures.
Design considerations for power supplies
A typical unregulated power supply is shown in Figure 8.1. This is wholly
conventional in concept, though for optimal hum performance the wiring
Figure 8.1
A simple unregulated
power supply,
including rectifiersnubbing and
Power supplies and PSRR
topology and physical layout need close attention, and this point is rarely
For amplifiers of moderate power the total reservoir capacitance per rail
usually ranges from 4700 to 20,000 µF, though some designs have much
more. Ripple current ratings must be taken seriously. It is often claimed that
large amounts of reservoir capacitance give firmer bass; this is untrue for all
normal amplifier designs below clipping.
I do not propose to go through the details of designing a simple PSU, as
such data can be found in standard textbooks, but I instead offer some hints
and warnings that are either rarely published or are especially relevant to
audio amplifier design.
Mains transformers
The mains transformer will normally be either the traditional E-&-I frame
type, or a toroid. The frame type is used where price is more important than
compactness or external field, and vice-versa. There are various other types
of transformer, such as C-core, or R-core, but they do not seem to be able
to match the low external field of the toroid, while being significantly more
expensive than the frame type.
The external field of a frame transformer can be significantly reduced by
specifying a hum strap, or belly-band as it is sometimes rather indelicately
called. This is a wide strip of copper that forms a closed circuit around the
outside of the core and windings, so it does not form a shorted turn in the
main transformer flux. Instead it intersects with the leakage flux, partially
cancelling it.
The design of the mains transformer for a given voltage at a given current
is simple in principle, but in practice always seems to involve a degree of
trial and error. The main reason for this is that the voltage developed on the
reservoir capacitors depends on losses that are not easily predicted, and
this is inherent in any rectifier circuit where the current flows only in short
sharp peaks at the crest of the AC waveform.
Firstly the voltage developed depends on the transformer regulation, i.e. the
amount the voltage drops as more current is drawn. (The word regulation
in this context has nothing to do with negative-feedback voltage control –
unfortunate and confusing, but there it is.) Transformer manufactures are
usually reluctant to predict anything more than a very approximate figure
for this.
Voltage losses also depend strongly on the peak amplitude of the charging
pulses from the rectifier to the reservoir; these peaks cause voltage drops in
the AC wiring, transformer winding resistances, and rectifiers that are rather
larger than might be expected. Unfortunately the peak current value is
poorly defined, by wiring resistance and transformer leakage reactance (a
Audio Power Amplifier Design Handbook
parameter that transformer manufacturers are even more reluctant to
predict) and any calculations are so rough that they are really valueless.
There may also be uncertainties in the voltage efficiency of the amplifier
itself, and there are so many variables that it is only realistic to expect to try
two or three transformer designs before the exact output power required is
Since most amplifiers are intended to reproduce music and speech, with
high peak-to-average power ratios, they will operate satisfactorily with
transformers rated to supply only 70% of the current required for extended
sinewave operation, and in a competitive market the cost savings are
significant. Trouble comes when the amplifiers are subjected to sinewave
testing, and a transformer so rated will probably fail from internal
overheating, though it may take an hour or more for the temperatures to
climb high enough. The usual symptom is breakdown of the interlayer
winding insulation, the resultant shorted turns causing the primary mains
fuse to blow. This process is usually undramatic, without visible transformer
damage or the evolution of smoke, but it does of course ruin an expensive
To prevent such failures when a mains transformer is deliberately
underrated, some form of thermal cutout is essential. Self-resetting cutouts
based on snap-action bimetal discs are physically small enough to be
buried in the outer winding layers and work very well. They are usually
chosen to act at 100 or 110°C, as transformer materials are usually rated to
120°C unless special construction is required.
If the primary side of the mains transformer has multiple taps for multicountry operation, remember that some of the primary wiring will carry
much greater currents at low voltage tappings; the mains current drawn
on 90 V input will be nearly 3 times that at 240 V, for the same power
Fusing and rectification
The rectifier (almost always a packaged bridge) must be generously rated to
withstand the initial current surge as the reservoirs charge from empty on
switch-on. Rectifier heatsinking is definitely required for most sizes of
amplifier; the voltage drop in a silicon rectifier may be low (1 V per diode
is a good approximation for rough calculation) but the current pulses are
large and the total dissipation is significant.
Reservoir capacitors must have the incoming wiring from the rectifier going
directly to the capacitor terminals; likewise the outgoing wiring to the HT
rails must leave from these terminals. In other words, do not run a tee off
to the cap, because if you do its resistance combined with the high-current
charging pulses adds narrow extra peaks to the ripple crests on the DC
output and may worsen the hum/ripple level on the audio.
Power supplies and PSRR
The cabling to and from the rectifiers carry charging pulses that have a
considerably higher peak value than the DC output current. Conductor
heating is therefore much greater due to the higher value of I-squared-R.
Heating is likely to be especially severe if connectors are involved.
Fuseholders may also heat up and consideration should be given to using
heavy-duty types. Keep an eye on the fuses; if the fusewire sags at turn-on,
or during transients, the fuse will fail after a few dozen hours, and the rated
value needs to be increased.
When selecting the value of the mains fuse in the transformer primary
circuit, remember that toroidal transformers take a large current surge at
switch-on. The fuse will definitely need to be of the slow-blow type.
The bridge rectifier must be adequately rated for long-term reliability, and
it needs proper heat-sinking.
RF emissions from bridge rectifiers
Bridge rectifiers, even the massive ones intended solely for 100 Hz power
rectification, generate surprising quantities of RF. This happens when the
bridge diodes turn off; the charge carriers are swept rapidly from the junction
and the current flow stops with a sudden jolt that generates harmonics well
into the RF bands. The greater the current, the more RF produced, though it is
not generally possible to predict how steep this increase will be. The effect
can often be heard by placing a transistor radio (long or medium wave) near
the amplifier mains cable. It is the only area in a conventional power
amplifier likely to give trouble in EMC emissions testing [3].
Even if the amplifier is built into a solidly-grounded metal case, and the
mains transformer has a grounded electrostatic screen, RF will be emitted
via the live and neutral mains connections. The first line of defence against
this is usually four snubbing capacitors of approx. 100 nF across each diode
of the bridge, to reduce the abruptness of the turn-off. If these are to do any
good, it is vital that they are all as close as possible to the bridge rectifier
connections. (Never forget that such capacitors must be of the type
intended to withstand continuous AC stress.)
The second line of defence against RF egress is an X-capacitor wired
between Live and Neutral, as near to the mains inlet as possible (see Figure
8.1). This is usually only required on larger power amplifiers of 300 W total
and above. The capacitor must be of the special type that can withstand
direct mains connection. 100 nF is usually effective; some safety standards
set a maximum of 470 nF.
Power supply-rail rejection in amplifiers
The literature on power amplifiers frequently discusses the importance of
power-supply rejection in audio amplifiers, particularly in reference to its
possible effects on distortion [4].
Audio Power Amplifier Design Handbook
I hope I have shown in Chapters 5 and 6 that regulated power supplies are
just not unnecessary for an exemplary THD performance. I want to confirm
this by examining just how supply-rail disturbances insinuate themselves
into an amplifier output, and the ways in which this rail-injection can be
effectively eliminated. My aim is not just the production of hum-free
amplifiers, but also to show that there is nothing inherently mysterious in
power-supply effects, no matter what Subjectivists may say on the
The effects of inadequate power-supply rejection ratio (PSRR) in a typical
Class-B power amplifier with a simple unregulated supply, may be twofold:
1 a proportion of the 100 Hz ripple on the rails will appear at the output,
degrading the noise/hum performance. Most people find this much more
disturbing than the equivalent amount of distortion,
2 the rails also carry a signal-related component, due to their finite
impedance. In a Class-B amplifier this will be in the form of half-wave
pulses, as the output current is drawn from the two supply-rails
alternately; if this enters the signal path it will degrade the THD
The second possibility, the intrusion of distortion by supply-rail injection,
can be eliminated in practice, at least in the conventional amplifier
architecture so far examined. The most common defect seems to be
misconnected rail bypass capacitors, which add copious ripple and
distortion into the signal if their return lines share the signal ground; this
was denoted No. 5 (Rail Decoupling Distortion) on my list of distortion
mechanisms in Chapter 3.
This must not be confused with distortion caused by inductive coupling of
halfwave supply currents into the signal path – this effect is wholly
unrelated and is completely determined by the care put into physical
layout; I labelled this Distortion No. 6 (Induction Distortion).
Assuming the rail bypass capacitors are connected correctly, with a
separate ground return, ripple and distortion can only enter the amplifier
directly through the circuitry. It is my experience that if the amplifier is
made ripple-proof under load, then it is proof against distortion-components from the rails as well; this bold statement does however require a
couple of qualifications:
Firstly, the output must be ripple-free under load, i.e. with a substantial
ripple amplitude on the rails. If a Class-B amplifier is measured for ripple
output when quiescent, there will be a very low amplitude on the supplyrails and the measurement may be very good; but this gives no assurance
that hum will not be added to the signal when the amplifier is operating and
drawing significant current from the reservoir capacitors. Spectrum analysis
could be used to sort the ripple from the signal under drive, but it is simpler
Power supplies and PSRR
Figure 8.2
Diagram of a
generic power
amplifier, with
diode biasing for
input tail and VAS
to leave the amplifier undriven and artificially provoke ripple on the HT
rails by loading them with a sizeable power resistor; in my work I have
standardised on drawing 1 A. Thus one rail at a time can be loaded; since
the rail rejection mechanisms are quite different for V+ and V–, this is a
great advantage.
Drawing 1 A from the V– rail of the typical power amplifier in Figure 8.2
degraded the measured ripple output from –88 dBu (mostly noise) to
–80 dBu.
Secondly, I assume that any rail filtering arrangements will work with
constant or increasing effectiveness as frequency increases; this is clearly
true for resistor-capacitor (RC) filtering, but is by no means certain for
electronic decoupling such as the NFB current-source biasing used in the
design in Chapter 6. (These will show declining effectiveness with
frequency as internal loop-gains fall.) Thus, if 100 Hz components are
below the noise in the THD residual, it can usually be assumed that
disturbances at higher frequencies will also be invisible, and not
contributing to the total distortion.
To start with some hard experimental facts, I took a power amplifier –
similar to Figure 8.2 – powered by an unregulated supply on the same PCB
Audio Power Amplifier Design Handbook
(the significance of this proximity will become clear in a moment) driving
140 W rms into 8 at 1 kHz. The PSU was a conventional bridge rectifier
feeding 10,000 µF reservoir capacity per rail.
The 100 Hz rail ripple under these conditions was 1 V pk–pk. Superimposed on this were the expected halfwave pulses at signal frequency;
measured at the PCB track just before the HT fuse, their amplitude was
about 100 mV peak-peak. This doubled to 200 mV on the downstream side
of the fuse – the small resistance of a 6.3 A slow-blow fuse is sufficient to
double this aspect of the PSRR problem, and so the fine details of PCB
layout and PSU wiring could well have a major effect. (The 100 Hz ripple
amplitude is of course unchanged by the fuse resistance.)
It is thus clear that improving the transmitting end of the problem is likely
to be difficult and expensive, requiring extra-heavy wire, etc. to minimise
the resistance between the reservoirs and the amplifier. It is much cheaper
and easier to attack the receiving end, by improving the power-amp’s PSRR.
The same applies to 100 Hz ripple; the only way to reduce its amplitude is
to increase reservoir capacity, and this is expensive.
A design philosophy for rail rejection
Firstly ensure there is a negligible ripple component in the noise output of
the quiescent amplifier. This should be pretty simple, as the supply ripple
will be minimal; any 50 Hz components are probably due to magnetic
induction from the transformer, and must be removed first by attention to
physical layout.
Secondly, the THD residual is examined under full drive; the ripple
components here are obvious as they slide evilly along the distortion
waveform (assuming that the scope is sync’ed to the test signal). As another
general rule, if an amplifier is made visually free of ripple-synchronous
artefacts on the THD residual, then it will not suffer detectable distortion
from the supply-rails.
PSRR is usually best dealt with by RC filtering in a discrete-component
power amplifier. This will however be ineffective against the sub-50 Hz VLF
signals that result from short-term mains voltage variations being reflected
in the HT rails. A design relying wholly on RC filtering might have low AC
ripple figures, but would show irregular jumps and twitches of the THD
residual; hence the use of constant-current sources in the input tail and VAS
to establish operating conditions more firmly.
The standard op-amp definition of PSRR is the dB loss between each
supply-rail and the effective differential signal at the inputs, giving a figure
independent of closed-loop gain. However, here I use the dB loss between
rail and output, in the usual non-inverting configuration with a C/L gain of
26.4 dB. This is the gain of the amplifier circuit under consideration, and
allows dB figures to be directly related to testgear readings.
Power supplies and PSRR
Looking at Figure 8.2, we must assume that any connection to either HT rail
is a possible entry point for ripple injection. The PSRR behaviour for each
rail is quite different, so the two rails are examined separately.
Positive supply-rail rejection
The V+ rail injection points that must be eyed warily are the input-pair tail
and the VAS collector load. There is little temptation to use a simple resistor
tail for the input; the cost saving is negligible and the ripple performance
inadequate, even with a decoupled mid-point. A practical value for such a
tail-resistor would be 22k, which in SPICE simulation gives a lowfrequency PSRR of –120 dB for an undegenerated differential pair with
Replacing this tail resistor with the usual current source improves this to
–164 dB, assuming the source has a clean bias voltage. The improvement of
44 dB is directly attributable to the greater output impedance of a current
source compared with a tail resistor; with the values shown this is 4.6 M,
and 4.6 M/22k is 46 dB, which is a very reasonable agreement. Since the
rail signal is unlikely to exceed +10 dBu, this would result in a maximum
output ripple of –154 dBu.
The measured noise floor of a real amplifier, (ripple excluded) was
–94.2 dBu (EIN = –121.4 dBu) which is mostly Johnson noise from the
emitter degeneration resistors and the global NFB network. The tail ripple
contribution would be therefore 60 dB below the noise, where I think it is
safe to neglect it.
However, the tail-source bias voltage in reality will not be perfect; it will be
developed from V+, with ripple hopefully excluded. The classic method is
a pair of silicon diodes; LED biasing provides excellent temperature
compensation, but such accuracy in setting DC conditions is probably
unnecessary. It may be desirable to bias the VAS collector current-source
from the same voltage, which rules out anything above a volt or two. A 10 V
zener might be appropriate for biasing the tail-source (given suitable
precautions against noise generation) but this would seriously curtail the
positive VAS voltage swing.
The negative-feedback biasing system used in the design in Chapter 6
provides a better basic PSRR than diodes, at the cost of some betadependence. It is not quite as good as an LED, but the lower voltage
generated is more suitable for biasing a VAS source. These differences
become academic if the bias chain mid-point is filtered with 47 µF to V+,
as Table 8.1 shows; this is C11 in Figure 8.2.
As another example, the Figure 8.2 amplifier with diode-biasing and no
bias chain filtering gives an output ripple of –74 dBu; with 47 µF filtering
Audio Power Amplifier Design Handbook
Table 8.1
2 diodes
NFB low-beta
NFB high-beta
No decouple
Decoupled with 47 µF
–65 dB
–77 dB
–74 dB
–77 dB
–87 dB
–86 dB
–86 dB
–86 dB
this improves to –92 dBu, and 220 µF drops the reading into limbo below
the noise floor.
Figure 8.3 shows PSpice simulation of Figure 8.2, with a 0 dB sinewave
superimposed on V+ only. A large Cdecouple (such as 100 µF) improves LF
PSRR by about 20 dB, which should drop the residual ripple below the
noise. However, there remains another frequency-insensitive mechanism at
about –70 dB. The study of PSRR greatly resembles the peeling of onions,
because there is layer after layer, and often tears . . . There also remains an
HF injection route, starting at about 100 kHz in Figure 8.3, which is quite
unaffected by the bias-chain decoupling.
Rather than digging deeper into the precise mechanisms of the next layer,
it is simplest to RC filter the V+ supply to the input pair only (it makes very
little difference if the VAS source is decoupled or not) as a few volts lost
Figure 8.3
Positive-rail rejection;
decoupling the tail
current-source bias
chain R21, R22 with
0, 1, 10 and 100 µF
Power supplies and PSRR
Figure 8.4
Positive-rail rejection;
with input-stage supplyrail RC filtered with
100 and 0, 10 and
100 µF. Same scale as
Figure 8.3
here are of no consequence. Figure 8.4 shows the very beneficial effect of
this at middle frequencies, where the ear is most sensitive to ripple
Negative supply-rail rejection
The V– rail is the major route for injection, and a tough nut to analyse. The
well-tried Wolf-Fence approach is to divide the problem in half, and in this
case, the Fence is erected by applying RC filtering to the small-signal
section (i.e. input current-mirror and VAS emitter) leaving the unity-gain
output stage fully exposed to rail ripple. The output ripple promptly
disappears, indicating that our wolf is getting in via the VAS or the bottom
of the input pair, or both, and the output stage is effectively immune. We
can do no more fencing of this kind, for the mirror has to be at the same DC
potential as the VAS. SPICE simulation of the amplifier 1 with 1 V (0 dBV)
AC signal on V– gives the PSRR curves in Figure 8.5, with Cdom stepped
in value. As before there are two regimes, one flat at –50 dB, and one rising
at 6 dB per octave, implying at least two separate injection mechanisms.
This suspicion is powerfully reinforced because as Cdom is increased, the
HF PSRR around 100 kHz improves to a maximum and then degrades
again; i.e. there is an optimum value for Cdom at about 100 pF, indicating
some sort of cancellation effect. (In the V+ case, the value of Cdom made
very little difference.)
Audio Power Amplifier Design Handbook
Figure 8.5
Negative-rail rejection
varies with Cdom in a
complex fashion;
100 pF is the optimal
value. This implies
some sort of
concellation effect
A primary LF ripple injection mechanism is Early Effect in the input-pair
transistors, which determines the –50 dB LF floor of Curve 1 in Figure 8.7,
for the standard input circuit (as per Figure 8.5 with Cdom = 100 pF).
To remove this effect, a cascode structure can be added to the input stage,
as in Figure 8.6. This holds the Vce of the input pair at a constant 5 V, and
gives Curve 2 in Figure 8.7. The LF floor is now 30 dB lower, although HF
Figure 8.6
A cascoded input
stage; Q21, Q22
prevent AC on V– from
reaching TR2, TR3
collectors, and improve
LF PSRR. B is the
alternative Cdom
connection point for
cascode compensation
Power supplies and PSRR
PSRR is slightly worse. The response to Cdom’s value is now monotonic;
simply a matter of more Cdom, less PSRR. This is a good indication that one
of two partly-cancelling injection mechanisms has been deactivated.
There is a deep subtlety hidden here. It is natural to assume that Early effect
in the input pair is changing the signal current fed from the input stage to
the VAS, but it is not so; this current is in fact completely unaltered. What
is changed is the integrity of the feedback subtraction performed by the
input pair; modulating the Vce of TR1, TR2 causes the output to alter at LF
by global feedback action. Varying the amount of Early effect in TR1, TR2
by modifying VAF (Early intercept voltage) in the PSpice transistor model
alters the floor height for Curve 1; the worst injection is with the lowest VAF
(i.e. Vce has maximum effect on lc) which makes sense.
We still have a LF floor, though it is now at –80 rather than –50 dB.
Extensive experimentation showed that this is getting in via the collector
supply of TR12, the VAS beta-enhancer, modulating Vce and adding a
signal to the inner VAS loop by early effect once more. This is easily
squished by decoupling TR12 collector to V–, and the LF floor drops to
about –95 dB, where I think we can leave it for the time being. (Curve 3 in
Figure 8.7.)
Having peeled two layers from the LF PSRR onion, something needs to be
done about the rising injection with frequency above 100 Hz. Looking
again at Figure 8.2, the VAS immediately attracts attention as an entry
Figure 8.7
Curve 1 is negative-rail
PSRR for the standard
input. Curve 2 shows
how cascoding the
input stage improves
rail rejection. Curve 3
shows further
improvement by also
decoupling TR12
collector to V–
Audio Power Amplifier Design Handbook
Figure 8.8
Adding a Cdom buffer
A1 to prevent any
possibility of signal
entering directly from
the V– rail
route. It is often glibly stated that such stages suffer from ripple fed in
directly through Cdom, which certainly looks a prime suspect, connected
as it is from V– to the VAS collector. However, this bald statement is untrue.
In simulation it is possible to insert an ideal unity-gain buffer between the
VAS collector and Cdom, without stability problems (A1 in Figure 8.8) and
this absolutely prevents direct signal flow from V– to VAS collector through
Cdom; the PSRR is completely unchanged.
Cdom has been eliminated as a direct conduit for ripple injection, but the
PSRR remains very sensitive to its value. In fact the NFB factor available is
the determining factor in suppressing V– ripple-injection, and the two
quantities are often numerically equal across the audio band.
The conventional amplifier architecture we are examining inevitably has
the VAS sitting on one supply-rail; full voltage swing would otherwise be
impossible. Therefore the VAS input must be referenced to V–, and it is very
likely that this change-of-reference from ground to V– is the basic source of
injection. At first sight, it is hard to work out just what the VAS collector
signal is referenced to, since this circuit node consists of two transistor
collectors facing each other, with nothing to determine where it sits; the
answer is that the global NFB references it to ground.
Consider an amplifier reduced to the conceptual model in Figure 8.9, with
a real VAS combined with a perfect transconductance stage G, and unitygain buffer A1. The VAS beta-enhancer TR12 must be included, as it proves
to have a powerful effect on LF PSRR.
To start with, the global NFB is temporarily removed, and a DC input
voltage is critically set to keep the amplifier in the active region (an easy
trick in simulation). As frequency increases, the local NFB through Cdom
becomes steadily more effective, and the impedance at the VAS collector
Power supplies and PSRR
Figure 8.9
A conceptual SPICE
model for V– PSRR,
with only the VAS
made from real
components. R999
represents VAS loading
falls. Therefore the VAS collector becomes more and more closely bound
to the AC on V–, until at a sufficiently high frequency (typically 10 kHz) the
PSRR converges on 0 dB, and everything on the V– rail couples straight
through at unity gain, as shown in Figure 8.10.
There is an extra complication here; the TR12/TR4 combination actually
shows gain from V– to the output at low frequencies; this is due to Early
effect, mostly in TR12. If TR12 was omitted the LF open-loop gain drops to
about –6 dB.
Figure 8.10
Open-loop PSRR from
the model in Figure
8.8, with Cdom
value stepped. There
is actual gain below
1 kHz
Audio Power Amplifier Design Handbook
Figure 8.11
Closed-loop PSRR from
Figure 8.9, with Cdom
stepped to alter the
closed-loop NFB factor
Reconnecting the global NFB, Figure 8.11 shows a good emulation of the
PSRR for the complete amplifier in Figure 8.7. The 10–15 dB open-loopgain is flattened out by the global NFB, and no trace of it can be seen in
Figure 8.11.
Now the NFB attempts to determine the amplifier output via the VAS
collector, and if this control was perfect the PSRR would be infinite. It is not,
because the NFB factor is finite, and falls with rising frequency, so PSRR
deteriorates at exactly the same rate as the open-loop gain falls. This can be
seen on many op-amp spec sheets, where V– PSRR falls off from the
dominant-pole frequency, assuming conventional op-amp design with a
VAS on V–.
Clearly a high global NFB factor at LF is vital to keep out V– disturbances.
In Chapter 4 I rather tendentiously suggested that apparent open-loop
bandwidth could be extended quite remarkably (without changing the
amount of NFB at HF where it matters) by reducing LF loop gain; a highvalue resistor Rnfb in parallel with Cdom works the trick. What I did not say
was that a high global NFB factor at LF is also invaluable for keeping the
hum out; a point overlooked by those advocating low NFB factors as a
matter of faith rather than reason.
Table 8.2 shows how reducing global NFB by decreasing the value of Rnfb
degraded ripple rejection in a real amplifier.
Power supplies and PSRR
Table 8.2
Ripple Out
83.3 dBu
85.0 dBu
80.1 dBu
73.9 dBu
Having got to the bottom of the V– PSRR mechanism, in a just world our
reward would be a new and elegant way of preventing such ripple
injection. Such a method indeed exists, though I believe it has never before
been applied to power amplifiers [5],[6]. The trick is to change the reference,
as far as Cdom is concerned, to ground. Figure 8.6 shows that cascodecompensation can be implemented simply by connecting Cdom to point B
rather than the usual VAS base connection at A. Figure 8.12 demonstrates
that this is effective, PSRR at 1 kHz improving by about 20 dB.
Elegant or not, the simplest way to reduce ripple below the noise floor still
seems to be brute-force RC filtering of the V– supply to the input mirror and
VAS, removing the disturbances before they enter. It may be crude, but it is
effective, as shown in Figure 8.13. Good LF PSRR requires a large RC timeconstant, and the response at DC is naturally unimproved, but the real snag
is that the necessary voltage drop across R directly reduces amplifier output
Figure 8.12
Using an input
cascode to change the
reference for Cdom.
The LF PSRR is
unchanged, but
extends much higher in
frequency. (Compare
Curve 2 in Figure
8.7.) Note that Cdom
value now has little
Audio Power Amplifier Design Handbook
Figure 8.13
RC filtering of the V–
rail is effective at
medium frequencies,
but less good at LF,
even with 100 µF of
filtering. R = 10 swing, and since the magic number of watts available depends on voltage
squared, it can make a surprising difference to the raw commercial
numbers (though not, of course, to perceived loudness). With the circuit
values shown 10 is about the maximum tolerable value; even this gives
a measurable reduction in output. The accompanying C should be at least
220 µF, and a higher value is desirable if every trace of ripple is to be
1. Sinclair (ed) Audio and Hi-Fi Handbook pub Newnes 1993, p. 541.
2. Linsley-Hood, J Evolutionary Audio. Part 3 Electronics World, Jan 1990,
p. 18.
3. Williams, T EMC For Product Designers pub Newnes (ButterworthHeinemann) 1992, ISBN 0 7506 1264 9 p. 106.
4. Ball, G Distorting Power Supplies EW+WW, Dec 90, p. 1084.
5. Ribner and Copeland Design Techniques for Cascoded CMOS Opamps
IEEE J. Solid-State Circuits, Dec 1984, p. 919.
6. Ahuja, B K Improved Frequency Compensation Technique for CMOS
Opamps. IEEE J. Solid-State Circuits, Dec 1983, pp. 629–633.
Class-A power amplifiers
An introduction to class-A
The two salient facts about Class-A amplifiers are that they are inefficient,
and that they give the best possible distortion performance. They will never
supplant Class-B amplifiers; but they will always be around.
The quiescent dissipation of the classic Class-A amplifier is equal to twice
the maximum output power, making massive power outputs impractical, if
only because of the discomfort engendered in the summer months.
However, the nature of human hearing means that the power of an
amplifier must be considerably increased to sound significantly louder.
Doubling the sound pressure level (SPL) is not the same as doubling
subjective loudness, the latter being measured in Sones rather than dB
above threshold, and it appears that doubling subjective loudness requires
nearer a 10 dB rather than 6 dB rise in SPL [1]. This implies amplifier power
must be increased something like ten-fold, rather than merely quadrupled,
to double subjective loudness. Thus a 40 W Class-B amplifier does not
sound much larger than its 20 W Class-A cousin.
There is an attractive simplicity and purity about Class A. Most of the
distortion mechanisms studied so far stem from Class B, and we can
thankfully forget crossover and switchoff phenomena (Distortions 3b, 3c),
non-linear VAS loading (Distortion 4), injection of supply-rail signals
(Distortion 5), induction from supply currents (Distortion 6), and erroneous
feedback connections (Distortion 7). Beta-mismatch in the output devices
can also be ignored.
The only real disadvantage of Class-A is inefficiency, so inevitably efforts
have been made to compromise between A and B. As compromises go,
traditional Class-AB is not a happy one (see Chapters 5 and 6) because
when the AB region is entered the step-change in gain generates
significantly greater high-order distortion than that from optimally-biased
Audio Power Amplifier Design Handbook
Class-B. However, a well-designed AB amplifier does give pure Class-A
performance below the AB threshold, something a Class-B amp cannot
Another possible compromise is the so-called non-switching amplifier, with
its output devices clamped to always pass a minimum current. However, it
is not obvious that a sudden halt in current-change as opposed to complete
turn-off makes a better crossover region. Those residual oscillograms that
have been published seem to show that some kind of discontinuity still
exists at crossover [2].
One potential problem is the presence of maximum ripple on the supplyrails at zero signal output; the PSRR must be taken seriously if good noise
and ripple figures are to be obtained. This problem is simply solved by the
measures proposed for Class-B designs in Chapter 8.
Class-A configurations and efficiency
There is a canonical sequence of efficiency in Class-A amplifiers. The
simplest version is single-ended and resistively-loaded, as at Figure 9.1a.
When it sinks output current, there is an inevitable voltage drop across the
emitter resistance, limiting the negative output capability, and resulting in
an efficiency of 12.5% (erroneously quoted in at least one textbook as 25%,
apparently on the grounds that power not dissipated in silicon doesn’t
count). This would be of purely theoretical interest – and not much of that
– except that a single-ended design by Fuller Audio has recently appeared.
This reportedly produces a 10 W output for a dissipation of 120 W, with
output swing predictably curtailed in one direction [3].
A better method – Constant-current Class-A – is shown in Figure 9.1b. The
current sunk by the lower constant-current source is no longer related to the
voltage across it, and so the output voltage can approach the negative rail
with a practicable quiescent current. (Hereafter shortened to Iq). Maximum
efficiency is doubled to 25% at maximum output; for an example with
20 W output (and a big fan) see Nelson [4]. Some versions (Krell) make the
current-source value switchable, controlling it with a kind of noise-gate.
Push-pull operation once more doubles full-power efficiency, getting us to
a more practical 50%; most commercial Class-A amplifiers have been of
this type. Both output halves now swing from zero to twice the Iq, and least
voltage corresponds with maximum current, reducing dissipation. There is
also the intriguing prospect of cancelling the even-order harmonics
generated by the output devices.
Push-pull action can be induced in several ways. Figures 9.1c, d show the
lower constant current-source replaced by a voltage-controlled currentsource (VCIS). This can be driven directly by the amplifier forward path, as
in Figure 9.1c [5], or by a current-control negative-feedback loop, as at
Class-A power amplifiers
Figure 9.1
The canonical
sequence of
configurations. c, d
and e are push-pull
variants, and
achieve 50%
efficiency. e is
simply a Class-B
stage with higher
Audio Power Amplifier Design Handbook
Figure 9.1d [6]. The first of these methods has the drawback that the stage
generates gain, phase-splitter TR1 doubling as the VAS; hence there is no
circuit node that can be treated as the input to a unity-gain output stage,
making the circuit hard to analyse, as VAS distortion cannot be separated
from output stage non-linearity. There is also no guarantee that upper and
lower output devices will be driven appropriately for Class-A; in LinsleyHood [5] the effective quiescent varies by more than 40% over the cycle.
The second push-pull method in Figure 9.1d is more dependable, and I
have designed several versions that worked well. The disadvantage with
the simple version shown is that a regulated supply is required to prevent
rail ripple from disrupting the current-loop control. Designs of this type
have a limited current-control range – in Figure 9.1d TR3 cannot be turned
on any further once the upper device is fully off – so the lower VCIS will not
be able to respond to an unforeseen increase in the output loading. In this
event there is no way of resorting to Class-AB to keep the show going and
the amplifier will show some form of asymmetrical hard clipping.
The best push-pull stage seems to be that in Figure 9.1e, which probably
looks rather familiar. Like all the conventional Class-B stages examined in
Chapters 5 and 6, this one will operate effectively in pure push-pull Class-A if
the quiescent bias voltage is sufficiently increased; the increment over ClassB is typically 700 mV, depending on the value of the emitter resistors. For an
example of high-biased Class B see Nelson-Jones [7]. This topology has the
great advantage that, when confronted with an unexpectedly low load
impedance, it will operate in Class-AB. The distortion performance will be
inferior not only to Class-A but also to optimally-biased Class-B, once above
the AB transition level, but can still be made very low by proper design.
The push-pull concept has a maximum efficiency of 50%, but this is only
achieved at maximum sinewave output; due to the high peak/average ratio
of music, the true average efficiency probably does not exceed 10%, even
at maximum volume before obvious clipping.
Other possibilities are signal-controlled variation of the Class-A amplifier
rail voltages, either by a separate Class-B amplifier, or a modulated switchmode supply. Both approaches are capable of high power output, but
involve extensive extra circuitry, and present some daunting design
A Class-B amplifier has a limited voltage output capability, but is flexible
about load impedances; more current is simply turned on when required.
However, Class-A has also a current limitation, after which it enters Class
AB, and so loses its raison d’être. The choice of quiescent value has a major
effect on thermal design and parts cost; so Class-A design demands a very
clear idea of what load impedance is to be driven in pure A before we
begin. The calculations to determine the required Iq are straightforward,
though lengthy if supply ripple, Vce(sat)s, and Re losses, etc. are all
Class-A power amplifiers
considered, so I just give the results here. (An unregulated supply with
10,000 µF reservoirs is assumed.)
A 20 W/8 amplifier will require rails of approx. +/–24 V and a quiescent
of 1.15 A. If this is extended to give roughly the same voltage swing into
4 , then the output power becomes 37 W, and to deliver this in Class-A the
quiescent must increase to 2.16 A, almost doubling dissipation. If however
full voltage swing into 6 will do (which it will for many reputable
speakers) then the quiescent only needs to increase to 1.5 A; from here on
I assume a quiescent of 1.6 A to give a margin of safety.
Output stages in Class-A
I consider here only the increased-bias Class-B topology, because it is
probably the best approach, effectively solving the problems presented by
the other methods. Figure 9.2 shows a Spice simulation of the collector
currents in the output devices versus output voltage, and also the sum of
these currents. This sum of device currents is in principle constant in ClassA, though it need not be so for low THD; the output signal is the difference
of device currents, and is not inherently related to the sum. However, a
large deviation from this constant-sum condition means increased inefficiency, as the stage must be conducting more current than it needs to for
some part of the cycle.
Figure 9.2
How output device
current varies in pushpull Class-A. The sum
of the currents is nearconstant, simplifying
Audio Power Amplifier Design Handbook
The constancy of this sum-of-currents is important because it shows that the
voltage measured across Re1 and Re2 together is also effectively constant
so long as the amplifier stays in Class-A. This in turn means that quiescent
current can be simply set with a constant-voltage bias generator, in very
much the same way as Class-B.
Figures 9.3, 9.4 and 9.5 show Spice gain plots for open-loop output stages,
with 8 loading and 1.6 A quiescent; the circuitry is exactly as for Class-B
in Chapter 6. The upper traces show Class-A gain, and the lower traces
optimal-bias Class-B gain for comparison. Figure 9.3 shows an emitterfollower output, Figure 9.4 a simple quasi-complementary stage, and
Figure 9.5 a CFP output.
We would expect Class-A stages to be more linear than B, and they are.
(Harmonic and THD figures for the three configurations, at 20 V Pk, are
shown in Table 9.1.) There is absolutely no gain wobble around 0 V, as in
Class-B, and push-pull Class-A really can and does cancel even-order
It is at once clear that the emitter-follower has more gain variation, and
therefore worse linearity, than the CFP, while the quasi-comp circuit shows
an interesting mix of the two. The more curved side of the quasi gain plot
is on the –ve side, where the CFP half of the quasi circuit is passing most of
the current; however we know by comparing Figure 9.3 and Figure 9.5 that
the CFP is the more linear structure. Therefore it appears that the shape of
Figure 9.3
Gain linearity of the
Class-A emitter-follower
output stage. Load is
8 , and quiescent
current (Iq) is 1.6 A
Class-A power amplifiers
Figure 9.4
Gain linearity of the
Class-A quasicomplementary output
stage. Conditions as
Figure 9.3
Figure 9.5
Gain linearity of the
Class-A CFP output
Audio Power Amplifier Design Handbook
Table 9.1
Emitter Follower
CFP Output
(THD is calculated from the first nine harmonics, though levels above the fifth are
very small)
the gain curve is determined by the output half that is turning off,
presumably because this shows the biggest gm changes. The CFP structure
maintains gm better as current decreases, and so gives a flatter gain curve
with less rounding of the extremes.
The gain behaviour of these stages is reflected in their harmonic generation;
Table 9.1 reveals that the two symmetrical topologies give mostly oddorder harmonics, as expected. The asymmetry of the quasi-comp version
causes a large increase in even-order harmonics, and this is reflected in the
higher THD figure. Nonetheless all the THD figures are still 2 to 3 times
lower than for their Class-B equivalents.
This modest factor of improvement may seem a poor return for the extra
dissipation of Class-A, but not so. The crucial point about the distortion
from a Class-A output stage is not just that it is low in magnitude, but that
it is low-order, and so benefits much more from the typical NFB factor that
falls with frequency than does high-order crossover distortion.
The choice of Class-A output topology is now simple. For best performance, use the CFP; apart from greater basic linearity, the effects of output
device temperature on Iq are servoed-out by local feedback, as in Class B.
For utmost economy, use the quasi-complementary with two NPN devices;
these need only a low Vce(max) for a typical Class-A amp, so here is an
opportunity to recoup some of the money spent on heatsinking. The rules
here are somewhat different from Class-B; the simple quasi-complementary
configuration gives first-class results with moderate NFB, and adding a
Baxandall diode to simulate a complementary emitter-follower stage gives
little improvement in linearity. See however Nelson-Jones [7] for an example
of its use.
