The Microflown - Universiteit Twente

The Microflown - Universiteit Twente
The Microflown
Hans-Elias de Bree
Second Edition
The Research described in this thesis has been possible due to the support of:
Micro Mechanics group of the University of Twente, Van den Hul B.V., The Dutch
Technology Foundation (STW) and ing. M.J.M. van de Wolfshaar.
De promotiecommissie:
Voorzitter:
Prof. dr. ir. J. van Amerongen
Universiteit Twente
Secretaris:
Prof. dr. ir. J. van Amerongen
Universiteit Twente
Promotor:
Prof. dr. M.C. Elwenspoek
Universiteit Twente
Leden:
Prof. dr. J. Sennheiser
Universität Hannover
Prof. dr. ir. H. Tijdeman
Universiteit Twente (WB)
Prof. dr. ir. P. Bergveld
Universiteit Twente (EL)
Prof. dr. ir. P.P.L. Regtien
Universiteit Twente (EL)
Cover:
Various symbols and pictures which have the personal interest of the writer.
Cover Design:
WELMOED SCHMIDT & mArt in dEsign
Layout:
mArt in dEsign
ISBN 9036509262
Copyright  by Hans-Elias de Bree, Enschede, The Netherlands.
All rights reserved. No part of this publication may be reproduced, stored in retrieval system, or
transmitted in any form or by any means - electronic, mechanical, photocopying or otherwise, without
prior written permission of the copyright owner.
SUMMARY
SAMENVATTING
CHAPTER 1: INTRODUCTION
1.1 GENERAL INTRODUCTION ....................................................................................... 1
1.2 MICROPHONES AND MICRO-MECHANICS ...................................................................... 6
1.3 OUTLINE OF THE THESIS ......................................................................................... 8
REFERENCES ......................................................................................................... 10
CHAPTER 2: ACOUSTICS
SUMMARY ............................................................................................................
2.1 INTRODUCTION .................................................................................................
2.2 AN INTRODUCTION TO ACOUSTICS ...........................................................................
Definitions .......................................................................................................
The one dimensional wave equation .........................................................................
Some specific acoustic impedances ..........................................................................
2.3 HOW TO CALIBRATE THE µ-FLOWN ..........................................................................
The 'infinite' tube ..............................................................................................
The acoustical short-cut .......................................................................................
The acoustical displacement setup ...........................................................................
The flow step setup ............................................................................................
The standing wave tube .......................................................................................
The silence setup ...............................................................................................
2.4 PRESENT-DAY ACOUSTIC MEASUREMENTS ..................................................................
Measuring sound intensity ....................................................................................
Measuring the acoustic impedance of a horn loudspeaker ...............................................
CONCLUSIONS AND DISCUSSION ...................................................................................
REFERENCES .........................................................................................................
13
14
15
15
18
20
23
24
26
27
28
29
29
30
30
33
36
37
CHAPTER 3: ELECTRONICS
SUMMARY ............................................................................................................
3.1 INTRODUCTION .................................................................................................
3.2 MEASURING OHMIC IMPEDANCES ............................................................................
3.3 THE WHEATSTONE BRIDGE ....................................................................................
3.4 THE GADGET ....................................................................................................
The Basic Gadget ...............................................................................................
The Transfer function of The Basic Gadget ................................................................
Linearity of The Basic Gadget ...............................................................................
Signal to noise ratio of The Basic Gadget ..................................................................
Implementations of The Gadget ..............................................................................
3.5 OTHER PRACTICAL CIRCUITS ..................................................................................
CONCLUSIONS AND DISCUSSION ...................................................................................
REFERENCES .........................................................................................................
39
40
42
44
45
45
45
48
50
53
57
60
61
CHAPTER 4: THE µ-FLOWN
SUMMARY. ............................................................................................................
4.1 INTRODUCTION...................................................................................................
4.2 A QUALITATIVE MODEL OF THE MICROFLOWN. .............................................................
The Hot Wire Anemometer (HWA). .........................................................................
The Mass Flow Sensor (MFS).................................................................................
The sensor part...................................................................................................
The Two Sensor Microflown (TSM). ........................................................................
Model of the sensitivity of the TSM. .........................................................................
4.3 MEASUREMENTS.................................................................................................
Calibration measurements. .....................................................................................
The Burn In procedure..........................................................................................
The temperature coefficient of resistivity. ...................................................................
The Power Curve. ...............................................................................................
The corner frequency. ..........................................................................................
The Sensitivity Curve. ..........................................................................................
The noise measurement. ........................................................................................
The signal to noise ratio. .......................................................................................
CONCLUSIONS AND DISCUSSION. ...................................................................................
REFERENCES. .........................................................................................................
63
64
65
66
70
71
72
73
76
78
79
80
82
83
83
84
85
87
88
CHAPTER 5: REALISATION
SUMMARY ............................................................................................................. 91
5.1 INTRODUCTION .................................................................................................. 92
5.2 WHAT PARAMETERS ARE IMPORTANT? ...................................................................... 92
µ-flown model aspects ......................................................................................... 92
Electrical aspects ................................................................................................ 93
Constructional aspects .......................................................................................... 94
Cost aspects ...................................................................................................... 95
Other production process considerations .................................................................... 95
5.3 THE FABRICATION PROCESSES ................................................................................. 96
The Bridges (type I process) .................................................................................. 96
The Cantilevers (type II process) ............................................................................. 98
The single metal process (type III process) ............................................................... 101
The One Mask Process (type IV process) ................................................................. 103
Summary of processes ....................................................................................... 106
The process steps ............................................................................................. 107
5.5 SEPARATION OF DICES ........................................................................................ 110
CONCLUSIONS AND DISCUSSION ................................................................................. 111
REFERENCES ........................................................................................................ 112
CHAPTER 6: APPLICATIONS
SUMMARY ...........................................................................................................
6.1 INTRODUCTION ................................................................................................
6.2 PROPERTIES OF THE µ-FLOWN ...............................................................................
Acoustic properties ...........................................................................................
Properties of conventional microphones ...................................................................
Acoustic properties of the microflown .....................................................................
Other featuring properties of the microflown .............................................................
6.3 APPLICATIONS USING THE µ-FLOWN .......................................................................
A telecommunication microphone ..........................................................................
A base drum microphone ....................................................................................
Stereo ‘in one point’ microphone ...........................................................................
An acoustic intensity probe ..................................................................................
CONCLUSIONS AND DISCUSSION .................................................................................
REFERENCES ........................................................................................................
115
116
116
116
119
121
124
128
128
130
130
132
141
142
CHAPTER 7: GENERAL CONCLUSIONS
APPENDIX 1: LIST OF SYMBOLS
APPENDIX 2: INTRODUCTION IN TRANSISTOR MODELS
APPENDIX 3: NOISE CALCULATIONS
Introduction in noise theory ..................................................................................
BJT noise generators ..........................................................................................
Noise of the BJT in Forward Biased Diode configuration ..............................................
Noise of the BJT in a Common Emitter configuration ..................................................
Noise of the BJT in an Emitter Coupled Pair configuration ............................................
Signal to Noise ratio of the Wheatstone Bridge ...........................................................
Noise of The Gadget ..........................................................................................
REFERENCES ........................................................................................................
APPENDIX 4: MICROPHONES, A COMPARISON BASED ON NOISE
APPENDIX 5: PICTURES OF PROBES
APPENDIX 6: ELECTRONIC CIRCUIT
LEVENSLOOP
DANKWOORD
159
161
162
163
165
166
168
170
SUMMARY
This thesis deals with a novel acoustic sensor, the microflown. This micromachined sensor is capable of measuring the particle velocity directly. When both
particle velocity and acoustic pressure variations are known an acoustic phenomena
can be fully described. The microflown is a microphone which consists of two
temperature sensors and a heater. The particle velocity alters the temperature
distribution and thus the temperature of both the sensors. The temperature difference
of both sensors is proportional with the particle velocity.
The various aspects to understand the microflown are divided into six chapters.
The first chapter is a general introduction. In this chapter some other micro machined
acoustic sensors are described.
To understand how particle velocity and acoustic pressure variations are
related in chapter two an introduction into acoustics is given. Methods to calibrate the
microflown are also treated in this chapter.
The microflown consists of two resistive temperature sensors. When the
temperature alters, the resistance of the sensors will alter. The differential resistance
variation of the sensors has to be measured. In chapter three the electronic circuits
which are capable of measuring this quantity are treated. Signal to noise and linearity
are the main issues in this chapter.
In chapter four a model of the acoustic behaviour of the microflown is
presented. Furthermore a set of measurements which fully document the acoustic
behaviour is introduced. These measurements will result in two quality figures: the
performance and the corner frequency.
Chapter five deals with the realisation of the microflown. Four methods of
manufacturing are presented.
Chapter six focuses on the applications of the microflown. Since it is a new type
of microphone there are many new features awaiting to be exploited. The sound
intensity probe is the main application for this moment.
SAMENVATTING
In dit proefschrift wordt de microflown, een nieuw soort akoestische sensor
beschreven. Deze micro-mechanische sensor is in staat om de particle velocity
(akoestische deeltjessnelheid) direct te meten. Als zowel de akoestische drukvariaties
alsmede de particle velocity bekend is, is een akoestisch fenomeen in het algemeen
volledig te beschrijven. De microflown is een microfoon die bestaat uit twee
temperatuursensoren en een verwarmingselement. De particle velocity verandert de
warmteverdeling
en
dus
ook
de
temperatuur
van
beide
sensoren.
Het
temperatuurverschil tussen beide sensoren is evenredig met de aangelegde particle
velocity.
Om inzicht te krijgen in de microflown worden er verschillende onderwerpen
behandeld. Deze onderwerpen worden behandeld in zes hoofdstukken. Hoofdstuk één
is een algemene inleiding waarin ook andere akoestische micro-mechanische sensoren
beschreven worden.
In hoofdstuk twee wordt een introductie in de akoestiek gegeven om ondermeer
inzicht te krijgen in de relatie tussen akoestische drukvariaties en particle velocity.
Verder worden er verschillende methoden aangereikt om de microflown te kalibreren.
De microflown bestaat uit twee ohmse temperatuursensoren. Als de temperatuur
verandert, verandert ook de weerstandwaarde. De verschilwaarde in weerstand van de
beide sensoren dient gemeten te worden. In hoofdstuk drie worden electrische
schakelingen behandeld die de ohmse verschil waarde omzetten in een stroom of
spanning. Signaal ruis verhouding en lineariteit zijn belangrijke begrippen in dit
hoofdstuk.
In hoofdstuk vier wordt een model voor het akoestische gedrag van de
microflown gepresenteerd. Verder wordt er een serie metingen gegeven welke
volledig de akoestische eigenschappen van de microflown beschrijft. Deze metingen
resulteren in twee kwaliteits-kentallen: de performance (de prestatie) en de kantel
frequentie.
Hoofdstuk vijf behandelt de realisatie van de microflown. Vier methoden om
haar te maken worden gepresenteerd.
Hoofdstuk zes richt zich op de applicaties met gebruikmaking van de
microflown. De geluid intensiteit opnemer is op dit moment een van de belangrijkste
applicaties.
General introduction
CHAPTER 1: INTRODUCTION
1.1 G ENERAL
INTRODUCTION
As probably most inventions the subject of this thesis is discovered by accident.
It was clear that flow sensors where very sensitive transducers and the idea popped
up: “shouldn’t it possible to use such a sensor as a microphone”. A flow sensor was
connected to an amplifier and a loudspeaker and it appeared that it was possible to use
the flow sensor as a microphone. A very bad one but still, it functioned.
1
I Introduction
The subject of this thesis is a very small particle velocity sensitive microphone
made with micro-machining technologies. Particle velocity is the other component of
an acoustical wave besides acoustic pressure variations. The operating principle of this
sensor is different from normal microphones. In general pressure microphones detect
the deflection caused by a force due to a pressure difference. The sensor described in
this work, the microflown, measures a temperature difference caused by a thermal
unbalance due to the present particle velocity. The word “microflown” is a
combination of the words “micro” and “flow” while particle velocity is also called
acoustical flow and the sensor can be used as a small microphone.
The goals of the research were to get an understanding of the working principles
of the microflown, to improve the properties of the microflown and to investigate if
the microflown has got a chance to be an economical success.
A lot of aspects have to be considered to get an understanding of the above
formulated goals and, as a matter of fact, all aspects have to be carried out at almost
the same time preferably. This has two reasons, when working on one aspect one can
learn about another aspect and if all subjects were carried out successively the project
would take years to get the first good results. There is only a limited time since, for
instance, patent costs are increasing dramatically after two and a half years [1.17].
For an international patent in the first period only national appliance costs have to be
paid. After this period for all the countries of choice the patent appliance costs have to
be paid.
More than twenty students have worked on the microflown project together with
several scientific, legal and financial advisors. In the research period (of two years)
nobody was legally responsible, the people who were working on the microflown
together have been called The Microflown Team.
The acoustic performance of the microflown has been improved more than a
factor hundred during this research (both the corner frequency and the sensitivity
increased over a factor ten, see chapter 4). To make it a high performance
microphone it has to be improved by another factor hundred. To reach such goals a
lot of work has to be done, however the microflown has some special properties, it
has already been used in several applications.
Other improvements in the last two years are for example that the production
process has been simplified. To manufacture the first microflowns three masks and
2
General introduction
two metals were used and the yield was not very high. Now the microflown can be
made by using a single metal, one mask and high yield process (chapter 5).
As mentioned a lot of aspects are of interest, the areas that have been
investigated are depicted in Fig. 1.1.
Fig. 1.1: Pictogram of The Microflown Team activities.
The fundamental section is the part in where questions about the behaviour of
the microflown are formalised. To get an answer on questions as “what is the transfer
function?” or “has it got a linear behaviour?”, measurement set-ups have to be
developed and for that acoustic theory has to be understood. The acoustic theory and
measurement set-ups will be treated in chapter 2, the research results in chapter 4.
Also an important aspect of this research area are the tricky questions like “our
microphone has a sensitivity of two milli-Volt per Pascal, what is the sensitivity of the
microflown?”. What is tricky about this question and what the answer is can be found
in chapter 6: Applications.
The electronics part deals with the question what is the best possible
measurement result and what type of circuit can reach these specifications. Therefore
noise and “signal to noise ratio” are the key concepts in chapter 3.
In the technology part of the investigation the best way to construct a
microflown is the central question. Quality of manufacturing processes concerns the
robustness, yield, easy processing and acoustical performance. The microflown has to
be robust to survive “normal” use. The easy processing is important while for an easy
process in general the yield will be high and the number of process steps will be low
which has a positive effect on the price per microflown. At last the acoustical
3
I Introduction
performance is considered. This very important quantity is quantified in chapter 4.
The quality rules and manufacturing processes can be found in chapter 5: Realisation.
Several applications that have been investigated, utilise features of the
microflown. For the direct measurement of acoustic impedance and acoustic intensity
the capability to measure particle velocity is of crucial importance [1.3]&[1.22]. The
ease to fabricate many microflowns with a very similar behaviour and the great
linearity of the device makes it possible to measure the apparent pressure relatively
easily. The acoustic pressure is then determined from the signal of exclusively
microflowns.
The last part of the pictogram (Fig. 1.1) contains the public relations and sales.
The public relations part contains writing of articles and giving lectures to guests and
the press. The sales part is not an academic issue, but with sales in mind all
previously mentioned research areas will be affected. To sell a microflown it has to
reach specifications that are accurately specified, it has to improve an application or
maintain the quality for a lower price.
Nowadays many electronic devices have been miniaturised compared to their
models sold in the eighties. Especially audio visual equipment as for instance a
cordless phone, a video recorder, computers and so on. It is not very surprising that
considerable effort is put in miniaturising microphones. A possible technique to
fabricate these miniature microphones is by using the planar micro-machining
technology [1.1], [1.4], [1.8]. Another trend is the digital recording and transmission
of sound which allows an improved quality of sound, specially regarding the signal to
noise ratio and noise levels. Therefore the demand on small, cheap and high quality
microphones is rising [1.17/1.21]. Small and very high quality microphones are
difficult to manufacture and therefore expensive. Quality of microphones is specified
in a different way for different applications. For telecommunication purposes the
bandwidth is relatively small and for music recording the bandwidth has to exceed the
bandwidth of human hearing. The application defines if the specifications of a
microphone are good or bad.
Markets where not price but size of microphones is the most important matter,
are for instance the acting music area or talk shows [1.21]. Because in those areas it is
desirable that the microphone is not seen. In music shows like operas or musicals the
microphone is worn on the forehead. Condenser microphones that are used for this
4
General introduction
purpose are very sensitive to humidity. The air is very moisture when actors are
performing under hot stage lights. These microphones can therefore only be used once
ore twice before replacement. For this market a complete new concept of sound
sensor is desirable [1.18].
One important issue concerning the economical success of the microflown is the
legal protection of the microflown [1.18], [1.19], [1.20]. While copying a product is
relatively easy compared with developing it, manufacturers also need a patent to
protect their future product. The working principle of the microflown has been written
down in a world wide patent.
Several thousands of microflowns have been made and several hundreds have
been (more ore less) packaged. Quite a few applications have been tested. The sound
intensity probe and the use of the microflown as a “normal” microphone are most eye
catching [1.3], [1.5], [1.15]. Applications as sound reinforcement for the use in a
flute and with guitars have been tried because the microflown is very small.
Exploiting the capability to easily make identical microflowns, measurements in
standing wave tubes for determining the acoustic impedance of a material have been
performed. While the microflown can withstand high temperatures (up to 250°C) also
the measurement of sound waves in the exhaust of an engine becomes possible.
To obtain some insight how micro-machined microphones operate some
examples will be presented below.
5
I Introduction
1.2 M ICROPHONES
AND MICRO - MECHANICS
Microphones (acoustic pressure sensors) are usually consisting of a membrane
which deflects as a result of an applied acoustic pressure. The omni-polar (sensitive in
all directions) microphone is the best known. This type of microphone consists of a
cavity, also called back chamber, which has been sealed with a membrane. When the
pressure outside the chamber differs of the pressure inside, the membrane deflects.
The microphone is normally sensitive for pressure variations in a range from twenty
Pascal down to twenty micro Pascal. Very low frequency pressure variations, for
instance variations in atmospheric pressure due to weather changes or altitude
variations are associated with variations of several hundred Pascal. To make the
microphone insensitive for these low frequency variations a hole has been made in the
back chamber. Therefore microphones will have got a high pass character, normal
corner frequencies are several Hertz. The mass and strain of the membrane are
causing an upper limit for the frequency response, normal corner frequencies are
above five kilo Hertz. If the back chamber is completely open the microphone is
sensitive for pressure gradients in the acoustic wave.
Fig. 1.2: A schematic view of a capacitive pressure microphone.
As mentioned the deflection of a membrane is measured. This can be done in
several ways. Electromagnetic microphones consist of a coil that has been connected
to the membrane. The movement of the membrane will cause the coil to move in a
magnetic field that will result in an electrical signal. This type of microphone was first
developed in 1860 by the German teacher Phillipp Reis [1.14]. This type of
microphone is not suitable for micro-machining due to the three dimensional
properties. A type of microphone which is suitable for micro-machining is the
capacitive microphone [1.1], [1.6], [1.7], [1.9], [1.10]. The acoustic pressure
variation is determined by means of a condenser. The membrane is used as one plate
of the capacitor and a perforated-rigid-back-electrode is used as the other plate. The
6
Microphones and micro-mechanics
deflection of the membrane causes a variation of the capacitance. This type of
microphone needs an additional (bias) voltage for operation and is called the
condenser microphone. To avoid an external bias voltage it is also possible to provide
one of the plates with an electret, creating a so called electret microphone. The
capacitive microphones do have good noise properties, which is one of the most
important parameters of a microphone. The first condenser (electret) microphone was
build in 1918 [1.2].
Piezoelectric and piezo-resistive microphones are easier to make compared to
the capacitive microphones since the deflection can be measured directly. Compared
to condenser microphones the noise performance however is worse.
The FET microphone consists of a field effect transistor (FET). The membrane
vibrations modulate the gate-channel capacitance and thus the drain current [1.11].
The noise performance is not good yet, but it is expected that this will be improved
significantly [1.2]. Optical-wave-guide microphones operate on the principle that the
phase of a light wave propagating in an optical wave-guide depends on variations in
the vicinity of the wave-guide [1.13].
Practically all types of microphones make use of the fact that an acoustic
pressure deflects a membrane and this deflection is measured in the previous
mentioned ways. The microflown is a completely other type of acoustic sensor. When
talking into the microflown it appears that it records the same as a pressure
microphone (namely sound). However acoustic measurements show that it does not
measure the acoustic pressure but the particle velocity, which is besides the acoustic
pressure fundamentally the other quantity of an acoustic wave. This particle velocity
is not measured by deflection of a membrane like pressure microphones but by using a
thermal principle. Two wires are heated and the particle velocity causes one wire to
cool down and the other to rise in temperature simultaneously. The temperature
difference is measured and values the particle velocity.
An other facet of the microflown is that it is very easy to realise it by using
micro-mechanic fabrication methods [1.8], [1.12]. In the eighties one was capable to
make microphones on a silicon wafer with the advantage to make a lot of small
microphones at once. This way it should be possible to manufacture cheap
microphones but until now cheap micro-machined microphones are not been sold
commercially, indicating that it is difficult to make high quality and low cost
7
I Introduction
microphones with micro-machining methods. The process to make a microflown is
less complex and the microflown is smaller than a micro-machined microphone.
These two parameters are determining the price and therefore it can be expected that
the production costs of a micro-machined microflown will be considerable lower
compared to a micro-machined microphone.
1.3 O UTLINE
OF THE THESIS
This thesis presents the mechanical design, the electronic optimisation, some
modelling, the fabrication, calibration and applications of a new acoustic (particle
velocity) sensor, the microflown. Because of the variety of subjects a foreknowledge
on all subjects is not expected. Therefore all theoretical subjects will be introduced in,
for an expert in that particular field, rather basic way.
The goal of chapter two is to give an answer to the question how to calibrate the
microflown. While this is a new sensor, no other particle velocity sensors exist, it is
not trivial to find a calibrating method. Therefore this chapter presents also an
introduction in acoustics. Measurement set-ups covering the complete acoustic
bandwidth will be presented to calibrate the microflown.
At last two present day acoustic measurements will be shown to explain how
some acoustic properties nowadays are measured without an acoustic flow sensor and
what problems these methods encounter.
Chapter three focuses of the question how a resistance value can be measured optimal,
and how the noise of electrical circuits can be analysed. The latter is done by some
practical circuits. It appears that the signal to noise ratio and linearity are the most
important quantities. The proposed circuits are compared on these properties.
In chapter four a rough model of the microflown is obtained. The microflown is
a relative simple device, only a few parameters are involved to get a basic
understanding of the transfer function. It is however very difficult to obtain a
complete quantitative model of the microflown by using the fluid dynamics. Therefore
8
Outline of the thesis
only a qualitative model describing the frequency behaviour is given and a set of
measurements will complete the basic model.
In chapter five the realisation of the microflown is presented. First design rules
are extracted from previous chapters. This will resolve in knowledge of optimal
configuration dimensions and material constants. Knowing the physical requirements,
materials can be chosen to realise the structure.
It appears that it is very easy to realise a microflown. Two types of microflowns
have been developed, a channel type where two one millimetre long sensors cross a
channel and a cantilever type where the sensors are only connected at one side.
Several processes have been developed. It appears that the number of masks is an
important figure to measure the process complexity.
An advantage of micro-mechanical sensors is that it is possible to make a large
quantity on one wafer, which will enforce a low price per piece and a sensor with
uniform properties. It is now easy to make four hundred microflowns on one three
inch diameter silicon wafer. A problem is to separate all these sensors without
damaging them. For large volume production this problem is easily solved, the
complete process is automated. However for small scale production this will result in
a very high price per sensor that cancels the first mentioned advantage. Therefore
solutions for the separation of dices for small scale production have to be found. One
solution, separation by breaking, is presented.
Chapter six focuses on the applications of the microflown. Properties of the
microflown will be presented together with some applications. The acoustical intensity
probe will be discussed quite extensively.
Finally general conclusions are drawn in chapter seven.
9
I Introduction
R EFERENCES
[1.1] P. Scheeper, A Silicon Condensor Microphone: Materials and Technology, Ph.D. thesis 1993,