It is sometimes assumed that the different mode of operation of Class-A
makes it inherently short-circuit proof. This may be true with some
configurations, but the high-biased type studied here will continue
delivering current in time-honoured Class-B fashion until it bursts, and
overload protection seems to be no less essential.
Class-A power amplifiers
Quiescent current control systems
Unlike Class-B, precise control of quiescent current is not required to
optimise distortion; for good linearity there just has to be enough of it.
However, the Iq must be under some control to prevent thermal runaway,
particularly if the emitter-follower output is used. A badly designed
quiescent controller can ruin the linearity, and careful design is required.
There is also the point that a precisely held standing-current is considered
the mark of a well-bred Class-A amplifier; a quiescent that lurches around
like a drunken sailor does not inspire confidence.
Straightforward thermal compensation with a Vbe-multiplier bias generator
works [8], and will prevent thermal runaway. However, unlike Class-B,
Class-A gives the opportunity of tightly controlling Iq by negative feedback.
This is profoundly ironic because now that we can precisely control Iq, it
is no longer critical. Nevertheless it seems churlish to ignore the
opportunity, and so feedback quiescent control will be examined.
There are two basic methods of feedback current-control. In the first, the
current in one output device is monitored, either by measuring the voltage
across one emitter-resistor (Rs in Figure 9.6a), or by a collector sensing
resistor; the second method monitors the sum of the device currents, which
as described above, is constant in Class-A.
The first method as implemented in Figure 9.6a [7] compares the Vbe of TR4
with the voltage across Rs , with filtering by RF, CF. If quiescent is excessive,
then TR4 conducts more, turning on TR5 and reducing the bias voltage
between points A and B. In Figure 9.6b, which uses the VCIS approach, the
voltage across collector sensing resistor Rs is compared with Vref by TR4,
the value of Vref being chosen to allow for TR4 Vbe [9]. Filtering is once
more by RF, CF.
For either Figure 9.6a or b, the current being monitored contains large
amounts of signal, and must be low-pass filtered before being used for control
purposes. This is awkward as it adds one more time-constant to worry about if
the amplifier is driven into asymmetrical clipping. In the case of collectorsensing there are unavoidable losses in the extra sense resistor. It is also my
experience that imperfect filtering causes a serious rise in LF distortion.
The Better Way is to monitor current in both emitter resistors; as explained
above, the voltage across both is very nearly constant, and in practice
filtering is unnecessary. An example of this approach is shown in Figure 9.6c,
based on a concept originated by Nelson Pass [10]. Here TR4 compares its
own Vbe with the voltage between X and B; excessive quiescent turns on
TR4 and reduces the bias directly. Diode D is not essential to the concept, but
usefully increases the current-feedback loop-gain; omitting it more than
doubles Iq variation with TR7 temperature in the Pass circuit.
The trouble with this method is that TR3 Vbe directly affects the bias setting,
but is outside the current-control loop. A multiple of Vbe is established
Audio Power Amplifier Design Handbook
Figure 9.6
Current-control systems.
Only that at c avoids
the need to low-pass
filter the control signal;
C simply provides
feedforward to speed
up signal transfer to
Class-A power amplifiers
between X and B, when what we really want to control is the voltage
between X and Y. The temperature variations of TR4 and TR3 Vbe partly
cancel, but only partly. This method is best used with a CFP or quasi output so
that the difference between Y and B depends only on the driver temperature,
which can be kept low. The reference is TR4 Vbe, which is itself temperaturedependent; even if it is kept away from the hot bits it will react to ambient
temperature changes, and this explains the poor performance of the Pass
method for global temp changes (Table 9.2).
Table 9.2
Iq change per
degree C
TR7 temp only
Global temp
Quasi + Vbe-mult
Pass: as Figure 9.6c
Pass: no diode D
New system:
(assuming OR22 emitter resistors and 1.6 A Iq)
A novel quiescent current controller
To solve this problem, I would like to introduce the novel control method
in Figure 9.7. We need to compare the floating voltage between X and Y
with a fixed reference, which sounds like a requirement for two differential
amplifiers. This can be reduced to one by sitting the reference Vref on point
Y; this is a very low-impedance point and can easily swallow a reference
current of 1 mA or so. A simple differential pair TR15, 16 then compares the
reference voltage with that at point Y; excess quiescent turns on TR16,
causing TR13 to conduct more and reducing the bias voltage.
The circuitry looks enigmatic because of the high-impedance of TR13
collector would seem to prevent signal from reaching the upper half of the
output stage; this is in essence true, but the vital point is that TR13 is part
of an NFB loop that establishes a voltage at A that will keep the bias voltage
between A and B constant. This comes to the same thing as maintaining a
constant Vbias across TR5. As might be imagined, this loop does not shine
at transferring signals quickly, and this duty is done by feed-forward
capacitor C4. Without it, the loop (rather surprisingly) works correctly, but
HF oscillation at some part of the cycle is almost certain. With C4 in place
the current-loop does not need to move quickly, since it is not required to
transfer signal but rather to maintain a DC level.
The experimental study of Iq stability is not easy because of the inaccessibility of junction temperatures. Professional SPICE implementations like
Figure 9.7
A Blameless 20 W Class-A power amplifier, using the novel current-control system
Class-A power amplifiers
PSpice allow both the global circuit temperature and the temperature of
individual devices to be manipulated; this is another aspect where simulators shine. The exact relationships of component temperatures in an
amplifier is hard to predict, so I show here only the results of changing the
global temperature of all devices, and changing the junction temp of TR7
alone (Figure 9.7) with different current-controllers. TR7 will be one of the
hottest transistors and unlike TR9 it is not in a local NFB loop, which would
greatly reduce its thermal effects.
A Class-A design
A design example of a Blameless 20 W/8 Class-A power amplifier is
shown in Figure 9.7. This is as close as possible in operating parameters to
the previous Class-B design, to aid comparison; in particular the NFB factor
remains 30 dB at 20 kHz. The front-end is as for the Class-B version, which
should not be surprising as it does exactly the same job, input Distortion 1
being unaffected by output topology. As before the input pair uses a high
tail current, so that R2, 3 can be introduced to linearise the transfer
characteristic and set the transconductance. Distortion 2 (VAS) is dealt with
as before, the beta-enhancer TR12 increasing the local feedback through
Cdom. There is no need to worry about Distortion 4 (non-linear loading by
output stage) as the input impedance of a Class-A output, while not
constant, does not have the sharp variations shown by Class-B.
Figure 9.7 uses a standard quasi output. This may be replaced by a CFP
stage without problems. In both cases the distortion is extremely low, but
gratifyingly the CFP proves even better than the quasi, confirming the
simulation results for output stages in isolation.
The operation of the current regulator TR13, 15, 16 has already been
described. The reference used is a National LM385/1.2. Its output voltage
is fixed at 1.223 V nominal; this is reduced to approx. 0.6 V by a 1k–1k
divider (not shown). Using this band-gap reference, a 1.6 A Iq is held to
within +/–2 mA from a second or two after switch-on. Looking at Table 9.2,
there seems no doubt that the new system is effective.
As before, a simple unregulated power supply with 10,000 µF reservoirs
was used, and despite the higher prevailing ripple, no PSRR difficulties
were encountered once the usual decoupling precautions were taken.
The closed-loop distortion performance (with conventional compensation)
is shown in Figure 9.8 for the quasi-comp output stage, and in Figure 9.9
for a CFP output version. The THD residual is pure noise for almost all of
the audio spectrum, and only above 10 kHz do small amounts of thirdharmonic appear. The expected source is the input pair, but this so far
remains unconfirmed.
The distortion generated by the Class-B and A design examples is
summarised in Table 9.3, which shows a pleasing reduction as various
Audio Power Amplifier Design Handbook
Figure 9.8
Class-A amplifier
THD performance
with quasi-comp
output stage. The
steps in the LF portion
of the trace are
Figure 9.9
Class-A distortion
performance with
CFP output stage
Table 9.3
B EF 2-pole
A quasi
A CFP 2-pole
1 kHz
10 kHz
20 kHz
50 W
50 W
50 W
20 W
20 W
20 W
(All for 8 loads and 80 kHz bandwidth. Single-pole compensation unless otherwise
Class-A power amplifiers
Figure 9.10
performance for CFP
output stage with
2-pole compensation.
The THD drops to
0.0012% at 20 kHz,
but the extra VAS
loading has
compromised the
positive-going slew
measures are taken to deal with it. As a final fling two-pole compensation
was applied to the most linear (CFP) of the Class-A versions, reducing
distortion to a rather small .0012% at 20 kHz, at some cost in slew-rate.
(Figure 9.10). While this may not be the fabled Distortionless Amplifier, it
must be a near relation . . .
The trimodal amplifier
I present here my own contribution to global warming in the shape of an
improved Class-A amplifier; it is believed to be unique in that it not only
copes with load impedance dips by means of the most linear form of ClassAB possible, but will also operate as a Blameless Class-B engine. The
power output in pure Class-A is 20 to 30 W into 8 , depending on the
supply-rails chosen.
This amplifier uses a Complementary-Feedback-Pair (CFP) output stage for
best possible linearity, and some incremental improvements have been
made to noise, slew-rate and maximum DC offset. The circuit naturally
bears a very close resemblance to a Blameless Class-B amplifier, and so it
was decided to retain the Class-B Vbe-multiplier, and use it as a safetycircuit to prevent catastrophe if the relatively complex Class-A currentregulator failed. From this the idea arose of making the amplifier instantly
switchable between Class-A and Class-B modes, which gives two kinds of
amplifier for the price of one, and permits of some interesting listening tests.
Now you really can do an A/B comparison . . .
In the Class-B mode the amplifier has the usual negligible quiescent
dissipation. In Class-A the thermal dissipation is naturally considerable, as
true Class-A operation is extended down to 6 resistive loads for the full
output voltage swing, by suitable choice of the quiescent current; with
heavier loading the amplifier gracefully enters Class-AB, in which it will
give full output down to 3 before the Safe-Operating-Area (SOAR)
Audio Power Amplifier Design Handbook
limiting begins to act. Output into 2 is severely curtailed, as it must be
with one output pair, and this kind of load is definitely not
In short, the amplifier allows a choice between:
1 being very linear all the time (Blameless Class-B) and
2 ultra-linear most of the time (Class-A) with occasional excursions into
Class-AB. The AB mode is still extremely linear by current standards,
though inherently it can never be quite as good as properly-handled
Class-B. Since there are three classes of operation I have decided to call
the design a trimodal power amplifier.
It is impossible to be sure that you have read all the literature; however, to
the best of my knowledge this is the first ever Trimodal amplifier.
As previously said, designing a low-distortion Class-A amplifier is in
general a good deal simpler than the same exercise for Class-B, as all the
difficulties of arranging the best possible crossover between the output
devices disappear. Because of this it is hard to define exactly what
Blameless means for a Class-A amplifier. In Class-B the situation is quite
different, and Blameless has a very specific meaning; when each of the
eight or more distortion mechanisms has been minimised in effect, there
always remains the crossover distortion inherent in Class-B, and there
appears to be no way to reduce it without departing radically from what
might be called the generic Lin amplifier configuration. Therefore the
Blameless state appears to represent some sort of theoretical limit for ClassB, but not for Class-A.
However, Class-B considerations cannot be ignored, even in a design
intended to be Class-A only, because if the amplifier does find itself driving
a lower load impedance than expected, it will move into Class-AB, and
then all the additional Class-B requirements are just as significant as for a
Class-B design proper. Class-AB can never give distortion as low as
optimally-biased Class-B, but it can be made to approach it reasonably
closely, if the extra distortion mechanisms are correctly handled.
In a class-A amplifier, certain sacrifices are made in the name of quality,
and so it is reasonable not to be satisfied with anything less than the best
possible linearity. The amplifier described here therefore uses the Complementary-Feedback-Pair (CFP) type of output stage, which has the
lowest distortion due to the local feedback loops wrapped around the
output devices. It also has the advantage of better output efficiency than
the emitter-follower (EF) version, and inherently superior quiescent
current stability. It will shortly be seen that these are both important for
this design.
Half-serious thought was given to labelling the Class-A mode Distortionless
as the THD is completely unmeasurable across most of the audio band.
Class-A power amplifiers
However, detectable distortion products do exist above 10 kHz, so this
provocative idea was regretfully abandoned.
It seemed appropriate to take another look at the Class-A design, to see if
it could be inched a few steps nearer perfection. The result is a slight
improvement in efficiency, and a 2 dB improvement in noise performance.
In addition the expected range of output DC offset has been reduced from
+/–50 mV to +/–15 mV, still without any adjustment.
Load impedance and operating mode
The amplifier is 4 capable in both A/AB and B operating modes, though
it is the nature of things that the distortion performance is not quite so good.
All solid-state amplifiers (without qualification, as far as I am aware) are
much happier with an 8 load, both in terms of linearity and efficiency;
loudspeaker designers please note. With a 4 load, Class-B operation
gives better THD than Class-A/AB, because the latter will always be in AB
mode, and therefore generating extra output stage distortion through gmdoubling. (Which should really be called gain-deficit-halving, but somehow I don’t see this term catching on.) These not entirely obvious
relationships are summarised in Table 9.4.
Table 9.4
Very low
(Note: High distortion in the context of this sort of amplifier means about 0.002%
THD at 1 kHz and 0.01% at 10 kHz)
Figure 9.11 attempts to show diagrammatically just how power, load
resistance, and operating mode are related. The rails have been set to
+/–20 V, which just allows 20 W into 8 in Class-A. The curves are lines
of constant power (i.e. V × I in the load), the upper horizontal line
represents maximum voltage output, allowing for Vce(sat)s, and the sloping
line on the right is the SOAR protection locus; the output can never move
outside this area in either mode. The intersection between the load
resistance lines sloping up from the origin and the ultimate limits of
voltage-clip and SOAR protection define which of the curved constantpower lines is reached.
Audio Power Amplifier Design Handbook
Figure 9.11
The relationships
between load,
mode, and power
output. The
intersection between
the sloping load
resistance lines and
the ultimate limits of
voltage-clipping and
SOAR protection
define which of the
curved constantpower lines is
reached. In A/AB
mode, the operating
point must be to the
left of the vertical
push-pull current-limit
line for true Class-A
In A/AB mode, the operating point must be left of the vertical push-pull
current-limit line (at 3 A, twice the quiescent current) for Class-A. If we
move to the right of this limit along one of the impedance lines, the output
devices will begin turning off for part of the cycle; this is the AB operation
zone. In Class-B mode, the 3 A line has no significance and the amplifier
remains in optimal Class-B until clipping or SOAR limiting occurs. Note
that the diagram axes represent instantaneous power in the load, but the
curves show sinewave RMS power, and that is the reason for the apparent
factor-of-two discrepancy between them.
Concern for efficiency in Class-A may seem paradoxical, but one way of
looking at it is that Class-A Watts are precious things, wrought in great heat
and dissipation, and so for a given quiescent power it makes sense to
ensure that the amplifier approaches its limited theoretical efficiency as
closely as possible. I was confirmed in this course by reading of another
recent design [11] which seems to throw efficiency to the winds by using a
hybrid BJT/FET cascode output stage. The voltage losses inherent in this
arrangement demand +/–50 V rails and six-fold output devices for a 100 W
Class-A capability; such rail voltages would give 156 W from a 100%
efficient amplifier.
The voltage efficiency of a power amplifier is the fraction of the supply-rail
voltage which can actually be delivered as peak-to-peak voltage swing into
Class-A power amplifiers
a specified load; efficiency is invariably less into 4 due to the greater
resistive voltage drops with increased current.
The Class-B amplifier I described in Chapter 6 has a voltage efficiency of
91.7% for positive swings, and 92.5% for negative, into 8 . Amplifiers are
not in general completely symmetrical, and so two figures need to be
quoted; alternatively the lower of the two can be given as this defines the
maximum undistorted sinewave. These figures above are for an emitterfollower output stage, and a CFP output does better, the positive and
negative efficiencies being 94.0% and 94.7% respectively. The EF version
gives a lower output swing because it has two more Vbe drops in series to
be accommodated between the supply-rails; the CFP is always more
voltage-efficient, and so selecting it over the EF for the current Class-A
design is the first step in maximising efficiency.
Figure 9.12 shows the basic CFP output stage, together with its two biasing
elements. In Class-A the quiescent current is rigidly controlled by negativefeedback; this is possible because in Class-A the total voltage across both
emitter resistors Re is constant throughout the cycle. In Class-B this is not
the case, and we must rely on thermal feedback from the output stage,
though to be strictly accurate this is not feedback at all, but a kind of
feedforward (Chapter 12). Another big advantage of the CFP configuration
Figure 9.12
The basic CFP output
stage, equally suited to
operating Class B, AB
and A, depending on
the magnitude of
Vbias. The emitter
resistors Re may be
from 0.1 to 0.47 273
Audio Power Amplifier Design Handbook
is that Iq depends only on driver temperature, and this is important in the
Class-B mode, where true feedback control of quiescent current is not
possible, especially if low-value Re’s such as 0.1 , are chosen, rather than
the more usual 0.22 ; the motivation for doing this will soon become
The voltage efficiency for the quasi-complementary Class-A circuit of the
circuit on page 266 into 8 is 89.8% positive and 92.2% negative.
Converting this to the CFP output stage increases this to 92.9% positive and
93.6% negative. Note that a Class-A quiescent current (Iq) of 1.5 A is
assumed throughout; this allows 31 W into 8 in push-pull, if the supplyrails are adequately high. However the assumption that loudspeaker
impedance never drops below 8 is distinctly doubtful, to put it mildly,
and so as before this design allows for full Class-A output voltage swing into
loads down to 6 .
So how else can we improve efficiency? The addition of extra and higher
supply-rails for the small-signal section of the amplifier surprisingly does
not give a significant increase in output; examination of Figure 9.13 shows
why. In this region, the output device TR6 base is at a virtually constant
880 mV from the V+ rail, and as TR7 driver base rises it passes this level,
and keeps going up; clipping has not yet occurred. The driver emitter
follows the driver base up, until the voltage difference between this emitter
and the output base (i.e. the driver Vce) becomes too small to allow further
conduction; this choke point is indicated by the arrows A–A. At this point
the driver base is forced to level off, although it is still about 500 mV below
the level of V+. Note also how the voltage between V+ and TR5 emitter
Figure 9.13
PSpice simulation
showing how
positive clipping
occurs in the CFP
output. A higher subrail for the VAS
cannot increase the
output swing, as the
limit is set by the
minimum driver Vce,
and not the VAS
output swing
Class-A power amplifiers
collapses. Thus a higher rail will give no extra voltage swing, which I must
admit came as something of a surprise. Higher sub-rails for small-signal
sections only come into their own in FET amplifiers, where the high Vgs for
FET conduction (5 V or more) makes their use almost mandatory.
The efficiency figures given so far are all greater for negative rather than
positive voltage swings. The approach to the rail for negative clipping is
slightly closer because there is no equivalent to the 0.6 V bias established
across R13; however this advantage is absorbed by the need to lose a little
voltage in the RC filtering of the V– supply to the current-mirror and VAS.
This is essential if really good ripple/hum performance is to be obtained
(see Chapter 8).
In the quest for efficiency, an obvious variable is the value of the output
emitter resistors Re. The performance of the current-regulator described,
especially when combined with a CFP output stage, is more than good
enough to allow these resistors to be reduced while retaining first-class Iq
stability. I took 0.1 as the lowest practicable value, and even this is
comparable with PCB track resistance, so some care in the exact details of
physical layout is essential; in particular the emitter resistors must be
treated as four-terminal components to exclude unwanted voltage drops in
the tracks leading to the resistor pads.
If Re is reduced from 0.22 to 0.1 then voltage efficiency improves from
92.9%/93.6%, to 94.2%/95.0%. Is this improvement worth having? Well,
the voltage-limited power output into 8 is increased from 31.2 to 32.2 W
with +/–24 V rails, at zero cost, but it would be idle to pretend that the
resulting increase in SPL is highly significant; it does however provide the
philosophical satisfaction that as much Class-A power as possible is being
produced for a given dissipation; a delicate pleasure.
The linearity of the CFP output stage in Class-A is very slightly worse with
0.1 emitter resistors, though the difference is small and only detectable
open-loop; the simulated THD for 20 V pk–pk into 8 is only increased
from 0.0027% to 0.0029%. This is probably due simply to the slightly
lower total resistance seen by the output stage.
However, at the same time, reducing the emitter resistors to 0R1 provides
much lower distortion when the amplifier runs out of Class-A; it halves the
size of the step gain changes inherent in Class-AB, and so effectively
reduces distortion into 4 loads. See Figures 9.14 and 9.15 for output
linearity simulations; the measured results from a real and Blameless
Trimodal amplifier are shown in Figure 9.16, where it can be clearly seen
that THD has been halved by this simple change. To the best of my
knowledge this is a new result; if you must work in Class-AB, then keep the
emitter resistors as low as possible, to minimise the gain changes.
Having considered the linearity of Class-A and AB, we must not neglect
what effect this radical Re change has on Class-B linearity. The answer is,
Audio Power Amplifier Design Handbook
Figure 9.14
CFP output stage
linearity with
Re = 0R22. Upper
trace is Class-A into
8 , lower is ClassAB operation into
4 , showing step
changes in gain of
.024 units
Figure 9.15
CFP output linearity
with Re = 0R1,
re-biased to keep Iq at
1.5 A. There is slightly
poorer linearity in the
flat-topped Class-A
region than for
Re = 0R22, but the
4 AB steps are
halved in size at .012
units. Note that both
gains are now closer to
unity; same scale as
Figure 9.14
Class-A power amplifiers
Figure 9.16
Distortion in Class-AB
is reduced by
lowering the value of
Figure 9.17
Proving that emitter
resistors matter much
less in Class-B. Output
was 20 W in 8 ,
with optimal bias.
Interestingly, the bias
does not need
adjusting as the value
of Re changes
not very much; see Figure 9.17, where crossover distortion seems to be
slightly higher with Re = 0.2 than for either 0.1 or 0.4 . Whether this is
a consistent effect (for CFP stages anyway) remains to be seen.
The detailed mechanisms of bias control and mode-switching are
described on pages 277–282.
On Trimodal biasing
Figure 9.18 shows a simplified rendering of the Trimodal biasing system;
the full version appears in Figure 9.19. The voltage between points A and
B is determined by one of two controller systems, only one of which can be
in command at a time. Since both are basically shunt voltage regulators
sitting between A and B, the result is that the lowest voltage wins. The novel
Class-A current-controller introduced on page 265 is used here adapted for
0.1 emitter resistors, mainly by reducing the reference voltage to 300 mV,
which gives a quiescent current (Iq) of 1.5 A when established across the
total emitter resistance of 0.2 .
Audio Power Amplifier Design Handbook
Figure 9.18
The simplified currentcontroller in action,
showing typical DC
voltages in Class-A.
Points A, B, X and Y
are in Figure 9.6 on
page 000
In parallel with the current-controller is the Vbe-multiplier TR13. In Class-B
mode, the current-controller is disabled, and critical biasing for minimal
crossover distortion is provided in the usual way by adjusting preset PR1 to
set the voltage across TR13. In Class-A/AB mode, the voltage TR13 attempts
to establish is increased (by shorting out PR1) to a value greater than that
required for Class-A. The current-controller therefore takes charge of the
voltage between X and Y, and unless it fails TR13 does not conduct. Points
A, B, X, and Y are the same circuit nodes as in the simple Class-A design
(see Figure 9.6c).
Class-A/AB mode
In Class-A/AB mode, the current-controller (TR14, 15, 16 in Figure 9.18) is
active and TR13 is off, as TR20 has shorted out PR1. TR15, 16 form a
simple differential amplifier that compares the reference voltage across R31
with the Vbias voltage across output emitter resistors R16 and R17; as
explained above, in Class-A this voltage remains constant despite delivery
of current into the load. If the voltage across R16, 17 tends to rise, then
TR16 conducts more, turning TR14 more on and reducing the voltage
between A and B. TR14, 15 and 16 all move up and down with the
amplifier output, and so a tail current-source (TR17) is used.
I am very aware that the current-controller is more complex than the simple
Vbe-multiplier used in most Class-B designs. There is an obvious risk that
an assembly error could cause a massive current that would prompt the
Figure 9.19
The complete circuit diagram of Trimodal amplifier, including the optional bootstrapping components, R47 and C15
Audio Power Amplifier Design Handbook
output devices to lay down their lives to save the rail fuses. The tail-source
TR17 is particularly vulnerable because any fault that extinguishes the tailcurrent removes the drive to TR14, the controller is disabled, and the
current in the output stage will be very large. In Figure 9.18 the Vbemultiplier TR13 acts as a safety-circuit which limits Vbias to about 600 mV
rather than the normal 300 mV, even if the current-controller is completely
non-functional and TR14 fully off. This gives a quiescent of 3.0 A, and I can
testify this is a survivable experience for the output devices in the shortterm; however they may eventually fail from overheating if the condition is
allowed to persist.
There are some important points about the current-controller. The entire
tail-current for the error-amplifier, determined by TR17, is syphoned off
from VAS current source TR5, and must be taken into account when
ensuring that the upper output half gets enough drive current.
There must be enough tail-current available to turn on TR14, remembering
that most of TR16 collector-current flows through R15, to keep the pair
roughly balanced. If you feel moved to alter the VAS current, remember
also that the base current for driver TR6 is higher in Class-A than Class-B,
so the positive slew-rate is slightly reduced in going from Class-A to B.
The original Class-A amplifier used a National LM385/1.2, its output
voltage fixed at 1.223 V nominal; this was reduced to approx. 0.6 V by a
1k–1k divider. The circuit also worked well with Vref provided by a silicon
diode, 0.6 V being an appropriate Vbias drop across two 0.22 output
emitter resistors. This is simple, and retains the immunity of Iq to heatsink
and output device temperatures, but it does sacrifice the total immunity to
ambient temperature that a band-gap reference gives.
The LM385/1.2 is the lowest voltage band-gap reference commonly
available; however, the voltages shown in Figure 9.18 reveal a difficulty
with the new lower Vbias value and the CFP stage; points A and Y are now
only 960 mV apart, which does not give the reference room to work in if it
is powered from node A, as in the original circuit. The solution is to power
the reference from the V+ rail, via R42 and R43. The mid-point of these two
resistors is bootstrapped from the amplifier output rail by C5, keeping the
voltage across R43 effectively constant. Alternatively, a current-source
could be used, but this might reduce positive headroom. Since there is no
longer a strict upper limit on the reference voltage, a more easily obtainable
2.56 V device could be used providing R30 is suitably increased to 5k to
maintain Vref at 300 mV across R31.
In practical use, Iq stability is very good, staying within 1% for long periods.
The most obvious limitation on stability is differential heating of TR15, 16
due to heat radiation from the main heatsink. TR14 should also be sited
with this in mind, as heating it will increase its beta and slightly imbalance
TR15, 16.
Class-A power amplifiers
Class-B mode
In Class-B mode, the current-controller is disabled, by turning off tailsource TR17 so TR14 is firmly off, and critical biasing for minimal crossover
distortion is provided as usual by Vbe-multiplier TR13. With 0.1 emitter
resistors Vbias (between X and Y) is approx. 10 mV. I would emphasise that
in Class-B this design, if constructed correctly, will be as Blameless as a
purpose-built Class-B amplifier. No compromises have been made in
adding the mode-switching.
As in the previous Class-B design, the addition of R14 to the Vbe-multiplier
compensates against drift of the VAS current-source TR5. To make an old
but much-neglected point, the preset should always be in the bottom arm
of the Vbe divider R10, 11, because when presets fail it is usually by the
wiper going open; in the bottom arm this gives minimum Vbias, but in the
upper it would give maximum.
In Class-B, temperature compensation for changes in driver dissipation
remains vital. Thermal runaway with the CFP is most unlikely, but accurate
quiescent setting is the only way to minimise cross-over distortion. TR13 is
therefore mounted on the same small heatsink as driver TR6. This is often
called thermal feedback, but it is no such thing as TR13 in no way controls
the temperature of TR6; thermal feedforward would be a more accurate
The mode-switching system
The dual nature of the biasing system means Class-A/Class-B switching can
be implemented fairly simply. A Class-A amplifier is an uneasy companion
in hot weather, and so I have been unable to resist the temptation to subtitle the mode switch Summer/Winter, by analogy with a car air intake.
The switchover is DC-controlled, as it is not desirable to have more signal
than necessary running around inside the box, possibly compromising
interchannel crosstalk. In Class-A/AB mode, SW1 is closed, so TR17 is
biased normally by D5, 6, and TR20 is held on via R33, shorting out preset
PR1 and setting TR13 to safety mode, maintaining a maximum Vbias limit
of 600 mV. For Class-B, SW1 is opened, turning off TR17 and therefore
TR15, 16 and 14. TR20 also ceases to conduct, protected against reversebias by D9, and reduces the voltage set by TR13 to a suitable level for
Class-B. The two control pins of a stereo amplifier can be connected
together, and the switching performed with a single-pole switch, without
interaction or increased crosstalk.
The mode-switching affects the current flowing in the output devices, but
not the output voltage, which is controlled by the global feedback loop,
and so it is completely silent in operation. The mode may be freely
switched while the amplifier is handling audio, which allows some
interesting A/B listening tests.
Audio Power Amplifier Design Handbook
It may be questioned why it is necessary to explicitly disable the currentcontroller in Class-B; TR13 is establishing a lower voltage than the currentcontroller which latter subsystem will therefore turn TR14 off as it strives
futilely to increase Vbias. This is true for 8 loads, but 4 impedances
increase the currents flowing in R16, 17 so they are transiently greater than
the Class-A Iq, and the controller will therefore intermittently take control
in an attempt to reduce the average current to 1.5 A. Disabling the
controller by turning off TR17 via R44 prevents this.
If the Class-A controller is enabled, but the preset PR1 is left in circuit (e.g.
by shorting TR20 base-emitter) we have a test mode which allows suitably
cautious testing; Iq is zero with the preset fully down, as TR13 over-rides
the current-controller, but increases steadily as PR1 is advanced, until it
suddenly locks at the desired quiescent current. If the current-controller is
faulty then Iq continues to increase to the defined maximum of 3.0 A.
Thermal design
Class-A amplifiers are hot almost by definition, and careful thermal design
is needed if they are to be reliable, and not take the varnish off the
Sheraton. The designer has one good card to play; since the internal
dissipation of the amplifier is maximal with no signal, simply turning on the
prototype and leaving it to idle for several hours will give an excellent idea
of worst-case component temperatures. In Class-B the power dissipation is
very program-dependent, and estimates of actual device temperatures in
realistic use are notoriously hard to make.
Table 9.5 shows the output power available in the various modes, with
typical transformer regulation, etc.; the output mode diagram in Figure 9.11
shows exactly how the amplifier changes mode from A to AB with
decreasing load resistance. Remember that in this context high distortion
means 0.002% at 1 kHz. This diagram was produced in the analysis section
of PSpice simply by typing in equations, and without actually simulating
anything at all.
The most important thermal decision is the size of the heatsink; it is going
to be expensive, so there is a powerful incentive to make it no bigger than
Table 9.5
Power capability
Load resistance
20 W
21 W
27 W
28 W
15 W
39 W
39 W
Class-A power amplifiers
necessary. I have ruled out fan cooling as it tends to make concern for ultralow electrical noise look rather foolish; let us rather spend the cost of the
fan on extra cooling fins and convect in ghostly silence. The exact thermal
design calculations are simple but tedious, with many parameters to enter;
the perfect job for a spreadsheet. The final answer is the margin between
the predicted junction temperatures and the rated maximum. Once power
output and impedance range are decided, the heatsink thermal resistance
to ambient is the main variable to manipulate; and this is a compromise
between coolness and cost, for high junction temperatures always reduce
semiconductor reliability. Looking at it very roughly:
Thermal resistance Heat flow Temp rise
Juncn to TO3 Case
36 W
Case to Sink
36 W
Sink to air
72 W
100 junction
75 TO3 case
67 Heatsink
20 Ambient
This shows that the transistor junctions will be 80 degrees above ambient,
i.e. at around 100°C; the rated junction maximum is 200°C, but it really
isn’t wise to get anywhere close to this very real limit. Note the Case-Sink
thermal washers were high-efficiency material, and standard versions have
a slightly higher thermal resistance.
The heatsinks used in the prototype had a thermal resistance of 0.65°C/W
per channel. This is a substantial chunk of metal, and since aluminium is
basically congealed electricity, it’s bound to be expensive.
A complete Trimodal amplifier circuit
The complete Class-A amplifier is shown in Figure 9.19, complete with
optional input bootstrapping. It may look a little complex, but we have only
added four low-cost transistors to realise a high-accuracy Class-A quiescent
controller, and one more for mode-switching. Since the biasing system has
been described above, only the remaining amplifier subsystems are dealt
with here.
The input stage follows my design methodology by using a high tail current
to maximise transconductance, and then linearising by adding input
degeneration resistors R2, 3 to reduce the final transconductance to a
Audio Power Amplifier Design Handbook
suitable level. Current-mirror TR10, 11 forces the collector currents of the
two input devices TR2, 3 to be equal, balancing the input stage to prevent
the generation of second-harmonic distortion. The mirror is degenerated by
R6, 7 to eliminate the effects of Vbe mismatches in TR10, 11. With some
misgivings I added the input network R9, C15, which is definitely not
intended to define the system bandwidth, unless fed from a buffer stage;
with practical values the HF roll-off could vary widely with the source
impedance driving the amplifier. It is intended rather to give the possibility
of dealing with RF interference without having to cut tracks. R9 could be
increased for bandwidth definition if the source impedance is known, fixed,
and taken into account when choosing R9; bear in mind that any value
over 47 will measurably degrade the noise performance. The values
given roll off above 150 MHz to keep out UHF.
The input-stage tail current is increased from 4 to 6 mA, and the VAS
standing current from 6 to 10 mA over the original Chapter 6 circuit. This
increases maximum positive and negative slew-rates from +21, –48 V/µsec
to +37, –52 V/µsec; as described in Chapter 7, this amplifier architecture is
bound to slew asymmetrically. One reason is feedthrough in the VAS
current source; in the original circuit an unexpected slew-rate limit was set
by fast edges coupling through the current-source c-b capacitance to
reduce the bias voltage during positive slewing. This effect is minimised
here by using the negative-feedback type of current source bias generator,
with VAS collector current chosen as the controlled variable. TR21 senses
the voltage across R13, and if it attempts to exceed Vbe, turns on further to
pull up the bases of TR1 and TR5. C11 filters the DC supply to this circuit
and prevents ripple injection from the V+ rail. R5, C14 provide decoupling
to prevent TR5 from disturbing the tail-current while controlling the VAS
The input tail-current increase also slightly improves input-stage linearity,
as it raises the basic transistor gm and allows R2, 3 to apply more local
The VAS is linearised by beta-enhancing stage TR12, which increases
the amount of local NFB through Miller dominant-pole capacitor C3
(i.e. Cdom). R36 has been increased to 2k2 to minimise power dissipation,
as there seems no significant effect on linearity or slewing. Do not omit it
altogether, or linearity will be affected and slewing much compromised.
As described in Chapter 8, the simplest way to prevent ripple from entering
the VAS via the V– rail is old-fashioned RC decoupling, with a small R and
a big C. We have some 200 mV in hand (see page 274) in the negative
direction, compared with the positive, and expending this as the voltagedrop through the RC decoupling will give symmetrical clipping. R37 and
C12 perform this function; the low rail voltages in this design allow the
1000 µF C12 to be a fairly compact component.
Class-A power amplifiers
The output stage is of the Complementary Feedback Pair (CFP) type,
which as previously described, gives the best linearity and quiescent
stability, due to the two local negative feedback loops around driver and
output device. Quiescent stability is particularly important with R16, 17
at 0.1 , and this low value might be rather dicey in a double emitterfollower (EF) output stage. The CFP voltage efficiency is also higher than
the EF version. R25, 26 define a suitable quiescent collector current for
the drivers TR6, 8, and pull charge carriers from the output device bases
when they are turning off. The lower driver is now a BD136; this has a
higher fT than the MJE350, and seems to be more immune to odd
parasitics at negative clipping.
The new lower values for the output emitter resistors R16, 17 halve the
distortion in Class-AB. This is equally effective when in Class-A with too
low a load impedance, or in Class-B but with Iq maladjusted too high. It is
now true in the latter case that too much Iq really is better than too little –
but not much better, and AB still comes a poor third in linearity to Classes
A and B.
SOAR (Safe Operating ARea) protection is given by the networks around
TR18, TR19. This is a single-slope SOAR system that is simpler than twoslope SOAR, and therefore somewhat less efficient in terms of getting the
limiting characteristic close to the true SOAR of the output transistor. In this
application, with low rail voltages, maximum utilisation of the transistor
SOAR is not really an issue; the important thing is to observe maximum
junction temperatures in the A/AB mode.
The global negative-feedback factor is 32 dB at 20 kHz, and this should
give a good margin of safety against Nyquist-type oscillation. Global NFB
increases at 6 dB/octave with decreasing frequency to a plateau of around
64 dB, the corner being at a rather ill-defined 300 Hz; this is then
maintained down to 10 Hz. It is fortunate that magnitude and frequency
here are non-critical, as they depend on transistor beta and other doubtful
It is often stated in hi-fi magazines that semiconductor amplifiers sound
better after hours or days of warm-up. If this is true (which it certainly isn’t
in most cases) it represents truly spectacular design incompetence. This sort
of accusation is applied with particular venom to Class-A designs, because
it is obvious that the large heatsinks required take time to reach final
temperature, so I thought it important to state that in Class-A this design
stabilises its electrical operating conditions in less than a second, giving the
full intended performance. No warm-up time beyond this is required;
obviously the heatsinks take time to reach thermal equilibrium, but as
described above, measures have been taken to ensure that component
temperature has no significant effect on operating conditions or
Audio Power Amplifier Design Handbook
The power supply
A suitable unregulated power supply is that shown in Figure 8.1; a
transformer secondary voltage of 20–0–20 V rms and reservoirs totalling
20,000 µF per rail will give approx. +/–24 V. This supply must be designed
for continuous operation at maximum current, so the bridge rectifier must be
properly heat-sunk, and careful consideration given to the ripple-current
ratings of the reservoirs. This is one reason why reservoir capacitance has
been doubled to 20,000 µF per rail, over the 10,000 µF that was adequate for
the Class-B design; the ripple voltage is halved, which improves voltage
efficiency as it is the ripple troughs that determine clipping onset, but in
addition the ripple current, although unchanged in total value, is now split
between two components. (The capacitance was not increased to reduce
ripple injection, which is dealt with far more efficiently and economically by
making the PSRR high.) Do not omit the secondary fuses; even in these
modern times rectifiers do fail, and transformers are horribly expensive . . .
The performance
The performance of a properly-designed Class-A amplifier challenges the
ability of even the Audio Precision measurement system. To give some
perspective on this, Figure 9.20 shows the distortion of the AP oscillator
driving the analyser section directly for various bandwidths. There appear
to be internal mode changes at 2 kHz and 20 kHz, causing step increases in
oscillator distortion content; these are just visible in the THD plots for
Class-A mode.
Figure 9.20
The distortion in the
AP-1 system at various
Figure 9.21 shows Class-B distortion for 20 W into 8 and 4 , while Figure
9.22 shows the same in Class-A/AB. Figure 9.23 shows distortion in Class-A
for varying measurement bandwidths. The lower bandwidths misleadingly
ignore the HF distortion, but give a much clearer view of the excellent
Class-A power amplifiers
Figure 9.21
Distortion in Class-B
(Summer) mode.
Distortion into 4 is
always worse. Power
was 20 W in 8 and 40 W in 4 ,
bandwidth 80 kHz
Figure 9.22
Distortion in ClassA/AB (Winter) mode,
same power and
bandwidth of Figure
9.21. The amplifier is
in AB mode for the
4 case, and so
distortion is higher
than for Class-B into
4 . At 80 kHz
bandwidth, the
Class-A plot below
10 kHz merely shows
the noise floor
Figure 9.23
Distortion in Class-A
only (20 W/8 ) for
varying measurement
bandwidths. The
lower bandwidths
ignore HF distortion,
but give a much
clearer view of the
excellent linearity
below 10 kHz
Audio Power Amplifier Design Handbook
Figure 9.24
Direct comparison of
Classes A and B
(20 W/8 ) at
30 kHz bandwidth.
The HF rise for B is
due to the inability of
negative feedback
that falls with
frequency to linearise
the high-order
crossover distortion in
the output stage
linearity below 10 kHz. Figure 9.24 gives a direct comparison of Classes A
and B. The HF rise for B is due to high-order crossover distortion being
poorly linearised by negative feedback that falls with frequency.
Further possibilities
One interesting extension of the ideas presented here is the Adaptive
Trimodal Amplifier. This would switch into Class-B on detecting device or
heatsink overtemperature, and would be a unique example of an amplifier
that changed mode to suit the operating conditions. The thermal protection
would need to be latching; flipping from Class-A to Class-B every few
minutes would subject the output devices to unnecessary thermal
1. Moore, B J An Introduction To The Psychology of Hearing Academic
Press, 1982, pp. 48–50.
2. Tanaka, S A New Biasing Circuit for Class-B Operation Journ. Audio
Eng. Soc. Jan/Feb 1981, p. 27.
3. Fuller, S Private communication.
4. Nelson Pass Build A Class-A Amplifier Audio, Feb 1977, p. 28
5. Linsley-Hood, J Simple Class-A Amplifier Wireless World, April 1969,
p. 148.
6. Self, D High-Performance Preamplifier Wireless World, Feb 1979,
p. 41.
7. Nelson-Jones, L Ultra-Low Distortion Class-A Amplifier Wireless
World, March 1970, p. 98.
Class-A power amplifiers
8. Giffard, T Class-A Power Amplifier Elektor Nov 1991, p. 37.
9. Linsley-Hood, J High-Quality Headphone Amp HiFi News and RR, Jan
1979, p. 81.
10. Nelson Pass The Pass/A40 Power Amplifier The Audio Amateur, 1978,
p. 4 (Push-pull).
11. Thagard, N Build a 100 W Class-A Mono Amp Audio, Jan 95, p. 43.
Class-G power amplifiers
Most types of audio power amplifier are less efficient than Class-B; for
example, Class-AB is markedly less efficient at the low end of its power
capability, while it is clear that Class-A wastes virtually all the energy put
into it. Building amplifiers with higher efficiency is more difficult. Class-D,
using ultrasonic pulse-width modulation, promises high efficiency and
sometimes even delivers it, but it is undeniably a difficult technology. The
practical efficiency of Class-D rests on details of circuit design and device
characteristics. The apparently unavoidable LC output filter – second order
at least – can only give a flat response into one load impedance, and its
magnetics are neither cheap nor easy to design. There are likely to be some
daunting EMC difficulties with emissions. Class-D is not an attractive
proposition for high-quality domestic amplifiers that must work with
separate speakers of unknown impedance characteristics.
There is, however, the Class-G method. Power is drawn from either high- or
low-voltage rails as the signal level demands. This technology has taken a
long time to come to fruition, but is now used in very-high-power
amplifiers for large PA systems, where the power savings are important, and
is also making its presence felt in home theatre sytems; if you have seven
or eight power amplifiers instead of two their losses are rather more
significant. Class-G is firmly established in powered subwoofers, and even
in ADSL telephone-line drivers. It is a technology whose time has come.
The principles of Class-G
Music has a large peak-to-mean level ratio. For most of the time the power
output is a long way below the peak levels, and this makes possible the
improved efficiency of Class-G. Even rudimentary statistics for this ratio for
various genres of music are surprisingly hard to find, but it is widely
accepted that the range between 10 dB for compressed rock, and 30 dB for
classical material, covers most circumstances.
Class-G power amplifiers
If a signal spends most of its time at low power, then while this is true a lowpower amplifier will be much more efficient. For most of the time lower
output levels are supplied from the lowest-voltage rails, with a low voltage
drop between rail and output, and correspondingly low dissipation. The
most popular Class-G configurations have two or three pairs of supply rails,
two being usual for hi-fi, while three is more common in high-power PA
When the relatively rare high-power peaks do occur they must be handled
by some mechanism that can draw high power, causing high internal
dissipation, but which only does so for brief periods. These infrequent
peaks above the transition level are supplied from the high-voltage pair of
rails. Clearly the switching between rails is the heart of the matter, and
anyone who has ever done any circuit design will immediately start
thinking about how easy or otherwise it will be to make this happen cleanly
with a 20 kHz signal.
There are two main ways to arrange the dual-rail system: series and parallel
(i.e. shunt). This chapter deals only with the series configuration, as it seems
to have had the greatest application to hi-fi. The parallel version is more
often used in high-power PA amplifiers.
Introducing series class-G
A series configuration Class-G output stage using two rail voltages is shown
in Figure 10.1 The so-called inner devices are those that work in Class-B;
those that perform the rail-switching on signal peaks are called the outer
devices – by me, anyway. In this design study the EF type of output stage is
chosen because of its greater robustness against local HF instability, though
the CFP configuration could be used instead for inner, outer, or both sets of
output devices, given suitable care. For maximum power efficiency the
inner stage normally runs in Class-B, though there is absolutely no reason
why it could not be run in Class-AB or even Class-A; there will be more
discussion of these intriguing possibilities later. If the inner power devices
are in Class-B, and the outer ones conduct for much less than 50% of a
cycle, being effectively in Class-C, then according to the classification
scheme I proposed [1], this should be denoted Class B + C. The plus sign
indicates the series rather than shunt connection of the outer and inner
power devices. This basic configuration was developed by Hitachi to
reduce amplifier heat dissipation [2,3]. Musical signals spend most of their
time at low levels, having a high peak/mean ratio, and power dissipation is
greatly reduced by drawing from the lower ±V1 supply rails at these
The inner stage TR3, 4 operates in normal Class-B. TR1, 2 are the usual
drivers and R1 is their shared emitter resistor. The usual temperature
compensated Vbias generator is required, shown here theoretically split in
Audio Power Amplifier Design Handbook
Figure 10.1
A series Class-G output
stage, alternatively
Class B + C. Voltages
and component values
are typical. The inner
stage is Class-B EF.
Biasing by my method
half to maintain circuit symmetry when the stage is SPICE simulated; since
the inner power devices work in Class-B it is their temperature which must
be tracked to maintain quiescent conditions. Power from the lower supply
is drawn through D3 and D4, often called the commutating diodes, to
emphasise their rail-switching action. The word ‘commutation’ avoids
confusion with the usual Class-B crossover at zero volts. I have called the
level at which rail-switching occurs the transition level.
When a positive-going instantaneous signal exceeds low rail +V1, D1
conducts, TR5 and TR6 turn on and D3 turns off, so the entire output
current is now taken from the high-voltage +V2 rail, with the voltage drop
and hence power dissipation shared between TR4 and TR6. Negative-going
signals are handled in exactly the same way. Figure 10.2 shows how the
collector voltages of the inner power devices retreat away from the output
rail as it approaches the lower supply level.
Class-G power amplifiers
Figure 10.2
The output of a ClassG stage and the
voltages on the
collectors of the inner
output devices
Class-G is commonly said to have worse linearity than Class-B, the blame
usually being loaded onto the diodes and problems with their commutation. As usual, received wisdom is only half of the story, if that, and there
are other linearity problems that are not due to sluggish diodes, as will be
revealed shortly. It is inherent in the Class-G principle that if switching
glitches do occur they only happen at moderate power or above, and are
well displaced away from the critical crossover region where the amplifier
spends most of its time. A Class-G amplifier has a low-power region of true
Class-B linearity, just as a Class-AB amplifier has a low-power region of true
Class-A performance.
Efficiency of Class-G
The standard mathematical derivation of Class-B efficiency with sinewave
drive uses straightforward integration over a half-cycle to calculate internal
dissipation against voltage fraction, i.e. the fraction of possible output
voltage swing. As is well known, in Class-B the maximum heat dissipation
is about 40% of maximum output power, at an output voltage fraction of
63%, which also delivers 40% of the maximum output power to the
The mathematics is simple because the waveforms do not vary in shape
with output level. Every possible idealisation is assumed, such as zero
quiescent current, no emitter resistors, no Vce(sat) losses and so on. In
Audio Power Amplifier Design Handbook
Class-G, on the other hand, the waveforms are a strong function of output
level, requiring variable limits of integration and so on, and it all gets very
The SPICE simulation method described by Self[4] is much simpler, if
somewhat laborious, and can use any input waveform, yielding a Power
Partition Diagram, (PPD) which shows how the power drawn from the
supply is distributed between output device dissipation and useful power in
the load.
No one disputes that sinewaves are poor simulations of music for this
purpose, and their main advantage is that they allow direct comparison
with the purely mathematical approach. However, since the whole point of
Class-G is power saving, and the waveform used has a strong effect on the
results, I have concentrated here on the PPD of an amplifier with real
musical signals, or at any rate, their statistical representation. The triangular
Probability Distribution Function (PDF) approach is described in Self[5].
Figure 10.3 shows the triangular PDF PPD for conventional Class-B EF, while
Figure 10.4 is that for Class-G with ±V2 = 50 V and ±V1 = 15 V, i.e. with the
ratio of V1/V2 set to 30%. The PPD plots power dissipated in all four output
devices, the load, and the total drawn from the supply rails. It shows how the
input power is partitioned between the load and the output devices. The total
sums to slightly less than the input power, the remainder being accounted for
as usual by losses in the drivers and Re’s. Note that in Class-G power
dissipation is shared, though not very equally, between the inner and outer
devices, and this helps with efficient utilisation of the silicon.
Figure 10.3
Power partition
diagram for a
conventional Class-B
amplifier handling a
typical music signal
with a triangular
Probability Density
Function. X-axis is
Class-G power amplifiers
Figure 10.4
Power partition
diagram for Class-G
with V1/V2 = 30%.
Signal has a
triangular PDF. X-axis
is volume; outer
devices dissipate
nothing until –15 dB
is reached
In Figure 10.4 the lower area represents the power dissipated in the inner
devices and the larger area just above represents that in the outer devices;
there is only one area for each because in Class-B and Class-G only one
side of the amplifier conducts at a time. Outer device dissipation is zero
below the rail-switching threshold at –15 dB below maximum output. The
total device dissipation at full output power is reduced from 48 W in ClassB to 40 W, which may not appear at first to be a very good return for
doubling the power transistors and drivers.
Figure 10.5 shows the same PPD but with ±V2 = 50 V and ±V1 = 30 V, i.e.
with V1/V2 set to 60%. The low-voltage region now extends up to –6 dB ref
Figure 10.5
Power partition
diagram for Class-G
with V1/V2 = 60%.
Triangular PDF.
Compared with
Figure 10.4, the
inner devices
dissipate more and
the outer devices
almost nothing
except at maximum
Audio Power Amplifier Design Handbook
full power, but the inner device dissipation is higher due to the higher V1
rail voltages. The result is that total device power at full output is reduced
from 48 W in Class-B to 34 W, which is a definite improvement. The
efficiency figure is highly sensitive to the way the ratio of rail voltages
compares with the signal characteristics. Domestic hi-fi amplifiers are not
operated at full volume all the time, and in real life the lower option for the
V1 voltage is likely to give lower general dissipation. I do not suggest that
V1/V2 = 30% is the optimum lower-rail voltage for all situations, but it
looks about right for most domestic hi-fi.
In my time I have wrestled with many ‘new and improved’ output stages
that proved to be anything but. When faced with a new and intriguing
possibility, I believe the first thing to do is sketch out a plausible circuit such
as Figure 10.1 and see if it works in SPICE simulation. It duly did.
The next stage is to build it, power it from low supply rails to minimise any
resulting explosions, and see if it works for real at 1 kHz. This is a bigger
step than it looks.
SPICE simulation is incredibly useful but it is not a substitute for testing a
real prototype. It is easy to design clever and complex output stages that
work beautifully in simulation but in reality prove impossible to stabilise at
high frequencies. Some of the most interesting output-triple configurations
seem to suffer from this.
The final step – and again it is a bigger one than it appears – is to prove real
operation at 20 kHz and above. Again it is perfectly possible to come up
with a circuit configuration that either just does not work at 20 kHz, due to
limitations on power transistor speeds, or is provoked into oscillation or
other misbehaviour that is not set off by a 1 kHz testing.
Only when these vital questions are resolved is it time to start considering
circuit details, and assessing just how good the amplifier performance is
likely to be.
The biasing requirements
The output stage bias requirements are more complex than for Class-B. Two
extra bias generators Vbias3, Vbias4 are required to make TR6 turn on
before TR3 runs out of collector voltage. These extra bias voltages are not
critical, but must not fall too low, or become much too high. Should these
bias voltages be set too low, so the outer devices turn on too late, then the
Vce across TR3 becomes too low, and its current sourcing capability is
reduced. When evaluating this issue bear in mind the lowest impedance
load the amplifier is planned to drive, and the currents this will draw from
the output devices. Fixed Zener diodes of normal commercial tolerance are
quite accurate and stable enough for setting Vbias3 and Vbias4.
Class-G power amplifiers
Alternatively, if the bias voltage is set too low, then the outer transistors will
turn on too early, and the heat dissipation in the inner power devices
becomes greater than it need be for correct operation. The latter case is
rather less of a problem so if in doubt this bias should be chosen to be on
the high side rather than the low.
The original Hitachi circuit [1] put Zeners in series with the signal path to the
inner drivers to set the output quiescent bias, their voltage being subtracted
from the main bias generator which was set at 10 V or so, a much higher
voltage than usual (see Figure 10.6). SPICE simulation showed me that the
presence of Zener diodes in the forward path to the inner power devices gave
poor linearity, which is not exactly a surprise. There is also the problem that
the quiescent conditions will be affected by changes in the Zener voltage.
The 10 V bias generator, if it is the usual Vbe multiplier, will have much too
high a temperature coefficient for proper thermal tracking.
I therefore rearrange the biasing as in Figure 10.1. The amplifier forward
path now goes directly to the inner devices, and the two extra bias voltages
Figure 10.6
The original Hitachi
Class-G biasing
system, with inner
device bias derived by
subtracting Vbias3, 4
from the main bias
Audio Power Amplifier Design Handbook
are in the path to the outer devices; since these do not control the output
directly, the linearity of this path is of little importance. The Zeners are out
of the forward path and the bias generator can be the standard sort. It must
be thermally coupled to the inner power devices; the outer ones have no
effect on the quiescent conditions.
The linearity issues of series Class-G
Series Class-G has often had its linearity called into question because of
difficulties with supply-rail commutation. Diodes D3, D4 must be power
devices capable of handling a dozen amps or more, and conventional
silicon rectifier diodes that can handle such currents take a long time to
turn off due to their stored charge carriers. This has the following unhappy
effect: when the voltage on the cathode of D3 rises above V1, the diode
tries to turn off abruptly, but its charge carriers sustain a brief but large
reverse current as they are swept from its junction. This current is supplied
by TR6, attempting as an emitter-follower to keep its emitter up to the right
voltage. So far all is well.
However, when the diode current ceases, TR6 is still conducting heavily,
due to its own charge-carrier storage. The extra current it turned on to feed
D3 in reverse now goes through TR3 collector, which accepts it because of
TR3’s low Vce, and passes it onto the load via TR3 emitter and Re.
This process is readily demonstrated by a SPICE commutation transient
simulation; see Figures 10.7 and 10.8. Note there are only two of these
Figure 10.7
Spikes due to charge
storage of
conventional diodes,
simulated at 10 kHz.
They only occur
when the diodes turn
off, so there are only
two per cycle. These
spikes disappear
completely when
Schottky diodes are
used in the SPICE
Class-G power amplifiers
Figure 10.8
A close-up of the
diode transient.
Diode current rises as
output moves away
from zero, then
reverses abruptly as
charge carriers are
swept out by reversebiasing. The spike on
the output voltage is
aligned with the
sudden stop of the
diode reverse current
events per cycle – not four, as they only occur when the diodes turn off. In
the original Hitachi design this problem was reportedly tackled by using
fast transistors and relatively fast gold-doped diodes, but according to
Sampei et al [2] this was only partially successful.
It is now simple to eradicate this problem. Schottky power diodes are
readily available, as they were not in 1976, and are much faster due to their
lack of minority carriers and charge storage. They have the added
advantage of a low forward voltage drop at large currents of 10 A or more.
The main snag is a relatively low reverse withstand voltage, but fortunately
in Class-G usage the commutating diodes are only exposed at worst to the
difference between V2 and V1, and this only when the amplifier is in its
low power domain of operation. Another good point about Schottky power
diodes is that they do appear to be robust; I have subjected 50 amp
Motorola devices to 60 amps-plus repeatedly without a single failure. This
is a good sign. The spikes disappear completely from the SPICE plot if the
commutating diodes are Schottky rectifiers. Motorola MBR5025L diodes
capable of 50 A and 25 PIV were used in simulation.
The static linearity
SPICE simulation shows in Figure 10.9 that the static linearity (i.e. that
ignoring dynamic effects like diode charge-storage) is distinctly poorer than
for Class-B. There is the usual Class-B gain-wobble around the crossover
Audio Power Amplifier Design Handbook
Figure 10.9
SPICE simulation
shows variations in
the incremental gain
of an EF-type Class-G
series output stage.
The gain-steps at
transition (at ±16 V)
are due to Early
Effect in the
transistors. The ClassA trace is the top
one, with Class-B
optimal below. Here
the inner driver
collectors are
connected to the
switched inner rails,
i.e. the inner power
device collectors, as
in Figure 10.1
region, exactly the same size and shape as for conventional Class-B, but
also there are now gain-steps at ±16 V. The result with the inner devices
biased into push-pull Class-A is also shown, and proves that the gain-steps
are not in any way connected with crossover distortion. Since this is a DC
analysis the gain-steps cannot be due to diode switching-speed or other
dynamic phenomena, and Early Effect was immediately suspected. (Early
Effect is the increase in collector current when the collector voltage
increases, even though the Vbe remains constant.) When unexpected
distortion appears in a SPICE simulation of this kind, and effects due to
finite transistor beta and associated base currents seem unlikely, a most
useful diagnostic technique is to switch off the simulation of Early Effect for
each transistor in turn. In SPICE transistor models the Early Effect can be
totally disabled by setting the parameter VAF to a much higher value than
the default of 100, such as 50,000. This experiment demonstrated in short
order that the gain-steps were caused wholly by Early Effect acting on both
inner drivers and inner output devices. The gain-steps are completely
abolished. When TR6 begins to act, TR3 Vce is no longer decreasing as the
output moves positive, but substantially constant as the emitter of Q6
moves upwards at the same rate as the emitter of Q3. This has the effect of
a sudden change in gain, which naturally degrades the linearity.
This effect appears to occur in drivers and output devices to the same
extent. It can be easily eliminated in the drivers by powering them from the
outer rather than the inner supply rails. This prevents the sudden changes
Class-G power amplifiers
Figure 10.10
Connecting the inner
driver collectors to
the outer V2 rails
reduces Early Effect
non-linearities in
them, and halves the
transition gain-steps
Figure 10.11
A Class-G output stage
with the drivers
powered from the outer
supply rails
Audio Power Amplifier Design Handbook
in the rate in which driver Vce varies. The improvement in linearity is seen
in Figure 10.10, where the gain-steps have been halved in size. The
resulting circuit is shown in Figure 10.11. Driver power dissipation is
naturally increased by the increased driver Vce, but this is such a small
fraction of the power consumed that the overall efficiency is not
significantly reduced. It is obviously not practical to apply the same method
to the output devices, because then the low-voltage rail would never be
used and the amplifier is no longer working in Class-G. The small-signal
stages naturally have to work from the outer rails to be able to generate the
full voltage swing to drive the output stage.
We have now eliminated the commutating diode glitches, and halved the
size of the unwanted gain-steps in the output stage. With these improvements made it is practical to proceed with the design of a Class-G amplifier
with midband THD below 0.002%.
Practical Class-G design
The Class-G amplifier design expounded here uses very similar small-signal
circuitry to the Blameless Class-B power amplifier, as it is known to
generate very little distortion of its own. If the specified supply voltages of
±50 and ±15 V are used, the maximum power output is about 120 W into
8 , and the rail-switching transition occurs at 28 W.
This design incorporates various techniques described in this book, and
closely follows the Blameless Class-B amp described on page 176, though
some features derive from the Trimodal (page 279) and Load Invariant
(page 134) amplifiers. A notable example is the low-noise feedback
network, complete with its option of input bootstrapping to give a high
impedance when required. Single-slope VI limiting is incorporated for
overload protection; this is implemented by Q12, 13. Figure 10.12 shows
the circuit.
As usual in my amplifiers the global NFB factor is a modest 30 dB at
20 kHz.
Controlling small-signal distortion
The distortion from the small-signal stages is kept low by the same methods
as for the other amplifier designs in this book, and so this is only dealt with
briefly here. The input stage differential pair Q1, 2 is given local feedback
by R5 and R7 to delay the onset of third-harmonic Distortion 1. Internal re
variations in these devices are minimised by using an unusually high tail
current of 6 mA. Q3, 4 are a degenerated current-mirror that enforces
accurate balance of the Q1, 2 collector currents, preventing the production
of second-harmonic distortion. The input resistance (R3 + R4) and feedback
resistance R16 are made equal and made unusually low, so that base
Figure 10.12
The circuit diagram of the Class-G amplifier
Audio Power Amplifier Design Handbook
current mismatches stemming from input device beta variations give a
minimal DC offset. Vbe mismatches in Q1 and Q2 remain, but these are
much smaller than the effects of Ib. Even if Q1 and Q2 are high-voltage
types with relatively low beta, the DC offset voltage at the output should be
kept to less than ±50 mV. This is adequate for all but the most demanding
applications. This low-impedance technique eliminates the need for
balance presets or DC servo systems, which is most convenient.
A lower value for R16 implies a proportionally lower value for R15 to keep
the gain the same, and this reduction in the total impedance seen by Q2
improves noise performance markedly. However, the low value of R3 plus
R4 at 2k2 gives an input impedance which is not high enough for many
There is no problem if the amplifier is to have an additional input stage,
such as a balanced line receiver. Proper choice of opamp will allow the
stage to drive a 2k2 load impedance without generating additional
distortion. Be aware that adding such a stage – even if it is properly
designed and the best available opamps are used – will degrade the signalto-noise ratio significantly. This is because the noise generated by the
power amplifier itself is so very low – equivalent to the Johnson noise of a
resistor of a few hundred ohms – that almost anything you do upstream will
degrade it seriously.
If there is no separate input stage then other steps must be taken. What we
need at the input of the power amplifier is a low DC resistance, but a high
AC resistance; in other words we need either a 50 henry choke or recourse
to some form of bootstrapping. There is to my mind no doubt about the way
to go here, so bootstrapping it is. The signal at Q2 base is almost exactly the
same as the input, so if the mid-point of R3 and R4 is driven by C3, so far
as input signals are concerned R3 has a high AC impedance. When I first
used this arrangement I had doubts about its high-frequency stability, and
so added resistor R9 to give some isolation between the bases of Q1 and
Q2. In the event I have had no trouble with instability, and no reports of any
from the many constructors of the Trimodal and Load-Invariant designs,
which incorporate this option.
The presence of R9 limits the bootstrapping factor, as the signal at R3–R4
junction is thereby a little smaller than at Q2 base, but it is adequate. With
R9 set to 100R, the AC input impedance is raised to 13k, which should be
high enough for almost all purposes. Higher values than this mean that an
input buffer stage is required.
The value of C8 shown (1000 µF) gives an LF roll-off in conjunction with
R15 that is –3 dB at 1.4 Hz. The purpose is not impossibly extended subbass, but the avoidance of a low-frequency rise in distortion due to nonlinearity effects in C8. If a 100 µF capacitor is used here the THD at 10 Hz
worsens from <0.0006% to 0.0011%, and I regard this as unacceptable
Class-G power amplifiers
aesthetically – if not perhaps audibly. This is not the place to define the lowfrequency bandwidth of the system – this must be done earlier in the signal
chain, where it can be properly implemented with more accurate nonelectrolytic capacitors. The protection diodes D1 to D4 prevent damage to
C2 if the amplifier suffers a fault that makes it saturate in either direction;
it looks like an extremely dubious place to put diodes but since they
normally have no AC or DC voltage across them no measurable or
detectable distortion is generated.
The Voltage-Amplifier-Stage (VAS) Q11 is enhanced by emitter-follower
Q10 inside the Miller-compensation loop, so that the local negative
feedback that linearises the VAS is increased. This effectively eliminates
VAS non-linearity. Thus increasing the local feedback also reduces the VAS
collector impedance, so a VAS-buffer to prevent Distortion 4 (loading of
VAS collector by the non-linear input impedance of the output stage) is not
required. Miller capacitor Cdom is relatively big at 100 pF, to swamp
transistor internal capacitances and circuit strays, and make the design
predictable. The slew rate calculates as 40 V/µsec use in each direction.
VAS collector-load Q7 is a standard current source.
Almost all the THD from a Blameless amplifier derives from crossover
distortion, so keeping the quiescent conditions optimal to minimise this is
essential. The bias generator for an EF output stage, whether in Class-B or
Class-G, is required to cancel out the Vbe variations of four junctions in
series; those of the two drivers and the two output devices. This sounds
difficult, because the dissipation in the two types of devices is quite
different, but the problem is easier than it looks. In the EF type of output
stage the driver dissipation is almost constant as power output varies, and
so the problem is reduced to tracking the two output device junctions. The
bias generator Q8 is a standard Vbe-multiplier, with R23 chosen to
minimise variations in the quiescent conditions when the supply rails
change. The bias generator should be in contact with the top of one of the
inner output devices, and not the heatsink itself. This position gives much
faster and less attenuated thermal feedback to Q8. The VAS collector circuit
incorporates not only bias generator Q8 but also the two Zeners D8, D9
which determine how early rail-switching occurs as the inner device
emitters approach the inner (lower) voltage rails.
The output stage was selected as an EF (emitter-follower) type as this is
known to be less prone to parasitic or local oscillations than the CFP
configuration, and since this design was to the same extent heading into the
unknown it seemed wise to be cautious where possible. R32 is the usual
shared emitter resistor for the inner drivers. The outer drivers Q16 and Q17
have their own emitter resistors R33 and R36, which have their usual role
of establishing a reasonable current in the drivers as they turn on, to
increase driver transconductance, and also in speeding up turn-off of the
outer output devices by providing a route for charge-carriers to leave the
output device bases.
Audio Power Amplifier Design Handbook
As explained above, the inner driver collectors are connected to the outer
rails to minimise the gain-steps caused by the abrupt change in collector
voltage when rail transition occurs.
Deciding the size of heatsink required for this amplifier is not easy,
mainly because the heat dissipated by a Class-G amplifier depends very
much on the rail voltages chosen and the signal statistics. A Class-B
design giving 120 W into 8R would need a heatsink with thermal
resistance of the order of 1°C/W (per channel); a good starting point for
a Class-G version giving the same power would be about half the size,
i.e. 2°C/W. The Schottky commutating diodes do not require much
heatsinking, as they conduct only intermittently and have a low forward
voltage drop. It is usually convenient to mount them on the main
heatsink, even if this does mean that most of the time they are being
heated rather than cooled.
C15 and R38 make up the usual Zobel network. The coil L1, damped by
R39, isolates the amplifier from load capacitance. A component with 15 to
20 turns at 1 inch diameter should work well; the value of inductance for
stability is not all that critical.
The performance
Figure 10.13 shows the THD at 20 W/50 W (into 8 ) and I think this
demonstrates at once that the design is a practical competitor for Class-B
amplifiers. Compare these results with the upper trace of Figure 10.14,
taken from a Blameless Class-B amplifier at 50 W, 8 . Note the lower trace
of Figure 10.14 is for 30 kHz bandwidth, used to demonstrate the lack of
distortion below 1 kHz; the THD data above 30 kHz is in this case
meaningless as all the harmonics are filtered out. All the Class-G plots here
Figure 10.13
THD versus
frequency, at 20 W
(below transition) and
50 W into an 8 load. The joggle
around 8 kHz is due
to a cancellation of
harmonics from
crossover and
transition. 80 kHz
Class-G power amplifiers
Figure 10.14
THD versus frequency
for a Blameless
Class-B amplifier at
50 W, 8 Figure 10.15
The THD residual
waveform at 50 W
into 8 . This residual
may look rough, but
in fact it had to be
averaged eight times
to dig the glitches
and crossover out of
the noise; THD is
only 0.0012%. The
vertical lines show
where transition
are taken at 80 kHz to make sure any high-order glitching is properly
Figure 10.15 shows the actual THD residual at 50 W output power. The
glitches from the gain-steps are more jagged than the crossover disturbances, as would be expected from the output stage gain plot in Figures
10.9, 10.11. Figure 10.16 confirms that at 20 W, below transition, the
residual is indistinguishable from that of a Blameless Class-B amplifier; in
this region, where the amplifier is likely to spend most of its time, there are
no compromises on quality.
Audio Power Amplifier Design Handbook
Figure 10.16
The THD residual
waveform at 20 W
into 8 , below
transition. Only
crossover artefacts
are visible as there is
no rail-switching
Figure 10.17
THD versus level,
showing how THD
increases around
28 W as transition
begins. Class-A + C
is the lower and
Class-B + C the
upper trace
Figure 10.17 shows THD versus level, demonstrating how THD increases
around 28 W as transition begins. The steps at about 10 W are nothing to do
with the amplifier – they are artefacts due to internal range-switching in the
measuring system.
Figure 10.18 shows for real the benefits of powering the inner drivers from
the outer supply rails. In SPICE simulation (see above) the gain-steps were
roughly halved in size by this modification, and Figure 10.18 duly confirms
that the THD is halved in the HF region, the only area where it is
sufficiently clear of the noise floor to be measured with any confidence.
Class-G power amplifiers
Figure 10.18
THD plot of real
amplifier driving
50 W into 8 . Rails
were ±40 and
±25 V. Distortion at
HF is halved by
connecting the inner
drivers to the outer
supply rails rather
than the inner rails
Deriving a new kind of amplifier: Class-A + C
A conventional Class-B power amplifier can be almost instantly converted
to push-pull Class-A simply by increasing the bias voltage to make the
required quiescent current flow. This is the only real circuit change, though
naturally major increases in heatsinking and power-supply capability are
required for practical use. Exactly the same principle applies to the Class-G
amplifier. Recently I suggested a new and much more flexible system for
classifying amplifier types [6] and here it comes in very handy. Describing
Class-G operation as Class-B + C immediately indicates that only a bias
increase is required to transform it into Class-A + C, and a new type of
amplifier is born. This amplifier configuration combines the superb
linearity of classic Class-A up to the transition level, with only minor
distortion artefacts occurring at higher levels, as demonstrated for Class-B
+ C above. Using Class-A means that the simple Vbe-multiplier bias
generator can be replaced with precise negative feedback control of the
quiescent current, as implemented in the Trimodal amplifier in this book.
There is no reason why an amplifier could not be configured as a Class-G
Trimodal, i.e. manually switchable between Classes A and B. That would
indeed be an interesting machine.
In Figure 10.19 is shown the THD plot for such an A + C amplifier working
at 20 W and 30 W into 8 . At 20 W the distortion is very low indeed, no
higher than a pure Class-A amplifier. At 30 W the transition gain-steps
appear, but the THD remains very well controlled, and no higher than a
Blameless Class-B design. Note that as in Class-B, when the THD does start
to rise it only does so at 6 dB/octave. The quiescent current was set to
1.5 amps.
Audio Power Amplifier Design Handbook
Figure 10.19
The THD plot of the
Class-A + C amplifier
(30 W and 20 W
into 8 ). Inner
drivers powered from
outer rails
Figure 10.20
The THD residual
waveform of the
Class-A + C amplifier
above transition, at
30 W into 8 .
Switching artefacts
are visible but not
crossover distortion
Figure 10.20 reveals the THD residual during A + C operation. There are
absolutely no crossover artefacts, and the small disturbances that do occur
happen at such a high signal level that I really do think it is safe to assume
they could never be audible. Figure 10.21 shows the complete absence of
artefacts on the residual when this new type of amplifier is working below
transition; it gives pure Class-A linearity. Finally, Figure 10.22 gives the
THD when the amplifier is driving the full 50 W into 8 ; as before the A
+ C THD plot is hard to distinguish from Class-B, but there is the immense
advantage that there is no crossover distortion at low levels, and no critical
bias settings.
Class-G power amplifiers
Figure 10.21
The THD residual
waveform plot of the
Class-A + C amplifier
(20 W into 8 )
Figure 10.22
The THD plot of the
Class-A + C amplifier
(50 W into 8 ).
Inner drivers
powered from outer
Adding two-pole compensation
I have previously shown elsewhere in this book that amplifier distortion can
be very simply reduced by changes to the compensation; which means a
scheme more sophisticated than the near-universal dominant pole method.
It must be borne in mind that any departure from the conventional 6 dB/
octave-all-the-way compensation scheme is likely to be a move away from
unconditional stability. (I am using this phrase in its proper meaning; in
Control Theory unconditional stability means that increasing open-loop
gain above a threshold causes instability, but the system is stable for all
Audio Power Amplifier Design Handbook
lower values. Conditional Stability means that lower open-loop gains can
also be unstable.)
A conditionally stable amplifier may well be docile and stable into any
conceivable reactive load when in normal operation, but shows the cloven
hoof of oscillation at power-up and power-down, or when clipping. This is
because under these conditions the effective open-loop gain is reduced.
Class-G distortion artefacts are reduced by normal dominant-pole feedback
in much the same way as crossover non-linearities, i.e. not all that
effectively, because the artefacts take up a very small part of the cycle and
are therefore composed of high-order harmonics. Therefore a compensation system that increases the feedback factor at high audio frequencies will
be effective on switching artefacts, in the same way that it is for crossover
distortion. The simplest way to implement two-pole circuit compensation is
shown in Figure 10.23. Further details are given on page 188.
Figure 10.23
The circuit
modification for twopole compensation
Figure 10.24
The THD plot for B +
C operation with
compensation (20 W
and 30 W into 8 ).
Compare with
Figures 10.13
(B + C) and 10.19
(A + C)
Class-G power amplifiers
The results of two-pole compensation for B + C are shown in Figure 10.24;
comparing it with Figure 10.13 (the normally compensated B + C amplifier)
the above-transition (30 W) THD at 10 kHz has dropped from 0.008% to
0.005%; the sub-transition (20 W) THD at 10 kHz has fallen from 0.007%
to 0.003%. Comparisons have to be done at 10 kHz or thereabouts to
ensure there is enough to measure.
Now comparing the two-pole B + C amplifier with Figure 10.19 (the A + C
amplifier) the above-transition (30 W) THD at 10 kHz of the former is lower
at 0.005% compared with 0.008%. As I have demonstrated before, proper
use of two-pole compensation can give you a Class-B amplifier that is hard
to distinguish from Class-A – at least until you put your hand on the
Further variations on Class-G
This by no means exhausts the possible variations that can be played on
Class-G. For example, it is not necessary for the outer devices to operate
synchronously with the inner devices. So long as they turn on in time, they
can turn off much later without penalty except in terms of increased
dissipation. In so-called syllabic Class-G, the outer devices turn on fast but
then typically remain on for 100 msec or so to prevent glitching; see
Funada and Akiya[7] for one version. Given the good results obtained with
straight Class-G, this no longer seems a promising route to explore.