University of Twente, Enschede.
[1.2] G.M. Sessler, Silicon Microphones, J. Audio Eng. Soc., Vol. 44, No. 1/2, 1996.
[1.3] E.C. Wente, A condenser transmitter as a uniformly sensitive instrument for the absolute
measurement of sound intensity, Phys. Rev., 10-1917.
[1.4] J. Bergqvist, Modelling and Micromachining of Capacitive Microphones, Uppsala university,
1994.
[1.5] C.W. Reedyk, Noise cancelling electret microphone for light weight head telephone sets, J.
Acoust. Soc. Am. 53 (1973) 1609-1615.
[1.6] D. Hohm and G. Hess, A subminiature condenser microphone with silicon nitride membrane
and silicon back plate, J. Acoust. Soc. Am., 85 (1989) 476-480.
[1.7] J.A. Voorthuyzen, P. Bergveld and A.J. Sprenkels, Semiconductor-based electret sensors for
sound and pressure, IEEE Trans. Electr. Ins., 24 (1989) 267-276.
[1.8] A.J. Sprenkels, R.A. Groothengel, A.J. Verloop and P, Bergveld, Development of an electret
microphone in silicon, Sensors and Actuators, 17 (1989) 509-512.
[1.9] W. Kühnel and G. Hess, A silicon condenser microphone with structured back plate and silicon
nitride membrane, Sensors and Actuators A, 30 (1992) 251-258.
[1.10] W. Kühnel and G. Hess, Micromachined subminiature condensor microphones in silicon,
Sensors and Actuators A, 32 (1992) 560-564.
[1.11] W. Kühnel, Silicon condenser microphone with integrated field-effect transistor, Sensors and
Actuators A, 25-27 (1991) 521-525.
[1.12] D. Hohm and R. Gerhard-Multhaupt, Silicon-dioxide electret transducer, J. Acoust. Soc. Am.
75(4), 1984.
[1.13] D.K. Cheng, Field and Wave Electromagnetics, Reading, 1991.
[1.14] O. Brosze, Aufbau un wirkungsweise elektroakustischer Wandler, Der Fernmelde Ingenieur, 35
1981 Heft 6, 1-36, Heft 7, 1-35.
[1.15] S. Baker, An Acoustic Intensity Meter, The Journal of Ac. Soc. Of America, volume 27,
number 2, 1995.
[1.16] A.E.Perri G.L. Morrison, A study of the constant temperature hot wire anemometer, J. Fluid.
Mech., 47 (1971), 577-599.
[1.17] Private conversations Nederlandsch Octrooibureau.
[1.18] Private conversations AKG acoustics GmbH.
[1.19] Private conversations Brüel & kjær Denmark.
[1.20] Private conversations Sennheiser Electronic GmbH & Co. KG Germany.
[1.21] Private conversations Nederlands Omroep Bedrijf NV (J.W. vd Brink), The Netherlands.
[1.22] F.J.
10
Fahy,
Sound
Intensity,
sencond
edition,
E&FN
Spon,
london,
1995.
References
11
CHAPTER 2: ACOUSTICS
S UMMARY
The microflown is an acoustic sensor. Most acoustic
sensors measure acoustic pressure or acoustic pressure
gradient, however the microflown measures acoustical flow or
particle velocity, which makes it a unique sensor.
This chapter presents an introduction in acoustics to
obtain some insight in particle velocity, acoustic pressure, and
relations between both. Furthermore methods of calibration of
the microflown are presented. At last some conventional
measurement techniques (measuring sound intensity, acoustic
impedance) without a particle velocity sensor are presented.
13
II Acoustics
2.1 I NTRODUCTION
Originally acoustics was the study of small pressure waves in air that can be
detected by the human ear: sound. The scope of acoustics has been extended to higher
and lower frequencies: ultrasound and infrasound and to sound in other media as, for
example water. In such case acoustics is a part of fluid dynamics. A major problem of
fluid dynamics is that the equations of motion are non-linear. This implies that an
exact general solution of these equations is not available [2.2]. Acoustics is a first
order approximation in which non-linear effects are neglected.
Going into this matter is not the aim of this thesis but some acoustic principles
are necessary to understand what the microflown actually measures, how the
measurement set-ups are designed and why measuring acoustic flows can be useful.
This thesis starts with this chapter because of the fact that particle velocity is an
unknown phenomenon by a lot of people. An acoustic wave (sound) is mostly seen as
a pressure wave. This is not completely true. An acoustic wave consists of a pressure
and a particle velocity wave. The particle velocity wave is also called acoustical flow.
The acoustical pressure can be seen as a temporary increase and decrease of the
number of particles in a certain small volume. When a number of particles increase in
this certain volume, particles have to enter the volume: there has to be a movement of
particles. Particle velocity is associated with the movement of the particles.
The particles mentioned above are not single gas molecules or anything like
that. In acoustics a particle is defined as a volume which is small compared to the
dimensions of our measuring device (eardrum: 5 millimetre, microflown: 100
micrometer) or the wave length (minimal wavelength in air is at 20 kHz, 17
millimetre), but large compared to the molecular mean free path ( l = 5 ⋅ 10 −8 m )
[2.4].
14
An introduction to acoustics
2.2 A N
INTRODUCTION TO ACOUSTICS
As said in the introduction acoustical phenomena consist of acoustical pressure
variations and acoustical particle velocity. Definitions of, and relations between the
two will be described [2.1 & 2.2]. The wave equation is derived to show that some
assumptions have to be made to obtain an usable formalisation. To obtain for instance
the specific acoustic impedance the wave equation can be used. While the microflown
will be calibrated by using this impedance, one has to be careful that all assumptions
are valid.
DEFINITIONS
The instantaneous sound pressure, p(t), is the incremental change from the static
pressure at a given instant caused by the presence of the sound wave. The effective
sound pressure, p, is the root mean square (rms.) value of the instantaneous sound
pressure.
p=
1 T /2 2
p ( t )dt [ N / m2 ]
∫
/
2
T
−
T →∞ T
lim
(2.1)
Using T as the averaging time. The instantaneous particle velocity u(t), (or
instantaneous acoustic flow) is the velocity due to a sound wave only of a given
infinitesimal part of the medium (the above mentioned particle) at a given instant,
while the effective particle velocity u, is the root mean square of the instantaneous
particle velocity.
u=
1 T /2 2
∫ u ( t )dt [ m / s ]
T →∞ T −T / 2
lim
(2.2)
Note that pressure is a scalar while the particle velocity is a vector quantity. Acoustic
phenomena are in the frequency range from 20 Hz up to 20 kHz. The wavelength λ,
is given by the speed of propagation of the wave, c, divided by the frequency of
vibration:
λ=
c
[ m]
f
(2.3)
15
II Acoustics
Where f is the frequency. In air acoustic wavelengths are from 17 millimetres to 17
meters. The fluid particle displacement, ∆, corresponding to the harmonic wave
propagation at a frequency:
∆ =
u
[m]
2π f
(2.4)
The specific acoustical impedance at a point in a sound field is defined as the ratio of
the complex amplitude of an individual frequency component of sound pressure, at
that point, to the complex amplitude of the associated component of particle velocity.
Zs =
p
[ Ns / m3 ]
u
(2.5)
Note that the specific acoustical impedance is not a vector quantity. The characteristic
impedance is the ratio of the effective sound pressure at a given point to the effective
particle velocity at that point in a free, plane, progressive sound wave. It is equal to
the product of the density ρ, of the medium times the speed of sound in the medium.
A plane wave is an acoustic disturbance for which the pressure is uniform in a
direction normal to the direction of propagation. When measured far from the acoustic
source in the free field one obtains a plane wave. The sound intensity in a specified
direction at a point is the average rate at which sound energy is transmitted through a
unit area perpendicular to the specified direction at the point considered.
I [ W / m2 ] =
1 T/2
u( t ) ⋅ p( t )dt
T ∫−T / 2
(2.6)
In some cases it is convenient to express a quantity without dimensions.
Therefore reference values are given. The most known sound pressure level, given in
decibels, is defined as twenty times the logarithm to the base ten of the ratio of the
measured sound pressure of this sound to a reference effective sound pressure of 20
micro Pascal.
SPL = 20 Log10
16
p
pref .
( re. = 20 µPa ) [ dB ]
(2.7)
An introduction to acoustics
The particle velocity level, also given in decibels, has a reference effective particle
velocity 50 nano-meter per second.
PVL = 20 Log10
u
uref
( re. = 50 nm ⋅ s −1 ) [ dB ]
(2.8)
The sound intensity level has a reference intensity of one pico Watt.
SIL = 10 Log10
I
Iref
( re. = 1 pW ) [ dB ]
(2.9)
To gain some insight into the magnitudes of the mentioned quantities some
values are given in Table 2.1. It this case it is assumed that the specific acoustic
impedance equals the characteristic impedance and therefore the values of PVL and
SIL are equal to the SPL.
Table 2.1: Some acoustic values.
Description
SPL,
p
u
I
f=100 Hz
PVL & SIL
[Pa]
[dB]
∆
[m/s]
[W]
[m]
120
2×10
1
4.5×10-2
1×10-6
7.2×10-5
Reference level
94
1×10
0
2.5×10-3
5×10-8
3.6×10-6
Vacuum cleaner
80
2×10
-1
4.5×10-4
1×10-8
7.2×10-7
Whispering
40
2×10
-3
4.5×10-6
1×10-10
7.2×10-9
0
2×10
-5
4.5×10-8
1×10-12
7.2×10-11
Rock concert
Threshold of hearing
The particle displacement depends on both frequency and particle velocity. If
the specific acoustic impedance is equal to the characteristic impedance the particle
displacement is in a range of 3.6×10-13 meter for a sound pressure level of 0 dB by 20
kHz and 360 µm by a frequency of 20 Hz and a sound pressure level of 120 dB. On
top of this enormous variation of the particle displacement, the specific acoustic
impedance can theoretically vary from zero to infinity, causing an even larger
variation.
The particle velocity is a vector but it will hereafter be noted as a scalar; the
modulus of the particle velocity in a certain direction. In chapter 6 the equations will
17
II Acoustics
be expanded in a three dimensional form when the 3D-Intensity probe will be
explained.
THE ONE DIMENSIONAL WAVE EQUATION
The one (and three) dimensional wave equations are explained in many books
[2.1] & [2.8]. This will be repeated briefly to gain insight in which neglections are
necessarily made. To obtain formal relations between the acoustic pressure p(t,x), the
acoustic flow u(t,x) in one direction and the instantaneous density ρ(t,x)=ρ0+∆ρ(t,x)
the wave equation is derived. Consider a fixed volume S⋅dx in where an acoustic
disturbance passes. The rate of mass inflow will be:
Mass inflow = −
∂ ( ρ( t , x ) ⋅ u( t , x ))
dx ⋅ S
∂x
(2.10)
The principle of mass conservation requires that this net inflow must be balanced by
an increase in mass of the element:
∂ρ( t ) ∂ ( ρ( t , x ) ⋅ u( t , x ))
+
=0
∂t
∂x
(2.11)
While ρ0 is not dependent on time, the first derivative will simplify into: ∂∆ρ(t)/∂t.
Observing now the second derivative ∂(ρ(x,t)⋅u(t,x))/∂x, the product ρ(x,t)⋅u(t,x) is
equal to (ρ0+∆ρ(t,x))⋅u(t,x)=ρ0⋅u(t,x)+∆ρ(t,x)⋅u(t,x). If the term ∆ρ(t,x) is assumed
small compared to ρ0 eq. (2.11) will simplify:
∂∆ρ( t )
∂ ( u( t , x ))
+ ρ0 ⋅
=0
∂t
∂x
(2.12)
This relationship is known as the linearised equation of mass conservation and is only
valid if the variation in density is small compared to the density itself.
Using the principle of momentum conservation to a fluid element and defining
the pressure as p(t,x)=p0+∆p(t,x) the net force in the positive x direction on the
element is given by:
Net force = −
18
∂p( t , x )
dxS
∂x
(2.13)
An introduction to acoustics
This net force has to be balanced by the product of mass and acceleration. The
acceleration of the fluid element is given by:
du( t , x ) ∂u( t , x ) ∂x ∂u( t , x )
=
+
dt
∂x ∂t
∂t
(2.14)
The derivative ∂x/∂t equals u(t,x). For a harmonic particle velocity u(t,x)⋅∂u(t,x)/∂x is
u(t,x)/c smaller as ∂u(t,x)/∂t [2.2] and therefore eq. (2.14) will simplify:
du( t , x ) ∂u( t , x )
≈
dt
∂t
(2.15)
The mass times acceleration can now be approximated by ρ0⋅dx⋅S⋅(∂u(t,x)/∂t).
Equating the rate of change of momentum to the net force on the fluid element
therefore results in:
ρ0
∂u( t , x ) ∂p( t , x )
+
=0
∂x
∂x
(2.16)
This relationship is known as the linearised equation of momentum conservation and
is only valid if the particle velocity is small compared to the velocity of sound.
Differentiating eq. (2.12) with respect to time and eq. (2.16) with respect to x
then the combination of the two resulting relations shows:
∂ 2 p( t , x )
∂x 2
−
∂ 2 ρ( t , x )
∂t 2
=0
(2.17)
It is assumed that the acoustic compressions are such that the increase in pressure and
increase in density are linearly related and the square of the speed of sound is the
constant of proportionality such that p(t,x)=c2 ρ. Substitution of this in eq. (2.17) the
one-dimensional wave equation is achieved:
∂ 2 p( t , x )
∂x 2
1 ∂ 2 p( t , x )
− 2
=0
c
∂t 2
(2.18)
For harmonic varying acoustic pressures and flows a complex transformation is
suitable:
p( t , x ) = Re{ Aei(ωt − kx ) } = Re{ p( x )e iωt }
(2.19)
19
II Acoustics
k=ω/c=2π/λ is known as the wavenumber. A positive direction travelling harmonic
plane wave is represented by p(x)=e-ikx and a negative direction travelling harmonic
plane wave p(x)=eikx. Substituting this in the wave equation the one-dimensional
Helmholtz equation is obtained:
∂ 2 p( x )
∂x
2
+ k 2 p( x ) = 0
(2.20)
The harmonic particle velocity can be expressed similar. Substituting this in eq. (2.16)
the relation between the acoustic pressure and the acoustic flow is obtained:
∂p( x )
= − iωρu( x )
∂x
(2.21)
Now it is possible to calculate both acoustic pressure and flow, the specific acoustic
impedance can be calculated by dividing both:
Zs =
p( x )
u( x )
(2.22)
SOME SPECIFIC ACOUSTIC IMPEDANCES
The specific acoustic impedance is in general not equal to the characteristic
impedance. One reason for this is that the sound wave is not a plane wave, when for
instance it is emitted by a point source and still relatively close to the source. An other
reason may be the presence of reflections.
The specific acoustic impedance can be calculated by solving the wave equation.
This will be done for a simplified case, a rigidly terminated tube with rigged side
walls, to get some insight into the matter and to show that solving the wave equation
can be difficult in practical situations. The closed tube is shown in Fig. 2.1. The fluid
is excited by a piston with an amplitude U at the left hand end and is terminated by a
rigid boundary at the right hand end.
20
An introduction to acoustics
Fig. 2.1: A tube that is rigidly terminated at x=l and in which the fluid is driven by a
vibrating piston at x=0.
For harmonic excitation, one solution that will satisfy the wave equation is given by
the superposition of the complex pressures associated with a positive-travelling and a
negative-travelling plane wave. The plane wave approximation is allowed for
frequencies lower than the cut off frequency (see eq. (2.35)). In general the pressure
is given by:
p( x ) = Ae− ikx + Be ikx
(2.23)
Where A and B are arbitrary complex numbers which represent the amplitude and
relative phases of waves travelling in the positive and negative x direction
respectively. The particle velocity associated with this pressure wave can be found
using the linearised momentum equation, eq. (2.21):
u( x ) =
Ae − ikx Be ikx
−
ρc
ρc
(2.24)
Now the values of the complex constants A and B are solved knowing that the particle
velocity is zero at x=l:
Ae − ikl = Beikl
(2.25)
and at the left hand side of the tube the particle velocity is given by the movement of
the piston u(0)=U:
ρcU = A − B
(2.26)
The constants now are given by:
ρcUe ikl
A=
2i ⋅ sin( kl )
ρcUe − ikl
; B=
2i ⋅ sin( kl )
(2.27)
21
II Acoustics
Substituting the constants in eq. (2.23) and eq. (2.24) the acoustic pressure and the
acoustic flow are defined and the specific acoustic impedance can be found by:
Zs =
p( x )
= − i ⋅ ρc ⋅ cot( k ( l − x ))
u( x )
(2.28)
As can be seen the specific acoustic impedance in a closed tube does not equal the
characteristic impedance.
If the rigid end is replaced by a perfectly absorbing termination (or a tube of
infinite length), a backward-travelling wave will not occur. Hence eq. (2.23)
becomes:
p( x ) = Ae − ikx
(2.29)
Using eq. (21) to derive the particle velocity:
u( x ) =
Ak ⋅ e − ikx A ⋅ e− ikx
=
ωρ
ρc
(2.30)
Hence,
Z s = ρc
(2.31)
The specific acoustic impedance of a tube with a non reflecting termination (or an
infinite tube) is the same as the characteristic impedance (same impedance as a free
field measurement).
The specific acoustic impedance of a freely spherical wave is given by [2.2]:
Z s = ρc ⋅
irk
1 + irk
(2.32)
In where r is the distance to the source. This specific acoustic impedance is measured
in an anechoic room. For relatively large distances or high frequencies (r >> k-1) the
specific acoustic impedance becomes almost the same as the characteristic impedance.
While in an anechoic chamber (theoretically) no reflections are present, the
specific acoustic impedance in such environment equals eq. (2.32).
22
How to calibrate the microflown
2.3 H OW
TO CALIBRATE THE
µ - FLOWN
The simplest way to calibrate the microflown is using a reference particle
velocity microphone. Because of the lack of these type of sensors one has to use other
measuring equipment. The pressure microphone is an obvious one to use. The
problem reduces now to finding an environment with a known specific acoustical
impedance. If the sound pressure is measured the particle velocity can be calculated
by dividing this pressure by the specific acoustic impedance. If this impedance
depends on place and frequency, measurement set-ups get complex while a lot of
parameters involve the measurement and calculation of the particle velocity.
As shown above reflections cause a specific acoustic impedance depending on
place and frequency so these must be avoided. An anechoic chamber is an obvious
choice but it is a very expensive solution. Furthermore for low frequencies the
acoustical wave is a spherical one and eq. (2.32) shows that in this case the specific
acoustical impedance is also dependent of place and frequency.
Therefore other solutions have been developed. Observing eq. (2.31) the
specific acoustic impedance of an infinite tube is real and independent of frequency
and position. This fact will lead to a suitable measurement set-up for frequencies
between 50 Hz and 12 kHz. For frequencies below 50 Hz both the ‘acoustical shortcut’ as the ‘acoustical displacement’ set-ups are used. In the first set up two
loudspeakers gently move a quantity of air without generating acoustical waves and
the second set-up comprises a microflown that is harmonically moved through still
standing air. In this way it will be shown that the microflown also functions in a so
called ‘reversed principle’: the movement of the microflown is measured in air of
which is assumed to have no relative (macroscopic) movement. An other way of
characterising frequency dependent systems is measuring the step response of the
microflown. This last ‘flow step’ set-up is used to gain fast information about the
dynamic behaviour of the microflown and makes use of the ‘reversed principle’.
23
II Acoustics
THE ‘INFINITE’ TUBE
For measuring frequencies in the range from 50 Hz to 2.5 kHz a long tube is
used (ordinary PVC rain pipe). The idea behind this set-up is that the acoustical
impedance of a tube with no reflections at the end has a characteristic impedance
(Zs=ρc¸ same impedance as a free field measurement).
When a sine burst is applied a measurement can take place before a reflection
returns. To reduce measuring errors at least ten periods have to be measured. This
implies that the lowest possible frequency to measure is given by the following
formula:
f min =
10 ⋅ c 5 ⋅ c
=
2⋅l
l
(2.33)
Using l as the distance from the microflown and microphone and the end of the tube.
So for a forty meter long tube the lowest frequency which could be measured should
be about fifty Hertz. The two meter spacing is used to be sure that the acoustic waves
are plane. Non plane waves vanish exponentially [2.5]. The two meter length also
introduces a time delay between the generated burst and pressure and flow output
signal. This time delay ensures that the output signal of the µ-flown is not an electrodynamic transduction, while in this case the time delay will be much shorter. In order
to make the wave approximation the viscous boundary layers (the rigid tube wall)
have to be thin [2.2]:
f min >>
2υ
π ⋅ d2
(2.34)
Where d represents the diameter of the tube and υ the kinetic viscosity of air. Above
the cut-off frequency the specific acoustic impedance changes due to the existence of
standing waves perpendicular to the direction of the sound wave and the set-up will be
very difficult to use since the acoustic impedance is not constant anymore. For a tube
this cut-off frequency is given by [2.5]:
fc =
24
c
171
. ⋅d
(2.35)
How to calibrate the microflown
Two ‘infinite tube’ measurement set-ups are implemented. One has a diameter
of 7 cm and a length of 40 m and can be used in a frequency range from 50 Hz to 2.6
kHz. A thinner tube of 1.5 cm in diameter and 7 m long is used for the frequencies up
to 12 kHz. Both set-ups have a diameter large enough to fulfil the condition of eq.
(2.34).
It is rather difficult to measure high sound intensity levels below the 100 Hz in
the seven centimetre tube while the loudspeaker becomes very non linear as it has the
same (small) diameter as the tube. Using sound pressure levels below sixty deci-Bell
will result in reliable measurements. Because a dome tweeter is used in the one and a
half centimetre measurement set-up, the lowest frequency is 1.5 kHz. This is while
sound intensities is below the 1.5 kHz will damage the loudspeaker.
Fig. 2.2: The ‘infinite’ tube measurement set up is used to calibrate the microflown in
a frequency range from 100Hz to 2.5kHz.
The measurements are performed using acoustic bursts. A typical measurement
is shown in Fig. 2.3. One burst provides one point in the transfer function. Normally
four hundred measurements are made in the frequency range from one 50 Hz to 2.5
kHz in the seven centimetre set-up and four hundred measurements are made in the
frequency range from 1.5 kHz to 12 kHz.
25
II Acoustics
Fig. 2.3: A typical measurement in the ‘infinite’ tube providing one point of the
transfer function.
THE ACOUSTICAL SHORT-CUT
Conventional (pressure) microphones can be calibrated in a small cavity where
the pressure varies [2.9]. In this cavity no acoustic waves are generated. For the
calibration of the microflown the complementary equivalent is developed: the
“acoustical short-cut”, see Fig. 2.4. This measurement set-up is designed for a
frequency band from ‘zero’ Herz up to 200 Hz with the idea of generating a quasi
static flow. By moving slowly and harmonically a small volume of air no acoustic
waves will arise. In the “infinite tube” it is difficult to measure accurate a higher
particle velocity levels below 100 Hz and no steady state acoustic waves can be
generated. These problems are overcome using this set-up. Steady state acoustic
measurements can be useful to avoid possible transient behaviour effects.
Fig. 2.4: The acoustical short-cut set-up.
26
How to calibrate the microflown
The set-up is calibrated by using a displacement sensor and the assumption that the
amount of air moved is proportional to the displacement of the cones of both
loudspeakers. The acoustical short-cut set-up can be used until acoustic waves (the
existence of both acoustic flows as acoustic pressure waves) appear due to reflections.
This can be checked using a pressure microphone. It appears that this will happen
above 200 Hz.
THE ACOUSTICAL DISPLACEMENT SETUP
For the lower frequencies also an other measurement set-up can be used, the so
called acoustical displacement set-up. The general idea is that the microflown moves
harmonically through still standing air. The set-up is calibrated by measuring the
displacement as function of the input voltage at the adapted loudspeaker.
Fig. 2.5: The acoustical displacement set-up.
The displacement is dependent on the frequency. Up to approximately 30 Hz the
amplitude transfer function is nearly flat and after this corner frequency the response
decreases with forty deci-Bell per decade as can be expected for a second order
system.
Both ‘acoustic short cut’ as ‘acoustic displacement’ set-up provides almost the
same information about the low frequency behaviour of the microflown. As
mentioned in the ‘acoustic short cut’ the air moves and in the ‘acoustic displacement’
the microflown moves. Both set-ups have the same second order frequency behaviour
while the same type of loudspeaker is used.
Knowing the displacement the flow can be calculated by using eq. (2.4). After
the corner frequency of both the ‘acoustic short cut’ as the ‘acoustic displacement’ setup the generated flow has got a first order low pass behaviour (the amplitude will
decrease twenty deci-Bell per decade).
27
II Acoustics
THE FLOW STEP SETUP
Another way to analyse dynamic systems is by measuring the step response. The
step response contains theoretically the same information about the system as a
frequency response if the system is linear. A flow step means that perfectly still
standing air has to move instantly at a certain speed. This is very difficult to
accomplish. The problem is solved in the same way as the acoustical displacement setup, the microflown is moved through motionless air and stopped instantaneously. In
the flow step set up a µ-flown is stopped from ½ m/s to zero. The output signal
provides a semi-DC sensitivity and a corner frequency can be seen in Fig. 2.6.
Fig. 2.6: A characteristic flow step output.
The corner frequency is calculated under the assumption that the microflown has got a
first order low pass behaviour. The step response of a first order system is an
exponential curve. The time it takes to reach 66% of the end value of the step
response is called the relaxation time. The reciprocal relaxation time is equal to the
corner frequency of the first order system.
The frequency ranges of the various measurement set-ups are depicted in Fig.
2.7. The striped areas indicate that the set-up can be used limited.
28
How to calibrate the microflown
Fig. 2.7: Frequency range of the various measurement set-ups.
The previous mentioned measurements set-ups are meant to measure the
properties of the microflown. When calibrated one microflown it can be used as a
reference microphone. Multiple measurements show that the transfer function is stable
in time.
THE STANDING WAVE TUBE
Once a microflown is calibrated, it can be used as a reference particle velocity
microphone. Previous problems regarding for instance the specific acoustic impedance
are now reduced and a measurement set-up is realised in a short (2 meter) standing
wave tube. The advantage of this set-up is that it provides fast information of the
transfer function and that it is an inexpensive solution for time continuous
measurements. It is thus an inexpensive alternative for the anechoic chamber.
THE SILENCE SETUP
The name of this set-up is found by the fact that this set-up produces no sound.
The aim of the set-up is to shield the microflown from acoustic noise. The only signal
that is produced by the microflown when it is placed in the silence set-up will be
noise.
29
II Acoustics
2.4 P RESENT - DAY
ACOUSTIC MEASUREMENTS
To gain insight in acoustic subjects, examples of how acoustic measurements
like measuring sound intensity and specific acoustic impedance can be performed
without a particle velocity measuring microphone will be briefly described here. The
commercially available sound intensity probe estimates the particle velocity using two
matched microphones [2.4], [2.11]. The particle velocity has not always to be
estimated. An another way to derive acoustic properties is for instance to measure the
impedance of a horn type loudspeaker using a standing wave tube.
MEASURING SOUND INTENSITY
As said above for measuring the acoustic intensity the acoustic pressure will be
measured and the particle velocity be estimated. The method is based upon Newton's
second law, that is the equation of motion:
ρ⋅
∂ur
∂p
=−
∂t
∂r
(2.36)
Where ur is the particle velocity in one direction r. Since the pressure gradient is
proportional to the particle acceleration, the particle velocity can be obtained by
integrating the pressure gradient in respect to time [2.3].
ur = −
1 ∂p
dt
ρ ∫ ∂r
(2.37)
In practice, the pressure gradient is approximated by measuring the pressure at two
points at a close distance ∆r.
ur = −
1
( pa − pb )dt
ρ∆r ∫
(2.38)
This approximation is valid as long as the separation, ∆r, is small compared with the
wavelength.
A practical sound intensity probe can therefore consist of two closely spaced
pressure microphones (and therefore named the p-p method), as for instance the Brüel
30
Present-day acoustic measurements
& Kjær intensity probe type 3512 fitted with two ½" pressure microphones. The
probe outlines are given in Fig. 2.8 (a photograph of the probe is shown in chapter 6):
Fig. 2.8: A schematic drawing of the B&K 3512 acoustic intensity probe.
The Block diagram of the acoustic measuring probe is shown in Fig. 2.9.
Fig. 2.9: The block diagram of how to obtain the acoustical intensity from two
pressure microphone signals.
Estimating the acoustic flow using the pressure difference method has a few
disadvantages. If the intensity is not constant over ∆r, for instance performing
nearfield measurements, an estimation error will be made (the spacing of both
microphones varies in commercially available intensity probes from six millimetres to
fifty millimetres). If a phase mismatch exists between the two measuring channels, it
is most critical for low frequencies or small values of microphone spacing.
Typical properties of the Brüel & Kjær intensity probe type 3512 are given
below.
31
II Acoustics
Fig. 2.10: Proximity approximation error.
As can be seen in Fig. 2.10 the error increases very rapidly if the probe measures the
intensity near to a source. If the spacing of the two microphones is smaller the
proximity error becomes smaller. If the intensity can be measured in one point the
proximity error becomes zero.
Fig. 2.11: The error due to a phase mismatch of ϕ=0.3° for relatively low
frequencies.
A phase mismatch introduces large errors at low frequencies. This is due to the fact
that the difference signal of both signals is used to estimate the acoustic flow. For low
frequencies the wave length becomes very large compared to the spacer so a phase
mismatch becomes more important. This is a particular disadvantage of estimating the
acoustic flow by subtracting two signals.
These and more problems occur when the two microphone method is used for
measuring the acoustic intensity. By measuring the acoustic flow directly using a
microflown the above described problems can be avoided. In chapter 6 the intensity
probe using a µ-flown and a microphone is described [2.12].
32
Present-day acoustic measurements
MEASURING THE ACOUSTIC IMPEDANCE OF A HORN LOUDSPEAKER1
To measure an acoustic impedance the acoustic pressure has to be divided by the
particle velocity. Acoustical impedance is an important quantity to characterise, for
example, horn loudspeakers. A horn loudspeaker can be seen as an acoustic
transformer, when the acoustical impedance is an imaginary figure the acoustic energy
will not be optimal. It transforms a small area diaphragm into a large area diaphragm,
without the difficulties of cone resonances or break-up.
Fig. 2.12: A horn type loudspeaker.
The acoustical impedance (Z=R+jX) of a horn can be derived by a recurrent
calculation process [2.7], the result is shown in Fig. 2.13.
Fig. 2.13: The theoretical acoustic impedance of a horn.
1
Based on: H. Schurer, P. Annema, H-E. de Bree, C.H. Slump, O. Hermann, Comparison of two
methods for measurement of horn input impedance, presented at the 100th convention AES, 1996 May
11-14 Copenhagen.
33
II Acoustics
If the real part of the normalised impedance is one and the imaginary part is zero the
maximum acoustical power is transmitted.
The conventional method to measure this acoustical impedance is by measuring
standing wave patterns inside a tube driven by a loudspeaker that is acoustically
terminated by the horn of the loudspeaker [2.6]. The measurement set-up is depicted
in Fig. 2.14. A loudspeaker is attached at one end of a tube, while the other end is
terminated by the horn. The diameter of the tube is chosen in a manner that there is a
smooth transition from tube to horn throat, while the length of the tube has to be at
least one-half of the longest wavelength of interest. A probing microphone is needed
for measuring the sound pressure inside the tube. It is necessary to move it along the
axial axis to determine standing wave maxima and minima. Therefore two slots are
made where the probing microphone can move along, keeping the slot as tight as
possible by means of a covering tube. Two slots are necessary because a shorter
covering tube to measure near the throat of the horn is needed.
Fig. 2.14: Fahy’s measurement set up [2.6].
For the driving loudspeaker a normal electrodynamic loudspeaker has been used. The
lowest cut-off frequency of the tube is given by eq. (2.35). For determination of the
input impedance three values have to be determined. First the position of the sound
pressure minimum nearest to the throat, xmin, and next the maximum and minimum
sound pressure of the standing wave pattern in the tube, pmax and pmin, are determined.
The complex acoustic impedance for one measurement (i.e. for one frequency) is then
found by [2.6]:
34
Present-day acoustic measurements
Z = R + jX =
 1.52c 
2
 2 ( 1 − r )
 d 
1 + r 2 − 2r ⋅ cos( t )
+ j
 1.52c 
 2  2r ⋅ sin( t )
 d 
(2.39)
1 + r 2 − 2r ⋅ cos( t )
With r the pressure reflection coefficient and t the reflection phase angle which are
given by:
r=
p
a −1
 4x