With the unstoppable advance of multichannel amplifier and powered subwoofers, Class-G is at last coming into its own. It has recently even
appeared in a Texas ADSL driver IC. I hope I have shown how to make it
work, and then how to make it work better. From the results of a Web
search done today, I would modestly suggest that this might be the lowest
distortion Class-G amplifier so far.
1. Self, D Self On Audio Newnes, ISBN 0–7506–4765–5, p. 347.
2. Sampei et al ‘Highest Efficiency and Super Quality Audio Amplifier
Using MOS Power FETs in Class-G Operation’ IEEE Trans on Consumer
Electronics, Vol CE–24, #3 Aug 1978, p. 300.
3. Feldman ‘Class-G High Efficiency Hi-Fi Amplifier’ Radio Electronics,
Aug 1976, p. 47.
4. Self, D Self On Audio Newnes, ISBN 0–7506–4765–5, p. 369.
5. Self, D Self On Audio Newnes, ISBN 0–7506–4765–5, p. 386.
6. Self, D Self On Audio Newnes, ISBN 0–7506–4765–5 p. 293.
7. Funada & Akiya ‘A Study of High-Efficiency Audio Power Amplifiers
Using a Voltage Switching Method’ Journ. Audio Eng. Soc. Vol 32 #10,
Oct 1984, p. 755.
FET output stages
The characteristics of power FETS
An FET is essentially a voltage-controlled device. So are BJTs, despite the
conventional wisdom that persists in regarding them as current-controlled.
They are not, even if BJT base currents are non-negligible.
The power FETs normally used are enhancement devices – in other words,
with no voltage between gate and source they remain off. In contrast, the
junction FETs found in small-signal circuitry are depletion devices,
requiring the gate to be taken negative of the source (for the most common
N-channel devices) to reduce the drain current to usable proportions.
(Please note that the standard information on FET operation is in many
textbooks and will not be repeated here.)
Power FETs have large internal capacitances, both from gate to drain, and
from gate to source. The gate-source capacitance is effectively bootstrapped by the source-follower configuration, but the gate-drain capacitance, which can easily total 2000 pF, remains to be driven by the previous
stage. There is an obvious danger that this will compromise the amplifier
slew-rate if the VAS is not designed to cope.
FETs tend to have much larger bandwidths than BJT output devices. My
own experience is that this tends to manifest itself as a greater propensity
for parasitic oscillation rather than anything useful, but the tempting
prospect of higher global NFB factors due to a higher output stage pole
remains. The current state of knowledge does not yet permit a definitive
judgement on this.
A great deal has been said on the thermal coefficients of the Vbias voltage.
It is certainly true that the temp coefficient at high drain currents is negative
FET output stages
– in other words drain current falls with increasing temperature – but on the
other hand the coefficient reverses sign at low drain currents, and this
implies that precise quiescent-current setting will be very difficult. A
negative-temperature coefficient provides good protection against thermal
runaway, but this should never be a problem anyway.
FET vs BJT output stages
On beginning any power amplifier design, one of the first decisions that
must be made is whether to use BJTs or FETs in the output stage. This
decision may of course already have been taken for you by the marketing
department, as the general mood of the marketplace is that if FETs are more
expensive, they must be better. If however, you are lucky enough to have
this crucial decision left to you, then FETs normally disqualify themselves
on the same grounds of price. If the extra cost is not translated into either
better performance and/or a higher sustainable price for the product, then
it appears to be foolish to choose anything other than BJTs.
Power MOSFETS are often hailed as the solution to all amplifier problems,
but they have their own drawbacks, not the least being low transconductance, poor linearity, and a high ON-resistance that makes output
efficiency mediocre. The high-frequency response may be better, implying
that the second pole P2 of the amplifier response will be higher, allowing
the dominant pole P1 be raised with the same stability margin, and so in
turn giving more NFB to reduce distortion. However, we would need this
extra feedback (if it proves available in practice) to correct the worse openloop distortion, and even then the overall linearity would almost certainly
be worse. To complicate matters, the compensation cannot necessarily be
lighter because the higher output-resistance makes more likely the
lowering of the output pole by capacitative loading.
The extended FET frequency response is, like so many electronic swords,
two-edged if not worse, and the HF capabilities mean that rigorous care
must be taken to prevent parasitic oscillation, as this is often promptly
followed by an explosion of disconcerting violence. FETs should at least
give freedom from switchoff troubles (Distortion 3c) as they do not suffer
from BJT charge-storage effects.
Advantages of FETs
1 For a simple complementary FET output stage, drivers are not required.
This is somewhat negated by the need for gate-protection zener
2 There is no second-breakdown failure mechanism. This may simplify the
design of overload protection systems, especially when arranging for
them to cope with highly reactive loads.
3 There are no charge-storage effects to cause switchoff distortion.
Audio Power Amplifier Design Handbook
Disadvantages of FETs
1 Linearity is very poor by comparison with a BJT degenerated to give the
same transconductance. The Class-B conduction characteristics do not
cross over smoothly, and there is no equivalent to the optimal Class-B
bias condition that is very obvious with a BJT output stage.
2 The Vgs required for conduction is usually of the order of 4–6 V, which
is much greater than the 0.6–0.8 V required by a BJT for base drive. This
greatly reduces the voltage efficiency of the output stage unless the
preceding small-signal stages are run from separate and higher-voltage
supply rails.
3 The minimum channel resistance of the FET, known as Rds(on), is high
and gives a further reduction in efficiency compared with BJT outputs.
4 Power FETs are liable to parasitic oscillation. In severe cases a plasticpackage device will literally explode. This is normally controllable in the
simple complementary FET output stage by adding gate-stopper resistors,
but is a serious disincentive to trying radical experiments in output stage
circuit design.
5 Some commentators claim that FET parameters are predictable; I find this
hard to understand as they are notorious for being anything but. From
one manufacturer’s data (Harris), the Vgs for the IRF240 FET varies
between 2.0 and 4.0 V for an ld of 250 µA; this is a range of two to one.
In contrast the Vbe/lc relation in bipolars is fixed by a mathematical
equation for a given transistor type, and is much more reliable. Nobody
uses FETs in log converters.
6 Since the Vgs spreads are high, this will complicate putting devices in
parallel for greater power capability. Paralleled BJT stages rarely require
current-sharing resistors of greater than 0.1 , but for the FET case they
may need to be a good deal larger, reducing efficiency further.
7 At the time of writing, there is a significant economic penalty in
using FETs. Taking an amplifier of given power output, the cost of the
output semiconductors is increased by between 1.5 and 2 times with
Insulated-Gate Bipolar Transistors represent a relatively new option for the
amplifier designer. They have been held up as combining the best features
of FETs and BJTs. In my view this is a dubious proposition as I find the
advantages of FETs for audio to be heavily outweighed by the drawbacks,
and if IGBTs have any special advantages they have not so far emerged.
According to the Toshiba application notes [1], IGBTs consist of an FET
controlling a bipolar power transistor; I have no information on the linearity
of these devices, but the combination does not sound promising.
The most discouraging aspect of IGBTs is the presence of a parasitic BJT
that turns the device hard on above a critical current threshold. This inbuilt
Figure 11.1
Three MOSFET output
Audio Power Amplifier Design Handbook
self-destruct mechanism will at the very least make overload protection an
extremely critical matter; it seems unlikely that IGBTs will prove popular for
audio amplification.
Power FET output stages
Three types of FET output stage are shown in Figure 11.1, and Figures
11.2–11.5 show SPICE gain plots, using 2SK135/2SJ50 devices. Most FET
amplifiers use the simple source-follower configuration in Figure 11.1a; the
large-signal gain plot at Figure 11.2 shows that the gain for a given load is
lower (0.83 rather than 0.97 for bipolar, at 8 ) because of low gm, and
this, with the high on-resistance, reduces output efficiency seriously. Openloop distortion is markedly higher; however LSN does not increase with
heavier loading, there being no equivalent of Bipolar Gain-Droop. The
crossover region has sharper and larger gain deviations than a bipolar stage,
and generally looks pretty nasty; Figure 11.3 shows the impossibility of
finding a correct Vbias setting.
Figure 11.1b shows a hybrid (i.e. bipolar/FET) quasi-complementary
output stage, first described in Self [2]. This topology is intended to
maximise economy rather than performance, once the decision has been
made (presumably for marketing reasons) to use FETs, by making both
output devices cheap N-channel devices; complementary MOSFET pairs
remain relatively rare and expensive. The basic configuration is badly
asymmetrical, the hybrid lower half having a higher and more constant
Figure 11.2
Source-Follower FET
large-signal gain vs
FET output stages
Figure 11.3
Source-Follower FET
crossover region
+/–15 V range
Figure 11.4
Bipolar-FET gain vs
gain than the source-follower upper half. Increasing the value of Re2 gives
a reasonable match between the gains of the two halves, but leaves a
daunting crossover discontinuity.
The hybrid full-complementary stage in Figure 11.1c was conceived [3] to
maximise FET performance by linearising the output devices with local
Audio Power Amplifier Design Handbook
Figure 11.5
Complementary BJTFET crossover region
+/–15 V range
feedback and reducing Iq variations due to the low power dissipation of
the bipolar drivers. It is very linear, with no gain-droop at heavier
loadings (Figure 11.4), and promises freedom from switchoff distortions;
however, as shown, it is rather inefficient in voltage-swing. The crossover
region in Figure 11.5 still has some unpleasant sharp corners, but the total
crossover gain deviation (0.96–0.97 at 8 ) is much smaller than for the
quasi-hybrid (0.78–0.90) and so less high-order harmonic energy is
Table 11.1 summarises the SPICE curves for 4 and 8 loadings. Each was
subjected to Fourier analysis to calculate THD% results for a +/–40 V input.
The BJT results from Chapter 5 are included for comparison.
Table 11.1
FET output stages
Power FETs and bipolars: the linearity comparison
There has been much debate as to whether power FETs or bipolar junction
transistors (BJTs) are superior in power amplifier output stages, e.g.
Hawtin [4]. As the debate rages, or at any rate flickers, it has often been flatly
stated that power FETs are more linear than BJTs, usually in tones that
suggest that only the truly benighted are unaware of this.
In audio electronics it is a good rule of thumb that if an apparent fact is
repeated times without number, but also without any supporting data, it
needs to be looked at very carefully indeed. I therefore present my own
view of the situation here.
I suggest that it is now well-established that power FETs when used in
conventional Class-B output stages are a good deal less linear than BJTs. The
gain-deviations around the crossover region are far more severe for FETs than
the relatively modest wobbles of correctly biased BJTs, and the shape of the
FET gain-plot is inherently jagged, due to the way in which two square-law
devices overlap. The incremental gain range of a simple FET output stage
is 0.84–0.79 (range 0.05) and this is actually much greater than for the
Bipolar stages examined in Chapter 5; the EF stage gives 0.965–0.972 into
8 (range 0.007) and the CFP gives 0.967–0.970 (range 0.003). The smaller
ranges of gain-variation are reflected in the much lower THD figures when
PSpice data is subjected to Fourier analysis.
However, the most important difference may be that the bipolar gain
variations are gentle wobbles, while all FET plots seem to have abrupt
changes that are much harder to linearise with NFB that must decline with
rising frequency. The basically exponential Ic/Vbe characteristics of two
BJTs approach much more closely the ideal of conjugate (i.e. always adding
up to 1) mathematical functions, and this is the root cause of the much
lower crossover distortion.
A close-up examination of the way in which the two types of device begin
conducting as their input voltages increase shows that FETs move abruptly
into the square-law part of their characteristic, while the exponential
behaviour of bipolars actually gives a much slower and smoother start to
Similarly, recent work [5] shows that less conventional approaches, such as
the CC-CE configuration of Mr Bengt Olsson [6], also suffer from the nonconjugate nature of FETs, and show sharp changes in gain. Gevel [7] shows
that this holds for both versions of the stage proposed by Olsson, using both
N- and P-channel drivers. There are always sharp gain-changes.
FETs in Class-A stages
It occurred to me that the idea that FETs are more linear was based not on
Class-B power-amplifier applications, but on the behaviour of a single
Audio Power Amplifier Design Handbook
device in Class-A. It might be argued that the roughly square-law nature of
a FET’s Id/Vgs law is intuitively more linear than the exponential Ic/Vbe law
of a BJT, but it is a bit difficult to know quite how to define linear in this
context. Certainly a square-law device will generate predominantly loworder harmonics, but this says nothing about the relative amounts
In truth the BJT/FET contest is a comparison between apples and aardvarks,
the main problem being that the raw transconductance (gm) of a BJT is far
higher than for any power FET. Figure 11.6 illustrates the conceptual test
circuit; both a TO3 BJT (MJ802) and a power-FET (IRF240) have an
increasing DC voltage Vin applied to their base/gate, and the resulting
collector and drain currents from PSpice simulation are plotted in Figure
11.7. Voffset is used to increase the voltage applied to FET M1 by 3.0 V
because nothing much happens below Vgs = 4 V, and it is helpful to have
Figure 11.6
The linearity test circuit.
Voffset adds 3 V to the
DC level applied to the
FET gate, purely to
keep the current curves
helpfully adjacent on a
Figure 11.7
Graph of Ic and Id for
the BJT and the FET.
Curve A shows Ic for
the BJT alone, while
Curve B shows the
result for Re = 0.1 .
The curved line is the
Id result for a power
FET without any
FET output stages
the curves on roughly the same axis. Curve A, for the BJT, goes almost
vertically skywards, as a result of its far higher gm. To make the comparison
meaningful, a small amount of local negative feedback is added to Q1 by
Re, and as this emitter degeneration is increased from 0.01 to 0.1 , the
Ic curves become closer in slope to the Id curve.
Because of the curved nature of the FET Id plot, it is not possible to pick an
Re value that allows very close gm equivalence; Re = 0.1 was chosen as
a reasonable approximation; see Curve B. However, the important point is
that I think no-one could argue that the FET Id characteristic is more linear
than Curve B.
This is made clearer by Figure 11.8, which directly plots transconductance
against input voltage. There is no question that FET transconductance
increases in a beautifully linear manner – but this ‘linearity’ is what results
in a square-law Id increase. The near-constant gm lines for the BJT are a
much more promising basis for the design of a linear amplifier.
To forestall any objections that this comparison is all nonsense because a
BJT is a current-operated device, I add here a small reminder that this is
untrue. The BJT is a voltage operated device, and the base current that
flows is merely an inconvenient side-effect of the collector current induced
by said base voltage. This is why beta varies more than most BJT
parameters; the base current is an unavoidable error rather than the basis of
transistor operation.
The PSpice simulation shown here was checked against manufacturers’
curves for the devices, and the agreement was very good – almost
Figure 11.8
Graph of
versus input voltage for
BJT and FET. The nearhorizontal lines are
BJT gm for various Re
Audio Power Amplifier Design Handbook
unnervingly so. It therefore seems reasonable to rely on simulator output for
these kind of studies – it is certainly infinitely quicker than doing the real
measurements, and the comprehensive power FET component libraries that
are part of PSpice allow the testing to be generalised over a huge number
of component types without actually buying them.
To conclude, I think it is probably irrelevant to simply compare a naked BJT
with a naked FET. Perhaps the vital point is that a bipolar device has much
more raw transconductance gain to begin with, and this can be handily
converted into better linearity by local feedback, i.e. adding a little emitter
degeneration. If the transconductance is thus brought down roughly to FET
levels, the bipolar has far superior large-signal linearity. I must admit to a
sneaking feeling that if practical power BJTs had come along after FETs, they
would have been seized upon with glee as a major step forward in power
1. Langdon, S Audio amplifier designs using IGBT’s, MOSFETs, and BJTs
Toshiba Application Note X3504, V. 1 Mar 1991.
2. Self, D Sound MOSFET Design Electronics and Wireless World, Sept
1990, p. 760.
3. Self, D MOSFET Audio Output Letter, Electronics and Wireless World,
May 1989, p. 524 (see also reference 2 above).
4. Hawtin, V Letters, Electronics World Dec 1994, p. 1037.
5. Self, D Two-Stage Amplifiers and the Olsson Output Stage Electronics
World, Sept 1995, p. 762.
6. Olsson, B Better Audio From Non-Complements? Electronics World,
Dec 1994, p. 988.
7. Gevel, M Private communication, Jan 1995.
Thermal compensation
and thermal dynamics
Why quiescent conditions are critical
In earlier sections of this book we looked closely at the distortion produced
by amplifier output stages, and it emerged that a well-designed Class-B
amplifier with proper precautions taken against the easily-fixed sources of
non-linearity, but using basically conventional circuitry, can produce
startlingly low levels of THD. The distortion that actually is generated is
mainly due to the difficulty of reducing high-order crossover non-linearities
with a global negative-feedback factor that declines with frequency; for 8 loads this is the major source of distortion, and unfortunately crossover
distortion is generally regarded as the most pernicious of non-linearities. For
convenience, I have chosen to call such an amplifier, with its small signal
stages freed from unnecessary distortions, but still producing the crossover
distortion inherent in Class-B, a Blameless amplifier (see Chapter 3).
Page 145 suggests that the amount of crossover distortion produced by the
output stage is largely fixed for a given configuration and devices, so the
best we can do is ensure the output stage runs at optimal quiescent
conditions to minimise distortion.
Since it is our only option, it is therefore particularly important to minimise
the output-stage gain irregularities around the crossover point by holding
the quiescent conditions at their optimal value. This conclusion is
reinforced by the finding that for a Blameless amplifier increasing quiescent
current to move into Class-AB makes the distortion worse, not better, as gmdoubling artefacts are generated. In other words the quiescent setting will
only be correct over a relatively narrow band, and THD measurements
show that too much quiescent current is as bad (or at any rate very little
better) than too little.
Audio Power Amplifier Design Handbook
The initial quiescent setting is simple, given a THD analyser to get a good
view of the residual distortion; simply increase the bias setting from
minimum until the sharp crossover spikes on the residual merge into the
noise. Advancing the preset further produces edges on the residual that
move apart from the crossover point as bias increases; this is gm-doubling
at work, and is a sign that the bias must be reduced again.
It is easy to attain this optimal setting, but keeping it under varying
operating conditions is a much greater problem because quiescent current
(Iq) depends on the maintenance of an accurate voltage-drop Vq across
emitter resistors Re of tiny value, by means of hot transistors with varying
Vbe drops. It’s surprising it works as well as it does.
Some kinds of amplifier (e.g. Class-A or current-dumping types) manage to
evade the problem altogether, but in general the solution is some form of
thermal compensation, the output-stage bias voltage being set by a
temperature-sensor (usually a Vbe-multiplier transistor) coupled as closely
as possible to the power devices.
There are inherent inaccuracies and thermal lags in this sort of arrangement, leading to program-dependency of Iq. A sudden period of high
power dissipation will begin with the Iq increasing above the optimum, as
the junctions will heat up very quickly. Eventually the thermal mass of the
heatsink will respond, and the bias voltage will be reduced. When the
power dissipation falls again, the bias voltage will now be too low to match
the cooling junctions and the amplifier will be under-biased, producing
crossover spikes that may persist for some minutes. This is very well
illustrated in an important paper by Sato et al [1].
Accuracy required of thermal compensation
Quiescent stability depends on two main factors. The first is the stability of
the Vbias generator in the face of external perturbations, such as supply
voltage variations. The second and more important is the effect of
temperature changes in the drivers and output devices, and the accuracy
with which Vbias can cancel them out.
Vbias must cancel out temperature-induced changes in the voltage across
the transistor base-emitter junctions, so that Vq remains constant. From the
limited viewpoint of thermal compensation (and given a fixed Re) this is
very much the same as the traditional criterion that the quiescent current
must remain constant, and no relaxation in exactitude of setting is
I have reached some conclusions on how accurate the Vbias setting must
be to attain minimal distortion. The two major types of output stage, the EF
and the CFP, are quite different in their behaviour and bias requirements,
and this complicates matters considerably. The results are approximate,
Thermal compensation and thermal dynamics
depending partly on visual assessment of a noisy residual signal, and may
change slightly with transistor type, etc. Nonetheless, Table 12.1 gives a
much-needed starting point for the study of thermal compensation.
From these results, we can take the permissible error band for the EF stage
as about +/–100 mV, and for the CFP as about +/–10 mV. This goes some
way to explaining why the EF stage can give satisfactory quiescent stability
despite its dependence on the Vbe of hot power transistors.
Returning to the PSpice simulator, and taking Re = OR1, a quick check on
how the various transistor junction temperatures affect Vq yields:
The EF output stage has a Vq of 42 mV, with a Vq sensitivity of –2 mV/°C
to driver temperature, and –2 mV/°C to output junction temperature. No
surprises here.
The CFP stage has a much smaller Vq (3.1 mV) Vq sensitivity is –2 mV/°C
to driver temperature, and only –0.1 mV/°C to output device temperature. This confirms that local NFB in the stage makes Vq relatively
independent of output device temperature, which is just as well as Table
12.1 shows it needs to be about ten times more accurate.
The CFP output devices are about 20 times less sensitive to junction
temperature, but the Vq across Re is something like 10 times less; hence the
actual relationship between output junction temperature and crossover
distortion is not so very different for the two configurations, indicating that
as regards temperature stability the CFP may only be twice as good as the
EF, and not vastly better, which is perhaps the common assumption. In fact,
as will be described, the CFP may show poorer thermal performance in
In real life, with a continuously varying power output, the situation is
complicated by the different dissipation characteristics of the drivers as
output varies. See Figure 12.1, which shows that the CFP driver dissipation
is more variable with output, but on average runs cooler. For both
configurations driver temperature is equally important, but the EF driver
dissipation does not vary much with output power, though the initial drift
at switch-on is greater as the standing dissipation is higher. This, combined
with the two-times-greater sensitivity to output device temperature and the
Table 12.1
Vbias tolerance
for 8 Crossover spikes obvious
Spikes just visible
Optimal residual
gm-doubling just visible
gm-doubling obvious
EF output
CFP output
2.25 V
1.242 V
Audio Power Amplifier Design Handbook
Figure 12.1
Driver dissipation
versus output level. In
all variations on the
EF configuration,
power dissipation
varies little with
output; CFP driver
power however varies
by a factor of two or
greater self-heating of the EF output devices, may be the real reason why
most designers have a general feeling that the EF version has inferior
quiescent stability. The truth as to which type of stage is more thermally
stable is much more complex, and depends on several design choices and
Having assimilated this, we can speculate on the ideal thermal compensation system for the two output configurations. The EF stage has Vq set by the
subtraction of four dissimilar base-emitter junctions from Vbias, all having
an equal say, and so all four junction temperatures ought to be factored into
the final result. This would certainly be comprehensive, but four
temperature-sensors per channel is perhaps overdoing it. For the CFP stage,
we can ignore the output device temperatures and only sense the drivers,
which simplifies things and works well in practice.
If we can assume that the drivers and outputs come in complementary pairs
with similar Vbe behaviour, then symmetry prevails and we need only
consider one half of the output stage, so long as Vbias is halved to suit. This
assumes the audio signal is symmetrical over timescales of seconds to
minutes, so that equal dissipations and temperature rises occur in the top
and bottom halves of the output stage. This seems a pretty safe bet, but the
unaccompanied human voice has positive and negative peak values that
may differ by up to 8 dB, so prolonged acapella performances have at least
the potential to mislead any compensator that assumes symmetry. One
amplifier that does use separate sensors for the upper and lower output
sections is the Adcom GFA-565.
For the EF configuration, both drivers and outputs have an equal influence
on the quiescent Vq, but the output devices normally get much hotter than
Thermal compensation and thermal dynamics
the drivers, and their dissipation varies much more with output level. In this
case the sensor goes on or near one of the output devices, thermally close
to the output junction. It has been shown experimentally that the top of the
TO3 can is the best place to put it, see page 335. Recent experiments have
confirmed that this holds true also for the TO3P package, (a large flat plastic
package like an overgrown TO220, and nothing like TO3) which can easily
get 20 degrees hotter on its upper plastic surface than does the underlying
In the CFP the drivers have most effect and the output devices, although still
hot, have only one-twentieth the influence. Driver dissipation is also much
more variable, so now the correct place to put the thermal sensor is as near
to the driver junction as you can get it.
Schemes for the direct servo control of quiescent current have been
mooted [2], but all suffer from the difficulty that the quantity we wish to
control is not directly available for measurement, as except in the complete
absence of signal it is swamped by Class-B output currents. In contrast the
quiescent current of a Class-A amplifier is easily measured, allowing very
precise feedback control; ironically its value is not critical for distortion
So: just how accurately must quiescent current be held? This is not easy to
answer, not least because it is the wrong question. Page 151 established
that the crucial parameter is not quiescent current (hereafter Iq) as such, but
rather the quiescent voltage-drop Vq across the two emitter resistors Re.
This takes a little swallowing – after all people have been worrying about
quiescent current for 30 years or more – but it is actually good news, as the
value of Re does not complicate the picture. The voltage across the output
stage inputs (Vbias) is no less critical, for once Re is chosen Vq and Iq vary
proportionally. The two main types of output stage, the Emitter-Follower
(EF) and the Complementary Feedback Pair (CFP) are shown in Figure 12.2.
Their Vq tolerances are quite different.
From the measurements on page 327 above the permissible error band for
Vq in the EF stage is +/–100 mV, and for the CFP is +/–10 mV. These
tolerances are not defined for all time; I only claim that they are realistic
and reasonable. In terms of total Vbias, the EF needs 2.93 V +/–100 mV, and
the CFP 1.30 V +/–10 mV. Vbias must be higher in the EF as four Vbe’s are
subtracted from it to get Vq, while in the CFP only two driver Vbe’s are
The CFP stage appears to be more demanding of Vbias compensation than
EF, needing 1% rather than 3.5% accuracy, but things are not so simple. Vq
stability in the EF stage depends primarily on the hot output devices, as EF
driver dissipation varies only slightly with power output. Vq in the CFP
depends almost entirely on driver junction temperature, as the effect of
output device temperature is reduced by the local negative-feedback;
Figure 12.2
The Emitter-Follower
(EF) and
Feedback Pair
(CFP) output
showing Vbias and
Thermal compensation and thermal dynamics
however CFP driver dissipation varies strongly with power output so the
superiority of this configuration cannot be taken for granted.
Driver heatsinks are much smaller than those for output devices, so the CFP
Vq time-constants promise to be some ten times shorter.
Basic thermal compensation
In Class B, the usual method for reducing quiescent variations is thermal
feedback. Vbias is generated by a thermal sensor with a negative
temperature-coefficient, usually a Vbe-multiplier transistor mounted on the
main heatsink. This system has proved entirely workable over the last 30-odd
years, and usually prevents any possibility of thermal runaway. However, it
suffers from thermal losses and delays between output devices and
temperature sensor that make maintenance of optimal bias rather questionable, and in practice quiescent conditions are a function of recent signal
and thermal history. Thus the crossover linearity of most power amplifiers is
intimately bound up with their thermal dynamics, and it is surprising this
area has not been examined more closely; Sato et al [1] is one of the few
serious papers on the subject, though the conclusions it reaches appear to be
unworkable, depending on calculating power dissipation from amplifier
output voltage without considering load impedance.
As is almost routine in audio design, things are not as they appear. So-called
thermal feedback is not feedback at all – this implies the thermal sensor is
in some way controlling the output stage temperature; it is not. It is really
a form of approximate feedforward compensation, as shown in Figure 12.3.
The quiescent current (Iq) of a Class-B design causes a very small
dissipation compared with the signal, and so there is no meaningful
feedback path returning from Iq to the left of the diagram. (This might be
less true of Class-AB, where quiescent dissipation may be significant.)
Instead this system aspires to make the sensor junction temperature mimic
the driver or output junction temperature, though it can never do this
Figure 12.3
Thermal signal flow
of a typical power
amplifier, showing
that there is no
thermal feedback to
the bias generator.
There is instead
feedforward of driver
junction temperature,
so that the sensor Vbe
will hopefully match
the driver Vbe
Audio Power Amplifier Design Handbook
promptly or exactly because of the thermal resistances and thermal
capacities that lie between driver and sensor temperatures in Figure 12.3.
It does not place either junction temperature or quiescent current under
direct feedback control, but merely aims to cancel out the errors. Hereafter
I simply call this thermal compensation.
Assessing the bias errors
The temperature error must be converted to mV error in Vq, for comparison
with the tolerance bands suggested above. In the CFP stage this is
straightforward; both driver Vbe and the halved Vbias voltage decrease by
2 mV per °C, so temperature error converts to voltage error by multiplying
by .002 Only half of each output stage will be modelled, exploiting
symmetry, so most of this chapter deals in half-Vq errors, etc. To minimise
confusion this use of half-amplifiers is adhered to throughout, except at the
final stage when the calculated Vq error is doubled before comparison with
the tolerance bands quoted above.
The EF error conversion is more subtle. The EF Vbias generator must establish
four times Vbe plus Vq, so the Vbe of the temperature-sensing transistor is
multiplied by about 4.5 times, and so decreases at 9 mV/°C. The CFP Vbias
generator only multiplies 2.1 times, decreasing at 4 mV/°C. The corresponding values for a half-amplifier are 4.5 and 2 mV/°C.
However, the EF drivers are at near-constant temperature, so after two
driver Vbe’s have been subtracted from Vbias, the remaining voltage
decreases faster with temperature than does output device Vbe. This runs
counter to the tendency to under-compensation caused by thermal
attenuation between output junctions and thermal sensor; in effect the
compensator has thermal gain, and this has the potential to reduce longterm Vq errors. I suspect this is the real reason why the EF stage, despite
looking unpromising, can in practice give acceptable quiescent stability.
Thermal simulation
Designing an output stage requires some appreciation of how effective the
thermal compensation will be, in terms of how much delay and attenuation
the thermal signal suffers between the critical junctions and the Vbias
We need to predict the thermal behaviour of a heatsink assembly over time,
allowing for things like metals of dissimilar thermal conductivity, and the
very slow propagation of heat through a mass compared with near-instant
changes in electrical dissipation. Practical measurements are very timeconsuming, requiring special equipment such as multi-point thermocouple
recorders. A theoretical approach would be very useful.
Thermal compensation and thermal dynamics
For very simple models, such as heat flow down a uniform rod, we can
derive analytical solutions to the partial differential equations that describe
the situation; the answer is an equation directly relating temperature to
position along-the-rod and time. However, even slight complications (such
as a non-uniform rod) involve rapidly increasing mathematical complexities, and anyone who is not already deterred should consult Carslaw and
Jaeger [3]; this will deter them.
To avoid direct confrontation with higher mathematics, finite-element and
relaxation methods were developed; the snag is that Finite-ElementAnalysis is a rather specialised taste, and so commercial FEA software is
I therefore cast about for another method, and found I already had the
wherewithall to solve problems of thermal dynamics; the use of electrical
analogues is the key. If the thermal problem can be stated in terms of
lumped electrical elements, then a circuit simulator of the SPICE type can
handle it, and as a bonus has extensive capabilities for graphical display of
the output. The work here was done with PSpice. A more common use of
electrical analogues is in the electro-mechanical domain of loudspeakers;
see Murphy [4] for a virtuoso example.
The simulation approach treats temperature as voltage, and thermal energy
as electric charge, making thermal resistance analogous to electrical
resistance, and thermal capacity to electrical capacitance. Thermal
capacity is a measure of how much heat is required to raise the temperature
of a mass by 1°C. (And if anyone can work out what the thermal equivalent
of an inductor is, I would be interested to know.) With the right choice of
units the simulator output will be in Volts, with a one-to-one correspondence with degrees Celsius, and Amps, similarly representing Watts of heat
flow; see Table 12.2. It is then simple to produce graphs of temperature
against time.
Table 12.2
Heat quantity
Heat flowrate
Thermal resistance
Thermal capacity
Heat source
Joules (Watt-seconds)
Dissipative element,
e.g. transistor
Medium-sized planet
Coulombs (Amp-seconds)
Current source
Voltage source
Audio Power Amplifier Design Handbook
Since heat flow is represented by current, the inputs to the simulated system
are current sources. A voltage source would force large chunks of metal to
change temperature instantly, which is clearly wrong. The ambient is
modelled by a voltage source, as it can absorb any amount of heat without
changing temperature.
Modelling the EF output stage
The major characteristic of Emitter-Follower (EF) output stages is that the
output device junction temperatures are directly involved in setting Iq. This
junction temperature is not accessible to a thermal compensation system,
and measuring the heatsink temperature instead provides a poor approximation, attenuated by the thermal resistance from junction to heatsink
mass, and heavily time-averaged by heatsink thermal inertia. This can
cause serious production problems in initial setting up; any drift of Iq will
be very slow as a lot of metal must warm up.
For EF outputs, the bias generator must attempt to establish an output bias
voltage that is a summation of four driver and output Vbe’s. These do not
vary in the same way. It seems at first a bit of a mystery how the EF stage,
which still seems to be the most popular output topology, works as well as
it does. The probable answer is Figure 12.1, which shows how driver
dissipation (averaged over a cycle) varies with peak output level for the
three kinds of EF output described on page 113, and for the CFP
configuration. The SPICE simulations used to generate this graph used a
triangle waveform, to give a slightly closer approximation to the peakaverage ratio of real waveforms. The rails were +/–50 V, and the load
8 .
It is clear that the driver dissipation for the EF types is relatively constant
with power output, while the CFP driver dissipation, although generally
lower, varies strongly. This is a consequence of the different operation of
these two kinds of output. In general, the drivers of an EF output remain
conducting to some degree for most or all of a cycle, although the output
devices are certainly off half the time. In the CFP, however, the drivers turn
off almost in synchrony with the outputs, dissipating an amount of power
that varies much more with output. This implies that EF drivers will work at
roughly the same temperature, and can be neglected in arranging thermal
compensation; the temperature-dependent element is usually attached to
the main heatsink, in an attempt to compensate for the junction
temperature of the outputs alone. The Type I EF output keeps its drivers at
the most constant temperature; this may (or may not) have something to do
with why it is the most popular of the EF types.
(The above does not apply to integrated Darlington outputs, with drivers
and assorted emitter resistors combined in one ill-conceived package, as
the driver sections are directly heated by the output junctions. This would
Thermal compensation and thermal dynamics
seem to work directly against quiescent stability, and why these compound
devices are ever used in audio amplifiers remains a mystery to me.)
The drawback with most EF thermal compensation schemes is the slow
response of the heatsink mass to thermal transients, and the obvious
solution is to find some way of getting the sensor closer to one of the output
junctions (symmetry of dissipation is assumed). If TO3 devices are used,
then the flange on which the actual transistor is mounted is as close as we
can get without a hacksaw. This is however clamped to the heatsink, and
almost inaccessible, though it might be possible to hold a sensor under one
of the mounting bolts. A simpler solution is to mount the sensor on the top
of the TO3 can. This is probably not as accurate an estimate of junction
temperature as the flange would give, but measurement shows the top gets
much hotter much faster than the heatsink mass, so while it may appear
unconventional, it is probably the best sensor position for an EF output
stage. Figure 12.4 shows the results of an experiment designed to test this.
A TO3 device was mounted on a thick aluminium L-section thermal
coupler in turn clamped to a heatsink; this construction is representative of
many designs. Dissipation equivalent to 100 W/8 was suddenly initiated,
and the temperature of the various parts monitored with thermocouples.
The graph clearly shows that the top of the TO3 responds much faster, and
with a larger temperature change, though after the first two minutes the
temperatures are all increasing at the same rate. The whole assembly took
more than an hour to asymptote to thermal equilibrium.
Figure 12.5 shows a TO3 output device mounted on a thermal coupling
bar, with a silicone thermal washer giving electrical isolation. The coupler
is linked to the heatsink proper via a second conformal material; this need
not be electrically insulating so highly efficient materials like graphite foil
can be used. This is representative of many amplifier designs, though a
Figure 12.4
Thermal response of a
TO3 device on a
large heatsink when
power is suddenly
applied. The top of
the TO3 can responds
most rapidly
Audio Power Amplifier Design Handbook
Figure 12.5
A TO3 power
transistor attached to a
heatsink by a thermal
coupler. Thermal sensor
is shown on can top;
more usual position
would be on thermal
good number have the power devices mounted directly on the heatsink; the
results hardly differ. A simple thermal-analogue model of Figure 12.5 is
shown in Figure 12.6; the situation is radically simplified by treating each
mass in the system as being at a uniform temperature, i.e. isothermal, and
therefore representable by one capacity each. The boundaries between
parts of the system are modelled, but the thermal capacity of each mass is
concentrated at a notional point. In assuming this we give capacity
elements zero thermal resistance; e.g. both sides of the thermal coupler will
always be at the same temperature. Similarly, elements such as the thermal
washer are assumed to have zero heat capacity, because they are very thin
and have negligible mass compared with other elements in the system.
Thus the parts of the thermal system can be conveniently divided into two
categories; pure thermal resistances and pure thermal capacities. Often this
gives adequate results; if not, more sub-division will be needed. Heat losses
from parts other than the heatsink are neglected.
Real output stages have at least two power transistors; the simplifying
assumption is made that power dissipation will be symmetrical over
anything but the extreme short-term, and so one device can be studied by
slicing the output stage, heatsink, etc. in half.
It is convenient to read off the results directly in °C, rather than temperature
rise above ambient, so Figure 12.6 represents ambient temperature with a
voltage source Vamb that offsets the baseline (node 10) 25°C from
simulator ground, which is inherently at 0°C (0V).
Values of the notional components in Figure 12.6 have to be filled in with
a mixture of calculation and manufacturer’s data. The thermal resistance R1
from junction to case comes straight from the data book, as does the
resistance R2 of the TO3 thermal washer; also R4, the convection
coefficient of the heatsink itself, otherwise known as its thermal resistance
Thermal compensation and thermal dynamics
Figure 12.6
A thermal/electrical
model of Figure 12.5,
for half of one channel
only. Node 1 is
junction temperature,
node 2 flange
temperature, and so
on. Vamb sets the
baseline to 25°C.
Arrows show heat flow
to ambient. This is always assumed to be constant with temperature, which
it very nearly is. Here R4 is 1°C/W, so this is doubled to 2 as we cut the
stage in half to exploit symmetry.
R3 is the thermal resistance of the graphite foil; this is cut to size from a
sheet and the only data is the bulk thermal resistance of 3.85 W/mK, so R3
must be calculated. Thickness is 0.2 mm, and the rectangle area in this
example was 38 × 65 mm. We must be careful to convert all lengths to
Heat flow/°C =
3.85 × Area
3.83 × (.038 × .065)
= 47.3 W/°C
So thermal resistance =
Equation 12.1
= 0.021°C/W
Thermal resistance is the reciprocal of heat flow per degree, so R3 is
0.021°C/W, which just goes to show how efficient thermal washers can be
if they do not have to be electrical insulators as well.
In general all the thermal capacities will have to be calculated, sometimes
from rather inadequate data, thus:
Thermal capacity = Density × Volume × Specific heat
A power transistor has its own internal structure, and its own internal
thermal model (Figure 12.7). This represents the silicon die itself, the solder
that fixes it to the copper header, and part of the steel flange the header is
welded to. I am indebted to Motorola for the parameters, from an MJ15023
TO3 device [5]. The time-constants are all extremely short compared with
heatsinks, and it is unnecessary to simulate in such detail here.
Audio Power Amplifier Design Handbook
Figure 12.7
Internal thermal model
for a TO3 transistor. All
the heat is liberated in
the junction structure,
shown as N multiples
of C1 to represent a
typical interdigitated
power transistor
The thermal model of the TO3 junction is therefore reduced to lumped
component C1, estimated at 0.1J/°C; with a heat input of 1 W and no losses
its temperature would increase linearly by 10°C/second. The capacity C2
for the transistor package was calculated from the volume of the TO3 flange
(representing most of the mass) using the specific heat of mild steel. The
thermal coupler is known to be aluminium alloy (not pure aluminium,
which is too soft to be useful) and the calculated capacity of 70J/°C should
be reliable. A similar calculation gives 250 J/°C for the larger mass of the
aluminium heatsink. Our simplifying assumptions are rather sweeping
here, because we are dealing with a substantial chunk of finned metal
which will never be truly isothermal.
The derived parameters for both output TO3’s and TO-225 AA drivers are
summarised in Table 12.3. The drivers are assumed to be mounted onto
small individual heatsinks with an isolating thermal washer; the data is for
the popular Redpoint SW38-1 vertical heatsink.
Figures 12.8 and 12.9 show the result of a step-function in heat generation
Table 12.3
Output device
Junction capacity
Junction-case resistance
Transistor package capacity
Thermal washer res
Coupler capacity
Coupler-heatsink res
Heatsink capacity
Heatsink convective res
Thermal compensation and thermal dynamics
in the output transistor; 20 W dissipation is initiated, corresponding
approximately to a sudden demand for full sinewave power from a
quiescent 100 W amplifier. The junction temperature V(1) takes off nearvertically, due to its small mass and the substantial thermal resistance
between it and the TO3 flange; the flange temperature V(2) shows a similar
but smaller step as R2 is also significant. In contrast the thermal coupler,
which is so efficiently bonded to the heatsink by graphite foil that they
might almost be one piece of metal, begins a slow exponential rise that will
take a very long time to asymptote. Since after the effect of C1 and C2 have
died away the junction temp is offset by a constant amount from the temp
of C3 and C4, V(1) also shows a slow rise. Note the X-axis of Figure 12.9
must be in kilo-seconds, because of the relatively enormous thermal
capacity of the heatsink.
This shows that a temperature sensor mounted on the main heatsink can
never give accurate bias compensation for junction temperature, even if it
is assumed to be isothermal with the heatsink; in practice there will be
some sensor cooling which will make the sensor temperature slightly
under-read the heatsink temperature V(4). Initially the temperature error
V(1)–V(4) increases rapidly as the TO3 junction heats, reaching 13 degrees
in about 200 ms. The error then increases much more slowly, taking 6
seconds to reach the effective final value of 22 degrees. If we ignore the
thermal-gain effect mentioned above, the long-term Vq error is +44 mV,
i.e. Vq is too high. When this is doubled to allow for both halves of the
Figure 12.8
Results for Figure 12.6, with step heat input of 20 W to junction initiated at Time = 10 seconds. Upper plot
shows temperatures, lower the Vbias error for half of output stage
Audio Power Amplifier Design Handbook
output stage we get +88 mV, which uses up nearly all of the +/–100 mV
error band, without any other inaccuracies. (Hereafter all Vbias/Vq error
figures quoted have been doubled and so apply to a complete output
stage.) Including the thermal gain actually makes little difference over a
10-second timescale; the lower Vq-error trace in Figure 12.8 slowly decays
as the main heatsink warms up, but the effect is too slow to be useful.
The amplifier Vq and Iq will therefore rise under power, as the hot output
device Vbe voltages fall, but the cooler bias generator on the main heatsink
reduces its voltage by an insufficient amount to compensate.
Figure 12.9 shows the long-term response of the system. At least 2500
seconds pass before the heatsink is within a degree of final temperature.
In the past I have recommended that EF output stages should have the
thermal sensor mounted on the top of the TO3 can, despite the mechanical
difficulties. This is not easy to simulate as no data is available for the
thermal resistance between junction and can top. There must be an
additional thermal path from junction to can, as the top very definitely gets
hotter than the flange measured at the very base of the can. In view of the
relatively low temperatures, this path is probably due to internal
convection rather than radiation.
A similar situation arises with TO3P packages (a large plastic package,
twice the size of TO220) for the top plastic surface can get at least 20
degrees hotter than the heatsink just under the device.
Figure 12.9
The long-term version of Figure 12.8, showing that it takes over 40 minutes for the heatsink to get within 1
degree of final temperature
Thermal compensation and thermal dynamics
Figure 12.10
Model of EF output
stage with thermal
paths to TO3 can top
modelled by R20,
R21. C5 simulates can
capacity. R23 models
sensor convection
cooling; node 21 is
sensor temperature
Using the real thermocouple data from page 335, I have estimated the
parameters of the thermal paths to the TO3 top. This gives Figure 12.10,
where the values of elements R20, R21, C5 should be treated with
considerable caution, though the temperature results in Figure 12.11 match
reality fairly well; the can top (V20) gets hotter faster than any other
accessible point. R20 simulates the heating path from the junction to the TO3
can and R21 the can-to-flange cooling path, C5 being can thermal capacity.
Figure 12.11
The simulation results for Figure 12.10; lower plot shows Vbias errors for normal thermal pad under sensor,
and 80°C/W semi-insulator. The latter has near-zero long-term error
Audio Power Amplifier Design Handbook
Figure 12.10 includes approximate representation of the cooling of the
sensor transistor, which now matters. R22 is the thermal pad between
the TO3 top and the sensor, C6 the sensor thermal capacity, and R23 is the
convective cooling of the sensor, its value being taken as twice the
datasheet free-air thermal resistance as only one face is exposed.
Putting the sensor on top of the TO3 would be expected to reduce the
steady-state bias error dramatically. In fact, it overdoes it, as after factoring
in the thermal-gain of a Vbe-multiplier in an EF stage, the bottom-most
trace of Figure 12.11 shows that the bias is over-compensated; after the
initial positive transient error, Vbias falls too low giving an error of –30 mV,
slowly worsening as the main heatsink warms up. If thermal-gain had been
ignored, the simulated error would have apparently fallen from +44 (Figure
12.8) to +27 mV; apparently a useful improvement, but actually illusory.
Since the new sensor position over-compensates for thermal errors, there
should be an intermediate arrangement giving near-zero long-term error. I
found this condition occurs if R22 is increased to 80°C/W, requiring some
sort of semi-insulating material rather than a thermal pad, and gives the
upper error trace in the lower half of Figure 12.11. This peaks at +30 mV
after 2 seconds, and then decays to nothing over the next twenty. This is
much superior to the persistent error in Figure 12.8, so I suggest this new
technique may be useful.
Modelling the CFP output stage
In the CFP configuration, the output devices are inside a local feedback
loop, and play no significant part in setting Vq, which is dominated by
thermal changes in the driver Vbe’s. Such stages are virtually immune to
thermal runaway; I have found that assaulting the output devices with a
powerful heat gun induces only very small Iq changes. Thermal compensation is mechanically simpler as the Vbe-multiplier transistor is usually
mounted on one of the driver heatsinks, where it aspires to mimic the driver
junction temperature.
It is now practical to make the bias transistor of the same type as the drivers,
which should give the best matching of Vbe [6], though how important this
is in practice is uncertain. This also avoids the difficulty of trying to attach
a small-signal (probably TO92) transistor package to a heatsink.
Since it is the driver junctions that count, output device temperatures are
here neglected. The thermal parameters for a TO225AA driver (e.g.
MJE340/350) on the SW38-1 vertical heatsink are shown in Table 12.3; the
drivers are on individual heatsinks so their thermal resistance is used
directly, without doubling.
In the simulation circuit (Figure 12.12) V(3) is the heatsink temperature; the
sensor transistor (also MJE340) is mounted on this sink with thermal washer
Thermal compensation and thermal dynamics
Figure 12.12
Model of a CFP stage.
Driver transistor is
mounted on a small
heatsink, with sensor
transistor on the other
side. Sensor dynamics
and cooling are
modelled by R4, C4
and R5
R4, and has thermal capacity C4. R5 is convective cooling of the sensor. In
this case the resulting differences in Figure 12.13 between sink V(3) and
sensor V(4) are very small.
We might expect the CFP delay errors to be much shorter than in the EF;
however, simulation with a heat step-input suitably scaled down to 0.5 W
(Figure 12.13) shows changes in temperature error V(1)–V(4) that appear
rather paradoxical; the error reaches 5 degrees in 1.8 seconds, levelling out
at 6.5 degrees after about 6 seconds. This is markedly slower than the EF
case, and gives a total bias error of +13 mV, which after doubling to +26 mV
is well outside the CFP error band of +/–10 mV.
The initial transients are slowed down by the much smaller step heat
input, which takes longer to warm things up. The final temperature
however, is reached in 500 rather than 3000 seconds, and the timescale
is now in hundreds rather than thousands of seconds. The heat input is
Figure 12.13
Simulation results for
CFP stage, with step
heat input of 0.5 W.
Heatsink and sensor
are virtually
isothermal, but there
is a persistent error
as driver is always
hotter than heatsink
due to R1, R2
Audio Power Amplifier Design Handbook
smaller, but the driver heatsink capacity is also smaller, and the overall
time-constant is less.
It is notable that both timescales are much longer than musical
The integrated absolute error criterion
Since the thermal sensor is more or less remote from the junction whose
gyrations in temperature will hopefully be cancelled out, heat losses and
thermal resistances cause the temperature change reaching the sensor to be
generally too little and too late for complete compensation.
As in the previous section, all the voltages and errors here are for one-half
of an output stage, using symmetry to reduce the work involved. These
half-amplifiers are used throughout this chapter, for consistency, and the
error voltages are only doubled to represent reality (a complete output
stage) when they are compared against the tolerance bands previously
We are faced with errors that vary not only in magnitude, but also in their
persistence over time; judgement is required as to whether a prolonged
small error is better than a large error which quickly fades away.
The same issue faces most servomechanisms, and I borrow from Control
Theory the concept of an Error Criterion which combines magnitude and
time into one number [7],[8]. The most popular criterion is the Integrated
Absolute Error (IAE) which is computed by integrating the absolute-value of
the error over a specified period after giving the system a suitably
provocative stimulus; the absolute-value prevents positive and negative
errors cancelling over time. Another common criterion is the Integrated
Square Error (ISE) which solves the polarity problem by squaring the error
before integration – this also penalises large errors much more than small
ones. It is not immediately obvious which of these is most applicable to
bias-control and the psychoacoustics of crossover distortion that changes
with time, so I have chosen the popular IAE.
One difficulty is that the IAE error criterion for bias voltage tends to
accumulate over time, due to the integration process, so any constant bias
error quickly comes to dominate the IAE result. In this case, the IAE is little
more than a counter-intuitive way of stating the constant error, and must be
quoted over a specified integration time to mean anything at all. This is why
the IAE concept was not introduced earlier in this chapter.
Much more useful results are obtained when the IAE is applied to a
situation where the error decays to a very small value after the initial
transient, and stays there. This can sometimes be arranged in amplifiers, as
I hope to show. In an ideal system where the error decayed to zero without
overshoot, the IAE would asymptote to a constant value after the initial
Thermal compensation and thermal dynamics
transient. In real life, residual errors make the IAE vary slightly with time, so
for consistency all the IAE values given here are for 30 seconds after the
Improved thermal compensation: the emitter-follower stage
It was shown above that the basic emitter-follower (EF) stage with the
sensor on the main heatsink has significant thermal attenuation error and
therefore under-compensates temperature changes. (The Vq error is
+44 mV, the positive sign showing it is too high. If the sensor is on the TO3
can top it over-compensates instead) (Vq error –30 mV).
If an intermediate configuration is contrived by putting a layer of controlled
thermal resistance (80°C/W) between the TO3 top and the sensor, then the
50-second timescale component of the error can be reduced to near-zero.
This is the top error trace in bottom half of Figure 12.14; the lower trace
shows the wholly misleading result if sensor heat losses are neglected in
this configuration.
Despite this medium-term accuracy, if the heat input stimulus remains
constant over the very long-term (several kilo-seconds) there still remains a
Figure 12.14
EF behaviour with semi-insulating pad under sensor on TO3 can top. The sensor in the upper temperature plot
rises more slowly than the flange, but much faster than the main heatsink or coupler. In lower Vq-error section,
upper trace is for a 80°C/W thermal resistance under the sensor, giving near-zero error. Bottom trace shows
serious effect of ignoring sensor-cooling in TO3-top version
Audio Power Amplifier Design Handbook
Figure 12.15
Over a long timescale, the lower plot shows that the Vq error, although almost zero in Figure 12.14, slowly
drifts into over-compensation as the heatsink temperature (upper plot) reaches asymptote
very slow drift towards over-compensation due to the slow heating of the
main heatsink (Figure 12.15).
This long-term drift is a result of the large thermal inertia of the main
heatsink and since it takes 1500 seconds (25 minutes) to go from zero to
–32 mV is of doubtful relevance to the time-scales of music and signal level
changes. On doubling to –64 mV, it remains within the EF Vq tolerance of
+/–100 mV. On the shorter 50-second timescale, the half-amplifier error
remains within a +/–1 mV window from 5 seconds to 60 seconds after the
For the EF stage, a very-long-term drift component will always exist so long
as the output device junction temperature is kept down by means of a main
heatsink that is essentially a weighty chunk of finned metal.
The EF system stimulus is a 20 W step as before, being roughly worst-case
for a 100 W amplifier. Using the 80°C/W thermal semi-insulator described
above gives the upper error trace in Figure 12.16, and an IAE of 254 mV-sec
after 30 seconds. This is relatively large because of the extra time-delay
caused by the combination of an increased R22 with the unchanged sensor
thermal capacity C6. Once more, this figure is for a half-amplifier, as are all
IAEs in this chapter.
Thermal compensation and thermal dynamics
Figure 12.16
The transient error for
the semi-insulating pad
and the low-tempco
version. The latter
responds much faster,
with a lower peak
error, and gives less
than half the Integrated
Absolute Error (IAE)
Up to now I have assumed that the temperature coefficient of a Vbemultiplier bias generator is rigidly fixed at –2 mV/°C times the Vbemultiplication factor, which is about 4.5× for EF and 2× for CFP. The
reason for the extra thermal gain displayed by the EF was set out on
page 334.
The above figures are for both halves of the output stage, so the halfamplifier value for EF is –4.5 mV/°C, and for CFP –2 mV/°C. However . . .
if we boldly assume that the Vbias generator can have its thermal
coefficient varied at will, the insulator and its aggravated time-lag can be
eliminated. If a thermal pad of standard material is once more used
between the sensor and the TO3 top, the optimal Vbias coefficient for
minimum error over the first 40 seconds proves to be –2.8 mV/°C, which is
usefully less than –4.5. The resulting 30-second IAE is 102 mV-sec, more
than a two times improvement; see the lower trace in Figure 12.16, for
comparison with the semi-insulator method described above.
In view of the fixed time-constants, dependant upon a certain weight of
metal being required for heat dissipation, it appears that the only way this
performance could be significantly improved upon might be to introduce a
new kind of output transistor with an integral diode that would sense the
actual junction temperature, being built into the main transistor junction
structure. Although it would be of immense help to amplifier makers, noone seems to be keen to do this.
From here on I am going to assume that a variable-temperature-coefficient
(tempco) bias generator can be made when required; the details of how to
Audio Power Amplifier Design Handbook
do it are not given here. It is an extremely useful device, as thermal
attenuation can then be countered by increasing the thermal gain; it does
not however help with the problem of thermal delay.
In the second EF example above, the desired tempco is –2.8 mV/°C, while
an EF output stage plus Vbe-multiplier has an actual tempco of –4.5 mV/°C.
(This inherent thermal gain in the EF was explained on page 334.) In this
case we need a bias generator that has a smaller tempco than the standard
circuit. The conventional EF with its temp sensor on the relatively cool
main heatsink would require a larger tempco than standard.
A potential complication is that amplifiers should also be reasonably
immune to changes in ambient temperature, quite apart from changes due
to dissipation in the power devices. The standard tempco gives a close
approach to this automatically, as the Vbe-multiplication factor is naturally
almost the same as the number of junctions being biased. However, this
will no longer be true if the tempco is significantly different from standard,
so it is necessary to think about a bias generator that has one tempco for
power-device temperature changes, and another for ambient changes. This
sounds rather daunting, but is actually fairly simple.
Improved compensation for the CFP output stage
As revealed on page 329, the Complementary-Feedback-Pair (CFP) output
stage has a much smaller bias tolerance of +/–10 mV for a whole amplifier,
and surprisingly long time-constants. A standard CFP stage therefore has
larger relative errors than the conventional Emitter-Follower (EF) stage with
thermal sensor on the main heatsink; this is the opposite of conventional
wisdom. Moving the sensor to the top of the TO3 can was shown to
improve the EF performance markedly, so we shall attempt an analogous
improvement with driver compensation.
The standard CFP thermal compensation arrangements have the sensor
mounted on the driver heatsink, so that it senses the heatsink temperature
rather than that of the driver itself. (See Figure 12.17a for mechanical
arrangement, and Figure 12.18 for thermal model.) As in the EF, this gives
a constant long-term error due to the sustained temperature difference
between the driver junction and heatsink mass; see the upper traces in
Figure 12.20, plotted for different bias tempcos. The CFP stimulus is a
0.5 W step, as before. This constant error cannot be properly dealt with by
choosing a tempco that gives a bias error passing through a zero in the first
fifty seconds, as was done for the EF case with a TO3-top sensor, as the
heatsink thermal inertia causes it to pass through zero very quickly and
head rapidly South in the direction of ever-increasing negative error. This is
because it has allowed for thermal attenuation but has not decreased
thermal delay. It is therefore pointless to compute an IAE for this
Thermal compensation and thermal dynamics
Figure 12.17
a The sensor transistor
on the driver
b An improved
version, with the
sensor mounted on
top of the driver
itself, is more
c Using two sensors to
construct a junctionestimator
A better sensor position
By analogy with the TO3 and TO3P transistor packages examined earlier,
it will be found that driver packages such as TO225AA on a heatsink get
hotter faster on their exposed plastic face than any other accessible point.
It looks as if a faster response will result from putting the sensor on top of
the driver rather than on the other side of the sink as usual. With the
Redpoint SW 38-1 heatsink this is fairly easy as the spring-clips used to
Audio Power Amplifier Design Handbook
Figure 12.18
Thermal circuit of
normal CFP sensor
mounting on heatsink.
R3 is the convective
cooling of the
heatsink, while R5
models heat losses
from the sensor body
Figure 12.19
Thermal circuit of
driver-back mounting
of sensor. The large
heatsink time-constant
R2–C2 is no longer
in the direct thermal
path to the sensor, so
the compensation is
faster and more
secure one plastic package will hold a stack of two TO225AA’s with only
a little physical persuasion. A standard thermal pad is used between the top
of the driver and the metal face of the sensor, giving the sandwich shown
in Figure 12.17b. The thermal model is Figure 12.19. This scheme greatly
reduces both thermal attenuation and thermal delay (lower traces in Figure
12.20) giving an error that falls within a +/–1 mV window after about 15.5
seconds, when the tempco is set to –3.8 mV/°C. The IAE computes to
52 mV, as shown in Figure 12.21, which demonstrates how the IAE
criterion tends to grow without limit unless the error subsides to zero. This
value is a distinct improvement on the 112 mV IAE which is the best that
could be got from the EF output.
The effective delay is much less because the long heatsink time-constant is
now partly decoupled from the bias compensation system.
A junction-temperature estimator
It appears that we have reached the limit in what can be done, as it is hard
to get one transistor closer to another than they are in Figure 12.17b. It is
however possible to get better performance, not by moving the sensor
position, but by using more of the available information to make a better
estimate of the true driver junction temperature. Such estimator subsystems
are widely used in servo control systems where some vital variable is
inaccessible, or only knowable after such a time-delay as to render the data
useless [9]. It is often almost as useful to have a model system, usually just
Thermal compensation and thermal dynamics
Figure 12.20
The Vq errors for normal and improved sensor mounting, with various tempcos. The improved method can
have its tempco adjusted to give near-zero error over this timescale. Not so for the usual method
Figure 12.21
The Vq error and IAE for the improved sensor mounting method on driver back. Error is much smaller, due
both to lower thermal attenuation and less delay. Best IAE is 52 mV-sec (with gain = 0.0038); twice as good
as the best EF version
Audio Power Amplifier Design Handbook
an abstract set of gains and time-constants, which all give an estimate of
what the current value of the unknown variable must be, or ought to be.
The situation here is similar, and the first approach makes a better guess at
the junction temperature V(1) by using the known temperature drop
between the package and the heatsink. The inherent assumption is made
that the driver package is isothermal, as it is modelled by one temperature
value V(2).
If two sensors are used, one placed on the heatsink as usual, and the other
on top of the driver package, as described above, (Figure 12.17c), then
things get interesting. Looking at Figure 12.19, it can be seen that the
difference between the driver junction temperature and the heatsink is due
to R1 and R2; the value of R1 is known, but not the heat flow through it.
Neglecting small incidental losses, the temperature drop through R1 is
proportional to the drop through R2. Since C2 is much smaller than C3, this
should remain reasonably true even if there are large thermal transients.
Thus, measuring the difference between V(2) and V(3) allows a reasonable
estimate of the difference between V(1) and V(2); when this difference is
added to the known V(2), we get a rather good estimation of the
inaccessible V(1). This system is shown conceptually in Figure 12.22,
which gives only the basic method of operation; the details of the real
circuitry must wait until we have decided exactly what we want it to do.
We can only measure V(2) and V(3) by applying thermal sensors to them, as
in Figure 12.17c, so we actually have as data the sensor temperatures V(4)
and V(5). These are converted to bias voltage and subtracted, thus estimating
the temperature drop across R1. The computation is done by VoltageControlled-Voltage-Source E1, which in PSpice can have any equation
assigned to define its behaviour. Such definable VCVSs are very handy as
little analogue computers that do calculations as part of the simulation
model. The result is then multiplied by a scaling factor called estgain which
is incorporated into the defining equation for E1, and is adjusted to give the
minimum error; in other words the variable-tempco bias approach is used to
allow for the difference in resistance between R1 and R2.
The results are shown in Figure 12.23, where an estgain of 1.10 gives the
minimum IAE of 25 mV-sec. The transient error falls within a +/–1 mV
window after about 5 seconds. This is a major improvement, at what
promises to be little cost.
A junction estimator with dynamics
The remaining problem with the junction-estimator scheme is still its
relatively slow initial response; nothing can happen before heat flows
through R6 into C5, in Figure 12.22. It will take even longer for C4 to
respond, due to the inertia of C3, so we must find a way to speed up the
dynamics of the junction-estimator.
Figure 12.22
Conceptual diagram of
the junction-estimator.
Controlled-voltagesource E1 acts as an
analogue computer
performing the scaling
and subtraction of the
two sensor
temperatures V(4) and
V(5), to derive the bias
Audio Power Amplifier Design Handbook
Figure 12.23
Simulation results for the junction-estimator, for various values of estgain. The optimal IAE is halved to
25 mV-sec; compare with Figure 12.21
The first obvious possibility is the addition of phase-advance to the
forward bias-compensation path. This effectively gives a high gain
initially, to get things moving, which decays back over a carefully-set
time to the original gain value that gave near-zero error over the
50-second timescale. The conceptual circuit in Figure 12.24 shows the
phase-advance circuitry added to the compensation path; the signal is
attenuated 100× by R50 and R51, and then scaled back up to the same
level by VCVS E2, which is defined to give a gain of 110 times
incorporating estimated gain = 1.10. C causes fast changes to bypass the
attenuation, and its value in conjunction with R50, R51 sets the degree of
phase-advance or lead. The slow behaviour of the circuit is thus
unchanged, but transients pass through C and are greatly amplified by
comparison with steady-state signals.
The result on the initial error transient of varying C around its optimal value
can be seen in the expanded view of Figure 12.25. The initial rise in Vq
error is pulled down to less than a third of its value if C is made 10 µF; with
a lower C value the initial peak is still larger than it need be, while a higher
value introduces some serious undershoot that causes the IAE to rise again,
as seen in the upper traces in Figure 12.26. The big difference between no
phase-advance, and a situation where it is even approximately correct, is
very clear.
Figure 12.24
The conceptual circuit
of a junction-estimator
with dynamics. C gives
higher gain for fast
thermal transients and
greatly reduces the
effects of delay
Audio Power Amplifier Design Handbook
Figure 12.25
The initial transient errors for different values of C. Too high a value causes undershoot
Figure 12.26
The IAE for different values of C. 10 µF is clearly best for minimum integrated error (IAE = 7.3 mV-sec) but
even a rough value is a great improvement
Thermal compensation and thermal dynamics
With C set to 10 µF, the transient error falls within a +/–1 mV window
after only 0.6 seconds, which is more than twenty times faster than the
first improved CFP version (sensor put on driver) and gives a nicely
reduced IAE of 7.3 mV-sec at 50 seconds. The real-life circuitry to do this
has not been designed in detail, but presents no obvious difficulties. The
result should be the most accurately bias-compensated Class-B amplifier
ever conceived.
Some of the results of these simulations and tests were rather unexpected. I thought that the CFP would show relatively smaller bias errors
than the EF, but it is the EF that stays within its much wider tolerance
bands, with either heatsink or TO3-top mounted sensors. The thermalgain effect in the EF stage seems to be the root cause of this, and this in
turn is a consequence of the near-constant driver dissipation in the EF
However, the cumulative bias errors of the EF stage can only be reduced to
a certain extent, as the system is never free from the influence of the main
heatsink with its substantial thermal inertia. In contrast the CFP stage gives
much more freedom for sensor placement and gives scope for more
sophisticated approaches that reduce the errors considerably.
Hopefully it is clear that it is no longer necessary to accept Vbe-multiplier
on the heatsink as the only option for the crucial task of Vbias
compensation. The alternatives presented promise greatly superior compensation accuracy.
Variable-tempco bias generators
The standard Vbe-multiplier bias generator has a temperature coefficient
that is fixed by the multiplication factor used, and so ultimately by the value
of Vbias required. At many points in this chapter it has been assumed that
it is possible to make a bias generator with an arbitrary temperature
coefficient. This section shows how to do it.
Figure 12.27 shows two versions of the usual Vbe-multiplier bias generator.
Here the lower rails are shown as grounded to simplify the results. The first
version in Figure 12.27a is designed for an EF (Emitter-Follower) output
stage, where the voltage Vbias to be generated is (4 × Vbe) + Vq, which
totals +2.93 V. Recall that Vq is the small quiescent voltage across the
emitter-resistors Re; it is this quantity we are aiming to keep constant, rather
than the quiescent current, as is usually assumed. The optimal Vq for an EF
stage is in the region of 50 mV.
Audio Power Amplifier Design Handbook
Figure 12.27
The classical Vbe-multiplier bias generator. Two versions are shown: for biasing EF (a) and (b) CFP output
stages. The EF requires more than twice the bias voltage for optimal crossover performance
The second bias generator in Figure 12.27b is intended for a CFP
(Complementary-Feedback-Pair) output stage, for which the required Vbias
is less at (2 × Vbe) + Vq, or approx 1.30 V in total. Note that the optimal Vq
is also much smaller for the CFP type of output stage, being about 5 mV.
It is assumed that Vbias is trimmed by varying R2, which will in practice be
a preset with a series end-stop resistor to limit the maximum Vbias setting.
It is important that this is the case, because a preset normally fails by the
wiper becoming disconnected, and if it is in the R2 position the bias will
default to minimum. In the R1 position an open-circuit preset will give
maximum bias, which may blow fuses or damage the output stage. The
adjustment range provided should be no greater than that required to take
up production tolerances; it is, however, hard to predict just how big that
will be, so the range is normally made wide for pre-production
manufacture, and then tightened in the light of experience.
The EF version of the bias generator has a higher Vbias, so there is a larger
Vbe-multiplication factor to generate it. This is reflected in the higher
temperature coefficient (hereafter shortened to ‘tempco’). See Table 12.4.
Table 12.4
Thermal compensation and thermal dynamics
Creating a higher tempco
A higher (i.e. more negative) tempco than normal may be useful to
compensate for the inability to sense the actual output junction temperatures. Often the thermal losses to the temperature sensor are the major
source of steady-state Vbias error, and to reduce this a tempco is required
that is larger than the standard value given by: ‘Vbe-multiplication factor
times –2 mV/°C’. Many approaches are possible, but the problem is
complicated because in the CFP case the bias generator has to work within
two rails only 1.3 V apart. Additional circuitry outside this voltage band can
be accommodated by bootstrapping, as in the Trimodal amplifier biasing
system in Chapter 9, but this does add to the component count.
A simple new idea is shown in Figure 12.28. The aim is to increase the
multiplication factor (and hence the negative tempco) required to give the
same Vbias. The diagram shows a voltage source V1 inserted in the R2 arm.
To keep Vbias the same, R2 is reduced. Since the multiplication factor
(R1 + R2)/R2 is increased, the tempco is similarly increased. In Table 12.5,
Figure 12.28
Principle of a Vbe
multiplier with
increased tempco.
Adding voltage source
V1 means the voltagemultiplication factor
must be increased to
get the same Vbias.
The tempco is therefore
also increased, here to
–4.4 mV/°C
Table 12.5
Audio Power Amplifier Design Handbook
Figure 12.29
Shows a practical
version of a Vbe
multiplier with
increased tempco. The
extra voltage source is
derived from the
bandgap reference by
R6, R4. Tempco is
increased to
–5.3 mV/°C
a CFP bias circuit has its tempco varied by increasing V1 in 100 mV steps;
in each case the value of R2 is then reduced to bring Vbias back to the
desired value, and the tempco is increased.
A practical circuit is shown in Figure 12.29, using a 2.56 V bandgap reference to generate the extra voltage across R4. This reference has to work
outside the bias generator rails, so its power-feed resistors R7, R8 are bootstrapped by C from the amplifier output, as in the Trimodal amplifier design.
Ambient temperature changes
Power amplifiers must be reasonably immune to ambient temperature
changes, as well as changes due to dissipation in power devices.
The standard compensation system deals with this pretty well, as the
Figure 12.30
Practical Vbe multiplier
with increased tempco,
and also improved
correction for ambient
temperature changes,
by using diode D to
derive the extra voltage
Thermal compensation and thermal dynamics
Vbe-multiplication factor is inherently almost the same as the number of
junctions being biased. This is no longer true if the tempco is significantly
modified. Ideally we require a bias generator that has one increased
tempco for power-device temperature changes only, and another standard
tempco for ambient changes affecting all components. One approach to
this is Figure 12.30, where V1 is derived via R6, R4 from a silicon diode
rather than a bandgap reference, giving a voltage reducing with temperature. The tempco for temperature changes to Q1 only is –4.0 mV/°C,
while the tempco for global temperature changes to both Q1 and D1 is
lower at –3.3 mV/°C. Ambient temperatures vary much less than output
device junction temperatures, which may easily range over 100 °C.
Creating a lower tempco
Earlier in this chapter I showed that an EF output stage has ‘thermal gain’ in
that the thermal changes in Vq make it appear that the tempco of the Vbias
generator is higher than it really is. This is because the bias generator is set
up to compensate for four base-emitter junctions, but in the EF output
configuration the drivers have a roughly constant power dissipation with
changing output power, and therefore do not change much in junction
temperature. The full effect of the higher tempco is thus felt by the output
junctions, and if the sensor is placed on the power device itself rather than
the main heatsink, to reduce thermal delay, then the amplifier can be
seriously over compensated for temperature. In other words, after a burst of
power Vq will become too low rather than too high, and crossover
distortion will appear. We now need a Vbias generator with a lower tempco
than the standard circuit.
The principle is exactly analogous to the method of increasing the tempco.
In Figure 12.31, a voltage source is inserted in the upper leg of potential
Figure 12.31
The principle of a
Vbe multiplier with
reduced tempco. The
values shown give
–3.1 mV/°C
Audio Power Amplifier Design Handbook
Table 12.6
divider R1, R2; the required Vbe-multiplication factor for the same Vbias is
reduced, and so therefore is the tempco.
Table 12.6 shows how this works as V1 is increased in 100 mV steps. R1
has been varied to keep Vbias constant, in order to demonstrate the
symmetry of resistor values with Table 12.5; in reality R2 would be the
variable element, for the safety reasons described above.
Current compensation
Both bias generators in Figure 12.27 are fitted with a current-compensation
resistor R3. The Vbe multiplier is a very simple shunt regulator, with low
loop gain, and hence shows a significant series resistance. In other words,
the Vbias generated shows unwanted variations in voltage with changes in
the standing current through it. R3 is added to give first-order cancellation
of Vbias variations caused by these current changes. It subtracts a
correction voltage proportional to this current. Rather than complete
cancellation, this gives a peaking of the output voltage at a specified
current, so that current changes around this peak value cause only minor
voltage variations. This peaking philosophy is widely used in IC bias
R3 should never be omitted, as without it mains voltage fluctuations can
seriously affect Vq. Table 12.4 shows that the optimal value for peaking at
6 mA depends strongly on the Vbe multiplication factor.
Figure 6.14 demonstrates the application of this method to the Class-B
amplifier. The graph shows the variation of Vbias with current for different
values of R3. The slope of the uncompensated (R3 = 0) curve at 6 mA is
approx. 20 , and this linear term is cancelled by setting R3 to 18 in
Figure 6.13.
The current through the bias generator will vary because the VAS current
source is not a perfect circuit element. Biasing this current source with the
usual pair of silicon diodes does not make it wholly immune to supply-rail
Thermal compensation and thermal dynamics
variations. I measured a generic amplifier (essentially the original Class-B
Blameless design) and varied the incoming mains from 212 V to 263 V,
a range of 20%. This in these uncertain times is perfectly plausible for a
power amplifier travelling around Europe. The VAS current-source output
varied from 9.38 mA to 10.12 mA, which is a 7.3% range. Thanks to the
current-compensating resistor in the bias generator, the resulting change
in quiescent voltage Vq across the two Re’s is only from 1.1 mV (264 V
mains) to 1.5 mV (212 V mains). This is a very small absolute change of
0.4 mV, and within the Vq tolerance bands. The ratio of change is greater,
because Vbias has had a large fixed quantity (the device Vbe’s) subtracted
from it, so the residue varies much more. Vq variation could be further
suppressed by making the VAS current source more stable against supply
The finite ability of even the current-compensated bias generator to cope
with changing standing current makes a bootstrapped VAS collector load
much less attractive than the current-source version; from the above data,
it appears that Vq variations will be at least three times greater.
A quite different approach reduces Vbias variations by increasing the
loop gain in the Vbe multiplier. Figure 12.32 shows the circuit of a twotransistor version that reduces the basic resistance slope from 20 to 1.7 .
The first transistor is the sensor. An advantage is that Vbias variations will
be smaller for all values of VAS current, and no optimisation of a resistor
value is required. A drawback is slightly greater complexity in an area
where reliability is vital. Figure 12.33 compares the two-transistor
configuration with the standard version (without R3). Multi-transistor
feedback loops raise the possibility of instability and oscillation, and this
must be carefully guarded against, as it is unlikely to improve amplifier
Figure 12.32
Circuit of a twotransistor Vbe multiplier.
The increased loop
gain holds Vbias more
constant against current
Audio Power Amplifier Design Handbook
Figure 12.33
The two-transistor
configuration gives a
consistently lower
series resistance, and
hence Vbias variation
with current,
compared with the
standard version
without R3
This section of the Thermal Dynamics chapter describes simple Vbias
generators with tempcos ranging from –2.5 to –6.9 mV/°C. It is hoped that
this, in combination with the techniques described earlier, will enable the
design of Class-B amplifiers with greater bias accuracy, and therefore less
afflicted by crossover distortion.