; a = max ; t = π  min + 1
 c

pmin
a +1
(2.40)
Only the ratio of maximum and minimum pressure is observed, therefore the
microphone does not need a calibration.
Because it is necessary to seal the tube properly at each measurement, it is more
straightforward to perform a full frequency sweep of 401 frequency points at every
measurement spot in the range of x=0-393 mm, with a resolution of 1 mm. This is a
very tedious task which yields an enormous amount of measurement data, especially
as measurements have to be as accurate as possible, which means 394 separate
measurements, see Fig. 2.15B.
3
Real part
2
1
0
Imaginary part
-1
-2
0
1000
2000
3000
4000
5000
frequency [Hz]
3,0
2,5
Normalized impedance
Normalized impedance
4
2,0
Real part
1,5
1,0
0,5
Imaginary part
0,0
-0,5
-1,0
A
0
1000
2000
3000
4000
frequency [Hz]
5000
B
35
II Acoustics
Fig. 2.15: The acoustic impedance, measured using the direct method (see chapter 6)
and obtained by Fahy’s method.
36
Present-day acoustic measurements
C ONCLUSIONS
AND DISCUSSION
The relation between the acoustic pressure and acoustic flow is formalised. This
is done under certain assumptions which are not always justified in practice. The
assumptions are that the acoustic compressions are such that the increase in pressure
and increase in density are linearly related, variations in density are small compared to
the density itself and that the particle velocity is small compared to the velocity of
sound. Therefore one has always to be careful when using the specific acoustic
impedance to calibrate the microflown. Acoustic non-linearity in air becomes
significant at sound levels exceeding about 135 dB [2.8].
Of the measurement set-ups used obviously the ‘infinite tube’ type of set-ups are
the most important ones. This is because the frequency range from 50 Hz up to 12
kHz is of most interest. In this range the human ear is most sensitive. The ‘infinite
tube’ type of set-ups are an inexpensive solution to create an environment with and
known specific acoustic impedance.
For frequencies below one hundred Hertz both ‘acoustic short cut’ as ‘acoustic
displacement’ set-up provide information about the frequency dependent behaviour of
the microflown. Using the ‘acoustic short cut’ the air moves and using the ‘acoustic
displacement set-up’ the microflown moves.
Once a microflown is calibrated “the standing wave tube” measurement set-up is
used to gain fast and reliable information about the transfer function.
When observing how acoustic measurements are performed nowadays it shows
that it is possible to measure properties as acoustic impedance and intensity without
using a flow microphone. Sound intensity can be measured by using two closely
spaced and, in particular, phase matched pressure microphones. The disadvantage is
the fact that it is difficult to fabricate (phase) matched microphones which will result
in a high price for the probe. Also some specific problems incorporated with the
method have been presented.
Measuring the acoustic impedance is possible using a standing wave tube but
this will alter the system and the measurement is very time consuming and noise is
introduced in data handling.
37
II Acoustics
R EFERENCES
[2.1] L. L. Beranek, Acoustics, McGraw-Hill, New York, 1954.
[2.2] P.A. Nelson & S.J.Elliot, Active Control of Sound, Academic press, London,1992.
[2.3] L.E. Kinsler et al., Fundamentals of Acoustics, New York, 1982.
[2.4] Brüel & Kjær, Sound Intensity, Technical Review, No. 3, 1982.
[2.5] A.P. Dowling and J.E. Williams, "Sound and Sources of Sound", Ellis Horwood Pub.,
Chichester (1983).
[2.6] F.J. Fahy, “A Simple Method for Measuring Loudspeaker Cabinet Impedance”, J. Audio Eng.
Soc., vol 41, No 3, pp 154-156, March 1993.
[2.7] H.F. Olson, Acoustical engineering, Van Nostrand company inc, Princeton, NJ, 1967.
[2.8] F.J. Fahy, Sound Intensity, sencond edition, E&FN Spon, london, 1995.
[2.9] G.S.K. Wong, T.F.W. Embleton, AIP Handbook of condenser microhones, Theory,
calibration, and measurements, 1994, New York.
[2.10] H. Schurer et. Al. Comparison of two methods for measurement of horn input impedance,
presented at the 100th convention AES, 1996 May 11-14 Copenhagen.
[2.11] IEC 1043, International Standard; Electroacoustics - Instruments for the measurement of sound
intensity - Measurement with pairs of pressure microphones; First edition December 1993.
[2.12] H-E. de Bree, M.T. Korthorst, P.J. Leussink, H. Jansen, M. Elwenspoek, A Method To
Measure Apparent Acoustic Pressure, Flow Gradient and Acoustic Intensity Using Two
Micromachined Flow Microphones, proceedings Eurosensors X, Leuven, 1996.
38
The Gadget
CHAPTER 3: ELECTRONICS
S UMMARY
In this chapter two important issues are discussed. What
is the best possible way to detect a varying resistance and what
electronic implementations can be used to measure this
variation. Four circuits are presented and compared to each
other on the basis of linearity and noise performance.
Fig 3.0: First realisation of the microflown and Gadget [3.6].
39
III Electronics
3.1 I NTRODUCTION
To detect a physical quantity one uses a sensor which is sensitive to that
particular quantity. Generally the sensor produces an electrical output which is
proportional to that particular quantity. This looks very easy but there are at least a
few problems. At first most sensors do not measure the quantity only they are
supposed to, secondly most sensors are not linear. So when the (input) quantity
doubles the electrical output does not, the transfer function is normally dependent of
the frequency, and at last there is a fundamental problem with noise.
Let’s take an electromagnetic microphone also (called dynamic microphone) for
example. This sensor consist of a movable membrane connected to a coil in a
magnetic field. Whenever there is a pressure difference over the membrane it moves
and so will the coil. This causes an electric signal. The only thing to be detected is the
sound pressure. But, this microphone also measures acceleration (due to the mass of
the membrane and coil). The microphone is due to the coil, also sensitive for
electromagnetic signals. Furthermore a microphone is not a linear device. When the
sound level doubles the electronic signal does not, caused by the stiffness of the
membrane. For very low and very high frequencies the transfer function becomes
small, and most microphones have a resonant frequency, a frequency where the
transfer function becomes large. When the sound level is to low the only electronic
signal measured is noise.
The microflown is a sensor which consists of two resistive temperature sensors
and possibly a heating element. An (AC) acoustic flow causes one sensor to drop in
temperature and the other to rise, a differential resistance variation is the result. The
signal, defined as the output of the temperature sensors is a differential variation of
resistance. There is no energy transduction from the acoustic wave to the electrical
domain. In contrast to a conventional microphone the microflown is a modulator type
transducer.
It is clear that the electronics have to transduce the signal as good as possible,
the electronics must transduce the resistance variation only and do not add anything to
the signal.
Considering the preceding, noise reduction and optimisation of linearity are of
main interest. Normally in stead of noise reduction, signal to noise ratio (S/N)
40
Introduction
optimisation is used. To optimise linearity and S/N one has to know exactly how these
figures are defined.
A signal (S) is defined as the output voltage or current caused by an acoustical
flow. (The microflown is a sensor which has to be used for measuring acoustical
flows i.e. flows, having a frequency from twenty hertz to twenty kilo-hertz, see
chapter 2.)
Noise (N) is defined as an unwanted, non-correlated output signal. There are
several sources of noise. For instance there is thermal noise which is generated in
resistors and also the current through a semiconductor is affected with noise.
The linearity is quantified by using the total harmonic distortion (THD). Most
transducers have a non linear transfer function as could readily be seen with the
previous mentioned microphone. The electronics must not enlarge the non linearity of
the total device significantly. The non linearity of the electronics has to be negligible
compared to the sensor.
A sensor is defined here as a device which is capable of transducing a certain
physical quantity into an electronic signal. Mostly such a device consists of a
combination of transducers and electronic circuits. The total system of sensor and
necessary electronics is defined as a sensor.
The main goal of this chapter is introducing (electronic) noise principles. This
will be done by means of different circuits which each are capable of measuring
differential resistance variations [3.2].
41
III Electronics
3.2 M EASURING
OHMIC IMPEDANCES
The output of a µ-flown is a differential variation in resistance of two resistors.
The main noise source is the thermal noise, see appendix 3. The value of a resistor R
is given by:
R=
U
I
(3.1)
Using U as the electrical voltage and I as the electrical current. An electrical circuit
for measuring the resistance at a given time, R(t), is given in Fig. 3.1.
Fig. 3.1: A circuit for measuring the resistor value.
The varying resistance is given by:
R( t ) = R0 + ∆R( t )
(3.2)
Using R0 as the nominal value and ∆R(t) as the time dependent part. Applying a
constant current the output voltage is given by:
U ( t ) = IR0 + I∆R( t ) = U 0 + ∆U ( t )
(3.3)
The varying, time dependent part, is called signal due to the fact that the microflown
measures an acoustic phenomena (i.e. the signal has a frequency from 20 Hz to 20
kHz).
∆U = IR0
∆R ( t )
R0
= IR
∆R
R
(3.4)
Using ∆R(t) /R=∆R /R as the relative (time dependent) variation of the resistance.
The noise is given by the thermal noise of a resistor U noise , rms = 4 kTR ⋅ Bw (see
42
Measuring ohmic impedances
also appendix 3). The signal to noise ratio of the system depicted in Fig. 3.1 is given
by (assumed that there is no significant noise generated by the current source):
S
=
N
IR
∆R
R
4 kTs R ⋅ Bw
=
I R
∆R
R
4 kTs ⋅ Bw
=
P
∆R
R
4 kTs ⋅ Bw
(3.5)
Using Bw as the bandwidth of the signal (here approximately twenty kilo Hertz), Ts as
the absolute temperature of the sensor and k as Boltzmann’s constant. The signal to
noise ratio is proportional to the square root of the power, P, dissipated in the
resistor.
However the microflown produces a differential resistance output. This can be
measured with the electrical circuit shown in Fig. 3.2.
Fig. 3.2: Measuring a differential resistance variation.
The signal to noise ratio of this circuit, by differential variations, the same nominal
resistor value, ideal current sources and subtraction circuit is given by:
∆R
S
2 IR R
=
=
N
4 kTs ⋅ Bw + 4 kTs ⋅ Bw
∆R
P R
2 kTs ⋅ Bw
(3.6)
Using ∆R /R as the relative differential variation of both resistances:
∆R R1( t ) − R2 ( t )
=
R
R
(3.7)
The signal to noise ratio of differential varying resistors is proportional to the square
root of power dissipated in the resistor, not of the resistor value itself.
43
III Electronics
3.3 T HE W HEATSTONE
BRIDGE
Measuring differential resistance variations is often done by using the
Wheatstone bridge, see Fig. 3.3. Some additional electronics will perform the
subtraction. This subtraction circuit will add some extra noise which will be neglected
here.
Fig. 3.3: Measuring the differential resistance variations using the Wheatstone bridge.
The transfer function is optimal if the static values of the resistors are the same
(R≈R1≈R2). The output signal is then given by:
1
∆U =
2
E
∆R
R
 ∆R 
1+  
 2R
2
=
IR
∆R
R
 ∆R 
1+  
 2R
(3.8)
2
Using E as the power supply voltage and I as the current trough the resistors. As can
be seen in eq. (3.8) the transfer function is not linear. For small differential resistor
variations and a nominal value R1=R2=R, the variation of the output voltage will be:
∆U ≈ IR
∆R
R
(3.9)
The signal to noise ratio of the Wheatstone bridge with an ideal (no noise etc.)
subtraction circuit can be calculated as:
S
=
N
IR
∆R
R
4 kTav R ⋅ Bw
=
I R
∆R
R
4 kTav ⋅ Bw
=
P
∆R
R
4 kTav ⋅ Bw
(3.10)
Using Tav as the average temperature of the four resistors. This ratio is slightly worse
compare to the circuit of in Fig. 3.2.
44
The Wheatstone bridge
3.4 T HE G ADGET 1
In the previous paragraph it is shown that it is possible to improve the signal to
noise ratio using another circuit than the Wheatstone bridge. The subtraction circuit
was also not taken into account. Normally this circuit is implemented as one or more
operational amplifiers. This amplifier introduces noise, uses mostly two power
supplies and can be unstable. In this paragraph The Gadget, a new small circuit
measuring differential resistance variations, will be presented. It will be explained in
the most simple form: The Basic Gadget. The actual implementations are given below
[3.7], [3.8].
THE BASIC GADGET
The Basic Gadget (Fig. 3.4 A) uses a single power supply which can be almost
freely chosen. It is basically a Widlar current mirror [3.1], the output current is a
function of the input current and the emitter resistors. If this resistors have the same
value the output current will be approximately the same as the input current. By
studying this circuit, noise sources of active circuits will be presented.
THE TRANSFER FUNCTION OF THE BASIC GADGET
The Basic Gadget is shown in Fig. 3.4A. How this circuit functions will be
explained roughly at this point. A more detailed description follows later.
The base and the collector of transistor T1 are short-circuited. Therefore it acts
as a diode. Because of the current source the voltage across this diode is independent
of resistor variations (the variation in the base current of transistor T2 is considered
very small). Therefore transistor T1 can be seen as a voltage source UD, see Fig.
3.4B. Both resistors vary only a little, as described by eq. (3.2).
1
Based on: H-E. de Bree, P.J. Leussink, M.T. Korthorst, Y. Backlund, H. Jansen, The Wheatstone
Gadget, A simple circuit for measuring differential resistance variations, proceedings MME 1995,
Denmark, pp. 201-204.
45
III Electronics
Fig. 3.4A: The Basic Gadget, B and C: the functionality simply explained.
When a constant current is applied to R1(t), a varying voltage, ∆UR1=I⋅∆R, will
be caused, see Fig. 3.4B. A variation of resistance in resistor R2(t) will cause a
variation in the emitter current of T2, which can be seen as a varying current source
parallel to R2, the Norton equivalent of a (Thévenin) voltage source in series with a
resistor. This voltage source can be split (Blakesley [3.2]), one in series with the base
and the other one in series with the collector. This last voltage source can be
neglected because of the high impedance of the collector output.
How The basic Gadget operates will be explained in more detail below, some
basic principles of the transistor are given in appendix 2.
The relation between the base emitter voltage, UBE and the current IC, of a BJT
transistor in forward-active operation is given by:
U BE
 U 
IC = ICO ⋅  1 + CE  ⋅ e U T 2
UA 

(3.11)
in which UA is the Early voltage (UA≈60V..150V) and UT represents kT/q≈25mV. If
UA >> UCE the Early voltage can be neglected.
To calculate the transfer function, i.e. the output current as a function of the
input current and both microflown resistors, one has to start with the large-signal
equations. Looking at eq. (3.11) and Fig. 3.4A the expression for both collector
currents are:
46
The Gadget
α FE 2 + 1
R2
α FE 2
UT 2
U B − Iout
Iout = ICO 2 ⋅ e
IC1 = ICO1


I
U B −  I − out  R1
α FE 2 

UT 1
⋅e
(3.12)
(3.13)
Using αFE as the DC forward current gain. The collector current of transistor T1 is
slightly less than the input current I because of base current loss.

 α FE 1
I
IC1 =  I − out 
α FE 2  α FE 1 + 1

(3.14)
These three formulas combined, and assuming the transistors to be identical and
having the same temperature (i.e. UT1=UT2 and ICO1=ICO2) will result in:
I out




R1 U T  I out (α FE 1 + 1)  I out ( R1 + R2 )
ln
=I
−
 −α
R2 R2  
R2
I out 
FE 2
I −
 α FE 1 
α FE 2 


(3.15)
This transcendental equation can not be solved analytically. For differential resistor
variations, resistors having an equal nominal value and αFE1≈αFE2 >> 1 the last term
(the DC current offset term) can be neglected and eq. (3.15) simplifies to:
UT
 R + ∆R
 I 
Iout ≈ I ⋅ 
+
ln out  
 R − ∆R I ( R − ∆R )  I  
2


 ∆R 



U T  I out  
∆R
1
 R
= I ⋅ 1 + 2
+2
+
ln

∆R
∆R U R  I  
R

1−
(1 −
)



R
R
(3.16)
Using UR as the voltage across the nominal value of the resistor.
47
III Electronics
LINEARITY OF THE BASIC GADGET
Analysing the linearity of The Basic Gadget one has to observe the large signal
transfer function. The DC forward current gain is considered large so eq. (3.16) can
be used. Only the varying part of the output current will be observed:
2


 ∆R 




 R 
UT
∆Iout  

 ∆R
ln 1 +
+2
+
∆Iout = I  2

∆R
∆R

I 
R
1
(
1
)
−
U
−


R
R
R


(3.17)
It is not possible to rewrite eq. (3.17) in a polynomial way so it is difficult to use the
THD directly. It is however possible to solve it numerically. After simulating the
large signal transfer function a polynome can be fitted. The coefficients of this fitted
function can be used for calculating the THD. With this method it is possible to gain
some quantitative insight in the non-linearity. The transfer function can be derived
solving eq. (3.17):

 ∆R
H exact  I ,
,U R  : solve eq.( 3.17 )

 R
(3.18)
Another method is to estimate the transfer function. For small variations of ∆R/R and
UT/UR << 1 the logarithm can be simplified:
∆I 
∆R

ln 1 + out  ≈ ln( 1 + 2
)
R

I 
(3.19)
Now the transfer function is not transcendental anymore and an polynome can be
estimated using the Taylor polynome. The approximated transfer function using the
fifth order Tailor power series expansion will lead to eq. (3.20):
2
3
4
5




U  ∆R
8 U T   ∆R 
4 UT   ∆R 
76 UT   ∆R  
 ∆R

 ∆R 
H5  I ,
,U R  = I   2 + 2 T 
+ 2
 + 2 +

 + 2 −

 + 2 −

 
 R

 R
UR R
3 UR  R 
3 U R  R 
15 U R   R  




the relative error is defined by:
Re lative error =
48
H exact − H5
⋅ 100%
Hexact
(3.21)
The Gadget
Comparing the fifth order approximation with the numerically solved solution (UR=1;
i.e. UT/UR ≈ 0.025 ) Fig. 3.5 is derived.
0,6
Relative error [%]
0,4
0,2
0,0
-0,2
-0,1
0,0
0,1
0,2
∆ R /R
Fig. 3.5: Relative error of the Taylor series compared to the simulated transfer
function.
As can be seen in Fig. 3.5 the relative error of the fifth order Tailor power series
expansion is small if UR=1 and ∆R/R is below 20%. Since UT/UR << 1 is assumed the
Taylor approximation H5 eq. (3.20) can be simplified in:
 ∆R  ∆R  2  ∆R  3  ∆R  4  ∆R  5 
 ∆R 
= 2 I 
+   +   +   +   
H5  I , 
 R  U T <<1
 R  R
 R 
 R  R
(3.22)
UR
If ∆R/R is small the Taylor approximation H5 can be simplified to the linear
approximation:
∆R
 ∆R 
= 2I
Hlinear  I , 
 R  U T <<1
R
(3.23)
UR
For small ∆R/R values small signal analysis can be used to obtain the transfer
function of The Gadget. The transfer function for small differential resistance
variations (see eq. (3.7)) is approximately given by:
∆Iout
∆R
R
=
 UT 
1 +

 UR 
2I
(3.24)
If the condition UT/UR << 1 is not fulfilled this term can not be neglected and the
transfer function becomes a function of UR. However the resistance variations ∆R/R
are considered small and therefore UR(t)=UR,0(1+∆R/R) ≈ UR,0, the linearity will not
decrease dramatically.
49
III Electronics
SIGNAL TO NOISE RATIO OF THE BASIC GADGET
To calculate the signal to noise ratio of the Basic Gadget the standard circuits of
appendix 3 have to be combined. The Basic Gadget can be seen as a combination of a,
as diode configured transistor and a common emitter configuration. The noise of these
circuits is given in appendix 3. If the proper substitutions are made, the signal to noise
ratio of the Basic Gadget is given by (see appendix 3):
S
=
N Gadget
P
∆R
R


T r 
2 q UT  s + bb'  ⋅ Bw + ∫ Noise( I , R ) ⋅ df 
 T

R 


Bw
(3.25)
Using Bw=fmax-fmin, respectively the maximal and the minimal frequency of the signal.
Observing first the numerator of eq. (3.25). The noise fraction Noise(I,R) is
dependent on the bias current I, and the sensor R. It is given by eq. (3.26), (see
appendix 3):
1 U T2 
K 'F  U T
1 +
+
Noise( I , R ) ≈
2 U R 
f α FE  α FE
 rbb'

+2+
 R
2
K 'F  1 U R 
K'  
r
 +
 1 + F   1 +  1 + bb'  
f  2α
f 
R  
FE 
 
Using K’F as the corner frequency of the flicker and burst noise. Observing this noise
fraction a minimum can be found if UR is chosen correctly. The optimal value of UR
can be found by solving the following equation:
f max
∂
Noise( I , R ) df U = IR = 0
∫
R
∂U R f min
(3.27)
The optimal value for UR is now given by:
f
α FE ⋅ Bw + K'F ln max
f min
U R ,optimal = U T
  r  2

f
'
 Bw + K F ln max  1 +  1 + bb'  
f min   
R  

And the optimal signal to noise ratio is given by eq. (3.29):
50
(3.28)
The Gadget
S
=
N opt . f max
∫
f min
P

T r
1
2kT  s + bb' +
α FE
T
R

 rbb'
K' 

+ 2+ F  +
f 
 R
∆R
R
1 
1 +
α FE 
2 
K'F   
r

 1 +  1 + bb'    ⋅df
  1 +
f 
fα FE   
R   

K'F  
If R >> rbb’ and αFE >> 1 the term between the accolades can be simplified to:
1
Ts
+
T α FE

 2 +

K 'F 
2
+
f 
α FE

 1 +

K'F 

(3.30)
f 
These three factors are shown in Fig. 3.6 separately. The solid line represents the
factor Ts/T and the value is chosen 1.5, K’F is chosen 100Hz and αFE is chosen 100.
The dashed line represents the factor
2 
1 +
α FE 
K'F 
1
 , the dotted line
f 
α FE

 2 +

K'F 
.
f 
Fig. 3.6: Noise terms plotted as a function of the frequency.
As can be seen the 1/f terms become negligible at frequencies above 1 Hz.
Formalising this effect for αfe >> 1, R >> rbb’ and f << K’F:
K ''F ≈
1 T '
KF
α fe Ts
(3.31)
Only for frequencies below K’’F the 1/f noise becomes relevant (the simplification
(A3.11) in appendix 3, is therefore justified). Because of the fact that acoustic
51
III Electronics
frequencies are defined above 20 Hz it is assumed that the 1/f -terms can be
neglected. The optimal signal to noise ratio simplifies into:
S
=
N opt .
P ∆R
R
2 kTs ⋅ Bw
(3.32)
Observing eq. (3.32) it shows that it is possible to implement The Basic Gadget in a
manner that the noise contribution of the circuit is negligible. Eq. (3.28) provides an
optimal resistor value using:
Roptimal =
U R2 ,optimal
(3.33)
P
Eq. (3.33) can be solved analytically if R >> rbb’.
Roptimal =
U T2
2P
K 'F
f
α FE +
ln max
Bw
f min
⋅
'
K
f
1 + F ln max
Bw
f min
(3.34)
It is possible to find BJT transistors with a K’F <100Hz. If the bandwidth of the
signal is 20kHz. expression (3.34) can be simplified:
U 
U 2 ⋅ α FE
Roptimal ≈ T
⇔ α FE optimal ≈ 2 R 
2P
 UT 
2
⇔ I opt . =
UT
R
α FE
(3.35)
Note that eq. (3.35) is only valid if R >> rbb’. If this condition is not fulfilled, eq.
(3.28) has to be solved numerically.
The noise of The Gadget is simulated using PSPICE [3.8]. This is done with an
AC analysis and the DC bias current is altered stepwise. Here the noise (an AC
analysis) has to be calculated as a function of the bias current. The parameters of the
simulation where rbb’=100Ω, R=500Ω (reminding the condition rbb’ << R), Ts=T, the
sensors are not heated and αfe=100. As can be seen the current noise fraction
(Noise(I,R)) is dependent on the bias current and has a minimum at I=350 µA (see
eq. (3.35)).
52
The Gadget
Fig. 3.7: A PSPICE simulation showing the various noise fractions.
IMPLEMENTATIONS OF THE GADGET
In the most simple form The Gadget is implemented using two additional
resistors, the differential resistor variation will be transduced into a varying voltage.
The Gadget Duo Sensation can transduce two pairs of differential varying resistances
into a varying voltage or current. With this configuration two microflowns can be
read out. To transduce multiple microflowns the Cascade Gadget is used.
Using the formulas of The Basic Gadget it is easy to find an expression for the
transfer function of circuit in Fig. 3.8, the current source is simply implemented with
resistor R3 and the output current is converted to an output voltage with resistor R4.
Fig. 3.8: The Gadget.
The DC bias condition of The Gadget is (see Fig. 3.4) is given by Uout=(EI⋅R4)>UE,T2+UCE,min ≈ UB. The bias current is given by I=(E-UBE1)/(R3+R). Assumed
53
III Electronics
is R1 ≈ R2 ≈ R. The DC bias condition yields: R3 ≥ R4. The transfer function of The
Gadget is given by:
∆ uout = − 2 IR4
R ( E − U BE 1 ) ∆ R
∆R
= −2 ⋅ 4
⋅
R
R3 + R
R
(3.36)
If the value of R4 equals R3, a maximal transfer function for The Gadget can be
achieved. The common mode transfer function (CMRR; ∆R1=∆R2) is given by:
∆uout ,common =
I ⋅ R ⋅ R4 ∆R
R3
R
(3.37)
The combination of eq. (3.36) and eq. (3.37) provides the CMRR:
CMRR =
∆uout , diff .
R
≈2 3
∆uout , common
R
(3.38)
If the power supply increases by ∆E (see Fig. 3.8), the current through R3 will
increase with ∆I=∆E/(R3+R) and consequently the current through R4 will also
increase by ∆I. The output voltage alters with ∆E minus ∆I⋅R4. This will lead to a
PSRR of:

R4 
∆E
≈ 1 −

∆U out 
R3 + R 
−1
(3.39)
If R << R4≈R3 the effect of variations in the power supply will be minimised. In this
way it is possible to force a variation of the current by varying E without a variation
of the output voltage. This effect is used for the AM-Gadget and will be discussed
below.
The Gadget Duo Sensation (Fig. 3.9) consists of two complementary Gadgets.
This circuit is capable of measuring two pairs of differentially varying resistors and
can be used with voltage or current output. In this configuration it is a circuit like the
Wheatstone bridge with four varying resistors and a differential amplifier.
54
The Gadget
Fig. 3.9: The Gadget Duo Sensation.
The bias current is given by I=(E-2UBE)/(R1+ R3+ R5). Using eq. (3.23) the output
current due to differential variations of the resistors is given by:
 ∆R

∆R
∆Iout = 2 I   
−  

  R  NPN  R  PNP 
(3.40)
For voltage output the PNP-Gadget is an active load for the NPN-Gadget and vice
versa [3.1]. If IDC ≈ 0 (Uout ≈ ½E) the transfer function is given by:
∆U out = ∆Iout ( ro ,PNP ro,NPN ) =
U A ,NPN U A,PNP ∆Iout
U A ,NPN + U A ,PNP I
(3.41)
Using UA as the Early voltage.
Because the output of the Basic Gadget has the same dimension and magnitude
as its input it is possible to cascade it. Cascading n microflowns generating all the
same signal (if the microflowns are situated close together compared to the
wavelength, of the applied acoustical wave their signal will be phase matched) will
resolve in a signal to noise improvement of √n. The limiting factor for cascading is
the fact that the bias current will be reduced, because of the last term of eq. (3.15).
This limitation however can be overcome by, for instance, injecting currents or
adding a small resistance in series with R1 (see Fig. 3.8). If the resistors of each
55
III Electronics
individual Gadget vary little and differentially and assuming (∆R/R)2 ≈ 0, the transfer
function of The Cascade Gadget is:
N
N 

∆R
∆R
Iout + ∆I out = I ∏  1 + 2    ≈ I + I ∑ 2  
R  Gi
 R  Gi 
i =1 
i =1 
(3.42)
Condenser microphones are in fact capacitive sensors. The instantaneous
capacitance can be determined by creating an oscillator: the varying capacitance will
result in a varying frequency: a frequency modulated signal will be the result [3.3],
[3.4], [3.5]. If it is desirable to get a frequency modulated output signal The Gadget
can be used in the following way.
The transfer function of The Gadget is the product of the bias current and the
differential varying resistors. The bias current can thus also be seen as an input.
Supplying The Gadget with an alternating voltage, superimposed on a DC voltage,
(see Fig. 3.8) the current will have the same character and the output will generate an
AM signal with suppressed carrier (a double-side band signal [3.4]). This circuit can
transduce very low frequency variations (in the 1/f region) in a higher frequency
range and so create a higher signal to noise ratio. The voltage supply of The Gadget is
in this case: E=E0[1+α· cos(ωHF t)] using α (with α<1) as the ratio of the absolute
value of the carrier and the DC voltage. The current will be approximately be
I≈E0[1+αCos(ωHF t)]/(R3+R), the output of the AM Gadget:
∆uout = 2 IR4 ⋅ β cos(ω LF t ) + PSRR −1 ⋅ αE ⋅ Cos(ω HF t )
+ IR4αβ { Cos(ω LF t + ω HF t ) + Cos(ω LF t − ω HF t )}
(3.43)
Using β cos(ωLF t) as ∆R/R. The PSRR, eq. (3.39), indicates how much the carrier
will be suppressed.
56
The Gadget
3.5 O THER
PRACTICAL CIRCUITS
Another circuit which has been used frequently is the common emitter CE
configuration (see also appendix 3). This circuit is used for situations where a
compensation filter is desirable (audio applications). This is because the transfer
function of the microflown principally has got a high pass character. The microflown
is configured as a half of a Wheatstone bridge, see Fig. 3.10. The transfer function is
defined as:
Vbase = U out + ∆U out =
R0, 2 + ∆R2
E=
R0, 2 + ∆R2 + R0,1 + ∆R1
1
2
E + IR
∆R
R
(3.44)
Since for small signal behaviour both sensor resistances are situated parallel (the
equivalent input resistance is therefore ½R0) the generated noise at the base will be
δui2 = 2 kTs R0 . The varying input voltage of the BJT transistor Vbase is called signal
and consequently the signal to noise ratio of the half Wheatstone bridge is the same as
eq. (3.6) and therefore optimal. The DC base voltage Vbase is at the half of the supply
voltage (E), the bias collector current is given by: IC=(Vbase-UBE)/RE.
Fig. 3.10: CE configuration with a half Wheatstone bridge as input.
The input noise of the CE configuration at the base is given by (see eq. A3.15):
57
III Electronics

1
R
+r

2
1 2 µflown bb'
δub2


 + 2 qI B ( 1 Rµflown + rbb' )2
= 4 kTrbb' rbb' + 2 kTs Rµflown + 2 qIC  s +
α fe
2

∆


 2 kT
( 1 2 Rµflown + rbb' )2 
δub2
≈ 4 kTrbb' rbb' + 2 kTs Rµflown + 
+ 2 qI C

α fe
∆
 q IC

 kT

(3.45)
The 1/f noise is neglected here because this circuit is used for audio applications, the
noise is expressed using an “A” weighting filter, low frequency noise will be
suppressed. An optimum can be found for the bias current (minimal noise
contribution):
IC ,opt . = U T
α fe
1 R
2 µflown + rbb'
(3.46)
If this optimal current is chosen, the input noise will be given by:
2
δutot
−1 

. = ( 2 kT R
S µflown + 4 kTBJT rbb' ) 1 + α fe 
∆f
(3.47)
If the base series resistance (rbb’) is chosen much smaller than the nominal (hot)
resistance of the microflown the circuit will not significantly add noise and the signal
to noise ratio will remain at the optimal value as stated in eq. (3.6).
A disadvantage is the low PSRR: a stable power supply (for example a battery)
is therefore advisable. This circuit has been used for audio applications.
The last circuit presented is designed to have a large dynamic range. The circuit
is designed to have an optimal noise behaviour and to have a linear transfer function
up to large differential resistance variations.
The basis of the circuit, see Fig. 3.11, is an emitter coupled pair. Normally the
differential input is at both bases. And for instance, a Wheatstone bridge would
transduce the differential resistor variation into a differential voltage variation. If due
to the large resistance variations a large differential input is generated this emitter
coupled pair would not have a linear transfer function. Placing resistors in series with
the emitter can be a solution since this will cause the transfer function to be linear for
larger differential input voltages. A disadvantage however is that these resistors will
add noise in the same amount as the base series resistance will do, resulting in a worse
58
Other practical circuits
noise behaviour. The solution has been found by replacing the emitter series
resistances by both the microflown sensing resistances.
Fig. 3.11: Emitter coupled pair with emitter degeneration used for high differential
resistor variation measurements.
A disadvantage is that when the values of the resistors are not equally large the
proper DC bias condition will not be fulfilled. To be sure that this is not a problem a
feedback signal for low frequencies only is put on one of the bases which will take
care of the DC bias condition. The optimal bias current can be found in appendix 3:
Ioptimal =
UT
f
K 'F ln max
( rbb' + R )2
f min
+
Bw
α fe
≈
UT
R
α fe
(3.48)
If the optimal current is applied and the sensor resistance is chosen much larger as the
base series resistance the noise contribution of the electronic circuit is negligible.
59
III Electronics
C ONCLUSIONS
AND DISCUSSION
If the static resistance of the microflown is chosen much larger than the base
series input resistance of a BJT the electronics can be designed so that the noise of the
circuit is not the limiting factor when operating the microflown. In contrast to a
condenser microphones the 1/f noise density of the electronic circuit is not dominant
in the acoustic bandwidth [3.3].
The signal to noise ratio and linearity (combined in the dynamic range) are the
main quality figures of a microphone [3.3]. The output signal of the microflown is a
differential resistance variation. Considering the main noise factor of a resistor, the
thermal noise, an optimal signal to noise ratio has been derived. It shows that only the
dissipated power and the temperature of the resistor and not the resistance itself are of
relevance.
Multiple circuits which are capable to transduce differential resistance variations
to a varying voltage have been presented, the known Wheatstone bridge and The
Gadget, a half Wheatstone bridge and a modified emitter coupled pair. It is possible
to implement the circuits in a manner that they add practically no noise. The
Wheatstone bridge has a slightly less noise performance than the other circuits.
The Gadget is not very linear for large differential resistance variations and
therefore not very suitable for high sound level measurements. It is however a very
useful circuit for measurement purposes since the transfer function is easy to calculate
when the input bias current is monitored.
For larger signals the signal to noise ratio becomes less important and the
linearity becomes more important so in this case the Wheatstone bridge becomes more
appropriate.
For audio applications a half Wheatstone bridge in combination of a CE
configuration has been used, the linearity of this circuit is high as long as the CE
configuration is operating in the linear region.
The modified emitter coupled pair needs additional electronics to be stable but
besides it is the best performing circuit regarding the linearity.
To increase the signal to noise ratio it is also possible to implement more
microflowns. The improvement of applying a number of n microflowns will be
60
n.
Conclusions and discussion
R EFERENCES
[3.1] Gray and Mayer, Analysis and design of analogue integrated circuits, 1993, New York.
[3.2] J.
Davidse,
Ruisarm
ontwerpen
in
de
elektronica
en
communicatietechniek:
een
postacademische cursus van de TU-Delft, Kluwer Technische Boeken, 1988.
[3.3] G.S.K. Wong, T.F.W. Embleton, AIP Handbook of condenser microphones, Theory,
calibration, and measurements, 1994, New York.
[3.4] A. Bruce Carlson, Communication systems, 1986, New York.
[3.5] Sennheiser, Revue part 1, microphones, 1-1996, Germany.
[3.6] P. Roodenburg, The µ-flown, practical trainee report, 1994.
[3.7] P.J. Leussink and M.T. Korthorst; Inleiding flierefluiten; 250 hrs report; University of Twente;
1995.
[3.8] P.J. Leussink; Flierefluiten I, The amazing Microflown; M.Sc. Thesis; University of Twente;
1996.
[3.9] H-E. de Bree, P.J. Leussink, M.T. Korthorst, Y. Backlund, H.V. Jansen, The Wheatstone
Gadget, A simple circuit for measuring differential resistance variations, MME, Copenhagen,
1995 .
61
Introduction
CHAPTER 4: THE µ-FLOWN
S UMMARY
In this chapter a model of the microflown is derived.
First the frequency dependent behaviour of a hot wire
anemometer is given. A heat flow diagram shows how the
microflown functions and why the sensitivity alters when
certain parameters alter.
At last a set of measurements which fully describe the
acoustical behaviour of the microflown is presented. This set of
measurements will lead to two figures which can describe the
acoustical behaviour: the performance and the corner
frequency.
Fig. 4.0: A Two Sensor Microflown.
63
IV The µ-flown
4.1 I NTRODUCTION
In this chapter two main issues are investigated. An inquiry of the operating
principles of the microflown and a set of measurements which fully describes its
behaviour. The microflown is a modulator type of transducer. An acoustical flow will
alter the sensor resistance values. Consequently additional electronics is required to
convert or amplify the output of the microflown. In chapter 3 the electronics of the
microflown has been discussed and restrictions are formulated. The sensor part, the
transduction of an acoustic signal to an electrical signal, will be discussed in this
chapter.
As said the microflown is an acoustic sensor which is capable of measuring
particle velocity. This is done through the thermal domain. The microflown consists
of at least one heating element and two temperature sensors. The microflown is
derived from a mass-flow sensor [4.2], see Fig 3.0. A mass flow sensor consists of
three resistors located in the middle of a micro-machined channel. The two outermost
resistors are used as temperature sensor, while the resistor located in the middle is
used as a heater. When a flow is applied, the heat distribution around the heater will
change. This results in a temperature difference between the upstream and
downstream situated sensors, the resulting change in resistance of both resistors can
be measured and will lead to an electrical output (chapter 3) proportional to the
applied flow. As will be clarified in this chapter it is not necessary to use a heater, it
is also possible to create a microflown by using two heated temperature sensors. This
configuration is called the Two Sensor Microflown (TSM).
Measurements show that in the acoustic frequency range the microflown has a
first order low pass frequency behaviour. A system of this kind is characterised by a
corner frequency and a low frequency sensitivity (i.e. frequencies below the corner
frequency). In this chapter a qualitative model of the corner frequency of one heated
wire (an anemometer) will be given, since it is assumed that this can be extended to
the microflown, which consists of two or three heated wires close to each other.
The low frequency sensitivity of a microflown is dependent on the geometry and
dissipated power mainly, a simple model will be suggested to explain this.
4.2 A
64
QUALITATIVE MODEL OF THE MICROFLOWN 1
A qualitative model of the microflown
To measure small air flows, mass flow sensors (MFS) can be used. This type of
sensor consists of a heater and two temperature sensors equally spaced around the
heater. The flow alters the temperature distribution around the heater. This is detected
by the sensors. The temperature difference between the sensors will quantify the flow.
Another principle to measure a flow is a hot wire anemometer (HWA). This
sensor consists of a heated wire which is also used as a sensor. The heat loss, which is
dependent on the air flow, is measured when measuring the temperature. A major
disadvantage of the HWA is the low sensitivity for small DC flows [4.3] and the
direction of the flow can not be obtained.
The anemometer is much better understood in comparison to the MFS. Using
the model of the anemometer to find an expression for the frequency behaviour of one
sensor, and by using the insights of the mass flow sensor, a combination sensor is
developed.
The proposed sensor, the Two Sensor Microflown (TSM), consists of two
heated elements which are used both as sensor and heater (like the anemometer) and
uses the differential temperature as a representation of the flow (like the MFS).
First one heated wire, the anemometer, will be considered. This will lead to an
understanding of the frequency dependent behaviour of the sensors. In literature [4.2]
the mass flow sensor is treated as an anemometer. Only here the temperature of the
wire is not sensed but the temperature difference around the heater is monitored. The
MFS is used for steady state operation and therefore the signal to noise ratio and
frequency dependent behaviour is of less importance. For the microflown however the
signal to noise ratio and the frequency dependent behaviour are of major importance.
THE HOT WIRE ANEMOMETER (HWA)
Theory about the fundamentals of the HWA has been studied thoroughly and is
summarised quite clearly by C.G. Lomas, “Fundamentals of hot wire anemometry”
[4.3]. The HWA is a flow sensor suitable for relatively large flows, the lower limit of
detectable flows is around 0.15 m/s to 0.2 m/s [4.5]. The microflown is used for
much smaller flows, the differential temperature variation caused by an air-flow is
linear with the flow up to about 0.3 m/s. Because both sensors have a quite different
65
IV The µ-flown
operating flow range the models of the HWA can not be used for understanding the
working principles of the MFS directly. The theory of the HWA will be discussed
because its frequency dependent behaviour can be used for understanding the
quantitative frequency dependent behaviour of the microflown.
The HWA consist of one wire which is heated by an electrical current. At the
same time the electrical resistance of this wire is measured to determine the
temperature. When a flow is applied, the temperature of the wire will drop, and
therefore the resistance, because the convective heat loss increases. This effect can be
described by considering the heat balance for a hot wire (Fig. 4.1).
Fig. 4.1: The various heat losses of a hot wire.
Heat is generated electrically in the wire and lost by convection to the
surrounding fluid, by conduction to the bulk and radiation to the surroundings. In
addition, there is heat storage in the wire. An energy balance yields for the following
differential equation for the heat balance in a hot wire sensor:
A
∂T
∂  ∂Ts  I 2 ρr
− ρcA s − πdh(Ts − Tf ) − πdσε (Ts4 − Tf4 ) = 0
 ks
+
∂x  ∂x 
A'
∂t
(4.1)
Here ks is the coefficient of thermal conductivity for the sensor material, A the
surface of the total sensor, A’ the surface of the conducting part of the sensor, Ts the
sensor temperature, I the electrical current, ρr the resistivity of the sensor material, ρ
the density of the sensor material, c the specific heat, t the time, h the coefficient of
convective heat transfer, Tf the temperature of the surrounding fluid, σ the Stefan-
66
A qualitative model of the microflown
Boltzmann constant and ε the emissivity of the sensor. The first part of eq. (4.1)
represents the heat transfer by conduction in the wire, the second part the electrical
heat generation, the third part the heat storage, the fourth the convection loss and the
last part the emission loss. The last part is normally neglected since the emission loss
is assumed very small [4.1].
In order to develop an expression for the frequency response of a heated wire
sensor the heat balance is used. If the sensor is assumed long compared with the width
(i.e. a high aspect ratio) for the temperature profile to be constant (the first term
vanishes) and the heat loss by radiation can be neglected [4.1] & [4.7], eq. (4.1) will
simplify to:
I 2 ρr
∂T
= ρcA s + πdh(Ts − Tf )
∂t
A'
(4.2)
The coefficient of convective heat transfer is given by [4.3]:
h = H1 + H 2 u
(4.3)
Using H1 and H2 as constants and u represents the fluid velocity. Because for positive
and negative flows the heat loss is the same an AC flow can only be measured
completely with a DC bias flow [4.3]. The resistor value of the sensor is given by:
R=
ρr l
A'
(4.4)
And the dependence of the temperature can be approximated by:
Rs = R f + α( Ts − T f )R f
(4.5)
Using α as the first order temperature coefficient of resistivity, Tf as a certain
reference temperature (in this case the fluid temperature) and Rf as the resistance of
the resistor at the reference temperature. Substituting this in the previous relations, the
following relation yields:
I 2 Rs = P =
ρcAl ∂Rs πdl
+
( H1 + H 2 u )( Rs − R f )
αR f ∂t
αR f
(4.6)
67
IV The µ-flown
If it is assumed that all fluctuating quantities can be expressed by a sum of a mean
component and a fluctuating component, for example u(t)=u+∆u and Rs(t)=Rs+∆Rs
eq. (4.6) will alter in the following first order ordinary differential equation:

d∆Rs αR f  πlk f
2

+
(
H
+
H
u
)
−
I
1
2
 ∆Rs =
ρcAl  αR f
dt

 πk f 

 H 2 u ( Rs − R f )∆u
 2 ρcAu 
(4.7)
The associated time constant of this equation is easy to find and consequently the
corner frequency of this equation is given by [4.3]:
fc =
I 2 R 2f α
2πρcAl( Rs − R f )
=
P
2πρcAl( Ts − T f )[ 1 + α ( Ts − T f )]
(4.8)
The corner frequency is dependent on the sensor temperature and thus of the applied
flow. For steady state operation and using eq. (4.2), eq. (4.6) will alter:
Ts − T f =
P
πdhl
(4.9)
Substituting eq. (4.9) in (4.8) the expression for the corner frequency is given by:
fc =
h πdl
1
h πdl
1
⋅
⋅
=
⋅
⋅
Rs − R f
ρc 2πAl 1 + αP
ρc 2πAl
1+
lπdh
Rf
(4.10)
Eq. (4.10) consists of three parts. The first part is the ratio of the coefficient of
convective heat transfer and the product of the density of the sensor material and the
specific heat. The second part can be seen as a shape factor: the ratio of the surface
and the volume of the sensor. The last part is a reducing factor dependent on the
temperature. The coefficient of convective heat transfer is in almost the same manner
dependent on the temperature and consequently the corner frequency has
approximately no temperature dependence.
The anemometer can be described with an equivalent thermal circuit. The
electrical power (Pel.) generates a constant input heat rate. The product of ρc is
commonly termed as the volumetric heat capacity and measures the ability of a
68
A qualitative model of the microflown
material to store thermal energy. In this equivalent thermal circuit it will be noted as
C. The static rate of heat loss, the resistor Rstat. in Fig. 4.2, is defined as the
temperature rise of the sensor divided by the input heat rate by no-flow operation:
Rstat . =
Ts − T f
Pel .
(4.11)
u =0
The resistor Rconv.(u) in Fig. 4.2 models the heat loss due to the convection. For small
flows (u<0.2m/s) the temperature drop caused by the applied flow of one wire is
negligible to the static temperature. Therefore the thermal convection modelled by
Rconv. is much larger than the thermal static resistance.
A first order low pass filter is in the electrical domain a system with a similar
behaviour. The corner frequency is determined by the inverse of the capacitance times
the resistance of the system.
Fig. 4.2: Equivalent thermal circuit of an anemometer.
In Fig. 4.2 the different elements are shown. This thermal equivalent shows the
macroscopic behaviour of an anemometer.
THE MASS FLOW SENSOR (MFS)
The MFS has a different way of operating compared with the HWA. It measures
the differential temperature variation in stead of the absolute temperature. The HWA
is not sensitive for flows smaller than 0.15 m/s. This is caused by, so called, free
convection [4.3]. Due to the heated elements the warm air creates a self-flow. The
MFS is not affected by this because of its differential measuring method. This could
69
IV The µ-flown
be the explanation for the observed linear sensitivity (see Fig. 4.8) for flows below
0.15 m/s.
To give an impression, the expected temperature distribution for no-flow
operation (solid line) and for flow operation (dotted line) is shown in Fig. 4.3. The
location of both sensors and heater is shown by the letters S and H, the spacing with
∆X.
Fig. 4.3: Temperature distribution of a mass flow sensor.
The temperature sensors will alter this model, since they dissipate power and are
also a disturbance for the particle velocity profile. The power dissipated in the sensors
may be considerable low compared to the power consumption in the heater (the
temperature distribution will have a large resemblance with the one shown in Fig.
4.3) but as shown in chapter three and below, the quality of the detection of resistor
variations is proportional to the square root of the dissipated power in the sensor. This
leads to an urge to increase the power in the sensors but by doing this the previous
assumptions will no longer be valid anymore.
Looking into actual implementations of the MFS, it is possible to use a three
beam configuration, one heater and two sensors like Lammerink et al., see Fig. 4.4A,
hereafter called the SHS configuration, or a two beam configuration, the heater is
distributed and placed on the same carrier as the sensors. This has been done by
Johnson et al. [4.4], see Fig. 4.4B.
70
A qualitative model of the microflown
Fig. 4.4: Two implementations of mass flow sensors.
Comparing both implementations with a certain heater temperature the operating
sensor temperature is higher for the two beam configuration than the operating sensor
temperature of the three beam configuration. This is because the thermal conductivity
through the air is less than the conductivity through the carrier. A higher operating
temperature of the temperature sensors will cause a higher thermal noise. For the two
beam configuration the carrier for the sensor and heater has to be larger in order to
support two wires, resulting in an expected lower corner frequency, see eq. (4.10).
THE SENSOR PART
In present realisations of the microflown the temperature sensor is implemented
as a resistor. Including eq. (4.5) and eq. (4.8) the differential temperature variation
(∆T) is measured as a differential resistance variation:
∆R Rd − Ru
=
=
R
R
α∆T
1+
( )
f
2
(4.12)
fc
The differential resistance variation is linearly dependent of the first order temperature
coefficient of resistivity and has a first order low pass behaviour (see eq. (4.10)). In a
differential measurement set-up (see chapter 3) the signal due to an acoustic flow
equals IR⋅∆R/R. The minimal noise generated by the sensor resistors is given by the
thermal noise and is given by
2kTs R ⋅ Bw (k is the Boltzmann’s constant and Bw the
bandwidth, see chapter 3) and therefore the signal to noise ratio is given by:
71
IV The µ-flown
∆R
S
α
P
1
R
=
=
×
×
N
Ts ( P) Bw
2 kTs R ⋅ Bw
2 k ⋅ Bw
IR
 1
∫  1 + f
Bw 
2

 df × ∆T ( P) (4.13)