Thermal dynamics in reality
One of the main difficulties in the study of amplifier thermal dynamics is
that some of the crucial quantities, such as transistor junction temperatures,
are not directly measurable. The fact that bias conditions are altering is
usually recognised from changes in the THD residual as viewed on a scope.
However, these temperatures are only a means to an end – low distortion.
What really matters is the crossover distortion produced by the output
stage. Measuring this gets to the heart of the matter. The method is as
follows. The amplifier under study is deliberately underbiased by a modest
amount. I chose a bias setting that gave about 0.02% THD with a peak
responding measurement mode. This is to create crossover spikes that are
clear of the rest of the THD residual, to ensure the analyser is reading these
spikes and ignoring noise and other distortions at a lower level. The AP
System-1 has a mode that plots a quantity against time (it has to be said that
the way to do this is not at all obvious from the AP screen menus –
essentially ‘time’ is treated as an external stimulus – but it is in the manual)
and this effectively gives that most desirable of plots – crossover conditions
Thermal compensation and thermal dynamics
against time. In both cases below the amplifier was turned on with the input
signal already present, so that dissipation conditions stabilised within a
second or so.
The first test amplifier examined has a standard EF output stage. The drivers
have their own small heatsinks and have no thermal coupling with the
main output device heatsink. The most important feature is that the bias
sensor transistor is not mounted on the main heatsink, as is usual, but on
the back of one of the output devices, as I recommended above. This puts
the bias sensor much closer thermally to the output device junction. A
significant feature of this test amplifier is its relatively high supply rails. This
means that even under no load, there is a drift in the bias conditions due to
the drivers heating up to their working temperature. This drift can be
reduced by increasing the size of the driver heatsinks, but not eliminated.
Figure 12.34 shows the THD plot taken over 10 minutes, starting from cold
and initiating some serious power dissipation at t = 0. The crossover
distortion drops at once; Figure 12.1 shows that driver dissipation is not
much affected by output level, so this must be due to the output device
junctions heating up and increasing Vq. There is then a slower reduction
until the THS reading stabilises at about 3 minutes.
The second amplifier structure examined is more complex. It is a triple-EF
design with drivers and output devices mounted on a large heatsink with
considerable thermal inertia. The pre-drivers are TO220 devices mounted
separately without heatsinks. It may seem perverse to mount the drivers on
Figure 12.34
Peak THD vs time
over 10 minutes
Audio Power Amplifier Design Handbook
Figure 12.35
Circuit and thermal
paths of the triple-EF
output stage
the same heatsink as the outputs, because some of the time they are being
heated up rather than cooled down, which is exactly the opposite of what
is required to minimise Vbe changes. However, they need a heatsink of
some sort, and given the mechanical complications of providing a separate
thermally isolated heatsink just for the drivers, they usually end up on the
main heatsink. All that can be done (as in this case) is to put them in the
heatsink position that stays coolest in operation. Once more the bias sensor
transistor is not mounted on the main heatsink, but on the back of one of
the output devices. See Figure 12.35 for the electrical circuit and thermal
coupling paths.
The results are quite different. Figure 12.36 shows at A the THD plot taken
over 10 minutes, again starting from cold and initiating dissipation at t = 0.
Initially THD falls rapidly, as before, as the output device junctions heat. It
then commences a slow rise over 2 minutes, indicative of falling bias, and
this represents the timelag in heating the sensor transistor. After this there is
a much slower drift downwards, at about the same rate as the main
heatsink is warming up. There are clearly at least three mechanisms
operating with very different time-constants. The final time-constant is very
long, and the immediate suspicion is that it must be related to the slow
warming of the main heatsink. Nothing else appears to be changing over
this sort of timescale. In fact this long-term increase in bias is caused by
cooling of the bias sensor compared with the output device it is mounted
on. This effect was theoretically predicted above, and it is pleasing to see
that it really exists, although it does nothing but further complicate the
quest for optimal Class-B operation. As the main heatsink gets hotter, the
heat losses from the sensor become more significant, and its temperature is
lower than it should be. Therefore the bias voltage generated is too high,
and this effect grows over time as the heatsink warms up.
Thermal compensation and thermal dynamics
Figure 12.36
Peak THD vs time
over 10 seconds
Knowledge of how the long-term drift occurs leads at once to a strategy for
reducing it. Adding thermal insulation to cover the sensor transistor, in the
form of a simple pad of plastic foam, gives plot B, with the long-term
variation reduced. Plot C reduces it still further by more elaborate
insulation; a rectangular block of foam with a cutout for the sensor
transistor. This is about as far as it is possible to go with sensor insulation;
the long-term variation is reduced to about 40% of what it was. While this
technique certainly appears to improve bias control, bear in mind that it is
being tested with a steady sinewave. Music is noted for not being at the
same level all the time, and its variations are much faster than the slow
effect we are examining. It is very doubtful if elaborate efforts to reduce
sensor cooling are worthwhile. I must admit this is the first time I have
applied thermal lagging to an amplifier output stage.
Early effect in output stages
There is another factor that affects the accuracy with which quiescent
conditions can be maintained. If you take a typical power amplifier and
power it from a variable-voltage transformer, you are very likely to find that
Vq varies with the mains voltage applied. This at first seems to indicate that
the apparently straightforward business of compensating the bias generator
for changes in standing current has fallen somewhat short of success (see
page 178). However, even if this appears to be correct, and the constantcurrent source feeding the bias generator and VAS is made absolutely
stable, the quiescent conditions are still likely to vary. At first this seems
utterly mysterious, but the true reason is that the transistors in the output
Audio Power Amplifier Design Handbook
stage are reacting directly to the change in their collector–emitter voltage
(Vce). As Vce increases, so does the Vq and the quiescent current. This is
called Early Effect. It is a narrowing of the base-collector region as Vce
increases, which will cause an increase in the collector current Ic even if
Vbe and Ib are held constant. In a practical EF output stage the result is a
significant variation in quiescent conditions when the supply voltage is
varied over a range such as ±10%.
Table 12.7
changes with
supply rail voltage
(MJE340/50 and
MJ15022/3). All
devices held at
Q1 Vbe
Q3 Vbe
Q2 Vbe
Q4 Vbe
Table 12.7 shows the effect as demonstrated by SPICE simulation, using
MJE340/50 for drivers and MJ15022/23 as output devices, with fixed bias
voltage of 2.550 V, which gave optimal crossover in this case. It is
immediately obvious that (as usual) things are more complicated than they
at first appear. The Vq increases with rail voltage, which matches reality.
However, the way in which this occurs is rather unexpected. The Vbe’s of
the drivers Q1 and Q2 reduce with increasing Vce as expected. However,
the output devices Q3 and Q4 show a Vbe that increases – but by a lesser
amount, so that after subtracting all the Vbe drops from the fixed bias
voltage the aggregate effect is that Vq, and hence quiescent current Iq, both
increase. Note that the various voltages have been summed as a check that
they really do add up to 2.550 V in each case.
Table 12.8 has the results of real Vbe measurements. These are not easy to
do, because any increase in Iq increases the heating in the various
transistors, which will cause their Vbe’s to drift. This happens to such an
extent that sensible measurements are impossible. The measurement
technique was therefore slightly altered. The amplifier was powered up on
the minimum rail voltage, with its Vq set to 1.0 mV only. This is far too low
for good linearity, but minimises heating while at the same time ensuring
that the output devices are actually conducting. The various voltages were
measured, the rail voltage increased by 5 V, and then the bias control
turned down as quickly as possible to get Vq back to 1.0 mV, and the
process is repeated. The results are inevitably less tidy as the real Vbe’s are
prone to wander around by a millivolt or so, but it is clear that in reality, as
in SPICE, most of the Early Effect is in the drivers, and there is a general
Thermal compensation and thermal dynamics
reduction in aggregate Vbe as rail voltage increases. The sum of Vbe’s is no
longer constant as Vq has been constrained to be constant instead.
Table 12.8
Real Vbe changes
with supply rail
voltage (2SC4382,
2SA1668 drivers
and 2SC2922,
2SA1216 output)
Q1 Vbe
Q3 Vbe
Q2 Vbe
Q4 Vbe
It may seem at this point as if the whole business of quiescent control is just
too hopelessly complicated. Not so. The cure for the Early Effect problem
is to overcompensate for standing current changes, by making the value of
resistor R3 above larger than usual. The best and probably the only
practical way to find the right value is the empirical method. Wind the HT
up and down on the prototype design and adjust the value of R3 until the
Vq change is at a minimum. (Unfortunately this interacts with the bias
setting, so there is a bit of twiddling to do – however, for a given design you
only need to find the optimal value for R3 once.) This assumes that the
supply-rail rejection of the VAS current source is predictable and stable;
with the circuits normally used this seems to be the case, but some further
study in this area is required.
1. Sato et al Amplifier Transient Crossover Distortion Resulting from
Temperature Change of Output Power Transistors AES Preprint. AES
Preprint 1896 for 72nd Convention, Oct. 1982.
2. Brown, I Opto-Bias Basis for Better Power Amps Electronics World, Feb.
1992, p. 107.
3. Carslaw and Jaeger Conduction of Heat in Solids Oxford Univ. Press
1959, ISBN 0-19-853368-3.
4. Murphy, D Axisymmetric Model of a Moving-Coil Loudspeaker Journ.
AES, Sept. 1993, p. 679.
5. Motorola, Toulouse Private communication.
6. Evans, J Audio Amplifier Bias Current Letters Electronics & Wireless
World, Jan. 1991, p. 53.
7. Chen, C-T Analog & Digital Control System Design Saunders-HBJ 1993,
p. 346.
8. Harriot, P Process Control McGraw-Hill 1964, pp. 100–102.
9. Liptak, B, ed. Instrument Engineer’s Handbook-Process Control Butterworth-Heinemann 1995, p. 66.
Amplifier and
loudspeaker protection
Categories of amplifier protection
The protection of solid-state amplifiers against overload is largely a matter
of safeguarding them from load impedances that are too low and endanger
the output devices; the most common and most severe condition being a
short across the output. This must be distinguished from the casual use of
the word overload to mean excessive signal that causes clipping and
audible distortion.
Overload protection is not the only safety precaution required. An equally
vital requirement is DC-offset protection – though here it is the loudspeaker
load that is being protected from the amplifier, rather than the other way
Similarly, thermal protection is also required for a fully-equipped amplifier.
Since a well-designed product will not overheat in normal operation, this
is required to deal with two abnormal conditions:
1 The amplifier heatsinking is designed to be adequate for the reproduction of speech and music (which has a high peak-to-volume ratio, and
therefore brings about relatively small dissipation) but cannot sustain
long-term sinewave testing into the minimum specified load impedance
without excessive junction temperatures. Heatsinking forms a large part
of the cost of any amplifier, and so economics makes this a common state
of affairs.
Similar considerations apply to the rating of amplifier mains transformers,
which are often designed to indefinitely supply only 70% of the current
required for extended sinewave operation. Some form of thermal cut-out
in the transformer itself then becomes essential (see Chapter 8).
Amplifier and loudspeaker protection
2 The amplifier is designed to withstand indefinite sinewave testing, but is
vulnerable to having ventilation slots, etc. blocked, interfering either
with natural convection or fan operation.
Finally, all amplifiers require internal fusing to minimise the consequences
of a component failure – i.e. protecting the amplifier from itself – and to
maintain safety in the event of a mains wiring fault.
Semiconductor failure modes
Solid-state output devices have several main failure modes, including
excess current, excess power dissipation, and excess voltage. These are
specified in manufacturer’s data sheets as Absolute Maximum Ratings,
usually defined by some form of words such as exceeding these ratings
even momentarily may cause degradation of performance and/or reduction
in operating lifetime. For semiconductor power devices ratings are usually
plotted as a Safe Operating Area (SOA) which encloses all the permissible
combinations of voltage and current. Sometimes there are extra little areas,
notably those associated with second-breakdown in BJTs, with time limits
(usually in microseconds) on how long you can linger there before
something awful happens.
It is of course also possible to damage the base-emitter junction of a BJT by
exceeding its current or reverse voltage ratings, but this is unlikely in power
amplifier applications. In contrast the insulated gate of an FET is more
vulnerable and zener clamping of gate to source is usually considered
mandatory, especially since FET amplifiers often have separate higher
supply-rails for their small-signal sections.
BJTs have an additional important failure mode known as second
breakdown, which basically appears as a reduction in permissible power
dissipation at high voltages, due to local instability in current flow. The
details of this mechanism may be found in any textbook on transistor
Excessive current usually causes failure when the I2R heating in the bond
wires becomes too great and they fuse. This places a maximum on the
current-handling of the device no matter how low the voltage across it, and
hence the power dissipation. In a TO3 package only the emitter bond wire
is vulnerable, as the collector connection is made through the transistor
substrate and flange. If this wire fails with high excess current then on some
occasions the jet of vaporised metal will drill a neat hole through the top of
the TO3 can – an event which can prove utterly mystifying to those not in
the know.
Any solid-state device will fail from excess dissipation, as the internal
heating will raise the junction temperatures to levels where permanent
degradation occurs.
Audio Power Amplifier Design Handbook
Excess emitter-collector or source-drain voltage will also cause failure. This
failure mode does not usually require protection as such, because
designing against it should be fairly easy. With a resistive load the
maximum voltage is defined by the power supply-rails, and when the
amplifier output is hard against one rail the voltage across the device that
is turned off will be the sum of the two rails, assuming a DC-coupled
design. If devices with a Vce(max.) greater than this is selected there should
be no possibility of failure. However, practical amplifiers will be faced with
reactive load impedances, and this can double the Vce seen by the output
devices. It is therefore necessary to select a device that can withstand at
least twice the sum of the HT rail voltages, and allow for a further safety
margin on top of this. Even greater voltages may be generated by abrupt
current changes in inductive loads, and these may go outside the supplyrail range causing device failure by reverse biasing. This possibility is
usually dealt with by the addition of catching diodes to the circuit (see
below) and does not in itself affect the output device specification
Power semiconductors have another failure mode initiated by repeated
severe temperature changes. This is usually known as thermal cycling and
results from stresses set up in the silicon by the differing expansion
coefficients of the device chip and the header it is bonded to. This
constitutes the only real wearout mechanism that semiconductors are
subject to. The average lifetimes of a device subjected to temperature
variations delta–T can be approximately predicted by the equation:
N = 107 · e –0.05 · del–T
Equation 13.1
Where N = cycles to failure, and delta–T is the temperature change.
This shows clearly that the only way open to the designer to minimise the
risk of failure is to reduce the temperature range or the number of
temperature cycles. Reducing the junction temperature range requires
increasing heatsink size or improving the thermal coupling to it. Thermal
coupling can be quickly improved by using high-efficiency thermal
washers, assuming their increased fragility is acceptable in production, and
this is much more cost-effective than increasing the weight of heatsink. The
number of cycles can only be minimised by leaving equipment (such as
Class-A amplifiers) powered long-term, which has distinct disadvantages in
terms of energy consumption and possibly safety.
Overload protection
Solid-state output devices are much less tolerant to overload conditions
than valves, and often fail virtually instantaneously. Some failure modes
(such as overheating) take place slowly enough for human intervention, but
this can never be relied upon. Overload protection is therefore always an
important issue, except for specialised applications such as amplifiers built
Amplifier and loudspeaker protection
into powered loudspeakers, where there are no external connections and
no possibility of inadvertent short-circuits.
Driven by necessity, workable protection systems were devised relatively
early in the history of solid-state amplifiers; see Bailey [1], Becker [2] and
Motorola [3]. Part of the problem is defining what constitutes adequate
current delivery into a load. Otala [4] has shown that a complex impedance,
i.e. containing energy-storage elements, can be made to draw surprisingly
large currents if specially optimised pulse waveforms are used that catch
the load at the worst part of the cycle; however it seems to be the general
view that such waveforms rarely if ever occur in real life.
Verifying that overload protection works as intended over the wide range of
voltages, currents, and load impedances possible is not a light task. Peter
Baxandall introduced a most ingenious method of causing an amplifier to
plot its own limiting lines [5].
Overload protection by fuses
The use of fuses in series with the output line for overload protection is no
longer considered acceptable, as it is virtually impossible to design a fuse
that will blow fast enough to protect a semiconductor device, and yet be
sufficiently resistant to transients and turn-on surges. There are also the
obvious objections that the fuse must be replaced every time the protection
is brought into action, and there is every chance it will be replaced by a
higher value fuse which will leave the amplifier completely vulnerable.
Fuses can react only to the current flowing through them, and are unable
to take account of other important factors such as the voltage drop across
the device protected.
Series output fuses are sometimes advocated as a cheap means of DC offset
protection, but they are not dependable in this role.
Putting a fuse in series with the output will cause low-frequency distortion
due to cyclic thermal changes in the fuse resistance. The distortion problem
can, in theory at least, be side-stepped by putting the fuse inside the global
feedback loop; however what will the amplifier do when its feedback is
abruptly removed when the fuse blows? (See also page 384 on DC offset
protection below.)
One way of so enclosing fuses that I have seen advocated is to use them
instead of output emitter-resistors Re; I have no personal experience of this
technique, but since it appears to add extra time-dependent thermal
uncertainties (due to the exact fuse resistance being dependant upon its
immediate thermal history) to a part of the amplifier where they already
cause major difficulties, I don’t see this as a promising path to take. There
is the major difficulty that the failure of only one fuse will generate a
maximal DC offset, so we may have dealt with the overload, but there is
Audio Power Amplifier Design Handbook
now a major DC offset to protect the loudspeaker from. The other fuse may
blow as a consequence of the large DC current flow, but sizing a fuse to
protect properly against both overload and DC offset may prove
Amplifier circuitry should always include fuses in each HT line. These are
not intended to protect the output devices, but to minimise the damage when
the output devices have already failed. They can and should therefore be of
the slow-blow type, and rated with a good safety margin, so that they are
entirely reliable; a fuse operated anywhere near its nominal fusing current
has a short life-time, due to heating and oxidation of the fuse wire. HT fuses
cannot save the output devices, but they do protect the HT wiring and the
bridge rectifier, and prevent fire. There should be separate DC fuses for each
channel, as this gives better protection than one fuse of twice the size, and
allows one channel to keep working in an emergency.
Similarly, the mains transformer secondaries should also be fused. If this is
omitted, a failure of the rectifier will inevitably cause the mains transformer
to burn out, and this could produce a safety hazard. The secondary fuses
can be very conservatively rated to make them reliable, as the mains
transformer should be able to withstand a very large fault current for a short
time. The fuses must be of the slow-blow type to withstand the current
surge into the reservoir capacitors at switch-on.
The final fuse to consider is the mains fuse. The two functions of this are to
disconnect the live line if it becomes shorted to chassis, and to protect
against gross faults such as a short between live and neutral. This fuse must
also be of the slow-blow type, to cope with the transformer turn-on current
surge as well as charging the reservoirs. In the UK, there will be an
additional fuse in the moulded mains plug. This does not apply to mains
connectors in other countries and so a mains fuse built into the amplifier
itself is absolutely essential.
Electronic overload protection
There are various approaches possible to overload protection. The
commonest form (called electronic protection here to distinguish it from
fuse methods) uses transistors to detect the current and voltage conditions
in the output devices, and shunts away the base drive from the latter when
the conditions become excessive. This is cheap and easy to implement (at
least in principle) and since it is essentially a clamping method requires no
resetting. Normal output is resumed as soon as the fault conditions are
removed. The disadvantage is that a protection scheme that makes good
use of the device Safe Operating Area (SOA) may allow substantial
dissipation for as long as the fault persists undetected, and while this should
not cause short-term failure if the protection has been correctly designed,
the high temperatures generated may impair long-term reliability.
Amplifier and loudspeaker protection
An alternative approach drops out the DC protection relay when overload
is detected. The relay may either be opened for a few seconds delay, after
which it resets, or stay latched open until the protection circuit is reset. This
is normally done by cycling the mains power on and off, to avoid the
expense of a reset button that would rarely be used.
If the equipment is essentially operated unattended, so that an overload
condition may persist for some time, the self-resetting system will subject
the output semiconductors to severe temperature changes, which may
shorten their operational lifetime.
Plotting the protection locus
The standard method of representing the conditions experienced by output
devices, of whatever technology, is to draw loadlines onto a diagram of the
component’s SOA, to determine where they cross the limits of the area.
This is shown in Figure 13.1, for an amplifier with +/–40 V HT rails, which
would give 100 W into 8 and 200 W into 4 , ignoring losses; the power
transistor is a Motorola MJ15024. You do not need to fix the HT voltage
before drawing most of the diagram; the position of the SOA limits is fixed
by the device characteristics. The line AB represents the maximum current
rating of 16 A, and the reciprocal curve BC the maximum power dissipation
of 250 W. The maximum Vce is 250 V, and so is far off the diagram to the
right. Line CD defines the second-breakdown region, effectively an extra
Figure 13.1
The Safe Operating
Area (SOA) of a
typical TO3 highpower transistor, in
this case the Motorola
Audio Power Amplifier Design Handbook
area removed from the high-voltage end of the power-limited region.
Second-breakdown is an instability phenomenon that takes a little time to
develop, so manufacturer’s data often allows brief excursions into the
region between the second-breakdown line and the power limit. The
nearer these excursions go towards the power limit, the briefer they must be
if the device is to survive, and trying to exploit this latitude in amplifiers is
living dangerously, because the permitted times are very short (usually tens
of microseconds) compared with the duration of audio waveforms.
The resistive loadline XY represents an 8 load, and as a point moves
along it, the co-ordinates show the instantaneous voltage across the output
device and the current through it. At point X, the current is maximal at 5.0 A
with zero voltage across the device, as Vce(sats) and the like can be ignored
without significant error. The power dissipated in the device is zero, and
what matters is that point X is well below the current-limit line AB. This
represents conditions at clipping.
At the other end, at Y, the loadline has hit the X-axis and so the device
current is zero, with one rail voltage (40 V) across it. This represents the
normal quiescent state of an amplifier, with zero volts at its output, and zero
device dissipation once more. So long as Y is well to the left of the
maximum-voltage line all is well. Note that while you do not need to
decide the HT voltage when drawing the SOA for the device, you must do
so before the loadlines are drawn, as all lines for purely resistive loads
intersect the X-axis at a voltage representing one of the HT rails.
Intermediate points along XY represent instantaneous output voltages
between 0 V and clipping; voltage and current co-exist and so there is
significant device dissipation. If the line cuts the maximum-power rating
curve BC, the dissipation is too great and the device will fail.
Different load resistances are represented by lines of differing slope; ZY is
for a 4 load. The point Y must be common to both lines, for the current
is zero and the rail voltage unchanged no matter what load is connected to
a quiescent amplifier. Point Z is however at twice the current, and there is
clearly a greater chance of this low-resistance line intersecting the power
limit BC. Resistive loads cannot reach the second-breakdown region with
these rails.
Unwelcome complications are presented by reactive loading. Maximum
current no longer coincides with the maximum voltage, and vice-versa. A
typical reactive load turns the line XY into an ellipse, which gets much
nearer to the SOA limit. The width (actually the minor axis, to be
mathematical) of the ellipse is determined by the amount of reactance
involved, and since this is another independent variable, the diagram could
soon become over-complex. The solution is to take the worst-case for all
possible reactive loads of the form R + jX, and instead of trying to draw
hundreds of ellipses, to simply show the envelope made up of all their
closest approaches to the SOA limit. This is another straight line, drawn
from the same maximum current point Z to a point W at twice the rail
Amplifier and loudspeaker protection
voltage. There is clearly a much greater chance that the ZW line will hit the
power-limit or second-breakdown lines than the 4 resistive line ZY, and
the power devices must have an SOA large enough to give a clear safety
margin between its boundary and the reactive envelope line for the lowest
rated load impedance. The protection locus must fit into this gap, so it must
be large enough to allow for circuit tolerances.
The final step is plot the protection locus on the diagram. This locus, which
may be a straight line, a series of lines, or an arbitrary curve, represents the
maximum possible combinations of current and voltage that the protection
circuitry permits to exist in the output device. Most amplifiers use some
form of VI limiting, in which the permitted current reduces as the voltage
across the device increases, putting a rough limit on device power
dissipation. When this relationship between current and voltage is plotted,
it forms the protection locus.
This locus must always be above and to the right of the reactive envelope
line for the lowest rated load, or the power output will be restricted by the
protection circuitry operating prematurely. It must also always be to the left
and below the SOA limit, or it will allow forbidden combinations of voltage
and current that will cause device failure.
Simple current-limiting
The simplest form of overload protection is shown in Figure 13.2, with both
upper and lower sections shown. For positive output excursions, R1
samples the voltage drop across emitter-resistor Re1, and when it exceeds
the Vbe of approx. 0.6 V, TR1 conducts and shunts current away from TR2
base. The component values in Figure 13.2 give a 5.5 A constant-current
Figure 13.2
Simple current-limit
Audio Power Amplifier Design Handbook
regime as shown in Figure 13.3, which was simulated using a model like
Figure 13.8 below. The loadlines shown represent 8 and 4 resistive,
and 4 worst-case reactive (ZW). The current-limit line is exactly
horizontal, though it would probably show a slight slope if the simulation
was extended to include more of the real amplifier, such as real current
sources, etc.
The value of Re1 is usually determined by the requirements of efficiency or
quiescent stability, and so the threshold of current-limiting is set by R1 and
R2. This circuit can only operate at a finite speed, and so R1 must be large
enough to limit TR1 base current to a safe value. 100 seems sufficient in
practice. Re1 is usually the output emitter resistor, as well as current sensor,
and so does double duty.
The current drawn by TR1 in shunting away TR2 base drive is inherently
limited by I, the constant-current load of the VAS. There is no such limit
on TR4, which can draw large and indeterminate currents through VAS
transistor TR7. If this is a TO-92 device it will probably fail. It is therefore
essential to limit the VAS current in some way, and a common approach
is shown in Figure 13.2. There is now a secondary layer of currentlimiting, with TR8 protecting TR7 in the same way that TR1 protects TR2,
3. The addition of Rs to sense the VAS current does not significantly affect
VAS operation, and does not constitute local negative feedback. This is
because the input to TR7 is a current from the input stage, and not a
Figure 13.3
Current-limiting with
+/–40 V HT rails
Amplifier and loudspeaker protection
voltage; the development of a voltage across Rs does not affect the value
of this current, as it is effectively being supplied from a constant-current
It has to be faced that this arrangement often shows signs of HF instability
when current limiting, and this can prove difficult or impossible to
eradicate completely. (This applies to single and double-slope VI limiting
also.) The basic cause appears to be that under limiting conditions there are
two feedback systems active, each opposing the other. The global voltage
feedback is attempting to bring the output to the demanded voltage level,
while the overload protection must be able to override this to safeguard the
output devices. HF oscillation is often a danger to BJT output devices, but
in this case it does not seem to adversely affect survivability. Extensive tests
have shown that in a conventional BJT output stage, the oscillation seems
to reduce rather than increase the average current through the output
devices, and it is arguable that it does more good than harm. It has to be
said, however, that the exact oscillation mechanism remains obscure
despite several investigations, and the state of our knowledge in this area is
far from complete.
The diodes D1, D2 in the collectors of TR1, TR4 prevent them conducting
in the wrong half cycle if the Re voltage drops are large enough to make the
collector voltage go negative. Under some circumstances you may be able
to omit them, but the cost saving is negligible.
The loadline for an output short-circuit on the SOA plot is a vertical line,
starting upwards from Y, the HT rail voltage on the X-axis, and
representing that current increases indefinitely without any reduction of
the voltage drop across the output devices. An example is shown in
Figure 13.3 for +/–40 V rails. When the short-circuit line is prolonged
upwards it hits the 5.5 A limiting locus at 40 V and 5.5 A; at 220 W this
is just inside the power-limit section of the SOA. The devices are
therefore safe against short-circuits; however the 4 resistive loadline
also intersects the 5.5 A line, at Vce = 18 V and Ic = 5.5 A, limiting the
4 output capability to 12 V peak. This gives 18 W rather than 200 W in
the load, despite the fact that full 4 output would in fact be perfectly
safe. The full 8 output of 100 W is possible as the whole of XY lies
below 5.5 A.
With 4 reactive loads the situation is worse. The line ZW cuts the 5.5 A
line at 38 V, leaving only 2 V for output, and limiting the power to a feeble
0.5 W.
The other drawback of constant current protection is that if the HT rails
were increased only slightly, to +/–46 V, the intersection of a vertical line
from Y the X-axis centre would hit the power-limit line, and the amplifier
would no longer be short-circuit proof unless the current limit was
Audio Power Amplifier Design Handbook
Single-slope VI limiting
Simple current-limiting makes very poor use of the device SOA; singleslope VI limiting is greatly superior because it uses more of the available
information to determine if the output devices are endangered. The Vce as
well as the current is taken into account. The most popular circuit
arrangement is seen in Figure 13.4, where R3 has been added to reduce the
current-limit threshold as Vce increases. This simple summation of voltage
and current seems crude at first sight, but Figure 13.5 shows it to be an
enormous improvement over simply limiting the current.
Figure 13.4
Single-slope VI limiter
Figure 13.5
Single-slope locus
plotted on MJ15024
Amplifier and loudspeaker protection
The protection locus has now a variable slope, making it much easier to fit
between reactive load lines and the SOA boundary; the slope is set by R3.
In Figure 13.5, Locus 1 is for R3 = 15k, and Locus 2 for 10k. If Locus 2 is
chosen the short-circuit current is reduced to 2 A, while still allowing the
full 4 resistive output.
Current capability at Vce = 20 V is increased from 5.5 A to 7.5 A.
Dual-slope VI limiting
The motivation for more complex forms of protection than single-slope VI
limiting is usually the saving of money, by exploiting more of the output
device SOA. In a typical amplifier required to give 165 W into 8 and
250 W into 4 (assuming realistic losses) the number of device pairs in the
output stage can be reduced from three to two by the use of dual-slope
protection, and the cost saving is significant. The single-slope limiting line
is made dual-slope by introducing a breakpoint in the locus so it is made
of two straight-line sections as in Figure 13.7, allowing it to be moved
closer to the curved SOA limit; the current delivery possible at low device
voltages is further increased.
A dual-slope system is shown in Figure 13.6. The action of the Vce
component on sensing transistor TR1 is reduced when Vce is high enough
for Zener diode DZ1 to conduct. The series combination of R4 and R1 is
chosen to give the required initial slope with low Vce (i.e. the left-hand
slope) but as the voltage increases the Zener conducts and diverts current
through R5, whose value controls the right-hand slope of the protection
locus. Locii 1, 2 and 3 are for R5 = 2k7, 1k8 and 1k respectively.
Current capability at Vce = 20 V is further increased from 7.5 A to 9.5 A.
Figure 13.6
Dual-slope VI limiter
Audio Power Amplifier Design Handbook
Figure 13.7
Dual-slope locus
plotted on MJ15024
Simulating overload protection systems
The calculations for protection circuitry can be time-consuming. Simulation is quicker; Figure 13.8, shows a conceptual model of a dual-slope VI
limiter, which allows the simulated protection locus to be directly
compared with the loadline and the SOA. The amplifier output stage is
reduced to one half (the positive or upper half) by assuming symmetry, and
the combination of the actual output device and the load represented by
Figure 13.8
A conceptual model of
an overload protection
circuit that implements
dual-slope limiting
Amplifier and loudspeaker protection
voltage-controlled current-source G. The output current from controlledsource G is the same as the output device current in reality, and passes
through current-sense resistor Re1.
The 6 mA current-source I models the current from the previous stage that
TR1 must shunt away from the output device. Usually this is an accurate
model because the VAS collector load will indeed be a current-source. The
feedback loop is closed by making the voltage at the collector of TR1
control the current flowing through G and hence Re1.
In this version of VI-protection the device voltage is sensed by R4 and the
current thus engendered is added to that from R1 at the base of TR1. This
may seem a crude way of approximating a constant power curve, and
indeed it is, but it provides very effective protection for low and mediumpowered amplifiers.
Vin models the positive supply-rail, and exercises the simulation through
the possible output voltage range. In reality the emitter of TR1 and Re1
would be connected to the amplifier output, which would be move up and
down to vary the voltage across the output devices, and hence the voltage
applied across R1, R2. Here it is easier to alter the voltage source V, as the
only part of the circuit connected to HT+. V+ is fixed at a suitable HT
voltage, e.g. +50 V.
The simulation only produces the protection locus, and the other lines
making up the SOA plot are added at the display stage. Ic(max.) is drawn
by plotting a constant to give a horizontal line at 16 A. P(max.) is drawn as
a line of a constant power, by using the equation 250/Vce to give a 250 W
line. In PSpice there seems to be no way to draw a strictly vertical line to
represent Vce(max.), but in the case of the MJ15024 this is 250 V, and is for
most practical purposes off the right-hand end of the graph anyway. The
second-breakdown region is more difficult to show, for in the manufacturer’s data the region is shown as bounded by a non-linear curve. The
voltage/current co-ordinates of the boundary were read from manufacturer’s data, and approximately modelled by fitting a second order
polynomial. In this case it is:
I = 24.96 – 0.463 . Vce + 0.00224 . Vce 2
Equation 13.2
This is only valid for the portion that extends below the 250 W constantpower line, at the bottom right of the diagram.
Catching diodes
These are reverse-biased power diodes connected between the supply-rails
and the output of the amplifier, to allow it to absorb transients generated by
fast current-changes into an inductive load. All moving-coil loudspeakers
present an inductive impedance over some frequencies.
Audio Power Amplifier Design Handbook
When an amplifier attempts to rapidly change the current flowing in an
inductive load, the inductance can generate voltage spikes that drive the
amplifier output outside its HT rail voltages; in other words, if the HT
voltage is +/–50 V, then the output might be forced by the inductive backEMF to 80 V or more, with the likelihood of failure of the reverse-biased
output devices. Catching diodes prevent this by conducting and clamping
the output so it cannot move more than about 1 V outside the HT rails.
These diodes are presumably so-called because they catch the output line
if it attempts to move outside the rails.
Diode current rating should be not less than 2 A, and the PIV 200 V or
greater, and at least twice the sum of the HT rails. I usually specify 400 PIV
3 A diodes, and they never seem to fail.
DC-offset protection
In some respects, any DC-coupled power amplifier is an accident waiting
to happen. If the amplifier suffers a fault that causes its output to sit at a
significant distance away from ground, then a large current is likely to flow
through the loudspeaker system. This may cause damage either by driving
the loudspeaker cones beyond their mechanical limits or by causing
excessive thermal dissipation in the voice-coils, the latter probably being
the most likely. In either case the financial loss is likely to be serious. There
is also a safety issue, in that overheating of voice-coils or crossover
components could presumably cause a fire.
Since most power amplifiers consist of one global feedback loop, there are
many possible component failures that could produce a DC offset at the
output, and in most cases this will result in the output sitting at one of the
HT rail voltages. The only way to save the loudspeaker system from
damage is to remove this DC output as quickly as possible. The DC
protection system must be functionally quite separate from the power
amplifier itself or the same fault may disable both.
There are several possible ways to provide DC protection:
1 By fusing in the output line, the assumption being that a DC fault will
give a sustained current flow that will blow the fuse when music-type
current demands will not.
2 By means of a relay in the output line, which opens when a DC offset is
3 By triggering a crowbar that shunts the output line to ground, and blows
the HT fuses. The crowbar device is usually a triac, as the direction of
offset to be dealt with is unpredictable.
4 By shutting down the power supply when a DC fault is detected. This can
be done simply by an inhibit input if a switched-mode PSU is used.
Conventional supplies are less easy.
Amplifier and loudspeaker protection
DC protection by fuses
Fuses in series with the output line are sometimes recommended for DC
offset protection, but their only merit is cheapness. It may be true that they
have a slightly better chance of saving expensive loudspeakers than the HT
fuses, but there are at least three snags:
Selection of the correct fuse size is not at all easy. If the fuse rating is
small and fast enough to provide some real loudspeaker protection, then
it is likely to be liable to nuisance blowing on large bass transients. A
good visual warning is given by behaviour of the fuse wire; if this can be
seen sagging on transients, then it is going to fail sooner rather than later.
At least one writer on DIY Class-A amplifiers gave up on the problem,
and coolly left the tricky business of fuse selection to the constructor!
Fuses running within sight of their nominal rated current generate
distortion at LF due to cyclic changes in their resistance caused by I2R
heating; the THD would be expected to rise rapidly as frequency falls,
and Greiner [6] states that harmonic and intermodulation distortion near
the burn-out point can reach 4%. It should be possible to eradicate this
by including the fuse inside the global feedback network, for the
distortion will be generated at low frequencies where the feedback
factor is at its greatest, but there are problems with amplifier behaviour
after the fuse has blown.
In my tests, the distortion generated was fairly pure third harmonic. Figure
13.9 shows the THD measured before and after a T1A (slow-blow) fuse in
series with an 8 load at 25 W. Below 100 Hz the distortion completely
swamps that produced by the amplifier, reaching 0.007% at 20 Hz. The
distortion rises at rather less than 6 dB/octave as frequency falls. The fuse in
this test is running close to its rating, as increasing the power to 30 W
caused it to blow.
Figure 13.9
Fuse distortion. THD
measured before
and after the fuse
at 25 W into 8 385
Audio Power Amplifier Design Handbook
Fuses obviously have significant resistance (otherwise they wouldn’t
blow) so putting one in series with the output will degrade the
theoretical damping factor. However, whether this is of any audible
significance is very doubtful.