fc 
As can be seen the signal to noise ratio is a function characterised by the first order
temperature coefficient of resistivity, the square root of the dissipated power divided
by the absolute temperature of the sensors, the corner frequency of the sensors and the
differential temperature variation due to a given particle velocity. This differential
temperature variation is a function of the dissipated power and thus, for a certain
realisation of the microflown, the signal to noise ratio is a function of the power only.
THE TWO SENSOR MICROFLOWN (TSM)
The two sensor microflown (TSM) looks very much alike the two beam
configuration of Johnson et al. Instead of heating the sensors with a separate heater,
the power of the sensors can be increased so that the sensors dissipate enough power
to heat itself. This configuration is shown in Fig. 4.5.
Fig. 4.5: The Two Sensor Microflown.
The heater has become redundant. The power which was dissipated in the heater
can now be divided over both the sensors and an increase of the power in the sensors
will lead to an increase of the signal to noise ratio since the operating temperature of
the sensors stays the same, the ratio
P
Ts ( P)
in eq. (4.13) will increase. The
supporting carrier of the sensors now can be smaller than those of the configuration of
Johnson et al. resulting in a higher corner frequency.
72
A qualitative model of the microflown
MODEL OF THE SENSITIVITY OF THE TSM
A model will be presented to understand how the TSM functions. It will give an
understanding why the sensitivity alters with the spacing between the sensors. This
model can be extended to the SHS type of microflown but this will not be done here.
In this model the velocity boundary layers are neglected, the flow is assumed uniform
and the sensors are assumed to be of infinite length. The thermal effects of a
connected tip of the microflown are neglected. The microflown is very small in
comparison with the wavelength and therefore the applied acoustic flow is assumed
the same at both sensors (quasi static approach).
It is assumed that the first order low pass behaviour is caused by the volumetric
heat capacity and the thermal resistances only. The DC sensitivity of the TSM will be
described.
The microflown is a true particle velocity sensor and not a particle displacement
sensor. This can be proved since the particle displacement does have a 1/f behaviour.
As shown before the microflown has a 1/f behaviour for frequencies above the corner
frequency. The cause of the 1/f behaviour for higher frequencies is the thermal
capacitance and resistance of the sensors. In Fig. 4.6 a heat flow diagram the TSM is
shown. The sensors are presented as small spheres with a certain heat rate input and
output and operating temperature.
Fig. 4.6: Heat flow diagram of the Two Sensor Microflown in operation.
The several heat transfer rates are displayed for an AC flow during a small time
instant. Due to this flow (for instance from left to right) a heat loss rate (qconv. ) will
arise in both sensors. A certain amount of the heat of sensor 1 will be transferred to
sensor 2. This is modelled with the heat rate input source qconv.2:
73
IV The µ-flown
qconv.2 = ξ ⋅ qconv.1
ξ ≤1
(4.14)
Using ξ as the efficiency of the heat transfer.
The flow from left to right will cause an temperature difference in both sensors,
∆T=TS2-TS1 and therefore a heat transfer is existing from sensor 2 to sensor 1 by a
thermal conduction, modelled with the heat flow qc. This heat transfer rate has a
reducing effect on the sensitivity. Due to the particle velocity the convection heat
transfer rate causes a temperature difference between both sensors and the temperature
difference causes a conduction heat transfer in the opposite direction.
Because the TSM is symmetric the same is valid for a flow from right to left.
Therefore the efficiency is assumed the same in both directions.
Fig. 4.7 shows the a simplified equivalent thermal circuit of the Two Sensor
Microflown. The TSM is treated as two closely spaced anemometers. So in fact it is
an expansion of the model of the anemometer, see Fig. 4.2. Only three elements are
added: two heat transfer rate sources qconv.1 and qconv.2 and a thermal resistor Rc. Due to
the different geometry the value of the resistor Rstat. is different of the one in Fig. 4.2.
Fig. 4.7: Equivalent thermal circuit of the thermal behaviour of the TSM.
The sensor is heated by two heat sources: the electrical dissipated power (Pel.)
and the heat transfer rate from the other sensor due to convection multiplied with the
efficiency (qconv.). These heat sources dissipate in Rstat., the heat leakage rate in no-flow
steady state condition, and in a Rconv. the heat transfer rate due to forced convection
(particle velocity). The capacitor C represents the heat storage of the sensor, the
resistor Rc represents the conduction though the air and is given by:
74
A qualitative model of the microflown
Rc = K1
∆X
κ air
(4.15)
The coefficient of thermal conductance (κair) is dependent on the operating
temperature. The cross conductance is proportional to the spacing (∆X) and K1
represents a (positive) constant.
The equivalent thermal circuit of the thermal behaviour of a TSM will be
analysed now. Formulating the heat balance of both sensors (the heat flow is oriented
from S1 to S2):
T1 = ( Pel1 − qconv .1 − qstat .1 + qc )
Rstat . ⋅ Rconv .
R stat . + Rconv .
R ⋅R
T2 = ( Pel 2 − qconv .2 − qstat .2 − qc + ξ ⋅ qconv .1 ) stat . conv .
Rstat . + Rconv .
(4.16)
The thermal convection resistance is assumed larger than the thermal static resistance.
Because the sensor is symmetric both the rate of static heat loss as the rate of
convection heat loss of both sensors is assumed to be equal.
∆T = ξ( ∆X ) ⋅ qconv . (T , u) ⋅
1 Rstat . (T ) ⋅ Rc ( ∆X , T )
2 Rstat . (T ) + Rc ( ∆X , T )
(4.17)
Eq. (4.17) consists of three parts. The efficiency of the heat transfer, the convection
heat loss rate and the double static and cross conduction resistances parallel. All three
are dependent on the spacing and temperature difference of the sensor and the fluid.
As can be seen in eq. (4.17) to maximise the sensitivity, i.e. to obtain a
maximal temperature difference as function of the dynamic flow applied, the three
terms have to be maximised. To reach a high efficiency the heat transfer be optimal
which means a minimal spacing. Furthermore the heat transfer on both beginning and
end of the sensor will be less optimal, the sensor should be as long as possible. The
shape of the sensors have to be chosen so that the convection heat loss (qconv.) is
maximal.
This suggest a sensor with a large width. The last term represents the thermal static
resistance and the thermal conductance parallel. This last term is maximal when both
resistances are chosen equal.
75
IV The µ-flown
Analysing the models presented in literature [4.9/4.19], the model of the TSM
could not be extracted directly. In the model presented by Lammerink et al. it is
assumed that all heat is transported to the bulk of a channel around the sensor.
Furthermore the influence of the sensors is not included in the model while it is
assumed that no considerable amount of power is dissipated compared to the heater.
Since in the TSM the power is dissipated in the sensors only and no bulk is around the
sensor this model could not be used.
4.3 M EASUREMENTS
First measurements are presented regarding the model [4.17]. These are used for
validation and for gaining additional insight. The measurement (performed in the
“infinite tube”) depicted in Fig. 4.8 shows the amplitude of the differential
temperature variation as function of the particle velocity level for a certain realisation.
It shows that the TSM has a linear behaviour up to 135 dB PVL (which equals 0.25
m/s). Above the 135 dB PVL the output shows an irregular character. The noise
masks the sensitivity for lower PVL. Down to 0 dB PVL real time small bandwidth
measurements have been performed.
Fig. 4.8: The differential temperature variation as function of the particle velocity.
The sensitivity (the differential temperature variation due to a reference particle
velocity level) is dependent on the operating temperature. This could be expected
since all components of eq. (4.17) are temperature dependent. Fig. 4.9 shows a
typical dependence.
76
Measurements
Fig. 4.9: The differential temperature variation as function of the operating
temperature.
The temperature profile is not constant over the sensor. At both ends (at the tip
and at the bulk side) the temperature is lower than the temperature at the middle of the
sensor. This can be observed when the sensor is glowing. The middle part is glowing
(temperature is approximately 1000 K) and both ends are not glowing in the visible
range (consequently the temperature is below 900 K).
Fig. 4.10 shows the temperature of both sensors apart, the differential (normal)
output and the common output. This measurement is performed in the “infinite tube”,
i.e. the specific acoustic impedance is a real figure (see chapter 2); the particle
velocity signal is proportional with the pressure signal. As can be seen due to the
acoustic disturbance both sensors cool down. The common (sum) signal of both
sensors shows the characteristic double frequency of a HWA.
Fig. 4.10: The temperature of both sensors read apart.
77
IV The µ-flown
A variation in sensitivity is observed when altering the spacing of the TSM.
However not enough statistical measurements have been performed to find an optimal
spacing.
CALIBRATION MEASUREMENTS
The optimal transfer function of the microflown will be primarily empirically
determined. To compare microflowns one has to have a quality factor, a value which
reflects the performance of a microflown.
One of the main parameters of a microphone is the selfnoise, see chapter 6. The
selfnoise is a well defined parameter which is used for acoustic purposes. To exploit
the selfnoise in a more general way, the signal to noise ratio in a one Hertz bandwidth
will be used. When the signal to noise ratio is known the selfnoise can be easily
calculated.
In Fig. 4.11 the recurrent design process is shown. When a new design of
microflown is worked out it has to be realised. This part will be treated in chapter 6.
When it is possible to realise the microflown, the first step in determining the quality
is the so called burn in procedure, a constant voltage is put over the sensing resistors
of the microflown and the current is monitored. In this step a first opinion is formed
about the stability of the resistors of the microflown. When the resistor values are
stable, the first order temperature coefficient of resistivity (α) is determined. By
knowing the coefficient of resistivity the power curve can be obtained. The power is
increased and the resistance of the sensors (and, if present the heater) is monitored.
By using eq. (4.5) the temperature as a function of the dissipated power can be
calculated. The corner frequency is obtained by measuring the frequency response. At
last the sensitivity as a function of the dissipated power is obtained. For all
microflowns the noise is not measured but calculated by assuming that it is generated
by the thermal noise only. The signal to noise ratio can now be determined and used
as a quality factor of the new design.
78
Measurements
Fig. 4.11: Recurrent design process, the signal to noise ratio is the main quality
factor.
All steps now are treated briefly and will be discussed in more detail below. To
gain some insight, for one microflown the several measurement steps are shown.
After discussing all steps separately more general information about microflowns is
presented.
THE BURN IN PROCEDURE
In this paragraph the measurement steps will be discussed on basis of one
microflown (nr. 183). It is a Two Sensor Microflown made in a two mask process
consisting of a half micron silicon nitride and 10 nm chromium and 150 nm platinum
sensing material (see chapter 5). The spacing between both sensors is 80 micron, the
sensor width is 40 micron.
The Burn In procedure is used to ensure that the resistor values show no drift in
the following measurements. A constant voltage is presented to the microflown
sensors and the resistance is monitored. If the resistance does not vary anymore the
procedure is stopped.
Of a new microflown the resistor values vary in the first minutes of operation.
This is thought to be caused due to the formation of an alloy: the chromium and
platinum layer mix due to the high temperature. (For new materials this procedure is
the first step to ensure that this particular material can be used. Some materials react
with the air. This can be monitored using the Burn In procedure and, if so the
proposed material has to be rejected).
79
IV The µ-flown
Fig. 4.12: Typical Burn In measurement result.
Typically the (chromium/platinum) sensing materials are stable in a few
minutes. After the Burn In procedure the (cold) resistance value has been changed by
a few per cent (in the order of 10 %).
THE TEMPERATURE COEFFICIENT OF RESISTIVITY
For the measurement of the coefficient of resistivity of the sensor material two
measurement set-ups are used. The values are determined for only one or two samples
per wafer. Using the first method a microflown is heated up to 550°C and cooled
down slowly.
Fig. 4.13: Measurement set up for temperatures from 100°C up to 550°C.
A little stove is made from a steel shell with a little cavity in it which is heated
with a flame heater. The cavity is accessed through a little opening in the metal. The
microflown to be characterised can be inserted through this opening. Avoiding the
problems with, for instance, melting soldering tin the microflown has been
wirebonded to two small bars of copper having no full contact with these bars and
therefore the temperature of the microflown will be mainly governed by the
80
Measurements
temperature in the cavity instead of by the copper bars. A temperature sensor is
mounted to the metal with the cavity to monitor the oven temperature.
It takes a long time (ca. three hours) to perform one measurement with the high
temperature measurement set up. The lower the temperature the slower the steel shell
cools down. Therefore for lower temperatures up to 100°C the resistance is measured
in water and for temperatures up to 250°C the resistance is measured in olive oil
When the liquid is heated the temperature and resistance is monitored.
A typical measurement of the high temperature set up is shown in Fig. 4.14. As
can be seen the temperature coefficient of resistivity is very linear up to 500°C, the
value can be calculated by using eq. (4.5).
Fig. 4.14: Measurement of the resistance as function of the temperature to determine
the temperature coefficient of resistivity.
Mostly the coefficient of resistivity of the sensor material is measured in the
(non-destructive) olive oil measurement set-up. For the commonly applied
microflowns (chromium/platinum, see chapter 5) the first order temperature
coefficient of resistivity is in the order of one to four per mill per Kelvin.
THE POWER CURVE
To determine the relative resistance variation as a function of the dissipated
power the so called Power Curve is used. If the first order temperature coefficient of
resistivity is known the operating temperature can be calculated by using eq. (4.5).
Rewriting eq. (4.9) an expectation of the curve can be made:
81
IV The µ-flown
∆R
αP
(P) =
=α ( Ts − T f )
R
πlH1
(4.18)
The constant H1 (see eq. (4.3)) is linearly dependent on the coefficient of thermal
conductivity which is dependent on the operating temperature of the sensors:
κair=κair(T0)(Ts/T0)0.8 [4.3]. If a certain configuration is realised, a different metal layer
will not alter the denominator of eq. (4.18) and an estimation of the thermal
coefficient of resistivity can be made.
The measured curve is estimated with a fifth order polynomial fit, the data of
the power curve is now expressed in five numbers.
Fig. 4.15: The resistance variation of the two sensors as function of the dissipated
power per element.
One typical measurement is shown in Fig. 4.15. As predicted in eq. (4.18) the
temperature is not a linear function of the power. The platinum microflowns can be
heated until it is brightly glowing. The measurement is stopped if the microflown just
starts to glow: the maximal sensor temperature is then about 900K (the sensor
operating temperature is lower than the maximal sensor temperature since the
temperature profile is not constant over the sensor). Normally the relative resistance
variation is in the order of 100% and the microflown roughly starts to glow at 35 mW
per sensor for a two sensor microflown and 25 mW per sensor or heater for the SHS
type of microflown.
82
Measurements
THE CORNER FREQUENCY
The corner frequency is normally measured in the “infinite tube”, see chapter 2.
An anechoic chamber has also been used and it shows that both measurements are
consistent. The measurement depicted in Fig. 4.16 shows the transfer function as
function of several distances to the source. This measurement provides information
about the “proximity effect” (see chapter 6) which is important for the
telecommunication application of the microflown. All microflowns do have a first
order low pass behaviour as predicted in the theory above.
Fig. 4.16: A bode plot, measured in an anechoic chamber for several distances to the
source.
The corner frequency of the microflown is in the range of 50 Hz to 1 kHz, depending
on geometry and materials used.
THE SENSITIVITY CURVE
The sensitivity of the microflown is dependent of the temperature of the sensors
and therefore of the dissipated power of the elements. The sensitivity is measured as a
differential resistance variation as a result of an 120 dB PVL sound wave of one
hundred Hertz as a function of the dissipated power in one sensor. In chapter 6 a
more general definition of the sensitivity is presented. Of course both sensors (and
possibly the heater) are heated. As can be seen the resistance variation is in the order
of several per mill. The first order temperature coefficient of resistivity is also in the
83
IV The µ-flown
order of a few per mill and therefore the differential temperature variation is in the
order of one Kelvin (at 120 dB PVL).
Fig. 4.17: The differential resistance variation as function of the dissipated power per
element.
Similar to the result of the Power Curve a fifth order polynomial is fitted to the result
of the Sensitivity Curve to express the information in five numbers.
Typically the maximum of the power curve is found at roughly thirty per cent of
the power at where the sensors start to glow. An 120 dB PVL sound wave at one
hundred Hertz results in a differential resistance variation in the order of one to five
per mill.
THE NOISE MEASUREMENT
The selfnoise of the microflown is measured in an absolute silent environment,
see chapter 2. By observing the Power Curve, combined with the temperature
coefficient of resistivity the operating temperature (Ts) of the sensor resistances of the
microflown can be obtained. By measuring the current through and the voltage over
the sensors the dissipated power and the resistance are calculated.
The microflown is connected to an amplifier having a low noise, high gain and
frequency dependent behaviour (an “A”-type of filter, see chapter 6). The noise,
resistance of the sensors and the dissipated power in the sensors is measured and the
operating temperature of the sensors is estimated. The microflown is replaced with
two (metal film) dummy resistors having the same value and the noise is measured
again. The effect of the noise of the amplifiers is now eliminated, see Eq. (4.19).
84
Measurements
enoise , µ − flown
enoise , dummy
4 kTs Rµ − flown
∫
2
H amplifier( f ) df
Bw
=
4 kTamb. Rdummy
∫ H amplifier( f )
2
=
df
Ts
Tamb.
(4.19)
Bw
Due to the lower temperature of the dummy resistors (Tamb.) the thermal noise
produced is a factor
Ts
Tamb.
smaller compared with the thermal noise of the sensors
of the microflown. This factor is indeed measured and consequently the noise of the
microflown is generated by the thermal noise only.
THE SIGNAL TO NOISE RATIO
If all measurements are performed the signal to noise can be calculated as a
function of the power. As mentioned before the signal to noise ratio is calculated in a
one Hertz bandwidth. Using the results of the Power Curve and sensitivity expressed
in the polynomes Eq. (4.13) will alter:
S
1
(P)=
×
N
2k
P
5
∑
0
i
PCi ⋅ P
+ Tambiant
α
×
1
1+ f f
c
5
× ∑ S i ⋅ Pi
(4.20)
0
The coefficients PCi and Si can be found in Fig. 4.15 and Fig. 4.17. The signal to
noise ratio of the TSM (nr. 183) in one Hertz bandwidth is given in Fig. 4.18.
Fig. 4.18: The signal to noise ratio as function of the dissipated power per sensor.
85
IV The µ-flown
When the microflown dissipates 15 mW per sensor (the operating temperature of the
sensors is approximately 250ºC) the signal to noise ratio is 128 dB. That means that
the noise level is at -8 dB PVL/Hz (the signal is 120 dB PVL). So below the corner
frequency a particle velocity of 20 nm/s can be measured in one Hertz bandwidth.
The corresponding relative temperature variations are in the order of micro Kelvins.
As can be seen in Fig. 4.18 for the signal to noise ratio an optimal power can be
found. Three figures are important to determine the signal to noise ratio. The corner
frequency, the square root of the ratio of the dissipated power and the operating
temperature and the sensitivity below the corner frequency. It appears to be
convenient to have a dimensionless number combining these numbers. For this the
performance of a microflown is given by:
u

Popt .
 ref .

Performance = 20 Log10 
×
×SP 
opt .
TPopt .
 2 k

(4.21)
(The reference particle velocity uref.=50 nm/s, see chapter 2). The corner frequency is
not affecting the performance. This figure will be used in the noise factor, see also
chapter 6.
For the microflown number 183, the optimal power is found in Fig. 4.18
(15mW per sensor), the operating temperature is then estimated by using the thermal
coefficient of resistivity and Fig. 4.15 (500 K). The sensitivity at 15mW can be found
in Fig. 4.17 (0.05 s/m). The performance of microflown number 183 is 8.3 dB.
C ONCLUSIONS
AND DISCUSSION
By studying the hot wire anemometer it is understood that the sensors of the
microflown should have a first order low pass behaviour with a corner frequency in
the order of a few hundred Hertz. The microflown originally did consist of three
elements, two temperature sensors and a heater (SHS type of microflown). The new
proposed microflown (the Two Sensor Microflown, TSM) only contains two
elements: two heated temperature sensors. This new type of microflown has an
improved signal to noise ratio; the most important figure of an acoustical sensor.
A quantitative model of the TSM is presented and it explains why the static flow
sensitivity is dependent of the sensor spacing and operating temperature. The dynamic
86
Conclusions and discussion
behaviour is modelled with the volumetric heat capacity and the thermal resistances
only.
The model of the TSM is kept very simple. To obtain a more detailed model a
lot of effort has to be put into research about alternating temperature profiles in very
small flows around very small structures. To gain more insight in the operation
principles it was chosen to perform characteristic measurements on the behaviour of
the microflown.
A set of calibration measurements fully describes the acoustic properties of the
microflown and this will resolve in two figures. The performance, a dimensionless
figure which provides information about the low frequency self noise. And the corner
frequency, above this frequency the sensitivity drops with 6dB/oct.
87
IV The µ-flown
R EFERENCES
[4.1] R. Aigner et al; SI-Planar-Pellistor: Designs for temperature modulated operation, Transducers
‘95-Eurosensors IX, (1995), 213-PD5.
[4.2] T.S.J. Lammerink et al; Micro liquid flow sensor; Sensors and Actuators A, 37-38, (1993), 4550.
[4.3] C.G. Lomas, 'Fundamentals of hot wire anemometry', Cambridge University Press,
Cambridge, 1986.
[4.4] R.G. Johnson et al., A Highly sensitive silicon chip microtransducer for air flow and
differential pressure sensing applications, Sensors and Actuators, 63-72, 1987.
[4.5] F.E. jorgensen, An omnidirectional thin-film probe for indoor climate research. DISA Info.,
24, 24-29, 1979.
[4.6] F.P. Incropera and D.P. de Witt, Fundamentals of heat and mass transfer, John Wiley & sons,
New York, 1990.
[4.7] C.Yang et. al., Monolithic flow sensor for measuring milliliter per minute flow, Sensors and
Actuators A, 33, 1992, 143-153.
[4.8] K. Petersen et. al., High precision, High performance mass-flow sensor with integrated laminar
flow micro-channels, Sensors and Actuators. 1985, 361-363.
[4.9] G.B. Hocker, A microtransducer for air flow and differential pressure sensing applications,
Micromaching and micropackaging of transducers, 1985, 207-214.
[4.10] J. Branebjerg, A micromachined flow sensor for measuring small liquid flows, Sensors and
Actuators, 1991.
[4.11] E. Masayoshi, Micro flow sensor and integrated magnetic oxigen sensor using it, Sensors and
Actuators, 1991.
[4.12] B.W. van Oudheusden et. al., High sensitivity 2-D flow sensor with an etched thermal isolation
structure, Sensors and Actuators A, 1990, 425-430.
[4.13] G. Wachutka et. al., Analytical 2D model of CMOS micro-machined gas flow sensors, Sensors
and Actuators, 1991.
[4.14] B.W. van Oudheusden et. al., Integrated flow friction meter, transducers 1987, 368-371.
[4.15] P.J. Leussink; Flierefluiten I, The amazing Microflown; M.Sc. Thesis; University of Twente;
1996.
[4.16] P.J. Leussink and M.T. Korthorst; Inleiding flierefluiten; 250 hrs report; University of Twente;
1995.
[4.17] T.T. Veenstra; Flierefluiten III, characterization methods for the microflown; M.Sc. Thesis;
University of Twente; August 1996.
[4.18] B.J. Vreugdenhil, Een analytisch en nummeriek model van de microflown, M.Sc. Thesis;
University of Twente; March 1996.
[4.19] H-E. de Bree, P.J. Leussink, M.T. Korthorst, M. Elwenspoek, The Two Sensor Microflown,
an improved flow sensing principle, proceedings Eurosensors X, Leuven, 1996
88
References
[4.20] H-E. de Bree, P.J. Leussink, M.T. Korthorst, H.V. Jansen, T. Lammerink, M. Elwenspoek,
The microflown, a novel device measuring acoustical flows, Sensors and Actuators: A.
Physical, volume SNA 054/1-3, pp. 552-557.
89
CHAPTER 5: REALISATION
S UMMARY
In chapter four a method to quantify the acoustical
performance of the microflown is given. By using this number a
choice can be made regarding mechanical parameters. In this
chapter different methods to realise a microflown will be given.
A study is made of how long it takes to process a wafer.
As a result of this an estimation can be made on the costs of
the various processes.
Fig. 5.0: A part of a processed wafer containing Two Sensor Microflowns.
91
V Realisation
5.1 I NTRODUCTION
Realisation of the microflown is the most important issue in this research.
Nevertheless research issues about cleanroom techniques are not the main theme in
this chapter, the microflown is easy to make using straightforward cleanroom
techniques. The accent will be how to make a cheap and reliable device and what
rules have to be obeyed to create a device with the best acoustical properties.
The standard cleanroom techniques will be discussed briefly and four methods
of realisation are presented.
5.2 W HAT
PARAMETERS ARE IMPORTANT ?
There are three types of quality considerations distinguished. At first the
mechanical construction of the microflown, at second the acoustical performance of
the total device (i.e. the signal to noise ratio and frequency response) and last there
are economical considerations. In other words the goal is to make a strong and stable,
cheap and easy to fabricate sensor with the best acoustic behaviour possible.
µ-FLOWN MODEL ASPECTS
The main acoustic quality factor of the microflown is the signal to noise ratio. If
the microflown is operated at its optimal power this ratio is given by (see chapter 4):
S
=
N
Popt
4 kTs ,Popt ⋅ Bw
×
α
× ∆T ( Popt )
1 + f fc
(5.1)
The only parameters which can be optimised by using cleanroom techniques are the
corner frequency (fc) and the first order temperature coefficient of resistivity (α). The
signal to noise ratio appears to be proportional to the corner frequency (see also
chapter 6), and is given by (see chapter 4):
fc =
h πdl
1
⋅
⋅
ρc 2πAl 1 + α ( Ts − T f )
(5.2)
As can be seen in eq. (5.2) the corner frequency is inversely dependent of the specific
heat (c) and the density of the sensor material (ρ). The second part concerns the shape
92
What parameters are important?
factor, if the sensors are made thinner, the second part of eq. (5.2) will enlarge and
(also measurements have proven that) the corner frequency will increase. The third
part of eq. (5.2) will lower the corner frequency when the temperature coefficient of
resistivity increases. A large temperature coefficient of resistivity is however
advisable while the signal to noise ratio is linearly dependent on it.
Concerning the signal to noise ratio the best materials to use are materials with a
high value of α ρc . The sensors have to be as thin as possible, resulting in a low
thermal capacitance (see chapter 4).
ELECTRICAL ASPECTS
The microflown converts the particle velocity into a differential resistance
variation which has to be converted into an electrical output. The signal to noise ratio
is of major concern but also power consumption and power supply voltage are in
some applications important parameters.
To enable a low voltage supply the voltage over the resistors has to be minimal.
If the microflown is operated by the optimal power, Popt (see chapter 4), the sensor
resistance has to be as low as possible to get a low voltage supply (E), see eq. (5.3).
E = Rs ⋅ Popt
(5.3)
Chapter three shows that the static ohmic resistance of the sensors has no
influence on the signal to noise ratio. The ohmic resistance combined with the
operating temperature of the sensors causes electrical noise. If this noise is larger than
the equivalent input noise of the following pre-amplifier, this amplifier does not add
noise significantly. The electrical resistance of one sensor can be calculated by:
Rs = ρ r
h⋅w
l
(5.4)
Using h as the height, w as the width and l as the length of the resistor and ρr as the
resistivity. To create a higher resistance the height has to be decreased.
To get an optimal noise performance the resistor value has to be larger than the
ohmic base series resistance of a BJT transistor applied in the pre-amplifier (see
chapter 3). If this is accomplished the electrical circuit will not add noise
93
V Realisation
significantly. And to ensure that the voltage supply is as low as possible the resistance
has to be as low as possible. So the optimal resistance value is about twice the ohmic
base series resistance of the BJT transistor used, in the order of hundred ohms at
ambient temperature. When operating the microflown the temperature of the sensor
resistance and the static resistor value will increase and therefore the noise will
increase.
CONSTRUCTIONAL ASPECTS
The base construction material has been chosen to be silicon nitride since this
material has some exclusive parameters and has well known properties [5.1/5.9].
Silicon nitride is an electrical insulator which makes the design very easy since
otherwise the films have to be insulated from the silicon bulk. From silicon nitride it
is well know that it is more resistant against many, later mentioned, etching fluids
than other possibly suitable materials as silicon dioxide or silicon oxynitride (also
electrical insulators) [5.2]. Furthermore the stress of silicon nitride can be controlled
by adjusting the process parameters allowing to create a sensor film with a low stress.
To obtain a high corner frequency the sensors has to be made as thin as
possible. To allow a thin silicon nitride carrier the stress of the metal layer has to be
not too large. It shows that the effect of the stress of the metal layer can be reduced
by producing a thinner metal layer. The metal layer is normally made of platinum (see
below). It appears that an adhesion layer is necessary. This layer will interact with the
platinum and will form an alloy of which the temperature coefficient of resistivity is
substantially lower than of a pure platinum layer. Consequently when the platinum
layer is made too thin the percentage metal of the adhesion layer is too high and the
first order temperature coefficient of resistivity drops. A thinner metal layer also will
lead to a higher corner frequency.
Summarising, in order to allow a thin silicon nitride carrier the metal layer has
to be thin and therefore a single metal would be appropriate because then an alloy can
not be formed. When both the metal and the silicon nitride layer are as thin as
possible the corner frequency is as high as possible.
94
What parameters are important?
C OST
ASPECTS
To give an impression of the cost of a microflown the cleanroom costs is the
first matter to look into. If the process time and operator time for all processes are
given (for small batch production and using MESA facilities) for larger batches an
estimation can be made.
The number of masks is a good indication of the process costs [5.18], [5.19].
This is because lithography steps (using the masks), are time consuming and due to
for example misalignment the risk of failure is increased. Also the process time and
expenses of equipment will be involved in the price.
The size of a microflown has to be minimised to get a maximal number per
wafer. Because the number of bondpads is determining the width of the microflown
the two sensor microflown is the best candidate regarding the size.
Small production volume requires a low constant cost and a high variable cost,
the handling time for separation of dices and finishing will be high in order to keep
the constant cost low: no machines have to be paid and programmed. Dicing by
breaking is therefore the solution for small volume production. The microflown has to
be relatively large because the handling has to be done by hand. So for small volume
production the cleanroom cost and the handling time are relatively high.
For large volumes the dicing can be done by sawing and the handling has to be
done by a robot. The microflowns can now be as small as possible keeping the
cleanroom costs per sensor as low as possible.
OTHER PRODUCTION PROCESS CONSIDERATIONS
The cleanroom is a multi-user environment and has only a certain number of
machines. There is thus a limited set of machines which is not available at any time.
This fact requires a certain way of processing, the so called store and forward
processing. The general idea is to split the total process in to the smallest portions
possible. One of these portions contains a number of process steps that has to be done
before the wafer under process can be stored again.
95
V Realisation
5.3 T HE
FABRICATION PROCESSES
A total of four processes are developed to realise the microflown. The first
process creates the bridge type of microflown. The second type is designed to create
cantilever types of microflowns. The third method allows a single metal as sensor or
heater material and the last process is a one mask, single metal process. The
production process scheme is schematically represented in Fig. 5.12, the ‘M’ indicate
a mask step. The process steps will be briefly discussed here. All exact figures and
process parameters can be found in appendix 5.
THE BRIDGES (TYPE I PROCESS)
The first type of microflowns made were bridge types, silicon nitride bridges
with sensors and heater from gold thin films [5.15]. A chromium layer is used as
adhesion layer. In the first stadium of the research it was not clear what the width of
the heater had to be.
To make a very large heater (a width in the order of 200 µm) possible, a
sacrificial layer (of polycrystalline silicon) is used under the sensors and heater. After
deposition and patterning the polycrystalline silicon, low stress silicon nitride is
deposited on the wafer and the heater and sensors are deposited by sputtering and
patterned by lift off. The metal layer used is gold or platinum and chromium is used
as adhesion layer. The silicon nitride is patterned with Reactive Ion Etching (RIE) and
is used as mask for the anisotropic wet etching. This etching will release the sensors
and heater while the mono-crystalline silicon and polycrystalline silicon is etched only
where the silicon nitride is removed. To avoid through the wafer etching the etching
has to be stopped (KOH time stop).
If the width of the sensors and heater is not too large the structures can be
released by isotropic RIE etching and the sacrificial layer is not necessary.
96
The fabrication process
Fig. 5.1: Type I microflown, the width of the sensors is 5µm and of the heater 90µm.
In Fig. 5.2 the several production steps are shown in a cross-section of the
wafer. Step a: The optional LPCVD deposition of the polycrystalline sacrificial layer,
b: patterning by RIE, c: LPCVD deposition of low stress silicon nitride, d: deposition
of metal (chromium-gold or chromium-platinum) by sputtering and patterning by liftoff, f: anisotropic wet etching to create the channels and release the sensors and
heater. Dicing normally is done by sawing.
Fig. 5.2: Production steps of the Type I microflown.
97
V Realisation
THE CANTILEVERS (TYPE II PROCESS)
Fig. 5.3: Type II SHS microflown, the chromium gold metal layer causes tensile stress
and thus an upward bending of the cantilever. As can be seen (under the
microflown) the anisotropic wet etching has been stopped just too early.
Fig. 5.4: Type II TSM microflown, the chromium platinum metal layer causes
compressive stress and thus the downward bending of the cantilever.
98
The fabrication process
Fig. 5.5: Tip of the type II microflown. The metal acts as mask for the RIE, in the
middle of the sensors still a mask is used (to reduce the possibility of
redeposition of metal).
Fig. 5.6: Tip of the type II microflown. The metal acts as mask for the RIE, only to
connect the top a mask is used. At the bottom the remaining silicon nitride
layer can be seen.
99
V Realisation
The second process is developed to create cantilever type of microflowns [5.15],
[5.16]. While the stress of the sensors and heater could damage the microflown in a
bridge type configuration cantilevers where proposed as a solution to this problem.
The stress would simply bend the sensor and heater instead of damaging it. Also a
rigid plane near the sensors will decrease the sensitivity while the particle velocity will
reduce due to the boundary layer. As can be seen Fig. 5.3 and Fig. 5.4 the various
metals (chromium/gold and chromium/platinum) cause stress and the microflown will
bend.
To create type II microflowns first a silicon nitride layer is deposited. Then a
chromium and gold or chromium and platinum metal layer is sputtered and patterned
with lift off. The silicon nitride is patterned at the top and bottom with reactive ion
etching. The etching at the bottom can be omitted. Only a thin silicon nitride layer
will remain at the bottom which will usually disappear when dicing. If not, it can
easily be removed by hand. Anisotropic etching will free the sensors (and if present
the heater) starting at the top, a sacrificial layer therefore is not needed. Through the
wafer etching is desired, a time stop is not necessary.
One important goal is to maximise the corner frequency. This can be done by
making the sensors as thin as possible, see eq. (5.2). In case of the microflown the
metal layer is on top of the silicon nitride. To avoid that the aligning is not too
difficult the silicon nitride carrier is a bit overdimensioned, see Fig. 5.3 and Fig. 5.4.
The result of this overdimensioning is that the sensors are too large, resulting in, most
important, a lower corner frequency than possible. The chromium platinum metal
layer can be used as a mask in the RIE patterning of the nitride layer. This property is
used to create less bulky sensors, see Fig. 5.5 & Fig. 5.6, and this results indeed in a
higher corner frequency (see eq. 4.13). It has to be said that using a metal as mask in
the RIE is not as easy as it sounds. When the ion bombardment of the RIE process is
too high [5.20], the metal layer will be sputtered. This will lead to a reduced metal
thickness and more important, to re-deposition of the metal on the wafer. When redeposited the metal acts as a mask again. This problem can be solved [5.11] but it
restricts the possibilities of RIE.
As can be seen in Fig. 5.5 the silicon nitride is only present at the top and (this
can not be seen) under the metal layer. The top is still connected because in the
process the sensors without this connection sometimes intertwine [5.17]. The reduced
100
The fabrication process
amount of silicon nitride roughly leads to a twice higher corner frequency. Another
advantage of using the metal as a mask is that the process is “self aligned”. It appears
that if the top is not connected the corner frequency also increases. This is because the
sensor cross resistance decreases, see chapter 4.
The process steps of the type II microflowns is depicted in Fig. 5.7. Step a:
LPCVD deposition of low stress silicon nitride, b: deposition of metal (chromiumgold or chromium-platinum) by sputtering and patterning by lift-off, c: anisotropic
wet etching to release the sensors and heater and create breaking grooves. The silicon
nitride at the back is normally not removed. Dicing is normally done by breaking.
Fig. 5.7: Production steps of the Type II microflown.
THE SINGLE METAL PROCESS (TYPE III PROCESS)
For several reasons it is desirable to avoid an adhesion layer. The main reason is
that the adhesion layer interacts with the conducting metal layer and due to the high
operating temperature an alloy is formed which has always a lower temperature
coefficient of resistivity than the separate metals (gold or platinum). To increase the
corner frequency the metal film and silicon nitride layer has to be as thin as possible.
The adhesion layer is chosen as thin as possible (in the order of 10 nm). A thinner
sensing metal film forms an alloy with an even smaller temperature coefficient of
resistivity. A temperature coefficient of resistivity of 2.1‰K-1 was measured for an
150/10nm Pt/Cr, 1.53‰K-1 for a 100/10nm Pt/Cr layer and 1.32‰K-1 for a
50/10nm Pt/Cr layer. Decreasing the silicon nitride layer increases the corner
frequency, this is a wanted effect. But also the bending due to the stress of the metal
layer increases, which is a not wanted effect. Therefore if the metal layer is thinner
the silicon nitride layer can also be chosen thinner. A single metal would allow
thinner metal films and (thus) a thinner silicon nitride layer causing a higher corner
frequency and the temperature coefficient of resistivity will not decrease [5.9], [5.10].
101
V Realisation
The anisotropic (KOH) wet etching of silicon turns out to remove most metals
without a chromium adhesion layer. Chromium as single metal can not be used since
it oxidates and it is to brittle (it tends to break while bending). Therefore a process is
developed with the KOH etching of silicon before the metal deposition.
Like the previous process at first a layer of low stress silicon nitride is deposited
(step a in Fig. 5.8). This layer is patterned (with RIE) at the back side and anisotropic
wet etching will create a silicon nitride film at the top (b). A layer of single metal is
sputtered on the top and patterned with lift off (c). Another possibility is using a
shadow mask [5.12]. While the metal is deposited on only a thin film of silicon
nitride, the lift-off has to be done with great care because of the risk of breaking,
using a shadow mask the lift-off process step is not necessary and therefore the yield
will increase. The last step (d) is the removal of the silicon nitride top layer, the metal
layer is used as mask; under the metal the silicon nitride remains.
Since the RIE etching uses a plasma for etching and the silicon nitride is has
strong insulating properties the removal of silicon nitride film will only succeed when
a conducting layer is deposited on the back side. Chromium or aluminium can be
used. After RIE etching this metal layer has to be removed [5.17].
A disadvantage is that the metal deposition has to be done on the fragile thin
silicon nitride film (c). This process step is not very robust although one micron
silicon nitride films survive normally. A solution is to leave a few micron silicon
under the silicon nitride layer using a time stop during the anisotropic wet etching.
Fig. 5.8: Production steps of the type III microflown.
THE ONE MASK PROCESS (TYPE IV PROCESS)
As already mentioned before, one of the main cost-indicators of cleanroom
activities is the number of mask steps. This is because patterning is time consuming
and all masks have to be aligned. Aligning also often does have the disadvantage that
102
The fabrication process
a certain spread in positioning of the different layers is introduced, see Fig. 5.5. In
case of the microflown the metal layer is on top of the silicon nitride. To avoid that
the aligning is not too difficult the silicon nitride carrier is a bit over-dimensioned.
For the chromium platinum type of metal layer this layer can be used as a mask in the
RIE patterning of the nitride layer. This feature is used to create less bulky sensors,
see Fig. 5.6 and the result is indeed a higher corner frequency (see also eq. 4.13). It
is possible to design a one mask process using the metal layer as mask for the silicon
nitride layer. As mentioned before, a single metal is much sought after. While the
KOH etching will lift off a metal layer with out an adhesion layer the KOH etching
has to be carried out before the metal deposition. This excludes a metal mask method.
The solution is found in first patterning the silicon nitride layer, then KOH
etching and at last metal deposition [5.17]. To avoid short-circuiting of both sensors
the silicon nitride has to act as a shadow mask [5.13], [5.12]. This is easily done by
etching through the silicon nitride and etch isotropically a few micron into the silicon.
After KOH etching the silicon nitride acts a (very small) marquise over the silicon,
see Fig. 5.9. In this SEM photo one can see a part of the microflown between the
bondpads. The silicon nitride leans over a KOH etched groove. The dirt in the groove
is caused by the (polluted) KOH solution.
To create 800 µm long cantilevers the wafer is too thick, it takes much longer to
free the cantilevers than to etch through the wafer. The etch speed to free the
cantilevers appears to be three times as fast as the etch speed through the wafer.
Therefore of the back side of the wafer the silicon nitride is removed before the KOH
etching. The result is that both sides of the wafer are etched and the cantilevers are
free at the same time as the wafer is completely etched through.
103
V Realisation
Fig. 5.9: Silicon nitride marquises act as a shadow mask to prevent electrical short
circuiting.
Fig. 5.10: One mask microflowns.
104
The fabrication process
The metal layer is deposited not by sputtering but using an evaporation method. This
is because sputtering causes short circuiting of the bondpads. In this process step it is
crucial that the silicon nitride layer is of low stress while otherwise the metal layer is
not of the same thickness over the sensors.
The result of the one mask process is depicted in Fig. 5.10. Due to the KOH
etching at the backside the thickness of the bulk is in the order of 75 µm. In Fig. 5.11
the process steps are shown schematically. Step a: deposition of the silicon nitride
layer, b: removal (RIE) of the silicon nitride at the back side, c: releasing the
structures by KOH etching (time stop), d: single metal deposition by E-beam
evaporation.
Fig. 5.11: Production steps of the type IV microflown.
One process step in the one mask process is the removal of the silicon nitride at
the back side of the wafer. The silicon nitride is just deposited in the step before. One
could think of a way to deposit silicon nitride only at the front side of the wafer. This
is not done in this research.
105
V Realisation
SUMMARY OF PROCESSES
The four production methods of the microflown are represented in Fig. 5.12.
The several process steps are discussed separately below.
Fig. 5.12: Production process schemes for fabricating microflowns.
The grey areas can be omitted, the “M” indicates that a mask is used.
106
The fabrication process
THE PROCESS STEPS
How microflowns are processed has been discussed above, a discussion of all
process steps is presented below. The time which is required for each process step is
measured the processing of multiple wafers [5.14], [5.15], [5.17]. Each process step
has, regarding time, an optimal number of wafers. For example the nitride deposition
can be carried out with twenty wafers at a time and therefore the optimal number of
wafers is twenty. KOH etching (in the MESA facilities) is done with a maximum of
seven wafer at a time.
Table 5.1: List of the required process time (P.T.) and operator time (O.T.) of each
process step.
O.T.
P.T.
Nr. of
Time per one wafer
[min.]
[min.]
wafers
O.T. [min.]
P.T. [min.]
Standard cleaning
15
36
10
1.5
3.6
LPCVD polysilicon
20
150
20
1
7.5
LPCVD nitride
20
180
20
1
9
Lithography for lift-off
28
54
4
7
13.5
Sputtering
30
75
1
30
75
E-Beam evaporation
75
150
12
6.3
12.5
Lift-off
15
40
7
2.2
5.7
Lithography for RIE
27
79
4
6.8
20
RIE
20
20
3
6.7
6.7
Resist stripping
5
20
4
1.3
5
KOH etching
25
7
420
3.6
60
As can be found in Table 5.1 sputtering is this still the most time consuming
process step. This is because only one wafer can be processed at a time. When using
another sputter device this problem can be solved. If fact most processes can be
107
V Realisation
optimised regarding throughput. For instance the KOH etching can be performed in
larger batches.
If the process steps are optimised regarding throughput, the lithography step will
be the most time consuming process since the aligning of layers is a delicate matter
and this can only be done with one wafer at a time. It may be that the lithography of
the one mask process can be performed in a batch process. The mask has only be
aligned on the flat of the wafer which is not a very delicate job.
Looking at Fig. 5.12 and Table 5.1 the operator time (O.T.) and process time
(P.T.) of the various processes can be calculated (see Table 5.2).
Table 5.2: process time (P.T.) and operator time (O.T.) of process I, II and IV.
Type I
Type II
Type III
Type IV
O.T [min.] 75
60
70
35
P.T [min.]
200
200
90
150
As was expected total manufacturing time of a type IV microflown is the
shortest. These times are measured while the microflowns where processed. The
operator time is considerable less than the process time. Some processes are more
suitable to use this time difference to perform tasks than others. In calculations this
time has to be used as a minimal time. If the microflown is produced in large amounts
the operator time could reach this minimum. The processes however can be optimised
i.e. larger batches processed in one time. The process time therefore can be reduced.
• POLYSILICON
DEPOSITION
&
PATTERNING.
A layer of sixty nano-meter polysilicon
is deposited on a 380 µm single crystalline silicon (SCS) wafer. This is done by
low pressure chemical vapour deposition (LPCVD). This layer will be used as
sacrificial layer to free the nitride bridges by the anisotropic KOH etching step.
Patterning the polysilicon layer. First resist has to be deposited on the frond side of
the wafer by standard lithography, see appendix 5. After this the polysilicon will
be isotropic etched by reactive ion etching (RIE). The front side has to be locally
etched and on the back side the polysilicon has to be removed completely.
108
The fabrication process
• SILICON NITRIDE DEPOSITION &
PATTERNING.
Deposition of low stress nitride layer
is performed by Low Pressure Chemical Vapour Deposition (LPCVD). This layer
will be used as the construction material of the sensing element, to give it
mechanical strength and as an etching mask for the anisotropic KOH etching. The
patterning is performed by RIE etching.
• METAL DEPOSITION. Deposition of the metal pattern applied as resistors. Two ways
of metal deposition are used, E-Beam evaporation and sputtering. Process type I, II
and III normally use sputtering since gold and platinum are not allowed in the EBeam evaporation (at the MESA facilities). Before sputtering a standard
lithography step is done. After this a metal layer is deposited of the front side and
patterned by lift-off. In the MESA facilities the sputtering can not be considered as
a metal deposition from a point source, therefore another method, E-Beam
evaporation, is used for the one mask process. The silicon nitride layer is used as a
“shadow mask”.
• ANISOTROPIC
ETCHING OF SILICON.
This is done by KOH etching. The silicon
nitride will act as a mask. This results in a channel for type I microflowns and in
cantilevers and breaking grooves for type II microflowns. Type I uses a (critical)
time stop, after approximately five hours the wafer has to be removed from the
etching agent. The KOH etching appears to be a relatively destructive process for
the metal layer. Only when a chromium adhesion layer is used most metals stick
well enough to survive this process step. Platinum and gold are the metals which
are most commonly used in this research period. Platinum is the best metal of both
because of the high melting temperature. The mayor disadvantage of using an
adhesion layer is that the sensor material is not a single metal. Due to the high
operating temperature an alloy is created which has always a lower temperature
coefficient of resistivity than the gold, platinum or chromium. This is a very
unwanted effect. Using only chromium as a single metal appears not possible while
the layer is not resistant for bending of the cantilevers. To be able to use a single
metal process, the metal layer must be protected against the KOH or the KOH
etching must be done before the metal deposition. The first option can be realised
with a silicon nitride sealing layer. A disadvantage is that the sensors become
thicker and the corner frequency will decrease.
109
V Realisation
5.4 S EPARATION
OF DICES
Three ways of separation of dices have been investigated: two ways of dicing by
breaking and dicing by sawing.
The first way of dicing by breaking is to etch breaking grooves. If a scalpel is
pushed into the groove the dice is separated. This method has been used for over one
year to separate several hundreds of microflowns. An example of dicing by breaking
is shown in Fig 4.0.
The second way is through the wafer etching. The microflown is only held by
little bars of bulk material. The general idea is that the microflowns are broken out of
the grid. An example is shown in Fig. 5.10.
A disadvantage of the dicing by breaking is that the breaking grooves have to be
relatively large and consequently expensive. Therefore only for small batches the
dicing by breaking will be commercially attractive.
The most common way is sawing the wafer. Advantage is that the dicing
approximately cost only 50 µm, disadvantage is that only staff members are allowed
(in the MESA research institute) to use the sawing device. Because it is a well known
method and it is (for research purposes) a time consuming process step this method
has not been further investigated.
110
Conclusions and discussion
C ONCLUSIONS
AND DISCUSSION
Four methods of constructing a microflown are presented.
The bridge type of microflown was not used at the end of the research since it
appears that the sensitivity of the microflown decrease if the sensors are in the
neighbourhood of a rigid plane. In the realisation of the bridge type the bottom of the
channel is to near of the sensors.
In this research a few thousand microflowns are made using the type II process
because this process has the advantage that a lot of shapes are possible. For the
metalisation both sputtering as E-beam evaporation is possible. Most microflowns
where made with a one micron silicon nitride. A half micron nitride does have a
higher corner frequency but also a larger bending of the sensors since the metal
thickness is kept constant.
The type III process allows a single metal what makes it very suitable for
measurements on non-alloy metals. Both sputtering as E-beam evaporation is possible
and with this process the best metal can be found.
The mayor advantage of the one mask process (type IV process) is in the name;
only one mask is needed. Aligning problems will be reduced. The reduction of masks
and thus process time will lead to a substantial cost reduction of the microflowns as
they are on the wafer. The wafer however has become very thin which could lead to
damaging by further processing. In the one mask process it is not possible to use
(MESA) sputtering for metalisation when it can not be seen as a point source. This
reduces the number of possibilities using this method. If a good (metal) candidate is
found using the type III process, permission is asked to use the E-beam evaporation
method of deposition. The last step of the one mask process is the metalisation. This
can be done without the use of a mask since the silicon nitride layer is a bit under
etched and acts like a “shadow mask”. The effort which has be to put into creating
this under etching of the silicon nitride can be seen as a disadvantage compared to the
type II process. An advantage is that the metalisation is done at the last step. Due to
this the metal layer will stay as pure as possible. In the type II process the metal film
is a bit polluted and due to the lift-off process bent at the edges, see Fig. 5.5.
An advantage of the TSM compared to the SHS type of microflowns is that it is
better possible to leave the top not connected. This is because both sensors of the
111
V Realisation
TSM have the same operating temperature and therefore have the same amount of
bending. When operating the SHS, the heater is the hottest and therefore the heater
will bend more than the sensors, the three elements will therefore not be in one line.
R EFERENCES
[5.1] P.R. Scheeper; A silicon condenser microphone: Materials and technology; Ph. D. thesis;
University of Twente; April 1993.
[5.2] K.E. Petersen, Silicon as a mechanical material, Proc. IEEE, 70 (1982) 420-547.
[5.3] K. Allaert, A van Calser, H. loos and A. Lequesne, A comparison between silicon nitride films
made by PCVD of N2-SiH4/Ar and N2-SiH4/He, J. Electrochem. Soc., 132 (1985) 1763-1766.
[5.4] W.A.P Claassen, W.G.J.N. Valkenburg, M.F.C. Willemsen and W.M. v.d. Wijgert, Influence
of deposition temperature, gas pressure, gas phase composition and RF frequency on
composition and mechanical stress of plasma nitride layers, J Electrochem. Soc., 132 (1985)
893-898.
[5.5] H. Dun, P. Pan, F.R. White and R.W. Douse, Mechanisms of plasma-enhanced silicon nitride
deposition using SiH4/N2 mixture, J. Electrochem. Soc., 128 (1981) 1555-1563.
[5.6] G.M. Samuelson and K.M. Mar, The correlations between physical and electrical properties of
PECVD SiN with their composition ratios, J Electrochem. Soc.,129 (1982) 1773-1778.
[5.7] P.Pan and W. Berry, The composition and physical properties of LPCVD silicon nitride
deposited with different NH3/SiH2Cl2 gas ratios, J Electrochem. Soc., 129 (1982) 3001-3005.
[5.8] A.G. Noskov, E.B. Gorokov, G.A. Sokolova, E.M. Trukhanov and S.I. Stenin, Correlation
between stress and structure in chemically vapour deposition nitride films, Thin solid Films,
162 (1988) 129-143.
[5.9] R. Aigner et al; SI-Planar-Pellistor: Designs for temperature modulated operation, Transducers
‘95-Eurosensors IX, (1995), 213-PD5.
[5.10] E.A. Amerasekera, D.S. Campbell, Failure Mechanisms in Semiconductor Devices, University
of technology, Loughborough, UK.
[5.11] H.V. Jansen; Plasma etching in microtechnology; Ph. D. thesis; University of Twente;
February 1996.
[5.12] G.-J. Burger, A slider motion monitoring system, university of twente, 1995, thesis
[5.13] R. Legtenberg, Electrostatic actuators fabricated by surface micro machining techniques,
Thesis Universiteit Twente, Enschede, 1996.
[5.14] P.J. Leussink and M.T. Korthorst; Inleiding flierefluiten; 250 hrs report; University of Twente;
1995.
[5.15] P.J. Leussink; Flierefluiten I, The amazing Microflown; M.Sc. Thesis; University of Twente;
report.
[5.16] M.T. Korthorst, Flierefluiten II, A sound intensity probe, M.Sc. Thesis, August 1996.
112
References
[5.17] K.C. Ma; Flierefluiten IV, procesoptimalisatie en materiaalonderzoek t.b.v. de microflown;
M.Sc. Thesis; University of Twente; August 1996.
[5.18] Private discussion Twente Micro Products.
[5.19] Private discussion MESA.
[5.20] B. Chapman, Glow discharge processes: sputtering and plasma etching, Wiley, New York,
1980.
113
CHAPTER 6: APPLICATIONS
S UMMARY
In this chapter some applications using the microflown
are presented. First the acoustic properties of the microflown
as a particle velocity measuring device are given and methods
and criteria for comparing the microflown to a pressure
microphone derived.
Of course good acoustic properties are crucial but the
distinguishing features of the microflown are important to find
an application as a product. The features of the microflown are
summarised.
At last some applications using the microflown are given.
By combining it with a pressure microphone an acoustic
intensity probe, an acoustic impedance probe and a stereo
microphone are realised. By applying two microflowns the flow
gradient can be measured and the apparent pressure obtained.
This way the pressure microphone becomes redundant and both
the acoustic intensity probe and acoustic impedance probe are
realised by using only microflowns.
Fig. 6.0: The 3D u-u intensity probe.
VI
Applications
6.1 I NTRODUCTION
In this chapter some possible applications of the microflown are summarised and
some applications are investigated and realised. For a chance on a commercial success
of an application only one thing is crucial: it has to fulfil a certain need for less costs
than a competitive (mostly an already existing) product. If the application can be sold,
many aspects are involved. Funding, legal protection and long term credibility are just
a few aspects. A lot of literature on these subjects is available [6.13]. This chapter
will mainly focus on the technical aspects.
To establish the important aspects of microphones, the acoustical properties of
commercial microphones are investigated first and after this the properties of the
microflown are summarised and compared with conventional microphones.
6.2 P ROPERTIES
OF THE
µ - FLOWN
Two sorts of properties are important for microphones, the acoustic properties
and other properties like power consumption, robustness, long term stability, etcetera.
The acoustic properties will be discussed below and the other properties will be
discussed with the properties of the microflown.
ACOUSTIC PROPERTIES
The acoustic properties of the microflown can be described by a few parameters:
the sensitivity, the polar pattern, the noise level, the signal to noise ratio, the noise
spectrum and the dynamic range. These parameters are well defined for pressure
microphones and will be given for the µ-flown.
The sensitivity of a pressure microphone Sp, is given by the output voltage
divided by the applied acoustic pressure and is given in V/Pa and is normally
measured at one thousand Hertz. This is done since the transfer function is assumed
constant in the acoustic frequency band. The sensitivity of a microflown Sf, is given by
the differential resistance variation divided by the applied acoustic flow and is given
in s/m and has to be measured also at one thousand Hertz if the sensitivity of the
116
Properties of the microflown
microflown is flat from low frequencies to at least one thousand Hertz (1m/s equals
146dB PVL). Therefore the low pass behaviour has to be compensated using a certain
electrical compensation circuit.
The sensitivity of microphones depends on the angle of incidence. The polar
pattern is a relative representation of the angular dependency of the sensitivity. The
polar pattern of microflowns and microphones can be compared without conversions.
The equivalent noise level is given as a RMS signal in a certain frequency band
when no acoustic input is applied. This RMS output signal is calculated back (using
the sensitivity) to an input sound level (PVL or SPL) which would give an equivalent
RMS output signal.
∞
Noise level = S
−1
∫N
2
( f ) ⋅ W 2 ( f )df
(6.1)
0
Using N(f) as the frequency dependent noise density and W(f) as a certain frequency
dependent weighing curve. Although this expression is not mathematically correct (the
sensitivity is also a function of the frequency) it will give an impression of the noise
performance of a microphone. The “A” weighing curve is given in Fig. 6.1.
Fig. 6.1: The “A” weighing curve.
The formula of the “A” weighing curve is given by (6.2):
117
VI
Applications
WA ( f ) = 1.26
(12200 f 2 )2
(f 2 + 20.6 2 ) (f 2 + 12200 2 ) (f 2 + 107.7 2 ) (f 2 + 737.9 2 )
This equivalent noise level is noted in dB(A). The “A” weighing curve is used to
bring the sensitivity of the human ear into account. For noise calculations the
following integrals are convenient to know.
100kHz
∫10Hz
3.4 kHz
∫10Hz
2
WA df = 116 ; 20 Log10
2
WA df = 59.5 ;
20 Log10
100kHz
WA df = 413
.
3.4 kHz
WA df = 355
.
∫10Hz
∫10 Hz
2
2
The noise level of a microflown is defined in a same manner as the noise level
for a pressure microphone but now calculated back (using the sensitivity) to an input
particle velocity level. Therefore the “A” weighted noise level of a pressure
microphone is given in dB(A) SPL and of a microflown in dB(A) PVL.
The dynamic range of a microphone is given by twenty times the logarithm of
the ratio of the minimum level and maximum level which can be measured. The
minimum sound level normally equals the noise level (and is consequently dependent
on the weighing curve). The maximum sound level is defined by setting a certain
maximum distortion. For pressure microphones and for microflowns the dynamic
range is given by:

pmax
20 Log10
pmin

Dynamic range = 

umax
 20 Log10
umin

( pressure microphones)
(6.3)
(microflowns)
The dynamic range of both types microphones can be compared straightforwardly.
118
Properties of the microflown
PROPERTIES OF CONVENTIONAL MICROPHONES
In table 6.2 properties of some pressure microphones are given. At first
commercially available Brüel & Kjær measurement condenser microphones [6.1]. The
4179 is, concerning the “A” weighted equivalent noise level, the best performing
microphone and is used for extremely low pressure level measurements. In 3.16 Hertz
bandwidth, at 1 kHz an equivalent noise level of -35dB is measured. A bandwidth of
10 kHz is possible because a frequency response compensation network is used. The
resonance frequency of the microphone is at 7 kHz. The 4144 and 4133 are general
laboratory microphones, the 4135 a microphone for high pressure levels, high
frequency and for small scale model work, and finally the 4138 for high pressure
levels, very high frequency measurements, pulse measurements and model work.
The listed AKG microphones are used in studios [6.2]. The C12 VR is used for
vocals and soloists. The size of the membrane is not listed, the width of the
microphone is forty-two millimetres. The C 567 E1 is a miniature microphone having
a diameter of fourteen millimetres.
The Sennheiser MKE2PC is a high quality omni-directional miniature
microphone. It is an all purpose device and very robust [6.14].
The first micro-machined microphone was presented by Royer et al. [6.9] in
1982. It is based on the piezoelectric principle and has a noise level of 66 dB(A) SPL
[6.10]. The first micro-machined condenser microphone was made by Hohm et al. in
1984 [6.4], the noise level of the microphone is 54 dB(A) SPL [6.10]. W. Kühnel and
G. Hess made a micro-machined condenser type microphone with a very low noise
level of less than 25 dB(A) SPL [6.11]. It has to be noted that this noise level was
indirectly measured and therefore it is difficult to form an opinion about the
performance of the sensor including a pre-amplifier. The microphones made by
Bergqvist [6.5] and Scheeper [6.12] are performing relatively well as can be seen in
Table 6.2.
119
VI
Applications
Table 6.2: Some properties of various condenser microphones.
Manufacturer
Dynamic Sensitivity Noise
range
Size
Bandwidth
[mV/Pa]
[dB(A)]
[Hz]
(4179) 105*
100
-2.5
1”∅
10-10k
(4144) 130*
50
10
1”∅
2.6-8k
(4133) 140*
[dB]
Brüel & Kjær
12.5
22
1/2”∅
4-40k
(4135) 140
*
4
36
1/4”∅
4-100k
(4138) 125
*
1
55
1/8”∅
6.5-140k
(C 12 VR) 105**
10
22
-
30-20k
(C 567 E1) 110**
10
22
-
20-20k
Sennheiser (MKE2PC)
103***
10
27
4mm ∅
20-20k
W. Kühnel & G. Hess
NA
2
<25
.8×.8mm2
-20k
Bergqvist
NA
1-5
33
2×2mm2
-27k
Scheeper et al.
NA
5
30
2×2mm2
-14k
AKG
*
pmin equals the “A” weighted noise level, pmax the 10% distortion level.
**
pmin equals the “A” weighted noise level, pmax the 0.5% distortion level.
***
pmin equals the “A” weighted noise level, pmax the 1% distortion level.
Observing the properties in Table 6.2 it can be said that a noise level of 22
dB(A) SPL can be considered as good, a dynamic range of 110 dB is high (this
depends on the distortion level used), a normal sensitivity is about 5 mV/Pa, a size of
1 mm2 is small and a bandwidth of twenty kilo Hertz can be easily reached.
By knowing what is good and normal of conventional microphones, an opinion
about the properties of the microflown can be formed.
120
Properties of the microflown
A COUSTIC
PROPERTIES OF THE MICROFLOWN
THE POLAR PATTERN
Because of the operating principle of the microflown, the measurement of a
differential temperature variation, it can be expected that the polar pattern should be a
“figure of eight”. The acoustical wave can be de-composed in a component
perpendicular on the microflown and a component parallel to it. The first component
results in the known response and the latter will cause a common temperature
variation, and therefore no signal; the signal is determined in the form of a
differential resistance variation.
Fig. 6.2: The figure of eight type of polar pattern of the microflown measured at
150 Hz, 2 kHz and 4 kHz.
THE TRANSFER FUNCTION,
SENSITIVITY & SELF NOISE
To measure the “A”-weighed noise, the measurement set-up depicted in Fig.
6.3 can be used. The frequency fc is corresponding with the corner frequency of the
microflown, the frequency fLPF is the maximal frequency of the signal, above this
frequency both signal as noise are suppressed. The frequency fHPF is the minimal
frequency of the signal.
121
VI
Applications
Fig. 6.3: The measurement set-up to measure the “A” weighted noise.
Noise measurements however are rather complicated since for instance it is
desired that no acoustic signals reach the microflown. Therefore the theoretic minimal
noise can also be calculated and used for an estimation. This estimation is shown to be
quite good, see chapter 4. If for the electronic part of the microflown the (theoretical)
circuit of Fig. 3.2 is used, the quadratic noise density will be given by
δu 2 = 8kTs R ⋅ df . The compensation circuit transfer function is of the form
2
H ( f )comp .= 1 + f
f c2
. Therefore the “A”-weighed selfnoise will be described with the
following equation (see also eq. (6.2)):

8kTs R

Selfnoise = 20 Log10 
∆R
 uref . 2 IR R

f LPF
∫
f HPF
2
 f 
2
W A ( f ) ⋅ (1 +   ) ⋅ df
 fc 





u

Popt .
 f 
 ref .

= 10 Log10 ∫ W A2 ( f ) ⋅ (1 +   ) ⋅ df − 20 Log10 
×
× S P .
opt
TPopt .
 fc 
 2 k

f HPF
f LPF
(6.4)
2
1444444
424444444
3 14444442444444
3
=
Noise factor
−
Performance
All the quantities (including the performance, Eq. (4.21)) are found in chapter 4.
Using ∆R/R as the relative differential resistance variation, measured with an 120 dB
PVL and at a low frequency (acoustic frequencies below the corner frequency of the
microflown) and calculated to a resistance variation due to a particle velocity equal to
1 m/s. As shown in chapter 3 the nominal microflown sensor resistance is of no
influence in the selfnoise. The square root of the integral is called the noise factor.
Some practical values of this factor are calculated and depicted in Fig. 6.4.
122
Properties of the microflown
Fig. 6.4: The (“A”-weighed) noise factor as function of fLPF and corner frequency (fc).
For the microflown in a telecommunication application the maximal frequency
of interest (fLPF) is 3.4 kHz and the minimal frequency (fHPF) is 300 Hz since outside
this frequency band no signal will be transmitted [6.17].
If the corner frequency (fc) of a microflown is 300 Hz, the “A” weighted
noisefactor will be 53 dB (or 440 times), see Fig. 6.4. Suppose that the sensitivity is
measured ∆R/R=0.05 s/m, the optimal power is given by 15 mW per sensor and the
sensor operating temperature is 400K. The performance of the microflown will be 8.3
dB and consequently the “A” weighted selfnoise 44.6 dB. This selfnoise is, as can be
seen in Table 6.2, not good compared to the pressure microphones, see also
appendix 4.
THE DYNAMIC RANGE
The dynamic range of the microflown is determined by the minimal and
maximal particle velocity level which can be measured. The lower boundary will be
limited by the selfnoise level and is consequently dependent on the sort of filtering.
The higher boundary is limited by the harmonic distortion permissible. Fig. 6.5 shows
that the output of a TSM for higher sound levels is measured linear up to about 135
dB PVL. This measurement is performed in the “infinite tube” and as stated in
chapter two acoustic non-linearity in air becomes significant at sound levels exceeding
about 135 dB. It is not investigated yet if the microflown does have a linear behaviour
for sound levels higher than 135 dB.
123
VI
Applications
Fig. 6.5: The output of the microflown for high sound levels measured in the “infinite
tube”.
The selfnoise is dependent on the bandwidth and applied weighing curve. For
telecommunication purposes the bandwidth is limited to 3400 Hz. The selfnoise is
then approximately 40 dB(A) and the dynamic range 95 dB.
OTHER FEATURING PROPERTIES OF THE MICROFLOWN
The microflown is a particle velocity sensitive microphone. This is rather
special since all commercial available microphones measure pressure or pressure
gradient. There are systems available which are sensitive for particle velocity but
these are distributed sensors. One example of a particle velocity sensor is the circular
shaped part of the type 216 p-u intensity probe (Norwegian electronics, see Fig. 6.6).
The principle of this sensor is the differential Doppler shift of two ultrasonic beams
[6.15]. Another way to measure the particle velocity is using the differential pressure
method, see chapter 2 and below (Fig. 6.15). Both distributed sensors are large and
consequently the particle velocity is not measured at one point.
A realisation of the p-u probe is displayed in appendix 5.
124
Properties of the microflown
Fig. 6.6: Type 216 p-u intensity probe (Norwegian electronics).
Compared to conventional microphones the microflown is very small and in
contrast to the conventional microphones it is easy to manufacture an identical batch
of sensors (see also Fig. 5.0). These microflowns will have identical properties
especially regarding sensitivity and phase response. For conventional microphones the
latter is difficult to realise. For the p-p sound intensity probe the equal phase response
of the two pressure sensors is very important, see chapter 2.
The microflown is a low impedance sensor compared to the condenser
microphone.
Commercially available condenser microphones demonstrate a dominant 1/f
noise density behaviour for frequencies below the 100 Hz to 1 kHz. This is caused by
the electronics, see Fig. 6.7. When using the microflown one observes no 1/f noise in
the acoustic bandwidth.
To gain insight, the noise density of a microflown is theoretically determined
and compared with the 1 inch B&K condenser microphone (one of the best
performing microphones commercial available considered the noise behaviour), see
Fig. 6.7 and Fig. 6.8 and appendix 4. For this is a microflown is used which has a
corner frequency of 1kHz and a performance of 10 dB (Rmicroflown (hot)=400Ω, S=0.06
s/m, Popt=15 mW per sensor, Ts=500 K, see also chapter 4).
The preamplifier is based on a half Wheatstone bridge in combination of a CE
configuration and compensates for the low pass behaviour of the microflown. To
obtain the same sensitivity as the microphones used in Fig. 6.7 the voltage gain of the
125
VI
Applications
preamplifier equals 46 dB. The base series resistance of the transistor is assumed 40 Ω
and K’F=100 Hz (see chapter 3). The noise spectrum of the preamplifier equals
en ≈ 195 ⋅ 4 k ⋅ 300 ⋅ 40 = 159 nV
en = 195 ⋅ 2 k ⋅ 600 ⋅ 400 = 458 nV
Hz
Hz
and the noise density of the microflown equals
.
If is assumed that the specific acoustic impedance equals the characteristic
impedance (free field, see chapter 2) the PVL equals the SPL and the sensitivity can
be converted to 50 mV/Pa.
The noise density of the microflown and of the preamplifier are increasing with
6 dB/oct. above the 1 kHz since the sensitivity of the microflown is compensated. The
1/f noise fraction of the microflown and the preamplifier will not become dominant in
the acoustic bandwidth. The noise density of the microflown and preamplifier is much
higher than the noise density of the 1 inch B&K condenser microphone.
The microflown is relatively easy to manufacture, comparing other micromachined sensors but also in respect to conventional microphones.
Due to the fact that the microflown has an exact first order low pass transfer
function it has a well predictable behaviour which can be electrically compensated and
a flat frequency response can be easily obtained. Due to this behaviour no resonance
frequency is present. A conventional microphone does have a multi-order behaviour
and much effort has to be put in the design to get a reasonable flat frequency
response.
Due to the low mass of the microflown it is impact resistant i.e. the dropping of
the packaged microflown will not damage it.
The power consumption compared to conventional microphones is very large.
The power consumption of a conventional condenser microphone is in the order of
micro-watts, the power consumption of the microflown in normal operation is in the
order of 15 mW.
126
Properties of the microflown
Fig. 6.7: Noise voltage spectral density for a 1 inch condenser B&K microphone and
the preamplifier, see also appendix 4.
Fig. 6.8: Expected noise density of the microflown and preamplifier, see also
appendix 4.
127
VI
Applications
6.3 A PPLICATIONS
USING THE
µ - FLOWN
A frequently asked question is, what is the use or the significance of the
microflown? The idea which usually firstly pops up is an ultra miniature microphone
for espionage purposes. This idea is not worked out completely. One of the reasons is
the end of the cold war; the need for such microphones is strongly reduced (small
market).
Other ideas not worked out yet are: using the microflown in a feedback
(compensation) configuration in for instance a bass reflex port of a loudspeaker.
Measuring at the end of a tube (e.g. flute, organ) where a particle velocity maximum
can be expected. The microflown can stand an enormous pressure and no fundamental
problems are expected for using it (very deep) under water. Therefore a hydrophone
should be feasible.
Ideas of applications which are investigated can be found below.
A TELECOM MICROPHONE
The easy manufacturing, and by high volumes low unit cost of the microflown
makes it suitable for a mass market like the telecommunication. The self noise
requirements are within reach (34 dB(A) PVL; Bw=3400 Hz). The selfnoise is
defined as the absolute noise divided by the sensitivity. So if the sensitivity increases,
the selfnoise drops. The sensitivity of an acoustic sensor is obtained at a frequency of
one thousand Hertz, at one meter from the acoustic source, i.e. in the free field and
not in the near field. For telecommunication applications the acoustic sensor is near
the source (the mouth) and consequently in the near field.
u=
128
I
Zs
=
ω 
1 +  r
c 
I
ω
ρc
r
c
2