Note that the HT rail fuses, as opposed to fuses in the output line, are
intended only to minimise amplifier damage in the event of output device
failure. They must not be relied upon for speaker protection against DC
offset faults. Often when one HT fuse is caused to blow the other also does
so, but this cannot be relied upon, and obviously asymmetrical HT fuse
blowing will in itself give rise to a large DC offset.
Relay protection and muting control
Relay protection against DC offsets has the merit that, given careful relay
selection and control-circuitry design, it is virtually foolproof. The relay
should be of the normally-open type so that if the protection fails it will be
to a safe condition.
The first problem is to detect the fault condition as soon as possible. This is
usually done by low-pass filtering the audio output, to remove all signal
frequencies, before the resulting DC level is passed to a comparator that
trips when a set threshold is exceeded. This is commonly in the range of
1–2 V, well outside any possible DC-offsets associated with normal
operation; these will almost certainly be below 100 mV. Any low-pass filter
must introduce some delay between the appearance of the DC fault and the
comparator tripping, but with sensible design this will be too brief to
endanger normal loudspeakers. There are other ways of tackling the faultdetection problem, for example by detecting when the global negative
feedback has failed, but the filtering approach appears to be the simplest
method and is generally satisfactory. First-order filtering seems to be quite
adequate, though possibly a second-order active filter would give a faster
response time for the same discrimination against false-triggering on bass
transients. In general there is much to be said for keeping protection
circuitry as simple and reliable as possible.
Having paid for a DC protection relay, it seems only sensible to use it for
system muting as well, to prevent thuds and bangs from the upstream parts
of the audio system from reaching the speakers at power-up and power
down. Most power amplifiers, being dual-rail (i.e. DC-coupled) do not
generate enormous thumps themselves, but they cannot be guaranteed to be
completely silent, and will probably produce an audible turn-on thud.
An amplifier relay-control system should:
Leave the relay de-energised when muted. At power-up, there should be
a delay of at least 1 second before the relay closes. This can be increased
if required.
Amplifier and loudspeaker protection
Drop out the relay as fast as is possible at power-down, to stop the dying
moans of the pre-amp, etc. from reaching the outside world.
My preferred technique is a 2 msec (or thereabouts) timer which is held
reset by the AC on the mains transformer secondary, except for a brief
period around the AC zero-crossing, which is not long enough for the
timer to trigger. When the incoming AC disappears, the near-continuous
reset is removed, the timer fires, and the relay is dropped out within
10 msec. This will be long before the various reservoir capacitors in the
system can begin to discharge. However, if the mains switch contacts are
generating RF that is in turn reproduced as a click by the pre-amp, then
even this method may not be fast enough to mute it.
Drop out the relay as fast as is possible when a DC offset of more than
1–2 V, in either direction, is detected at the output of either power amp
channel; the exact threshold is not critical. This is normally done by lowpass filtering the output (47k and 47 µF works OK) and applying it to
some sort of absolute-value circuit to detect offsets in either direction.
The resulting signal is then OR-ed in some way with the muting signal
mentioned above.
Don’t forget that the contacts of a relay have a much lower current rating
for breaking DC rather than AC. This is an issue that doesn’t seem to
have attracted the attention it deserves.
A block diagram of a relay control system meeting the above requirements
is shown in Figure 13.10, which includes over-temperature protection. Any
of the three inhibit signals can override the turn-on delay and pull out the
Figure 13.10
Output relay control
combining DC offset
protection and poweron/off muting
Audio Power Amplifier Design Handbook
Distortion in output relays
Relays remain the only simple and effective method of disconnecting an
amplifier from its load. The contacts can carry substantial currents, and it
has been questioned whether they can introduce non-linearities.
My experience is that silver-based contacts in good condition show
effectively perfect linearity. Take a typical relay intended by its manufacturer for output-switching applications, with ‘silver alloy’ contacts –
whatever that means – rated at 10 A. Figure 13.11 shows THD before and
after the relay contacts while driving an 8 load to 91 W, giving a current
of 3.4 A rms. There is no significant difference; the only reason that the lines
do not fall exactly on top of each other is because of the minor bias changes
that Class B is heir to. This apparently perfect linearity can be badly
degraded if the contacts have been maltreated by allowing severe arcing –
typically while trying and failing to break a severe DC fault.
Figure 13.11
Demonstrating that
relay contacts in
themselves are
completely distortionfree. Current through
contacts was
3.4 A rms
Not everyone is convinced of this. If the contacts were non-linear for
whatever reason, an effective way of dealing with it would be to include
them in the amplifier feedback loop, as shown in Figure 13.12. R1 is the
main feedback resistor, and R2 is a subsidiary feedback path that remains
closed when the relay contacts open, and hopefully prevents the amplifier
from going completely berserk. With the values shown the normal gain is
15.4 times, and with the contacts open it is 151 times. There is a feedback
factor of about ten to linearise any relay problems.
Amplifier and loudspeaker protection
Figure 13.12
How to enclose relay
contacts in the
feedback loop. The
gain shoots up when
the relay contacts
open, so muting the
input signal is
The problem of course is that if there is to be a healthy amount of NFB
wrapped around the relay contacts, R2 must be fairly high and so the
closed-loop gain shoots up. If there is still an input signal, then the amplifier
will be driven heavily into clipping. Some designs object to this, but even
if the amplifier does not fail it is likely to accumulate various DC offsets on
its internal time-constants as a result of heavy clipping, and these could
cause unwanted noises when the relay contacts close again. One solution
to this is a muting circuit at the amplifier input that removes the signal
entirely and prevents clipping. This need not be a sophisticated circuit, as
huge amounts of muting are not required; –40 dB should be enough. It
must, however, pass the signal cleanly when not muting.
A much more insidious – unexpected – form of non-linearity can occur if
the relay is constructed so that its frame makes up part of the switched
electrical circuit as well as the magnetic circuit. (This is not the case with
the audio application relay discussed above.) A relay frame is made of soft
iron, to prevent it becoming permanently magnetised, and this appears to
present a non-linear resistance to a loudspeaker level signal, presumably
due to magnetisation and saturation of the material. (It should be said at
once that this is described by the manufacturer as a ‘power relay’ and is
apparently not intended for audio use.) A typical example of this
construction has massive contacts of silver/cadmium oxide, rated at 30 A
AC, which in themselves are linear. However, used as an amplifier output
relay, this component generates more – much more – distortion than the
power amplifier it is associated with.
The effect increases with increasing current; 4.0 A rms passing through the
relay gives 0.0033% THD and 10 A rms gives 0.018%. The distortion level
appears to increase with the square of the current. Experiment showed that
the distortion was worst where the frame width was narrowest, and hence
the current density greatest.
Audio Power Amplifier Design Handbook
Figure 13.13
A is amplifier
distortion alone, B
total distortion with
power relay in
circuit. C shows that
enclosing the relay in
the feedback loop is
not a complete cure
Figure 13.13 shows the effect at 200 W rms/2 (i.e. with 10 A rms through
the load) before and after the relay. Trace A is the amplifier alone. This is a
Blameless amplifier and so THD is undetectable below 3 kHz, being
submerged in the noise floor which sets a measurement limit of 0.007%.
Trace B adds in the extra distortion from the relay. It seems to be frequencydependent, but rises more slowly than the usual slope of 6 dB/octave. Trace
C shows the effect of closing the relay in the NFB loop using the circuit and
component values of Figure 13.12; the THD drops to about a tenth, which
is what simple NFB theory would predict. Note that from 10 kHz to 35 kHz
the distortion is now lower than before the relay was added; this is due to
cancellation of amplifier and relay distortion.
Figure 13.14 was obtained by sawing a 3 mm by 15 mm piece from a relay
frame and wiring it in series with the amplifier output, by means of copper
wires soldered at each end. As before the level was 200 W rms/2 , i.e. 10 A
rms. Trace A is the raw extra distortion; this is lower than shown in Figure
13.13 because the same current is passing through less of the frame
material. Trace B is the result of enclosing the frame fragment in the NFB
loop exactly as before. This removes all suspicion of interaction with coil
or contacts and proves it is the actual frame material itself that is nonlinear.
Wrapping feedback around the relay helps but, as usual, is not a complete
cure. Soldering on extra wires to the frame to bypass as much frame
material as possible is also useful, but it is awkward and there is the danger
of interfering with proper relay operation. No doubt any warranties would
Amplifier and loudspeaker protection
Figure 13.14
Trace A here is total
distortion with a
sample of the power
relay frame material
wired in circuit. B is
the same, enclosed
in the feedback loop
as before
be invalidated. Clearly it is best to avoid this sort of relay construction if you
possibly can, but if high-current switching is required, more than an audiointended relay can handle, the problem may have to be faced.
Output crowbar DC protection
Since relays are expensive and require control circuitry, and fuse protection
is very doubtful, there has for at least two decades been interest in simpler
and wholly solid-state solutions to the DC-protection problem. The circuit
of Figure 13.15 places a triac across the output, the output signal being
low-pass filtered by R and C. If sufficient DC voltage develops on C to fire
the diac, it triggers the triac, shorting the amplifier output to ground.
While this approach has the merit of simplicity, in my (wholly unhappy)
experience, it has proved unsatisfactory. The triac needs to be very big
indeed if it is to work more than once, because it must pass enough current
to blow the HT rail fuses. If these fuses were omitted the triac would have
to dump the entire contents of a power-supply reservoir capacitor to ground
through a low total resistance, and the demands on it become quite
An output crowbar is also likely to destroy the output devices; the
assumption behind this kamikaze crowbar system is that the DC offset is due
to blown output devices, and a short across the output can do no more harm.
This is quite wrong, because any fault in the small-signal part of the amplifier
will also cause the output to saturate positive or negative, with the output
devices in perfect working order. The operation of the crowbar under these
Audio Power Amplifier Design Handbook
Figure 13.15
Output crowbar DC
circumstances may destroy the output devices, for the overload protection
may not be adequate to cope with such a very direct short-circuit.
Protection by power-supply shutdown
If your amplifier is powered by a switch-mode supply, it may well have a
logic input that gives the option of near-instant shutdown. This can be
connected to a DC-detect low-pass filter, and the occurrence of a DC error
then gives an apparently foolproof shutdown of everything.
There are (as usual) snags to this. Firstly, the high relative cost of switchmode supplies means that one will be shared between two or more
amplifier channels, and so both channels are lost if one fails. Secondly, and
more worryingly, this provides very dubious protection against a fault in the
supply itself. If such a fault causes one of the HT rails to collapse, then it
may well also disable the shutdown facility, and all protection is lost.
Conventional transformer power supplies can also be shut down quickly by
firing crowbar SCRs across the supply-rails; this overcomes one of the
objections to output crowbars, as collateral damage to other parts of the
circuit is unlikely, assuming of course you are correctly trying to blow the
DC rail fuses, and not the transformer secondary fuses. The latter option
would severely endanger the bridge rectifier, and the crowbar circuitry
would have to handle enormous amounts of energy as it emptied the
reservoir capacitors. Even blowing the DC fuses will require SCRs with a
massive peak-current capability.
Thermal protection
This section deals only with protecting the output semiconductors against
excessive junction temperature; the thermal safeguarding of the mains
transformer is dealt with in Chapter 8.
Output devices that are fully protected against excess current, voltage and
power are by no means fully safeguarded. Most electronic overload
protection systems allow the devices to dissipate much more power than in
Amplifier and loudspeaker protection
normal operation; this can and should be well inside the rated capabilities
of the component itself, but this gives no assurance that the increased
dissipation will not cause the heatsink to eventually reach such temperatures that the crucial junction temperatures are exceeded and the
device fails. If no temperature protection is provided this can occur after
only a few minutes drive into a short. Heatsink over-temperature may also
occur if ventilation slots, etc. are blocked, or heatsink fins covered up.
The solution is a system that senses the heatsink temperature and intervenes
when it reaches a preset maximum. This intervention may be in the form of:
1 Causing an existing muting/DC-protection relay to drop out, breaking
the output path to the load. If such a relay is fitted, then it makes sense to
use it.
2 Muting or attenuating the input signal so the amplifier is no longer
dissipating significant power.
3 Removing the power-supply to the amplifier sections. This normally
implies using a bimetallic thermal switch to break the mains supply to the
transformer primary, as anywhere downstream of here requires two lines
to be broken simultaneously, e.g. the positive and negative HT rails.
Each of these actions may be either self-resetting or latching, requiring the
user to initiate a reset. The possibility that a self-resetting system will cycle on
and off for long periods, subjecting the output semiconductors to severe
temperature changes, must be borne in mind. Such thermal cycling can
severely shorten the life of semiconductors.
The two essential parts of a thermal protection system are the temperature
sensing element and whatever arrangement performs the intervention.
While temperature can be approximately sensed in many ways, e.g. by
thermistors, silicon diodes, transistor junctions, etc. these all require some
sort of setup or calibration procedure, due to manufacturing tolerances. This
is impractical in production, for it requires the heatsink (which normally has
substantial thermal inertia) to be brought up to the critical temperature
before the circuit is adjusted. This not only takes considerable time, but also
requires the output devices to reach a temperature at which they are
somewhat endangered.
A much better method is the use of integrated temperature sensors that do not
require any calibration. A good example is the National Semiconductor
LM35DZ, a three-terminal TO92 device which outputs 10 mV for each
degree Centigrade above Zero. Without any calibration procedure, the
output voltage may be compared against a fixed reference, usually by an opamp used as a comparator, and the resulting output used to pull out the
muting relay. This approach gives the most trouble-free temperature
protection in my experience. IC temperature sensors are more expensive
than thermistors, etc. but this is counterbalanced by their accurate and
trouble-free operation.
Audio Power Amplifier Design Handbook
Another pre-calibrated temperature sensor is the thermal switch, which
usually operates on the principle of a bistable bimetallic element. These
should not be confused with thermal fuses which are once-only components
that open the circuit by melting an internal fusible alloy; the trouble with
these is that they are relatively uncommon, and the chance of a blown
thermal fuse being replaced with the correct component in the field is not
The physical positioning of the temperature sensor requires some thought. In
an ideal world we would judge the danger to the output devices by assessing
the actual junction temperature; since this is impractical the sensor must get
as close as it can. It is shown elsewhere that the top of a TO3 transistor can
gets hotter than the flange, and as for quiescent biasing sensors, the top is the
best place for the protection sensor. This does however present some
mechanical problems in mounting. This approach may not be equally
effective with plastic flat-pack devices such as TO3P, for the outer surface is
an insulator; however it still gets hotter than the immediately adjacent
Alternatively, the protection sensor can be mounted on the main heatsink,
which is mechanically much simpler but imposes a considerable delay
between the onset of device heating and the sensor reacting. For this reason a
heatsink-mounted sensor will normally need to be set to a lower trip
temperature, usually in the region of 80°C, than if it is device-mounted. The
more closely the sensor is mounted to the devices, the better they are
protected. If two amplifiers share the same heatsink, the sensor should be
placed between them; if it was placed at one end the remote amplifier would
suffer a long delay between the onset of excess heating and the sensor
One well-known make of PA amplifiers implements temperature protection
by mounting a thermal switch in the live mains line on top of one of the TO3
cans in the output stage. This gains the advantage of fast response to
dangerous temperatures, but there is the obvious objection that lethal
voltages are brought right into the centre of the amplifier circuitry, where
they are not normally expected, and this represents a real hazard to service
Powering auxiliary circuitry
Whenever it is necessary to power auxiliary circuitry, such as the relay
control system described above, there is an obvious incentive to use the
main HT rails. A separate PSU requires a bridge rectifier, reservoir capacitor,
fusing and an extra transformer winding, all of which will cost a significant
amount of money.
The main disadvantage is that the HT rails are at an inconveniently high
voltage for powering control circuitry. For low-current sections of this
Amplifier and loudspeaker protection
circuitry, such as relay timing, the problem is not serious as the same highvoltage small-signal transistors can be used as in the amplifier small-signal
sections, and the power dissipation in collector loads, etc. can be controlled
simply by making them higher in value. The biggest problem is the relay
energising current; many relay types are not available with coil voltages
higher than 24 V, and this is not easy to power from a 50 V HT rail without
wasting power in a big dropper resistor. This causes unwanted heating of the
amplifier internals, and provides a place for service engineers to burn
One solution in a stereo amplifier is to run the two relays in series; the snag
(and for sound reinforcement work it may be a serious one) is that both relays
must switch together, so if one channel fails with a DC offset, both are muted.
In live work independent relay control is much to be preferred, even though
most of the relay control circuitry must be duplicated for each channel.
If the control circuitry is powered from the main HT rails, then its power
should be taken off before the amplifier HT fuses. The control circuitry
should then be able to mute the relays when appropriate, no matter what
faults have occurred in the amplifiers themselves.
If there is additional signal circuitry in the complete amplifier it is not
advisable to power it in this way, especially if it has high gain, e.g. a
microphone preamplifier. When such signal circuits are powered in this way,
it is usually by +/–15 V regulators from the HT rails, with series dropper
resistors to spread out some of the dissipation. However, bass transients in
the power amplifiers can pull down the HT rails alarmingly, and if the
regulators drop out large disturbances will appear on the nominally
regulated low-voltage rails, leading to very low frequency oscillations which
will be extremely destructive to loudspeakers. In this case the use of wholly
separate clean rails run from an extra transformer winding is strongly
recommended. There will be no significant coupling through the use of a
single transformer.
1. Bailey, A Output Transistor Protection in AF Amplifiers Wireless World,
June 1968, p. 154.
2. Becker, R High-Power Audio Amplifier Design Wireless World, Feb.
1972, p. 79.
3. Motorola High Power Audio Amplifiers With Sort Circuit Protection
Motorola Application Note AN-485 (1972).
4. Otala, M Peak Current Requirement of Commerical Loudspeaker Systems
Journ. Audio Eng. Soc. Vol. 35, June 1987, p. 455.
5. Baxandall, P Technique for Displaying Current and Voltage Capability of
Amplifiers Journ. Audio Eng. Soc. Vol. 36, Jan./Feb. 1988, p. 3.
6. Greiner, R Amplifier-Loudspeaker Interfacing Journ. Audio Eng. Soc.
Loudspeakers pp. 241–250.
Grounding and practical
Audio amplifier PCB design
This section addresses the special PCB design problems presented by
power amplifiers, particularly those operating in Class-B. All power
amplifier systems contain the power-amp stages themselves, and usually
associated control and protection circuitry; most also contain small-signal
audio sections such as balanced input amplifiers, subsonic filters, output
meters, and so on.
Other topics that are related to PCB design, such as grounding, safety,
reliability, etc. are also dealt with.
The performance of an audio power amplifier depends on many factors,
but in all cases the detailed design of the PCB is critical, because of the risk
of inductive distortion due to crosstalk between the supply-rails and the
signal circuitry; this can very easily be the ultimate limitation on amplifier
linearity, and it is hard to over-emphasise its importance. The PCB design
will to a great extent define both the distortion and crosstalk performance
of the amplifier.
Apart from these performance considerations, the PCB design can have
considerable influence on ease of manufacture, ease of testing and repair,
and reliability. All of these issues are addressed below.
Successful audio PCB layout requires enough electronic knowledge to fully
appreciate the points set out below, so that layout can proceed smoothly
and effectively. It is common in many electronic fields for PCB design to be
handed over to draughtspersons, who, while very skilled in the use of CAD,
have little or no understanding of the details of circuit operation. In some
fields this works fine; in power amplifier design it won’t, because basic
Grounding and practical matters
parameters such as crosstalk and distortion are so strongly layoutdependent. At the very least the PCB designer should understand the points
set out below.
All crosstalk has a transmitting end (which can be at any impedance) and
a receiving end, usually either at high impedance or virtual-earth. Either
way, it is sensitive to the injection of small currents. When interchannel
crosstalk is being discussed, the transmitting and receiving channels are
usually called the speaking and non-speaking channels respectively.
Crosstalk comes in various forms:
Capacitative crosstalk is due to the physical proximity of different
circuits, and may be represented by a small notional capacitor joining
the two circuits. It usually increases at the rate of 6 dB/octave, though
higher dB/octave rates are possible. Screening with any conductive
material is a complete cure, but physical distance is usually cheaper.
Resistive crosstalk usually occurs simply because ground tracks have a
non-zero resistance. Copper is not a room-temperature superconductor.
Resistive crosstalk is constant with frequency.
Inductive crosstalk is rarely a problem in general audio design; it might
occur if you have to mount two uncanned audio transformers close
together, but otherwise you can usually forget it. The notable exception
to this rule is . . . the Class-B audio power amplifier, where the rail
currents are halfwave sines that seriously degrade the distortion
performance if they are allowed to couple into the input, feedback or
output circuitry.
In most line-level audio circuitry the primary cause of crosstalk is unwanted
capacitative coupling between different parts of a circuit, and in most cases
this is defined solely by the PCB layout. Class-B power amplifiers, in
contrast, should suffer very low or negligible levels of crosstalk from
capacitative effects, as the circuit impedances tend to be low, and the
physical separation large; a much greater problem is inductive coupling
between the supply-rail currents and the signal circuitry. If coupling occurs
to the same channel it manifests itself as distortion, and can dominate
amplifier non-linearity. If it occurs to the other (non-speaking) channel it
will appear as crosstalk of a distorted signal. In either case it is thoroughly
undesirable, and precautions must be taken to prevent it.
The PCB layout is only one component of this, as crosstalk must be both
emitted and received. In general the emission is greatest from internal
wiring, due to its length and extent; wiring layout will probably be critical
for best performance, and needs to be fixed by cable ties, etc. The receiving
end is probably the input and feedback circuitry of the amplifier, which will
be fixed on the PCB. Designing these sections for maximum immunity is
critical to good performance.
Audio Power Amplifier Design Handbook
Rail induction distortion
The supply-rails of a Class-B power-amp carry large and very distorted
currents. As previously outlined, if these are allowed to crosstalk into the
audio path by induction the distortion performance will be severely
degraded. This applies to PCB conductors just as much as cabling, and it is
sadly true that it is easy to produce an amplifier PCB that is absolutely
satisfactory in every respect but this one, and the only solution is another
board iteration. The effect can be completely prevented but in the present
state of knowledge I cannot give detailed guidelines to suit every
constructional topology. The best approach is:
Minimise radiation from the supply rails by running the V+ and V– rails as
close together as possible. Keep them away from the input stages of the
amplifier, and the output connections; the best method is to bring the rails
up to the output stage from one side, with the rest of the amplifier on the
other side. Then run tracks from the output to power the rest of the amp;
these carry no halfwave currents and should cause no problems.
Minimise pickup of rail radiation by keeping the area of the input and
feedback circuits to a minimum. These form loops with the audio ground
and these loops must be as small in area as possible. This can often best be
done by straddling the feedback and input networks across the audio
ground track, which is taken across the centre of the PCB from input ground
to output ground.
Induction of distortion can also occur into the output and output-ground
cabling, and even the output inductor. The latter presents a problem as it is
usually difficult to change its orientation without a PCB update.
The mounting of output devices
The most important decision is whether or not to mount the power output
devices directly on the main amplifier PCB. There are strong arguments for
doing so, but it is not always the best choice.
The amplifier PCB can be constructed so as to form a complete
operational unit that can be thoroughly tested before being fixed into the
chassis. This makes testing much easier, as there is access from all sides;
it also minimises the possibility of cosmetic damage (scratches, etc.) to
the metalwork during testing.
It is impossible to connect the power devices wrongly, providing you get
the right devices in the right positions. This is important for such errors
usually destroy both output devices and cause other domino-effect faults
that are very time-consuming to correct.
The output device connections can be very short. This seems to help
stability of the output stage against HF parasitic oscillations.
Grounding and practical matters
If the output devices require frequent changing (which obviously
indicates something very wrong somewhere) then repeated resoldering
will damage the PCB tracks. However, if the worst happens the damaged
track can usually be bridged out with short sections of wire, so the PCB
need not be scrapped; make sure this is possible.
The output devices will probably get fairly hot, even if run well within
their ratings; a case temperature of 90°C is not unusual for a TO3 device.
If the mounting method does not have a degree of resilience, then
thermal expansion may set up stresses that push the pads off the PCB.
The heatsink will be heavy, and so there must be a solid structural fixing
between this and the PCB. Otherwise the assembly will flex when
handled, putting stress on soldered connections.
Single and double-sided PCBs
Single-sided PCBs are the usual choice for power amplifiers, because of
their lower cost; however the price differential between single and doublesided plated-through-hole (PTH) is much less than it used to be. It is not
usually necessary to go double-sided for reason of space or convoluted
connectivity, because power amplifier components tend to be physically
large, determining the PCB size, and in typical circuitry there are a large
number of discrete resistors, etc. that can be used for jumping tracks.
Bear in mind that single-sided boards need thicker tracks to ensure
adhesion in case desoldering is necessary. Adding one or more ears to pads
with only one track leading to them gives much better adhesion, and is
highly recommended for pads that may need resoldering during maintenance; unfortunately it is a very tedious task with most CAD systems.
The advantages of double-sided PTH for power amplifiers are as follows:
No links are required.
Double-sided PCBs may allow one side to be used primarily as a ground
plane, minimising crosstalk and EMC problems.
Much better pad adhesion on resoldering as the pads are retained by the
through-hole plating.
There is more total room for tracks, and so they can be wider, giving less
volt-drop and PCB heating.
The extra cost is small.
Power supply PCB layout
Power supply subsystems have special requirements due to the very high
capacitor-charging currents involved:
Tracks carrying the full supply-rail current must have generous widths.
The board material used should have not less than 2-oz copper. 4-oz
Audio Power Amplifier Design Handbook
copper can be obtained but it is expensive and has long lead-times; not
really recommended.
Reservoir capacitors must have the incoming tracks going directly to the
capacitor terminals; likewise the outgoing tracks to the regulator must
leave from these terminals. In other words, do not run a tee off to the
cap. Failure to observe this puts sharp pulses on the DC and tends to
worsen the hum level.
The tracks to and from the rectifiers carry charging pulses that have a
considerably higher peak value than the DC output current. Conductor
heating is therefore much greater due to the higher value of I2R. Heating
is likely to be especially severe at PC-mount fuseholders. Wire links may
also heat up and consideration should be given to two links in parallel;
this sounds crude but actually works very effectively.
Track heating can usually be detected simply by examining the state of
the solder mask after several hours of full-load operation; the green mask
materials currently in use discolour to brown on heating. If this occurs
then as a very rough rule the track is too hot. If the discoloration tends
to dark brown or black then the heating is serious and must definitely be
If there are PCB tracks on the primary side of the mains transformer, and
this has multiple taps for multi-country operation, then remember that
some of these tracks will carry much greater currents at low voltage
tappings; mains current drawn on 90 V input will be nearly 3 times that
at 240 V.
Be sure to observe the standard safety spacing of 60 thou between mains
tracks and other conductors, for creepage and clearance.
(This applies to all track-track, track-PCB edge, and track-metal-fixings
In general PCB tracks carrying mains voltages should be avoided, as
presenting an unacceptable safety risk to service personnel. If it must be
done, then warnings must be displayed very clearly on both sides of the
PCB. Mains-carrying tracks are unacceptable in equipment intended to
meet UL regulations in the USA, unless they are fully covered with
insulating material that is non-flammable and can withstand at least 120°C
(e.g. polycarbonate).
Power amplifier PCB layout details
A simple unregulated supply is assumed:
Power amplifiers have heavy currents flowing through the circuitry, and
all of the requirements for power supply design also apply here. Thick
tracks are essential, and 2-oz copper is highly desirable, especially if the
layout is cramped.
Grounding and practical matters
If attempting to thicken tracks by laying solder on top, remember that
ordinary 60:40 solder has a resistivity of about 6 times that of copper, so
even a thick layer may not be very effective.
The positive and negative rail reservoir caps will be joined together by
a thick earth connection; this is called Reservoir Ground (RG). Do not
attempt to use any point on this track as the audio-ground star-point, as
it carries heavy charging pulses and will induce ripple into the signal.
Instead take a thick tee from the centre of this track (through which the
charging pulses will not flow) and use the end of this as the starpoint.
Low-value resistors in the output stage are likely to get very hot in
operation – possibly up to 200°C. They must be spaced out as much as
possible and kept from contact with components such as electrolytic
capacitors. Keep them away from sensitive devices such as the driver
transistors and the bias-generator transistor.
Vertical power resistors. The use of these in power amplifiers appears at
first attractive, because of the small amount of PCB area they take up.
However the vertical construction means that any impact on the
component, such as might be received in normal handling, puts a very
great strain on the PCB pads, which are likely to be forced off the board.
This may result in it being scrapped. Single-sided boards are particularly
vulnerable, having much lower pad adhesion due to the absence of
Solderable metal clips to strengthen the vertical resistors are available in
some ranges, (e.g. Vitrohm) but this is not a complete solution, and the
conclusion must be that horizontal-format power resistors are
Rail decoupler capacitors must have a separate ground return to the
Reservoir Ground. This ground must not share any part of the audio
ground system, and must not be returned to the Starpoint. See Figure
The exact layout of the feedback takeoff point is criticial for proper
operation. Usually the output stage has an output rail that connects the
emitter power resistors together. This carries the full output current and
must be substantial. Take a tee from this track for the output connection,
and attach the feedback takeoff point to somewhere along this tee. Do
not attach it to the track joining the emitter resistors.
The input stages (usually a differential pair) should be at the other end of
the circuitry from the output stage. Never run input tracks close to the
output stage. Input stage ground, and the ground at the bottom of the
feedback network must be the same track running back to Starpoint. No
decoupling capacitors, etc. may be connected to this track, but it seems
to be permissible to connect input bias resistors, etc. that pass only very
small DC currents.
Put the input transistors close together. The closer the temperaturematch, the less the amplifier output DC offset due to Vbe mismatching.
If they can both be hidden from seeing the infra-red radiation from the
Audio Power Amplifier Design Handbook
Figure 14.1
Grounding system for
a typical power
heatsink (for example by hiding them behind a large electrolytic) then
DC drift is reduced.
Most power amplifiers will have additional control circuitry for muting
relays, thermal protection, etc. Grounds from this must take a separate
path back to Reservoir Ground, and not the audio Starpoint.
Unlike most audio boards, power amps will contain a mixture of
sensitive circuitry and a high-current power-supply. Be careful to keep
bridge-rectifier connections, etc. away from input circuitry.
Mains/chassis ground will need to be connected to the power amplifier
at some point. Do not do this at the transformer centre-tap as this is
spaced away from the input ground voltage by the return charging
pulses, and will create severe groundloop hum when the input ground is
connected to mains ground through another piece of equipment.
Connecting mains ground to starpoint is better, as the charging pulses are
excluded, but the track resistance between input ground and star will
carry any ground-loop currents and induce a buzz.
Connecting mains ground to the input ground gives maximal immunity
against groundloops.
If capacitors are installed the wrong way round the results are likely to
be explosive. Make every possible effort to put all capacitors in the same
orientation to allow efficient visual checking. Mark polarity clearly on
the PCB, positioned so it is still visible when the component is fitted.
Grounding and practical matters
Drivers and the bias generator are likely to be fitted to small vertical
heatsinks. Try to position them so that the transistor numbers are
All transistor positions should have emitter, base and collector or
whatever marked on the top-print to aid fault-finding. TO3 devices need
also to be identified on the copper side, as any screen-printing is covered
up when the devices are installed.
Any wire links should be numbered to make it easier to check they have
all been fitted.
The audio PCB layout sequence
PCB layout must be considered from an early stage of amplifier design. For
example, if a front-facial layout shows the volume control immediately
adjacent to a loudspeaker routing switch, then a satisfactory crosstalk
performance will be difficult to obtain because of the relatively high
impedance of the volume control wipers. Shielding metalwork may be
required for satisfactory performance and this adds cost. In many cases the
detailed electronic design has an effect on crosstalk, quite independently
from physical layout.
(a) Consider implications of facia layout for PCB layout.
(b) Circuitry designed to minimise crosstalk. At this stage try to look ahead
to see how op-amp halves, switch sections, etc. should be allocated to
keep signals away from sensitive areas. Consider crosstalk at abovePCB level; for example, when designing a module made up of two
parallel double-sided PCBs, it is desirable to place signal circuitry on
the inside faces of the boards, and power and grounds on the outside,
to minimise crosstalk and maximise RF immunity.
(c) Facia components (pots, switches, etc.) placed to partly define available
board area.
(d) Other fixed components such as power devices, driver heatsinks, input
and output connectors, and mounting holes placed. The area left
remains for the purely electronic parts of the circuitry that do not have
to align with metalwork, etc. and so may be moved about fairly
(e) Detailed layout of components in each circuit block, with consideration
towards manufacturability.
(f) Make efficient use of any spare PCB area to fatten grounds and highcurrent tracks as much as possible. It is not wise to fill in every spare
corner of a prototype board with copper as this can be time consuming,
(depending on the facilities of your PCB CAD system) and some of it
will probably have to be undone to allow modifications.
Ground tracks should always be as thick as practicable. Copper is
Audio Power Amplifier Design Handbook
Miscellaneous points
On double-sided PCBs, copper areas should be solid on the component
side, for minimum resistance and maximum screening, but will need to
be cross-hatched on the solder side to prevent distortion of the PCB is
flow-soldered. A common standard is 10 thou wide non-copper areas;
i.e. mostly copper with small square holes; this is determined in the CAD
package. If in doubt consult those doing the flow-soldering.
Do not bury component pads in large areas of copper, as this causes
soldering difficulties.
There is often a choice between running two tracks into a pad, or taking
off a tee so that only one track reaches it. The former is better because
it holds the pad more firmly to the board if desoldering is necessary. This
is particularly important for components like transistors that are
relatively likely to be replaced; for single-sided PCBs it is absolutely
If two parallel tracks are likely to crosstalk, then it is beneficial to run a
grounded screening track between them. However, the improvement is
likely to be disappointing, as electrostatic lines of force will curve over
the top of the screen track.
Jumper options must always be clearly labelled. Assume everyone loses
the manual the moment they get it.
Label pots and switches with their function on the screen-print layer, as
this is a great help when testing. If possible, also label circuit blocks, e.g.
DC offset detect. The labels must be bigger than component ident text to
be clearly readable.
Amplifier grounding
The grounding system of an amplifier must fulfil several requirements,
amongst which are:
The definition of a Star Point as the reference for all signal voltages.
In a stereo amplifier, grounds must be suitably segregated for good
crosstalk performance. A few inches of wire as a shared ground to the
output terminals will probably dominate the crosstalk behaviour.
Unwanted AC currents entering the amplifier on the signal ground, due
to external ground loops, must be diverted away from the critical signal
grounds, i.e. the input ground and the ground for the feedback arm. Any
voltage difference between these last two grounds appears directly in the
Charging currents for the PSU reservoir capacitors must be kept out of all
other grounds.
Ground is the point of reference for all signals, and it is vital that it is made
solid and kept clean; every ground track and wire must be treated as a
Grounding and practical matters
resistance across which signal currents will cause unwanted voltage-drops.
The best method is to keep ground currents apart by means of a suitable
connection topology, such as a separate ground return to the Star Point for
the local HT decoupling, but when this is not practical it is necessary to
make every ground track as thick as possible, and fattened up with copper
at every possible point. It is vital that the ground path has no necks or
narrow sections, as it is no stronger than the weakest part. If the ground
path changes board side then a single via-hole may be insufficient, and
several should be connected in parallel. Some CAD systems make this
difficult, but there is usually a way to fool them.
Power amplifiers rarely use double-insulated construction and so the
chassis and all metalwork must be permanently and solidly grounded for
safety; this aspect of grounding is covered in Chapter 15. One result of
permanent chassis grounding is that an amplifier with unbalanced inputs
may appear susceptible to ground loops. One solution is to connect audio
ground to chassis only through a 10 resistor, which is large enough to
prevent loop currents becoming significant. This is not very satisfactory
The audio system as a whole may thus not be solidly grounded.
If the resistor is burnt out due to misconnected speaker outputs, the
audio circuitry is floating and could become a safety hazard.
The RF rejection of the power amplifier is likely to be degraded. A 100 nF
capacitor across the resistor may help.
A better approach is to put the audio-chassis ground connection at the
input connector, so in Figure 14.1, ground-loop currents must flow through
A–B to the Protected Earth at B, and then to mains ground via B–C. They
cannot flow through the audio path E–F. This topology is very resistant to
ground-loops, even with an unbalanced input; the limitation on system
performance in the presence of a ground-loop is now determined by the
voltage-drop in the input cable ground, which is outside the control of the
amplifier designer. A balanced input could in theory cancel out this voltage
drop completely.
Figure 14.1 also shows how the other grounding requirements are met. The
reservoir charging pulses are confined to the connection D–E, and do not
flow E–F, as there is no other circuit path. E–F–H carries ripple, etc. from
the local HT decouplers, but likewise cannot contaminate the crucial audio
ground A–G.
Ground loops: how they work and how to deal with them
A ground loop is created whenever two or more pieces of mains-powered
equipment are connected together, so that mains-derived AC flows through
shields and ground conductors, degrading the noise floor of the system. The
effect is worst when two or more units are connected through mains ground
Audio Power Amplifier Design Handbook
as well as audio cabling, and this situation is what is normally meant by the
term ‘ground loop’. However, ground currents can also flow in systems that
are not galvanically grounded; they are of lower magnitude but can still
degrade the noise floor, so this scenario is also considered here.
The ground currents may either be inherent in the mains supply wiring (see
‘Hum injection by mains grounding currents’ below) or generated by one
or more of the pieces of equipment that make up the audio system (see
sections ‘Hum injection by transformer stray magnetic fields’ and ‘Hum
injection by ‘transformer stray capacitance’ below).
Once flowing in the ground wiring, these currents will give rise to voltage
drops that introduce hum and buzzing noises. This may occur either in the
audio interconnects, or inside the equipment itself if it is not well designed.
See section ‘Ground currents inside equipment’, on p. 410.
Here I have used the word ‘ground’ for conductors and so on, while ‘earth’
is reserved for the damp crumbly stuff into which copper rods are thrust.
Hum injection by mains grounding currents
Figure 14.2 shows what happens when a so-called ‘technical ground’ such
as a buried copper rod is attached to a grounding system which is already
connected to ‘mains ground’ at the power distribution board. The latter is
mandatory both legally and technically, so one might as well accept this
and denote as the reference ground. In many cases this ‘mains ground’ is
actually the neutral conductor, which is only grounded at the remote
transformer substation. AB is the cable from substation to consumer, which
serves many houses from connections tapped off along its length. There is
substantial current flowing down the N + E conductor, so point B is often
1 volt rms or more above earth. From B onwards, in the internal house
wiring, neutral and ground are always separate (in the UK, anyway).
Two pieces of audio equipment are connected to this mains wiring at C and
D, and joined to each other through an unbalanced cable F–G. Then an illadvised connection is made to earth at D; the 1 V rms is now impressed on
the path B–C–D, and substantial current is likely to flow through it,
depending on the total resistance of this path. There will be a voltage drop
from C to D, its magnitude depending on what fraction of the total BCDE
resistance is made up by the section C–D. The earth wire C–D will be of
at least 1.5 mm2 cross-section, and so the extra connection FG down the
audio cable is unlikely to reduce the interfering voltage much.
To get a feel for the magnitudes involved, take a plausible ground current
of 1 amp. The 1.5 mm2 ground conductor will have a resistance of
0.012 /metre, so if the mains sockets at C and D are one metre apart, the
voltage C–D will be 12 mV rms. Almost all of this will appear between F
and G, and will be indistinguishable from wanted signal to the input stage
Figure 14.2
The pitfalls of adding a ‘technical ground’ to a system which is already grounded via the mains
Audio Power Amplifier Design Handbook
of Unit 2, so the hum will be severe, probably only 30 dB below the
nominal signal level.
The best way to solve this problem is not to create it in the first place. If
some ground current is unavoidable then the use of balanced inputs (or
ground-cancel outputs – it is not necessary to use both) should give at least
40 dB of rejection at audio frequencies.
Figure 14.2 also shows a third earthing point, which fortunately does not
complicate the situation. Metal water pipes are bonded to the incoming
mains ground for safety reasons, and since they are usually electrically
connected to an incoming water supply current flows through B–W in the
same way as it does through the copper rod link D–E. This water-pipe
current does not, however, flow through C–D and cannot cause a groundloop problem. It may, however, cause the pipes to generate an AC magnetic
field which is picked up by other wiring.
Hum injection by transformer stray magnetic fields
Figure 14.3 shows a thoroughly bad piece of physical layout which will
cause ground currents to flow even if the system is correctly grounded to
just one point.
Figure 14.3
Poor cable layout in
the PSU at left wraps a
loop around the
transformer and
induces ground
Here Unit 1 has an external DC power supply; this makes it possible to use
an inexpensive frame-type transformer which will have a large stray field.
But note that the wire in the PSU which connects mains ground to the
outgoing 0 V takes a half-turn around the transformer, and significant
current will be induced into it, which will flow round the loop C–F–G–D,
and give an unwanted voltage drop between F and G. In this case
reinforcing the ground of the audio interconnection is likely to be of some
help, as it directly reduces the fraction of the total loop voltage which is
dropped between F and G.
It is difficult to put any magnitudes to this effect because it depends on
many imponderables such as the build quality of the transformer and the
exact physical arrangement of the ground cable in the PSU. If this cable is
Grounding and practical matters
rerouted to the dotted position in the diagram, the transformer is no longer
enclosed in a half-turn, and the effect will be much smaller.
Hum injection by transformer stray capacitance
It seems at first sight that the adoption of Class II (double-insulated)
equipment throughout an audio system will give inherent immunity to
ground-loop problems. Life is not so simple, though it has to be said that
when such problems do occur they are likely to be much less severe. This
problem afflicts all Class II equipment to a certain extent.
Figure 14.4 shows two Class II units connected together by an unbalanced
audio cable. The two mains transformers in the units have stray
capacitance from both live and neutral to the secondary. If these
capacitances were all identical no current would flow, but in practice they
are not, so 50 Hz currents are injected into the internal 0 V rail and flow
through the resistance of F–G, adding hum to the signal. A balanced input
or ground-cancelling output will remove or render negligible the ill-effects.
Figure 14.4
The injection of mains
current into the ground
wiring via transformer
Reducing the resistance of the interconnect ground path is also useful –
more so than with other types of ground loop, because the ground current
is essentially fixed by the small stray capacitances, and so halving the
resistance F–G will dependably halve the interfering voltage. There are
limits to how far you can take this – while a simple balanced input will give
40 dB of rejection at low cost, increasing the cross-sectional area of copper
in the ground of an audio cable by a factor of 100 times is not going to be
either easy or cheap. Figure 14.4 shows equipment with metal chassis
connected to the 0 V (this is quite acceptable for safety approvals – what
counts is the isolation between mains and everything else, not between
low-voltage circuitry and touchable metalwork); note the chassis connection, however, has no relevance to the basic effect, which would still occur
even if the equipment enclosure was completely non-conducting.
The magnitude of ground current varies with the details of transformer
construction, and increases as the size of the transformer grows. Therefore
the more power a unit draws, the larger the ground current it can sustain.
This is why many systems are subjectively hum-free until the connection of
Audio Power Amplifier Design Handbook
a powered subwoofer, which is likely to have a larger transformer than
other components of the system.
Equipment type
Turntable, CD, cassette deck
Tuners, amplifiers, small TVs
Big amplifiers, subwoofers, large TVs
20 W or less
20–100 W
More than 100 W
5 µA
100 uA
1 mA
Ground currents inside equipment
Once ground currents have been set flowing, they can degrade system
performance in two locations: outside the system units, by flowing in the
interconnect grounds, or inside the units, by flowing through internal PCB
tracks, etc. The first problem can be dealt with effectively by the use of
balanced inputs, but the internal effects of ground currents can be much
more severe if the equipment is poorly designed.
Figure 14.5 shows the situation. There is, for whatever reason, ground
current flowing through the ground conductor CD, causing an interfering
current to flow round the loop CFGD as before. Now, however, the
internal design of Unit 2 is such that the ground current flowing through
FG also flows through G–G’ before it encounters the ground wire going
to point D. G–G’ is almost certain to be a PCB track with higher
resistance than any of the cabling, and so the voltage drop across it can
be relatively large, and the hum performance correspondingly poor.
Exactly similar effects can occur at signal outputs; in this case the ground
current is flowing through F–F’.
Balanced inputs will have no effect on this; they can cancel out the voltage
drop along F–G, but if internal hum is introduced further down the internal
signal path, there is nothing they can do about it.
Figure 14.5
If ground current flows
through the path
F‘FGG’ then the
relatively high
resistance of the PCB
tracks produces
voltage drops between
the internal circuit
Grounding and practical matters
Figure 14.6
The correct method of
dealing with ground
currents; they are
diverted away from
internal circuitry
The correct method of handling this is shown in Figure 14.6. The
connection to mains ground is made right where the signal grounds leave
and enter the units, and are made as solidly as possible. The ground current
no longer flows through the internal circultry. It does, however, still flow
through the interconnection at FG, so either a balanced input or a groundcancelling output will be required to deal with this.
Balanced mains power
There has been speculation in recent times as to whether a balanced mains
supply is a good idea. This means that instead of live and neutral (230 V and
0 V) you have live and the other live (115 V–0–115 V) created by a centretapped transformer with the tap connected to Neutral. See Figure 14.7.
It has been suggested that balanced mains has miraculous effects on sound
quality, makes the sound stage ten dimensional, etc. This is obviously
nonsense. If a piece of gear is that fussy about its mains (and I don’t believe
any such gear exists) then dispose of it.
If there is severe RFI on the mains, an extra transformer in the path may tend
to filter it out. However, a proper mains RFI filter will almost certainly be
more effective – it is designed for the job, after all – and will definitely be
much cheaper.
Where you might gain a real benefit is in a Class II (i.e. double-insulated)
system with very feeble ground connections. Balanced mains would tend
Figure 14.7
Using a balanced
mains supply to cancel
ground currents
stemming from interwinding capacitance
in the mains
transformer. An
expensive solution
Audio Power Amplifier Design Handbook
to cancel out the ground currents caused by transformer capacitance (see
Figure 14.4 and above for more details on this) and so reduce hum. The
effectiveness of this will depend on C1 being equal to C2 in Figure 14.7,
which is determined by the details of transformer construction in the unit
being powered. I think that the effect would be small with well-designed
equipment and reasonably heavy ground conductors in interconnects.
Balanced audio connections are a much cheaper and better way of
handling this problem, but if none of the equipment has them then beefing
up the ground conductors should give an improvement. If the results are
not good enough then as a last resort, balanced mains may be worth
Finally, bear in mind that any transformer you add must be able to handle
the maximum power drawn by the audio system at full throttle. This can
mean a large and expensive component.
I wouldn’t be certain about the whole of Europe, but to the best of my
knowledge it’s the same as the UK, i.e. not balanced. The neutral line is at
earth potential, give or take a volt, and the live is 230 V above this. The
3-phase 11 kV distribution to substations is often described as ‘balanced’
but this just means that power delivered by each phase is kept as near equal
as possible for the most efficient use of the cables.
It has often occurred to me that balanced mains 115 V–0–115 V would be
a lot safer. Since I am one of those people that put their hands inside live
equipment a lot, I do have a kind of personal interest here.
Class I and Class II
Mains-powered equipment comes in two types: grounded and double
insulated. These are officially called Class I and Class II respectively.
Class I equipment has its external metalwork grounded. Safety against
electric shock is provided by limiting the current the live connection can
supply with a fuse. Therefore, if a fault causes a short-circuit between live
and metalwork, the fuse blows and the metalwork remains at ground
potential. A reasonably low resistance in the ground connection is essential
to guarantee the fuse blows. A three-core mains lead is mandatory. Twocore IEC mains leads are designed so they cannot be plugged into three-pin
Class I equipment. Class I mains transformers are tested to 1.5 kV rms.
Class II equipment is not grounded. Safety is maintained not by interrupting
the supply in case of a fault, but by preventing the fault happening in the
first place. Regulations require double insulation and a generally high
standard of construction to prevent any possible connection between live
and the chassis. A two-core IEC mains lead is mandatory; it is not permitted
to sell a three-core lead with a Class II product. This would present no
hazard in itself, but is presumably intended to prevent confusion as to what
Grounding and practical matters
kind of product is in use. Class II mains transformers are tested to 3 kV rms,
to give greater confidence against insulation breakdown.
Class II is often adopted in an attempt to avoid ground loops. Doing so
eliminates the possibility of major problems, at the expense of throwing
away all hope of fixing minor ones. There is no way to prevent capacitance
currents from the mains transformer flowing through the ground connections. (See section ‘Ground loops: how they work and how to deal with,
them’ on page 405). It is also no longer possible to put a grounded
electrostatic screen between the primary and secondary windings. This is
serious as it deprives you of your best weapon against mains noise coming
in and circuit RF emissions getting out. In Class II the external chassis may
be metallic, and connected to signal 0 V as often as you like.
If a Class II system is not connected to ground at any point, then the
capacitance between primaries and secondaries in the various mains
transformers can cause its potential to rise well above ground. If it is
touched by a grounded human, then current will flow, and this can
sometimes be perceptible, though not directly, as a painful shock like static
electricity. The usual complaint is that the front panel of equipment is
‘vibrating’, or that it feels ‘furry’. The maximum permitted touch current
(flowing to ground through the human body) permitted by current
regulations is 700 µA, but currents well below this are perceptible. It is
recommended, though not required, that this limit be halved in the tropics
where fingers are more likely to be damp. The current is measured through
a 50k resistance to ground.
When planning new equipment, remember that the larger the mains
transformer, the greater the capacitance between primary and secondary,
and the more likely this is to be a problem. To put the magnitudes into
perspective, I measured a 500 VA toroid (intended for Class II usage and
with no interwinding screen) and found 847 pF between the windings. At
50 Hz and 230 V this implies a maximum current of 63 µA flowing into the
signal circuitry, the actual figure depending on precisely how the windings
are arranged. A much larger 1500 VA toroidal transformer had 1.3 nF
between the windings, but this was meant for Class I use and had a screen,
which was left floating to get the figure above.
Please note that the legal requirements for electrical safety are always liable
to change. This book does not attempt to give a complete guide to what is
required for compliance. The information given here is correct at the time
of writing, but it is the designer’s responsibility to check for changes to
compliance requirements. The information is given here in good faith but
the author accepts no responsibility for loss or damage under any
Audio Power Amplifier Design Handbook
Mechanical layout and design considerations
The mechanical design adopted depends very much on the intended
market, and production and tooling resources, but I offer a few purely
technical points that need to be taken into account:
All power amplifiers will have a heatsink that needs cooling, usually by free
convection, and the mechanical design is often arranged around this
requirement. There are three main approaches to the problem:
(a) The heatsink is entirely internal, and relies on convected air entering
the bottom of the enclosure, and leaving near the top (passive
The heatsink may be connected to any voltage, and this may eliminate the
need for thermal washers between power device and sink. On the other
hand, some sort of conformal material is still needed between transistor and
heatsink. A thermal washer is much easier to handle than the traditional
white oxide-filled silicone compound, so you will be using them anyway.
There are no safety issues as to the heatsink temperatures.
This system is not suitable for large dissipations, due to the limited fin area
possible inside a normal-sized box, and the relatively restricted convection
(b) The heatsink is partly internal and partly external, as it forms one or
more sides of the enclosure. Advantages and disadvantages are much as
above; if any part of the heatsink can be touched then the restrictions on
temperature and voltage apply. Greater heat dissipation is possible.
(c) The heatsink is primarily internal, but is fan-cooled (active cooling).
Fans always create some noise, and this increases with the amount of
air they are asked to move. Fan noise is most unwelcome in a domestic
hi-fi environment, but is of little importance in PA applications.
This allows maximal heat dissipation, but requires an inlet filter to
prevent the build-up of dust and fluff internally. Persuading people to
regularly clean such filters is near-impossible.
Efficient passive heat removal requires extensive heatsinking with a free
convective air flow, and this indicates putting the sinks on the side of the
amplifier; the front will carry at least the mains switch and power indicator
light, while the back carries the in/out and mains connectors, so only the
sides are completely free.
Grounding and practical matters
The internal space in the enclosure will require some ventilation to prevent
heat build-up; slots or small holes are desirable to keep foreign bodies out.
Avoid openings on the top surface as these will allow the entry of spilled
liquids, and increase dust entry. BS415 is a good starting point for this sort
of safety consideration, and this specifies that slots should be no more than
3 mm wide.
Reservoir electrolytics, unlike most capacitors, suffer significant internal
heating due to ripple current. Electrolytic capacitor life is very sensitive to
temperature, so mount them in the coolest position available, and if
possible leave room for air to circulate between them to minimise the
temperature rise.
Convection cooling
It is important to realise that the buoyancy forces that drive natural
convection are very small, and even small obstructions to flow can
seriously reduce the rate of flow, and hence the cooling. If ventilation is by
slots in the top and bottom of an amplifier case, then the air must be drawn
under the unit, and then execute a sharp right-angle turn to go up through
the bottom slots. This change of direction is a major impediment to air flow,
and if you are planning to lose a lot of heat then it feeds into the design of
something so humble as the feet the unit stands on; the higher the better, for
air flow. In one instance the amplifier feet were made 13 mm taller and all
the internal amplifier temperatures dropped by 5°C. Standing such a unit
on a thick-pile carpet can be a really bad idea, but someone is bound to do
it (and then drop their coat on top of it); hence the need for overtemperature
cutouts if amplifiers are to be fully protected.
Mains transformers
A toroidal transformer is useful because of its low external field. It must
be mounted so that it can be rotated to minimise the effect of what stray
fields it does emit. Most suitable toroids have single-strand secondary
lead-outs, which are too stiff to allow rotation; these can be cut short and
connected to suitably-large flexible wire such as 32/02, with carefully
sleeved and insulated joints. One prototype amplifier I have built had a
sizeable toroid mounted immediately adjacent to the TO3 end of the
amplifier PCB; however complete cancellation of magnetic hum (hum
and ripple output level below –90 dBu) was possible on rotation of the
A more difficult problem is magnetic radiation caused by the reservoir
charging pulses (as opposed to the ordinary magnetisation of the core,
which would be essentially the same if the load current was sinusoidal)
which can be picked up by either the output connections or cabling to the
Audio Power Amplifier Design Handbook
power transistors if these are mounted off-board. For this reason the
transformer should be kept physically as far away as possible from even the
high-current section of the amplifier PCB.
As usual with toroids, ensure the bolt through the middle cannot form a
shorted turn by contacting the chassis in two places.
Wiring layout
There are several important points about the wiring for any power
Keep the + and – HT supply wires to the amplifiers close together. This
minimises the generation of distorted magnetic fields which may
otherwise couple into the signal wiring and degrade linearity. Sometimes
it seems more effective to include the 0 V line in this cable run; if so it
should be tightly braided to keep the wires in close proximity. For the
same reason, if the power transistors are mounted off the PCB, the
cabling to each device should be configured to minimise loop
The rectifier connections should go direct to the reservoir capacitor
terminals, and then away again to the amplifiers. Common impedance
in these connections superimposes charging pulses on the rail ripple
waveform, which may degrade amplifier PSRR.
Do not use the actual connection between the two reservoir capacitors
as any form of star point. It carries heavy capacitor-charging pulses that
generate a significant voltage drop even if thick wire is used. As Figure
14.1 shows, the star-point is tee-ed off from this connection. This is a
star-point only insofar as the amplifier ground connections split off from
here, so do not connect the input grounds to it, as distortion performance
will suffer.
Semiconductor installation
Driver transistor installation. These are usually mounted onto separate
heatsinks that are light enough to be soldered into the PCB without
further fixing. Silicone thermal washers ensure good thermal contact,
and spring clips are used to hold the package firmly against the sink.
Electrical isolation between device and heatsink is not normally
essential, as the PCB need not make any connection to the heatsink
fixing pads.
TO3P power transistor installation. These large flat plastic devices are
usually mounted on to the main heatsink with spring clips, which are not
only are rapid to install, but also generate less mechanical stress in the
package than bolting the device down by its mounting hole. They also
give a more uniform pressure onto the thermal washer material.
Grounding and practical matters
TO3 power transistor installation. The TO3 package is extremely
efficient at heat transfer, but notably more awkward to mount.
My preference is for TO3s to be mounted on an aluminium thermal-coupler
which is bolted against the component side of the PCB. The TO3 pins may
then be soldered directly on the PCB solder side. The thermal-coupler is
drilled with suitable holes to allow M3.5 fixing bolts to pass through the
TO3 flange holes, through the flange, and then be secured on the other side
of the PCB by nuts and crinkle washers which will ensure good contact
with the PCB mounting pads. For reliability the crinkle washers must cut
through the solder-tinning into the underlying copper; a solder contact
alone will creep under pressure and the contact force decay over time.
Insulating sleeves are essential around the fixing bolts where they pass
through the thermal-coupler; nylon is a good material for these as it has a
good high-temperature capability. Depending on the size of the holes
drilled in the thermal-coupler for the two TO3 package pins (and this
should be as small as practicable to maximise the area for heat transfer),
these are also likely to require insulation; silicone rubber sleeving carefully
cut to length is very suitable.
An insulating thermal washer must be used between TO3 and flange; these
tend to be delicate and the bolts must not be over-tightened. If you have a
torque-wrench, then 10 Newton/metre is an approximate upper limit for
M3.5 fixing bolts. Do not solder the two transistor pins to the PCB until the
TO3 is firmly and correctly mounted, fully bolted down, and checked for
electrical isolation from the heatsink. Soldering these pins and then
tightening the fixing bolts is likely to force the pads from the PCB. If this
should happen then it is quite in order to repair the relevant track or pad
with a small length of stranded wire to the pin; 7/02 size is suitable for a
very short run.
Alternatively, TO3s can be mounted off-PCB (e.g. if you already have a
large heatsink with TO3 drillings) with wires taken from the TO3 pads on
the PCB to the remote devices. These wires should be fastened together
(two bunches of three is fine) to prevent loop formation; see above. I cannot
give a maximum safe length for such cabling, but certainly 8 inches causes
no HF stability problems is my experience. The emitter and collector wires
should be substantial, e.g. 32/02, but the base connections can be as thin
as 7/02.
Testing and safety
Testing and fault-finding
Testing power amplifiers for correct operation is relatively easy; faultfinding
them when something is wrong is not. I have been professionally engaged
with power amplifiers for a long time, and I must admit I still sometimes
find it to be a difficult and frustrating business.
There are several reasons for this. Firstly, almost all small-signal audio
stages are IC-based, so the only part of the circuit likely to fail can be swiftly
replaced, so long as the IC is socketed. A power amplifier is the only place
where you are likely to encounter a large number of components all in one
big negative feedback loop. The failure of any components may (if you are
lucky) simply jam the amplifier output hard against one of the rails, or (if
you’re not) cause simultaneous failure of all the output devices, possibly
with a domino-theory trail of destruction winding through the small-signal
section. A certain make of high-power amplifier in the mid-70s was a
notorious example of the domino-effect, and when it failed (which was
often) the standard procedure was to replace all of the semiconductors,
back to and including the bridge rectifier. Component numbers here refer
to Figure 6.13.
By far the most important step to successful operation is a careful visual
inspection before switch-on. As in all power amplifier designs, a wronglyinstalled component may easily cause the immediate failure of several
others, making fault-finding difficult, and the whole experience generally
less than satisfactory. It is therefore most advisable to meticulously
Testing and safety
That the supply and ground wiring is correct.
That all transistors are installed in the correct positions.
That the drivers and TO3 output devices are not shorted to their
respective heatsinks through faulty insulating washers.
That the circuitry around the bias generator TR13 in particular is
correctly built. An error here that leaves TR13 turned off will cause large
currents to flow through the output devices and may damage them
before the rail fuses can act.
For the Trimodal amplifier in Chapter 9, I recommend that the initial testing
is done in Class-B mode. There is the minimum amount of circuitry to
debug (the Class-A current-controller can be left disconnected, or not built
at all until later) and at the same time the Class-B bias generator can be
checked for its operation as a safety-circuit on Class-A/AB mode.
The second stage is to obtain a good sinewave output with no load
connected. A fault may cause the output to sit hard up against either
rail; this should not in itself cause any damage to components. Since a
power-amp consists of one big feedback loop, localising a problem can
be difficult. The best approach is to take a copy of the circuit diagram
and mark on it the DC voltage present at every major point. It should
then be straightforward to find the place where two voltages fail to
agree; e.g. a transistor installed backwards usually turns fully on, so the
feedback loop will try to correct the output voltage by removing all
drive from the base. The clash between full-on and no base-drive signals
the error.
When checking voltages in circuit, bear in mind that C2 is protected against
reverse voltage in both directions by diodes which will conduct if the
amplifier saturates in either direction.
This DC-based approach can fail if the amplifier is subject to highfrequency oscillation, as this tends to cause apparently anomalous DC
voltages. In this situation the use of an oscilloscope is really essential. An
expensive oscilloscope is not necessary; a digital scope is at a disadvantage
here, because HF oscillation is likely to be aliased into nonsense and be
hard to interpret.
The third step is to obtain a good sinewave into a suitable high-wattage
load resistor. It is possible for faults to become evident under load that
are not shown up in Step 2 above.
Setting the quiescent conditions for any Class-B amplifier can only be
done accurately by using a distortion analyser. If you do not have access
to one, the best compromise is to set the quiescent voltage-drop across
both emitter resistors (R16, 17) to 10 mV when the amplifier is at
working temperature; disconnect the output load to prevent DC offsets
causing misleading current flow. This should be close to the correct
value, and the inherent distortion of this design is so low that minor
Audio Power Amplifier Design Handbook
deviations are not likely to be very significant. This implies a quiescent
current of approx. 50 mA.
It may simplify faultfinding if D7, D8 are not installed until the basic
amplifier is working correctly, as errors in the SOAR protection cannot then
confuse the issue. This demands some care in testing, as there is then no
short-circuit protection.
The overall safety record of audio equipment is very good, but no cause for
complacency. The price of safety, like that of liberty, is eternal vigilance.
Safety regulations are not in general hard to meet so long as they are taken
into account at the start of the mechanical design phase. This section
considers not only the safety of the user, but also of the service
Many low-powered amplifier designs are inherently safe because all the
DC voltages are too low to present any kind of electric-shock hazard.
However, high-powered models will have correspondingly high supplyrails which are a hazard in themselves, as a DC shock is normally
considered more dangerous than the equivalent AC voltage.
Unless the equipment is double-insulated, an essential safety requirement
is a solid connection between mains ground and chassis, to ensure that the
mains fuse blows if Live contacts the metalwork. British Standards on safety
require the mains earth to chassis connection to be a Protected Earth,
clearly labelled and with its own separate fixing. A typical implementation
has a welded ground stud onto which the mains-earth ring-terminal is held
by a nut and locking washer; all other internal grounds are installed on top
of this and secured with a second nut/washer combination. This discourages service personnel from removing the chassis ground in the
unlikely event of other grounds requiring disconnection for servicing. A
label warning against lifting the ground should be clearly displayed.
There are some specific points that should be considered:
1 An amplifier may have supply-rails of relatively low voltage, but the
reservoir capacitors will still store a significant amount of energy. If they
are shorted out by a metal finger-ring then a nasty burn is likely. If your
bodily adornment is metallic then it should be removed before diving
into an amplifier.
2 Any amplifier containing a mains power supply is potentially lethal. The
risks involved in working for some time on the powered-up chassis must
be considered. The metal chassis must be securely earthed to prevent it
becoming live if a mains connection falls off, but this presents the snag
that if one of your hands touches live, there is a good chance that the
other is leaning on chassis ground, so your well-insulated training shoes
Testing and safety
will not save you. All mains connections (neutral as well as live, in case
of mis-wired mains) must therefore be properly insulated so they cannot
be accidentally touched by finger or screwdriver. My own preference is
for double insulation; for example, the mains inlet connector not only
has its terminals sleeved, but there is also an overall plastic boot fitted
over the rear of the connector, and secured with a tie-wrap.
Note that this is a more severe requirement than BS415 which only requires
that mains should be inaccessible until you remove the cover. This assumes
a tool is required to remove the cover, rather than it being instantly
removable. In this context a coin counts as a tool if it is used to undo giant
3 A Class-A amplifier runs hot and the heatsinks may well rise above 70°C.
This is not likely to cause serious burns, but it is painful to touch. You
might consider this point when arranging the mechanical design. Safety
standards on permissible temperature rise of external parts will be the
dominant factor.
4 Note the comments on slots and louvres in the section on Mechanical
Design above.
5 Readers of hi-fi magazines are frequently advised to leave amplifiers
permanently powered for optimal performance. Unless your equipment
is afflicted with truly doubtful control over its own internal workings, this
is quite unnecessary. (And if it is so afflicted, personally I’d turn it off
now.) While there should be no real safety risk in leaving a soundlyconstructed power amplifier powered permanently, I see no point and
some potential risk in leaving unattended equipment powered; in ClassA mode there may of course be an impact on your electricity bill.
Absolute phase, 26–7
AC coupling, 41–2
Acronyms, listing, 27–8
Active load techniques, 95
Adaptive trimodal amplifier, 288
Ambient temperature changes,
accommodating, 360
three-stage, 31–2
two-stage, 32–3
Audio chain, effects of length, 18
Auxiliary circuitry, powering, 394
Baxandall cancellation technique, 17,
18, 111
Belcher intermodulation test, 10–11,
Beta-droop, 127
Bias errors, assessing, 332
Bias generator, 177
Bipolar junction transistors (BJTs):
failure modes, 371
in output stages, 123 and following
overheating, 372
Blameless amplifiers, 71
Blomley principle, 39–40
Blondlot, Rene, 8
Bode’s Second Law, 12
Bootstrapping, 96
Boucherot cell see Zobel network
Bridge rectifiers, 240
RF emissions, 241
Cable selection, loudspeaker, 202
Capacitor distortion, 13, 57, 177
Cascode compensation, 248
Catching diodes, for overload
protection, 383
Clamp diodes, see Catching diodes
Class-A amplifiers, 33–4, 107
A/AB mode, 271
Class B mode, 281
configurations, 257
constant-current, 256
design example, 279
disadvantages, 256
efficiency, 256, 272
load impedance, 272
mode-switching system, 281
operating mode, 272
output stages, 257
performance, 286
power supply, 286
quiescent current control, 263, 280
thermal design, 283
trimodal, 267, 283
Class-AB amplifiers, 34–5, 143
geometric mean, 40–41
Class-B amplifiers, 33, 35, 106, 176
50W design example, 176
efficiency, 256
variations, 38–9
Class-C amplifiers, 35, 291
Class-D amplifiers, 35
Class-E amplifiers, 35
Class-G amplifiers, 36–7
shunt, 37–8
Class-H amplifiers, 38
Class-S amplifiers, 38
Collector-load bootstrapping, 96
Common-mode distortion, 57–8
Common-mode rejection ratio, 61
Compensation, 184
dominant pole, 184
lag, 185
two-pole, 188, 312
Complementary feedback pair (CFP)
output, 114
large signal non-linearity, 115
thermal modelling, 342
Complementary output stages, 30–31
Contact degradation, 14
Cross-quad configuration, 76
Crossover distortion, 107
experiment, 145
harmonic generation, 109
Crosstalk, 397
interchannel, 10
Crowbar, protection system, 391
Current compensation, 362
Current limiting, for overload
protection, 374
Current timing factor, 221
Current-driven amplifiers, 39
Current-mirrors, 81
Damping factor, 25–6, 190
Darlington configuration, 104, 291
DC output offset, 89
DC-coupled amplifiers, 41, 42–4
DC-offset protection, 322, 336
by fuses, 385
by output crowbar, 391
relays, 386
Degradation effects, 7
Distortion, 24
capacitor see Capacitor distortion
in complete amplifiers, 158
induction see Induction distortion
mechanism types, 63
NFB takeoff point, 170
output stages, 56–7, 123
rail decoupling, 167
rail induction see Rail induction
distortion, 168
switching, 153
thermal see Thermal distortion
Type, 3a see Large signal nonlinearity, 123
Type, 3b see Crossover distortion
VAS loading, 163
Dominant pole compensation, 184
Dominant pole frequency, 62
Doubled output devices, 128
Dual-slope VI limiting, for overload
protection, 381
Early Effect, 367
Economic importance, 1–5
Emitter resister value, 135–8
Emitter-follower (EF) output, 113
large signal non-linearity, 123
modelling, 327
thermal compensation, 326
Error criterion, 344
Error-correcting amplifiers, 39
Failure modes, semiconductor, 371
Fault-finding, 419
Feedforward diodes, 131
Field effect transistor (FET) output
advantages, 314
amplifier failure modes, 203
characteristics, 318
in Class-A stages, 321
disadvantages, 316
hybrid, 318
hybrid full-complementary, 319
linearity comparison, 321
simple source-follower configuration,
Frequency compensation, 184
Frequency response capability, 23–4
for DC protection, 385
as overload protection, 373
sizing, 240
thermal, 394
Gain margin, 49
Generic principles, 52–4
advantages of convention, 54–5
distortions, 55–8
gm-doubling, 107
Grounding system, 402
Group delay, 10
Hafler straight-wire differential test, 18
Half-amplifiers, 344
Harmonic-mean AB operation, 41
Hearing limits, 9–12
designs, 414
for rectifier, 241
temperature sensing, 393
HF gain, 54
Hiraga, Jean, 9
Historical development, amplifiers, 30
Improvement factor, 45
Induction distortion, 57, 168
Input stage, 65
balance, 79
BJT/FET selection, 76
cascode configurations, 85
differential pair, 76
distortion, 64, 74–8
improving linearity, 82
noise reduction, 85
singleton, 76
slew-rate, 90
Instability, 222
HF, 222
LF, 223
Insulated-gate bipolar transistors
(IGBTs), 316
Integrated absolute error (IAE), 344
Integrated square error (ISE), 344
Johnson noise, 86
Junction-temperature estimator
subsystem, 350
with dynamics, 352
Lag compensation, 185
Large-signal non-linearity (LSN), 123
better output devices, 129
distortion, 127
doubled-output devices, 128
feed-forward diodes, 131
low loads, 132
mechanism, 127
output triples, 136
sustained beta devices, 129
Load-invariant design, 133
cable inductance, 13–14
cable selection, 202
enhanced currents, 220
loading modelling, 210
single-speaker load, 214
two-way speaker loads, 218
Mains transformers, 239
Messenger, Paul, 9
Microphony, 16
Miller capacitor compensation, 63
Miller dominant pole creation, 184
Misinformation, technical, 5–6, 21
Mode-switching system, Class-A
amplifiers, 281
Model amplifiers, 70
Monobloc construction, 15
Motorboating see Instability, LF
Muting control, 386
N-rays, 8
Negative feedback (NFB), 15, 44–6
factor maximising, 57
maximising linearity, 57
misconceptions, 46–8
takeoff distortion, 65, 170
Nested feedback, 187
Nesting differentiating feedback loops,
performance, 24
reduction, 24, 85
Non-switching amplifiers, 39
bandwidth, 101
gain measurement, 68
linearity, 67
Output networks, 190
Output stages, 106
alternative configurations, 103
CFP see Complementary feedback
pair (CFP) stages, 114
comparisons, 111
distortion, 123 and on
doubled, 128
emitter-folllower, 112
FET see Field effect transistor (FET)
output stages, 314
gm-doubling, 107
impedance, 192
improved, 296
low loads, 132
quasi-complementary, 119
quiescent conditions, 325
triple, 116, 136
use of inductors, 195
Overload protection, 372
by current limiting, 377
by dual-slope VI limiting, 381
by fuses, 373
by power supply shutdown, 340–41
by single-slope VI limiting, 38
catching diodes, 383
DC-offset, 384
electronic, 374
of output by thermal devices, 392
system simulation, 375
Parapsychology, 8
Performance requirements, 22–7
Phase delay, 10
Phase margin, 49
Phase shift, 15
Pole-splitting, 63
Power output capability, 22–3
Power supplies, 235
design, 15
design principles, 238
linear regulated, 236
mains transformers, 239
shutdown for overload protection,
simple unregulated, 235
switch-mode, 237
Power supply rejection ratio (PSRR),
Power supply-rail rejection, 241
design, 244
negative, 247
positive, 245
PCB and mechanical layout, 399
cooling requirements, 414
crosstalk, 397
grounding system, 404
layout details, 400
layout sequence, 403
mains transformers, 400
output device mounting, 398
plated-through-hole type, 399
power supply, 399
rail induction distortion, 398
semiconductor installation, 357–8
single/double-sided, 399
wiring layout, 416
DC-offset, 384
overload see Overload protection
plotting locus, 376
thermal, 393
Psychoacoustical research, 7, 9–12
Push-pull action, 256, 259
Quad 405, 39
Quasi-complementary output, 119
Quiescent conditions, 152, 325
Quiescent current, 146
Class-A amplifiers, 263
Quiescent voltage, 152, 235
Rail decoupling distortion, 65, 165
Rail induction distortion, 347
Rectifiers, 240
Regulated power supplies, 236
Relay protection:
against DC offsets, 386
for system muting, 388
Reliability, 22
Reservoir ground, 404
Resistive loads, 209
Ripple, 242
Safe operating area (SOA), 266, 323,
Safety requirements, 22, 420
Schottky diodes, 131, 298
failure modes, 371
installation, 416
Sensor position, 349
Sine wave signals, 13
Single-slope VI limiting, for overload
protection, 380
Slew rates, 48, 224
complications, 232
improving, 228
limiting, 225
measurement, 227
real-life limitations, 230
simulating, 228
Sound pressure level (SPL), 23
Speed see Slew rates
Standard amplifier performance, 71
Subjectivism, 6–9, 12–18
Switching distortion, 153
Switch-mode power supplies, 237
Sziklai pairs see Complementary
feedback pairs, 114
Temperature changes, ambient, 360
Temperature coefficient (tempco), 357
creating higher, 359
creating lower, 357
Temperature sensors, 393
Testing procedures, 418
Thermal behaviour:
basic compensation, 331
compensation accuracy, 332
EF stage compensation, 340
feedback/feedforward, 331
runaway, 30
sensor location, 349
simulation, 332
Thermal capacity, 333
Thermal cycling (failure mode), 372
Thermal distortion, 58, 66, 155
Thermal protection, 392
Thermal switch, 393
Tone-controls, 15
Total harmonic distortion (THD), 24–5
tests, 10
Transconductance, 78 et seq
Transformers, 220–21, 400
Translinear loop, 40–41
Trimodal amplifier, 269
biasing system, 280
Triple-based output, 116, 136
Two-pole compensation, 188, 312
Valve sound, 14
Variable-tempco bias generators, 357
Vbe multiplier, see Bias generator
Voltage amplifier stage (VAS), 31, 91
active load techniques, 95
balanced, 100
buffering, 99
distortion, 92, 95
enhancements, 97
linearising, 95
loading distortion, 99, 163
operation, 93
Wolf fence approach, supply-rail
rejection, 247
Zobel network, 194
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