I
 ω

rρc
 c
≈
 I

 ρc

ω
r < 1 (near field )
c
(6.5)
ω
r > 1 ( free field )
c
Applications using the microflown
As can be seen in eq. (6.5) due to the rising specific acoustic impedance in the near
field the particle velocity will drop proportional with the square root of the frequency.
In the near field the sensitivity of the microflown is higher compared to the sensitivity
measured in a free field.
A major disadvantage of the microflown in telecommunications applications is
the power consumption, since the mobile telephones are battery powered. Such a
telephone does have three modes of operation, switched off (only a very small power
is needed to monitor the on-off button) the stand-by mode (more power is needed to
communicate with the network) and actually transmitting and receiving. In the latter
mode the power consumption is in the order of a few Watts. Only in this last mode
the microflown will be used. In the last mode the power consumption is less than a
per cent of the total power consumption. (The previous is called the “Das
Tannenbaum Prinzip” referring to cellular telephone in operation: all kinds of lights
and sounds are switched on: it starts to look like a Christmas tree.)
With this in mind the maximal power consumption of the microflown in the
telecommunication application is put on 10 mW. Since these telephones are battery
powered, the operating voltage should be 2 V [6.17].
For more than half a year a microflown (performance is about 2 dB, corner
frequency about 300 Hz) was mounted in a normal telephone in such way that it is
was possible to toggle between the existing microphone and the microflown. The
performance of the microflown combined with a preamplifier was a slightly less
compared to a normal microphone, it has a noisier result. When the microphones
where altered in one conversation one could hear the difference. Telephone calls made
by only using the microflown did not lead to complains.
The Performance has been (mid-95) improved 17dB and the Noise Factor 7 dB.
129
VI
Applications
A BASE DRUM MICROPHONE
The acoustic properties of the microflown
suggest
low
frequency,
high
sound
level
applications. For this a bass drum microflown is
developed. As can be found in Fig. 6.5 for high
sound levels the output of the microflown is in the
order of ∆R/R=3 %.
Therefore an electronic circuit has to be
designed with a large dynamic range, see chapter 3
and appendix 6. The first realisation of the bass
drum microflown is shown in Fig. 6.9 on top of the
PCB the microflown and a LED power on indicator
can be seen. This realisation has an unbalanced
output. The second realisation made has a balanced
(differential) output and uses two microflowns (the
selfnoise therefore decreases by 3dB, see chapter 3).
An XLR plug provides the electrical link and
when connected the electronic circuit is activated.
The application has been tested in a pop studio
and acoustic technicians where satisfied with the Fig. 6.9: Bass drum microflown.
acoustic result [6.22].
STEREO ‘IN ONE POINT’ MICROPHONE
Using a pressure microphone and microflown a stereo microphone can be made.
Explaining the principles of this device two plane waves travelling in the opposite
direction are examined. A plane wave travelling in the positive direction (p+) and in
the negative direction (p- ) can be described as:
130
Applications using the microflown
A − ikx iω 1 t
e
e
ρc
B ikx iω 2 t
p− ( x , t ) = Be ikx e iω 2 t ; u− ( x , t ) =
e e
ρc
p+ ( x , t ) = Ae − ikx e iω 1 t ; u+ ( x , t ) =
(6.6)
The output of the microphone amplifier (Up) and the amplified microflown signal is
given by:
U p ( t ) = H M . A.( p+ ( x , t ) + p− ( x , t ))
U u ( t ) = Av ( u+ ( x , t) − u− ( x , t ))
(6.7)
Using HM.A. as the transfer function of the microphone amplifier and Av as the
amplification of the microflown signal.
It is possible to adjust the amplified microflown signal (Av) in such way that the
sum of Up(t) and Uu(t) will result in a signal proportional with the positive travelling
wave. Likewise, subtracting both signals Up(t) and Uu(t) will result in a signal
proportional with the negative travelling wave.
The previous theory is demonstrated by an experiment. The measurement set-up
is implemented using a tube with a loudspeaker at each end to be sure that the acoustic
waves are coming from opposite directions, see Fig. 6.10.
Fig. 6.10: Measurement set-up to demonstrate the stereo microphone.
One speaker generates a 150 Hz burst and the other a 200 Hz burst. The µ-flown and
microphone are situated in the middle measuring both acoustic waves travelling in
opposite directions (upper two curves, Fig. 6.11).
131
VI
Applications
Fig. 6.11: Measured signals of the stereo microphone.
AN ACOUSTIC INTENSITY PROBE
Measuring sound intensity seems to be a fundamental and scientific activity
only, but this is not true [6.6], [6.20]. For example the social relevance lies in the
fact that there are a lot of sound pollution laws. In The Netherlands all hotels, cafes,
bars, sports clubs or even social clubs have to show an acoustic report made by an
official acoustical consulting bureau that their sound pollution is not too large.
Considerable amounts of money are involved in rebuilding to meet the sound pollution
laws. Proper measurements are necessary to find out if this rebuilding is necessary
[6.18].
The measurement of sound intensity is required for many purposes. However
the probes are expensive while they are difficult to make. The microflown can make
the realisation of a sound intensity probe a lot easier and therefore also much cheaper.
This is emphasised with a quotation of F.J. Fahy from his book Sound Intensity:
“...The first patent for a device for the measurement of sound energy flux was
granted to Harry Olson of the RCA company in America in 1932. The first
commercial sound intensity measurement systems were put on the market in the early
1980s. Why the 50-year delay? ... It may be basically attributed to the technical
difficulty of devising a suitably stable linear wide frequency band transducer for the
accurate conversion of fluid particle velocity into an analogue electrical signal...”
[6.15].
132
Applications using the microflown
By using a pressure microphone and a microflown it should be possible to
construct a sound intensity probe.
THE DIRECT METHOD (P-U METHOD)
Looking at the definitions of sound intensity and the specific acoustic
impedance, the most obvious way to determining these quantities is measuring both
acoustic pressure and particle velocity and subsequently multiplying or dividing both
signals. An example of the measurement of the instantaneous sound intensity (nonaveraged) sound intensity is depicted in Fig. 6.12. This is a measurement result
obtained in the “infinite” tube (see chapter 2).
The p-p sound intensity probe consists of a couple pressure microphones which
is expensive because the microphones are phase matched. A phase mismatch of 0.3° is
considered large, see chapter 2. The pressure microphone which has to be used when
applying the direct method does not need to reach such requirements. The phase
mismatch between the microflown and pressure microphone may be much larger (6°
phase mismatch will lead to a measurement error of only 0.2dB [6.19]). While the p-u
method phase matching requirements are much less compared to the p-p method it is
assumed that the construction costs can be much lower compared to the construction
costs of a p-p probe, see also appendix 5.
Fig. 6.12: The instantaneous sound intensity obtained using the “Direct Method”.
133
VI
Applications
The measurement shown in Fig. 6.12 shows
the result of a one dimensional p-u probe. To
perform
three
dimensional
sound
intensity
measurements the particle velocity vector has to be
measured. For this a three dimensional particle
velocity probe is constructed, see Fig. 6.13. The
probe is made out of brass and three microflowns
and measures 5×5×3mm. To establish the electrical
connections
a
PCB
foil
is
used.
No
3D-
measurements are performed yet.
Fig. 6.13: 3D particle velocity probe
THE P-P
METHOD
Using two closely spaced microphones the acoustic pressure can be measured
and the particle velocity can be determined, see chapter 2. Two pressure sensors are
used, so it is called the p-p method [6.15]. Normally the sound intensity is measured
in one direction. This could lead to a measurement error. This will be explained
below, see Fig. 6.14.
Fig. 6.14: Three characteristic situations when using a p-p intensity probe.
The two dots represents the p-p intensity probe.
First situation: A sound wave (A) in the ex direction. The sound intensity
becomes (see chapter two):
I A = K ( P1 A + P2 A ) × ∫ ( P1 A − P2 A )dt
(6.8)
With K as an arbitrary constant. The intensity will be determined by multiplying the
estimated pressure (the average of the two pressure signals) and the estimated particle
velocity (proportional with the integrated difference of both pressure signals).
134
Applications using the microflown
Second situation: a sound wave (B) in the ey direction.
I B = K ( P1B + P2 B ) × ∫ ( P1 B − P2 B )dt = K ( P1B + P2 B ) × ∫ 0 dt = 0
(6.9)
Since (in a plane wave) both pressure signals do generate the same signal the pressure
difference signal is zero and consequently is the sound intensity.
Third situation: two sound waves perpendicular (A&B). The measured sound
intensity should be equal to the one measured in the first situation.
I A+ B = K ( P1 A + P1B + P2 A + P2 B ) × ∫ (( P1 A + P1 B ) − ( P2 A + P2 B ))dt
= K ( P1 A + P1B + P2 A + P2 B ) × ∫ ( P1 A − P2 A )dt
= K (( P1 A + P2 A ) × ∫ ( P1 A − P2 A )dt + ( P1 B + P2 B ) × ∫ ( P1 A − P2 A )dt )
(6.10)
= I A K (( P2 A + P2 B ) × ∫ ( P1 A − P2 A )dt ) ≠ I A + I B
Eq. (6.10) shows otherwise. Therefore an additional sound wave perpendicular to the
direction of the axis of the pressure probes will influence the measurement of a sound
wave in the direction of the axis of the pressure probes. This problem is in fact caused
by the non linearity of power measurements and can be mathematically eliminated by
methodical measurements.
Fig. 6.15: A Brüel and Kjær p-p sound intensity probe.
The p-p method is widely used. Microflowns produced in one batch will have
the same sensitivity and phase response. The phase matching problem is therefore
eliminated. Therefore the u-u method is investigated [6.19].
135
VI
Applications
THE U-U
METHOD
1
As stated above the power flux of a sound wave through a surface (sound
intensity) is given by the product of the sound pressure and the particle velocity.
Using three pairs of two closely spaced flow microphones, the acoustic flow can be
measured, but also the flow gradient, the apparent acoustic pressure and the sound
intensity can be determined.
The sound intensity at a point is the average rate at which sound energy is
transmitted through a unit area perpendicular to the specified direction at the point
under consideration (see chapter 2):
I=
1
T
T /2
∫ − T / 2 u( t ) ⋅ p( t )dt
(6.11)
The ratio of pressure and particle velocity is given by the specific acoustic
impedance. This impedance is normally a complex figure varying in place, indicating
that the pressure and flow are not in phase [6.7]. Therefore the pressure can not be
determined by simply multiplying the flow with a constant value (the impedance).
To obtain the apparent pressure a method using two closely spaced microflowns
can be used. This method is based upon the linearised equation of mass conservation
[6.8]:
∂ρ
= −ρ ∇ ⋅ u
∂t
(6.12)
Where ρ is the intrinsic density of the medium. For “normal” sound levels it is
assumed that the compressions are adiabatic such that the increase in pressure and
increase in density are linearly related:
p = c2 ⋅ ρ
(6.13)
Substituting eq. (6.13) in eq. (6.12):
1 ∂p
= −ρ ∇ ⋅ u
c 2 ∂t
1
(6.14)
Based on: H-E. de Bree, M. T. Korthorst, P.J. Leussink, H. Jansen, M. Elwenspoek., A Method To
Measure Apparent Acoustic Pressure, Flow Gradient and Acoustic Intensity Using Two
136
Applications using the microflown
Integrating both sides will result in:
∂u y ∂uz 
 ∂u
p = − ρ 0 ⋅ c 2 ⋅ ∫ ∇ ⋅ u dt = − ρ 0 ⋅ c 2 ⋅ ∫  x +
+
 dt
∂y
∂z 
 ∂x
(6.15)
In practice, the flow gradient in a certain direction, for example, ∂ux/∂x, can be
approximated by measuring the particle velocity, ua and ub in a line in the x-direction
at two closely spaced points, with a separation of ∆x. Dividing ub-ua, by the
separation ∆x will provide the following estimation for the apparent pressure p$ . If the
separation in all directions are equal ( ∆x = ∆y = ∆z = ∆r ):
ρ ⋅ c2
p$ = 0
⋅ ∫ ( ux ,b + u y ,b + uz ,b − ux ,a − u y ,a − uz ,a )dt
∆r
(6.16)
This approximation is valid as long as the separation ( ∆r ) is small compared to the
wavelength of interest.
Introductory measurements are performed with a one dimensional probe. This
measurement is justified when measured in an acoustic wave having only components
in one direction (for example a standing wave tube or the “infinite tube”, see chapter
two). In such case eq. (6.16) will simplify in:
ρ ⋅ c2
p$ = − 0
⋅ ∫ ( ub − ua )dt
∆r
(6.17)
The particle velocity component of the wave is measured by summing the signals of
both microflowns and dividing them by two. The sound intensity can be determined
by using the block diagram which is depicted Fig. 6.16.
The transfer function of the microflowns, Hµ-flown(ω), depends on the frequency
and shows a low pass characteristic. Only linear operations are performed on the
signals of both microflowns and these have been fabricated in the same batch, which
guarantees the sensors to be practically identical. Therefore the compensation for this
behaviour can be done after multiplying particle velocity and apparent pressure (point
Micromachined Flow Microphones, proceedings Eurosensors X, Leuven, 1996.
137
VI
Applications
E in Fig. 6.16). When subtracting (point B…C), the signal is very sensitive to a phase
mismatch. By shifting the compensation networks (filters), errors can be avoided.
Fig. 6.16: The block diagram of the one dimensional u-u sound intensity probe.
To measure the apparent pressure and the particle velocity a tube is used which
is closed rigidly at one end. This will deliver a standing wave, whereby the phase
shift between pressure and particle velocity is theoretically 90° [6.7]. The
measurement set-up is illustrated in Fig. 6.17.
Fig. 6.17: A standing wave tube.
In the rigidly terminated tube the RMS value of the minima and maxima have
been measured real time with a pressure microphone and with two spaced µ-flowns
(see Fig. 6.18).
Fig. 6.18: The first realised u-u intensity probe, the spacing between the µ-flowns is
five centimetres.
138
Applications using the microflown
Now observe point D in Fig. 6.16. The sum signal of the microflowns
represents the particle velocity and the integrated differential signal the apparent
pressure. The measured results in a standing wave can be seen in Fig. 6.19. At 550
Hz the minima in the pressure are separated by 30 centimetres as can be seen. The
minima in the particle velocity are shifted for ¼ wavelength, which is 15 cm. This
figure shows the possibility to measure the pressure incorporated in an acoustical
wave with two particle velocity sensors.
Fig. 6.19: The minima and maxima in a closed tube of the particle velocity, pressure
and apparent pressure.
In the ‘infinite tube’ the instantaneous sound intensity has been measured. The
results can be seen in Fig. 6.20, as expected the apparent pressure and particle
velocity are in phase (point D in Fig. 6.16).
The sound intensity before averaging is shown in the lower part of the graph
with a solid line. The result of the direct method is also shown (dashed line).
Fig. 6.20: Sound intensity in a tube without reflections.
139
VI
Applications
A three dimensional u-u sound intensity probe is realised, see Fig. 6.21. The
preamplifier is based on the half Wheatstone bridge and a CE configuration amplifier.
The spacing of the microflowns is 50 mm and consequently the probe is designed for
frequencies in the range from 20 Hz to 1.2 kHz. For higher frequencies the spacing is
too large and the probe too bulky. The three dimensional probe can be calibrated by
calibrating the three elements in the same way done above. No 3D sound intensity
measurements have been performed yet.
Fig. 6.21: Realisation of the3D u-u intensity probe.
140
Conclusions and discussion
C ONCLUSIONS
AND DISCUSSION
Some acoustic properties of microphones and microflowns are presented.
Comparing both, it shows that the microflown has some features which are competing
with the conventional microphones:
• True particle velocity (and not pressure) sensitive
• Very small
• Easy to fabricate
• Due to batch processing: similar response may be expected
• No-1/f noise in the acoustic bandwidth
• Low impedance
Other very important figures are not as good as conventional microphones:
• Low bandwidth
• High selfnoise
• High power consumption
Exploiting the competing features of the microflown three applications are
realised. A microphone for telecommunication purposes, a bass drum microflown and
a sound intensity probe. The latter application is realised using two methods: The
sound intensity obtained by the product of the measured acoustic pressure and
measured particle velocity. It is shown that it is possible to measure the apparent
pressure by using two closely spaced microflowns. The product of the apparent
pressure and the particle velocity provides the sound intensity.
The advantage of this method is the possibility of producing many identical
sensors in one process run. In contrast, for conventional pressure microphones it is
difficult to produce two phase matched sensors.
141
VI
Applications
R EFERENCES
[6.1] Master Catalogue, Electronic Instruments, Brüel & Kjær, may 1989.
[6.2] AKG acoustics, In the studio, prospectus 1995.
[6.3] E.C. Wente, A condenser as a uniformly sensitive instrument for the absolute measurement of
sound intensity, Phys. Rev., 10 (1917) 39-63.
[6.4] D. Hohm and R. Gerhard-Multhaupt, Silicon-dioxide electret transducer, J Acoust. Soc. Am.,
75 (1984) 1297-1298.
[6.5] J. Bergqvist et al., A silicon condenser microphone with a highly perforated backplate,
Proceedings of Transducers 1991, San Fransisco, USA, 408-411.
[6.6] Brüel & Kjær, Sound Intensity, Technical Review, No. 3, 1982.
[6.7] L. Beranek, Acoustics, New York, 1954.
[6.8] P.A. Nelson, Active Control of sound, academic press, London, 1992.
[6.9] M. Royer, J.O. Holmen, M.A. Wurm, O.S. Aadland and M. Glenn, ZnO on Si integrated
acoustic sensor, Sensors and Actuators, 4 (1983) 357-362.
[6.10] G.M. Sessler, Silicon Microphones, J. Audio Eng. Soc., Vol. 44, No. 1/2, 1996.
[6.11] W. Kühnel and G. Hess, A silicon condenser microphone with structured back plate and silicon
nitride membrane, Sensors and Actuators A, 30 (1992) 251-258.
[6.12] P. Scheeper, A Silicon Condensor Microphone: Materials and Technology, thesis 1993,
Enschede.
[6.13] G.A. moore, Inside the tornado, Marketing strategies from the silicon valley’s cutting edge,
HarperBusiness 1995.
[6.14] Sennheiser, Revue part 1, microphones, 1-1996, Germany.
[6.15] F.J. Fahy; Sound Intensity, second edition; E&FN Spon; London; 1995.
[6.16] V.Tarnow, thermal noise in microphones and preamplifiers, B&K Technical Review, 3-1972.
[6.17] Private conversations Sennheisser electronic GmbH.
[6.18] B. van Osch, De wet van de stilte, intermediair nr 26, 28 June 1996.
[6.19] M.T. Korthorst, Flierefluiten II, A sound intensity probe, M.Sc. Thesis, August 1996.
[6.20] IEC 1043, International Standard; Electroacoustics - Instruments for the measurement of sound
intensity - Measurement with pairs of pressure microphones; First edition December 1993.
[6.21] H-E. de Bree, T. Korthorst, P.J. Leussink, H. Jansen, M. Elwenspoek., A Method To Measure
Apparent Acoustic Pressure, Flow Gradient and Acoustic Intensity Using Two Micromachined
Flow Microphones, proceedings Eurosensors X, Leuven, 1996.
[6.22] Private conversations Atak poppodium, Enschede, The Netherlands.
142
143
GENERAL CONCLUSIONS
One of the central questions in this research is “has the microflown a chance to
be an economical success?”. This question can be answered positive: it has a chance.
The main reasons for the positive answer are:
• The microflown is a sensor that is small in dimensions and easy to make.
• It measures particle velocity directly, which makes it unique.
• The working principle of microflown is legally protected.
• Large companies are interested and are willing to invest for further research.
145
VII General conclusions
“What is the quality of the microflown”, is a frequently asked question. To give
a proper answer to this question, quality has to be specified. The microflown as an
acoustical sensor, a sensor to transduce for example speech, is not of high quality.
The dynamic range is of normal quality but the selfnoise is bad compared to the
simplest (i.e. cheapest) pressure microphone. The selfnoise of the microflown is just
good enough that it can be used for telecommunication applications.
The quality of the microflown as a particle velocity sensor will be compared to
the common commercially available ones which contain two pressure sensors (see
chapter 6: the P-P method). The selfnoise of such probe is worse than the selfnoise of
the pressure sensors apart. This is because the signal of the two pressure probes is
subtracted: the resulting signal will be much smaller and the resulting (self-) noise
will be increased. The selfnoise of the microflown is still worse than the selfnoise of
the P-P probe but is in close range. The size of the microflown is much smaller than
the P-P probe. Advantages are that the acoustic wave will be disturbed less and that
the particle velocity can be measured in one place. A P-P probe is costly while the
method requires a set of phase matched pressure microphones for proper operation.
The cost prize of the microflown should be considerate lower as a P-P probe.
The quality of the microflown when used in a sound intensity measuring system
is almost equivalent with the quality of the microflown used as a particle velocity
sensor. Multiple systems now can be compared: the microflown in combination with a
pressure sensor resulting in the P-U probe (see chapter 6) and a sound intensity
measuring probe consisting of two microflowns the U-U probe (see chapter 6).
Starting with the latter, of this probe the selfnoise is worse that the selfnoise of a P-P
probe. Both U-U as P-P probes are distributed sensors and thus the U-U probe has the
same disadvantages as the P-P probe. One advantage of the U-U probe is that due to
the manufacturing method the phase matching of the particle velocity sensors (the
microflowns) is a smaller problem compared to the phase matching of the pressure
sensors in the P-P probe.
When comparing the P-U intensity probe (a system containing a microflown and
a pressure microphone) with the P-P probe (a system which consist of two pressure
microphones) it turn out shows that the total system can be much smaller, due to the
method the phase matching is of less importance and the sound intensity can be
measured at one place in space.
146
General conclusions
GENERAL CONCLUSIONS TO CHAPTER 2
The relation between the acoustic pressure and acoustic flow is formalised. This
is done under certain assumptions which are not always justified in practice. The
assumptions are that the acoustic compressions are such that the increase in pressure
and increase in density are linearly related, variations in density are small compared to
the density itself and that the particle velocity is small compared to the velocity of
sound. Therefore one has always to be careful when using the specific acoustic
impedance to calibrate the microflown. Acoustic non-linearity in air becomes
significant at sound levels exceeding about 135 dB. The linearity of the microflown is
determined up to 135 dB (PVL). Measurements which are valid above the 135 dB are
not performed.
Of the measurement set-ups used obviously the ‘infinite tube’ type of set-ups are
the important ones. This is because the frequency range from 50 Hz up to 12 kHz is
of most interest. In this range the human ear is sensitive. The ‘infinite tube’ type of
set-ups are an inexpensive solution to create an environment with and known specific
acoustic impedance.
For frequencies below one hundred Hertz both ‘acoustic short cut’ as ‘acoustic
displacement’ set-up provide information about the frequency dependent behaviour of
the microflown. Using the ‘acoustic short cut’ the air moves and using the ‘acoustic
displacement set-up’ the microflown moves.
Once a microflown is calibrated “the standing wave tube” measurement set-up is
used to gain fast and reliable information about the transfer function.
When observing how acoustic measurements are performed nowadays it shows
that it is possible to measure properties as acoustic impedance and intensity without
using a flow microphone. Sound intensity can be measured by using two closely
spaced and, in particular, phase matched pressure microphones. The disadvantage is
the fact that it is difficult to fabricate (phase) matched microphones which will result
in a high price for the probe. Also some specific problems incorporated with the
method have been presented.
Measuring the acoustic impedance is possible using a standing wave tube but
this will alter the system and the measurement is very time consuming and noise is
introduced in data handling.
147
VII General conclusions
GENERAL CONCLUSIONS TO CHAPTER 3
If the static resistance of the microflown is chosen much larger than the base
series input resistance of a BJT the electronics can be designed so that the noise of the
circuit is not the limiting factor when operating the microflown. In contrast to a
condenser microphones the 1/f noise density of the electronic circuit is not dominant
in the acoustic bandwidth.
The signal to noise ratio and linearity (combined in the dynamic range) are the
main quality figures of a microphone. The output signal of the microflown is a
differential resistance variation. Considering the main noise factor of a resistor, the
thermal noise, an optimal signal to noise ratio has been derived. It shows that only the
dissipated power and the temperature of the resistor and not the resistance itself are of
relevance.
Multiple circuits which are capable to transduce differential resistance variations
to a varying voltage have been presented, the known Wheatstone bridge and The
Gadget, a half Wheatstone bridge and a modified emitter coupled pair. It is possible
to implement the circuits in a manner that they add practically no noise.
The regular Wheatstone bridge has a slightly less noise performance than the
other circuits.
The Gadget is not very linear for large differential resistance variations and
therefore not very suitable for high sound level measurements. It is however a very
useful circuit for measurement purposes since the transfer function is easy to calculate
when the input bias current is monitored.
For larger signals the signal to noise ratio becomes less important and the
linearity becomes more important so in this case the Wheatstone bridge becomes more
appropriate.
For audio applications a half Wheatstone bridge in combination of a CE
configuration has been used, the linearity of this circuit is high as long as the CE
configuration is operating in the linear region.
The modified emitter coupled pair needs additional electronics to be stable but
besides it is the best performing circuit regarding the linearity.
To increase the signal to noise ratio it is also possible to implement more
microflowns. The improvement of applying a number of n microflowns will be √n.
148
General conclusions
GENERAL CONCLUSIONS TO CHAPTER 4
By studying the hot wire anemometer it is understood that the sensors of the
microflown should have a first order low pass behaviour with a corner frequency in
the order of a few hundred Hertz. The microflown originally did consist of three
elements, two temperature sensors and a heater (SHS type of microflown). The new
proposed microflown (the Two Sensor Microflown, TSM) only contains two
elements: two heated temperature sensors. This new type of microflown has an
improved signal to noise ratio; the most important figure of an acoustical sensor.
A quantitative model of the TSM is presented and it explains why the static flow
sensitivity is dependent of the sensor spacing and operating temperature. The dynamic
behaviour is modelled with the volumetric heat capacity and the thermal resistances
only.
The model of the TSM is kept very simple. To obtain a more detailed model a
lot of effort has to be put into research about alternating temperature profiles in very
small flows around very small structures. To gain more insight in the operation
principles it was chosen to perform characteristic measurements on the behaviour of
the microflown.
A set of calibration measurements fully describes the acoustic properties of the
microflown and this will resolve in two figures. The performance, a dimensionless
figure which provides information about the low frequency self noise. And the corner
frequency, above this frequency the sensitivity drops with 6dB/oct.
GENERAL CONCLUSIONS TO CHAPTER 5
Four methods of constructing a microflown are presented:
The bridge type of microflown was not used at the end of the research while it
appears that the sensitivity of the microflown decrease if the sensors are in the
neighbourhood of a rigid plane. In the realisation of the bridge type the bottom of the
channel is to near of the sensors.
In this research a few thousand microflowns are made using the type II process
because this process has the advantage that a lot of shapes are possible. For the
149
VII General conclusions
metalisation both sputtering as E-beam evaporation is possible. Most microflowns
where made with a one micron silicon nitride. A half micron nitride does have a
higher corner frequency but also a larger bending of the sensors while the metal
thickness is kept constant.
The type III process allows a single metal what makes it very suitable for
measurements on non-alloy metals. Both sputtering as E-beam evaporation is possible
and with this process the best metal can be found.
The mayor advantage of the one mask process (type IV process) is in the name;
only one mask is needed. Aligning problems will be reduced. The reduction of masks
and thus process time will lead to a substantial cost reduction of the microflowns as
they are on the wafer. The wafer however is become very thin which could lead to
damaging by further processing. In the one mask process it is not possible to use
(MESA) sputtering for metalisation when it can not be seen as a point source. This
reduces the number of possibilities using this method. If a good (metal) candidate is
found using the type III process, permission is asked to use the E-beam evaporation
method of deposition. The last step of the one mask process is the metalisation. This
can be done without the use of a mask while the silicon nitride layer is a bit under
etched and acts like a “shadow mask”. The effort which has be to put into creating
this under etching of the silicon nitride can be seen as a disadvantage compared to the
type II process. An advantage is that the metalisation is done at the last step. Due to
this the metal layer will stay as pure as possible.
Advantage of the TSM compared to the SHS type of microflowns is that it is
better possible to leave the top not connected than the SHS type of microflown. This
is because both sensors of the TSM have the same operating temperature and therefore
have the same amount of bending. When operating the SHS, the heater is the hottest
and therefore the heater will bend more than the sensors, the three elements will
therefore not be in one line.
150
General conclusions
GENERAL CONCLUSIONS TO CHAPTER 6
Some acoustical properties of microphones and microflowns are presented.
Comparing both, it shows that the microflown has some features which are competing
with the conventional microphones:
• True particle velocity (and not pressure) sensitive
• Very small
• Easy to fabricate
• Due to batch processing: similar response
• No-1/f noise in the acoustic bandwidth
• Low impedance
Other very important figures are not as good as conventional microphones:
• Low bandwidth
• High selfnoise
• High power consumption
Exploiting the competing features of the microflown three applications are
realised. A microphone for telecommunication purposes, a bass drum microflown and
a sound intensity probe. The latter application is realised using two methods: The
sound intensity obtained by the product of the measured acoustic pressure and
measured particle velocity. It is shown that it is possible to measure the apparent
pressure by using two closely spaced microflowns. The product of the apparent
pressure and the particle velocity provides the sound intensity.
The advantage of this method is the possibility of producing many identical
sensors in one process run. In contrast, for conventional pressure microphones it is
difficult to produce two phase matched sensors.
151
VII General conclusions
SUGGESTIONS FOR FURTHER RESEARCH
The microflown now is operated in the “constant power mode”: an almost
constant power is dissipated in the sensors (and, if present the heater) and the varying
temperature is monitored. Another way of operating the microflown is the “constant
temperature mode”: the sensors will be kept on almost constant temperature due to a
feedback loop. This mode is used in the anemometry and one feature of the complete
system is that the corner frequency increases considerable. It is not clear yet what the
influence is on the noise behaviour. In this research some preliminary measurements
have been performed and the results where promising.
Until now, only metals where used to measure the temperature difference of
both sensors. Other temperature detection materials could be used like for instance
doped polysilicon, a PN junction or a bi-metal.
Long term stability is an important requirement for sensors. Although the
materials of which the microflown is composed are stable measurements are required
to observe the assumed stability.
Concerning the commercial aspects a lot of work has to be done. One of the
first priorities are: statistical research, to get a clear picture of the composition of the
cost prize of a microflown and a market research, to find the best way to exploit the
features of the microflown.
152
153
154
List of Symbols
APPENDIX 1: LIST OF SYMBOLS
Chapter 2: Acoustics
λ
p(t)
p
u(t)
u
∆
Zs
I
SPL
υ
k
wavelength
instantaneous sound pressure
effective sound pressure
instantaneous particle velocity
effective particle velocity
particle displacement
specific acoustical impedance
sound intensity
sound pressure level
kinetic viscosity (air 1.5⋅10-5)
m
N/m2
N/m2
m/s
m/s
m
Ns/ m3
W/m2
dB
m2/s
wavenumber (ω/c=2π/λ)
m-1
Chapter 3: Electronics
R
I
U
R0
∆R(t)
∆R /R
Bw
Ts
P
UT
UA
αFE
k
electrical resistance
electrical current
electrical voltage
nominal value of R
time dependant part of R (signal)
relative differential variation of two resistances
bandwidth
absolute temperature of the sensor
electrical power
kT/q≈25⋅10-3
Early voltage
DC forward current gain
Ω
A
V
Ω
Ω
Hz
K
W
V
V
-
Boltzmann’s constant
1,38 × 10-23 J/K
q
electronic charge
UR
αfe
rbb’
K’F
S
N
voltage over the nominal value of the resistor
AC forward current gain
1,6 × 10-19 C
V
-
base series resistance
corner frequency of the flicker and burst noise
Signal
Noise
Ω
Hz
155
AI List of Symbols
Chapter 4: The µ-flown
R
electrical resistance
I
electrical current
coefficient of thermal conductivity
κ
R0
nominal value of R
time dependent part of R (signal)
∆R(t)
∆R /R
Bw
Ts
P
ρr
ρ
c
h
relative differential variation of two resistances
bandwidth
absolute temperature (of the sensor)
electrical power
resistivity
ν
αd
density
specific heat
coefficient of convective heat transfer
Stefan-Boltzmann constant 5.67 10-8
emissivity
fluid velocity
kinematic viscosity
thermal diffusivity
α
S
N
linear temperature coefficient of resistivity
signal/ sensitivity
noise
σ
ε
U
Chapter 5: Realisation
R
electrical resistance
I
electrical current
k
Boltzmann’s constant (noise calculations
R0
nominal value of R
time dependent part of R (signal)
∆R(t)
relative differential variation of two resistances
∆R /R
Bw
bandwidth
Ts
absolute temperature (of the sensor)
P
electrical power
resistivity
ρr
density
ρ
c
specific heat
h
coefficient of convective heat transfer
Stefan-Boltzmann constant 5.67 10-8
σ
emissivity
ε
U
fluid velocity
kinematic viscosity
ν
thermal diffusivity
αd
linear temperature coefficient of resistivity
α
fc
corner frequency of the microflown
d
diameter of a cylinder
156
Ω
A
W/mK
Ω
Ω
Hz
K
W
Ωm
kg/m3
J/kg K
W/ m2 K
W/m2 K4
m/s
m2/s
m2/s
K-1
Ω
A
1,38 × 10-23 J/K
Ω
Ω
Hz
K
W
Ωm
kg/m3
J/kg K
W/ m2 K
W/m2 K4
m/s
m2/s
m2/s
K-1
Hz
m
Transistor Models
APPENDIX 2: TRANSISTOR MODELS
The large-signal behaviour of a BJT transistor can be summarised in a few
formulas.
Fig. A2.1: The BJT Transistor.
The devices can be seen as a two port, base emitter voltage UBE as input and
collector current IC as output. The relation between the two is given by:
U BE
U
I C = I CO ⋅ ( 1 + CE ) ⋅ e U T 2
UA
In where ICO is a arbitrary constant having a typical value of 10-14 to 10-16 A [1],
UA the Early voltage with a value of about 75V and UT the thermal voltage given by
kT/q≈25 mV. The collector current is a sum of both base as emitter current:
IC = I E + I B
At last the base and collector current are related as:
I C = α FE I B
Using αFE as the DC forward current gain having a typical value of 25 for high
power transistors to 400 for low power transistors. The small signal behaviour of
the BJT can be derived from the equations given above. This is done in Gray and
Mayer extensively [1] and this will be summarised here for frequencies below
20 kHz.
157
AII Transistor Models
Fig. A2.2: The small signal equivalent of the BJT.
The AC forward current gain (the small signal current gain) is approximately the
same as the DC forward current gain.
α fe ≈ α FE
The input resistance is given by:
ri =
α fe
s
=
α fe
α fe
≈
q
I C 40 I C
kT
The input resistance is reversibly dependent of the DC collector current. The
relation between the base emitter voltage, base current and collector current is given
by:
ic = sube ≈ 40 I C ube
= α feib
And at last the output resistance is given by:
ro =
UA
IC
Note that all small signal parameters are dependent on the DC collector current.
[1] Gray and Mayer, Analysis and design of analogue integrated circuits, 1993, New York.
158
Noise Calculations
APPENDIX 3: NOISE CALCULATIONS
INTRODUCTION IN NOISE THEORY
In this appendix the noise models of standard electronic circuits are presented.
The calculations are not very complicated but are strangely not given in any study
book whatsoever. Furthermore is the simulation of noise only limited possible with the
widely used programs as PSPICE or MicroCap.
Therefore the analyses of the basic electrical circuits is given here quite
extensive. Also the noise of the Wheatstone bridge, the emitter coupled pair, and The
Gadget is presented.
In order to be able to make the simulations a extra shell is designed for PSPICE
to be able to do the required simulations.
Noise is defined in a square spectral form, shown for example in the thermal
noise, noise due to the random thermal motion of the electrons in a resistor.
2
uthermal
= 4kTR
∆f
(A3.1)
Where k is Boltzmann’s constant and T the absolute temperature. To calculate the
rms. noise of an resistor in a frequency band one has to integrate over the frequency:
urms =
∫
fmax u 2
df
fmin ∆f
(A3.2)
This is quite easy for thermal noise while it is not dependent of the frequency.
Flicker noise, or 1/f noise, however is dependent of the frequency. This type of
noise is found in all active devices, as well as some discrete passive elements like
carbon resistors [A3.1]. Flicker noise is always associated with a flow of direct
current and displays a spectral density of the form:
i 2flicker
Ia
= K1 b
∆f
f
(A3.3)
159
AIII Noise Calculations
where I is the direct current, K1 is a constant for a particular device, a is a constant in
the range of 0.5 to 2 and b a constant of about unity.
Another noise source that always is associated with a direct current flow is the
shot noise. This source of noise is present in PN junctions, BJT transistors and diodes.
2
ishot
= 2qI
∆f
(A3.4)
In where q is the electronic charge.
The last noise source mentioned is burst noise. This is another type of low
frequency noise found in transistors. The source of this noise is not fully understood,
although it has been shown to be related to the presence of heavy metal ion
contamination [A3.1]. Gold doped devices show very high levels of burst noise.
2
iBurst
= K2
∆f
Ic
 f
1+  
 fc 
2
(A3.5)
Where K2 is a constant of a particular device, c is a constant in the range 0.5 to 2 and
fc is a particular frequency for a given noise process.
Noise calculations are not very complex, but in the calculation of all noise
sources to the output or input of a device often small errors are made. So the first
advice is to split up all calculations in small survivable pieces. A number of basic
circuits are presented below. The second thing that make noise calculations very
difficult is the fact that it is difficult to check the obtained answers. Simulation
program’s, like PSPICE, do not (yet) have the proper facilities to check the noise of a
circuit. At last a view mathematical rules have to be considered.
Summing noise sources:
2
utot
u12 u22
=
+
+...
∆f
∆f ∆f
(A3.6)
Calculating a transfer function:
ua2
u2
= Hb2→a ⋅ b
∆f
∆f
160
(A3.7)
Noise Calculations
Calculating the equivalent circuits shifting sources is often a simple and wise
thing to do. The Blakesley transformations are very convenient for this [A3.2]:
Fig. A3.1: The Blakesley voltage and current transformations.
BJT NOISE GENERATORS
In a BJT transistor a number of sources of noise are present. Those sources are
presented in Fig. A3, the small signal equivalent for relatively low frequencies.
Fig. A3.2: The noise generators shown in a small signal BJT model.
The transistor base resistor rbb’ is a physical resistor and thus has thermal noise.
δur2 '
bb
= 4 kTrbb'
∆f
(A3.8)
The collector noise contains only shot noise and is given by:
δiC2
= 2qI C
∆f
(A3.9)
161
AIII Noise Calculations
The base noise current is given by:
δiB
= 2qI B + K1
∆f
I Ba
+ K2
fb
I Bc
 f
1+  
 fc 
2
(A3.10)
The flicker and burst noise terms in bipolar transistors have been found
experimentally to be represented by current generators across the internal base emitter
junction. The parameters a, b, c, K1 and K2 are normally not specified for common
commercial available transistors and it is possible that they change during long time
operation. Accurate calculations therefore are very difficult. Therefore a rough
simplification will be made:
Ia
K1 Bb + K 2
f
I Bc
IB
2 ≈ KF f
 f 
(A3.11)
1+  
 fc 
Eq. will simplify and now becomes:

δiB
IB
K 'F 
K

 ; K 'F = F
= 2qI B + K F
= 2 qI B 1 +
∆f
f
f 
q

(A3.12)
Using K’F as the corner frequency of the flicker and burst noise. It is possible to find
transistors having a corner frequency K’F, as low as 100 Hertz.
NOISE OF THE BJT IN FORWARD BIASED DIODE CONFIGURATION
If the base and the collector are short circuited the BJT act as a diode. The noise
equivalent is calculated using eq. (A3.1).
Fig. A3.3: The BJT in Forward Biased Diode configuration.
If the transfer functions of all noise sources are known Fig. A3 can be simplified in to
Fig. A3.4:
162
Noise Calculations
Fig. A3.4: Small signal equivalent of the BJT-diode.
The values of Fig. A3.4 are:
IC
ICO
≈ 0.6 ...0.7V
U D ,BJT = U T e
1 r
rD ,BJT = + bb'
s α fe
(A3.13)
2
2
δuD

,BJT
2
21
= δurbb' + δiB  − rbb'  + δiC2 ⋅ rD2 ,BJT
s

∆f
2
1 r 

K'   1

= 4 kTrbb' + 2qI B  1 + F   − rbb'  + 2qIC ⋅  + bb' 

f  s

 s α fe 
2
NOISE OF THE BJT IN A COMMON EMITTER CONFIGURATION
The common emitter configuration is given in Fig. A3.5.
Fig. A3.5: Common Emitter configuration.
The small signal equivalent of Fig. A3.5 and all noise sources are given in Fig. A3.6:
163
AIII Noise Calculations
Fig. A3.6: Small signal equivalent of a Common Emitter configuration.
At first the transfer function of the CE circuit is calculated.
α fe


− ui − ib  Ri + rbb' +
+ RE  − iout RE = 0
s


(A3.14)
iout
−1
=
Ri + rbb' + RE
1
ui
+ RE +
α fe
s
Summarising the calculations above, the parameters of the CE become eq. (A3.15):
−1
i
A = out =
r
1
uin
bb' + + R + RE + Ri
E
α fe
α fe s
RCE = rbb' +
α fe
+ ( 1 + α fe ) RE
s
2
δuCE
= 4 k ( TRE RE + Trbb' rbb' ) + δui2
∆f
α fe


+ RE
Ri + rbb' +


s


+2 qI C
α fe


 Ri + rbb' +
+ ( 1 + α fe ) RE 


s
2
 1 Ri + rbb' + RE 



= 4 k ( TRE RE + Trbb' rbb' ) + δui2 + 2 qIC  s +
α fe

164
2
 rbb' 1

K'

 + 2 qI B ( 1 + F )( Ri + rbb' + RE )2
+
+
R
E
α

f
 fe s

2
+ 2 qI B ( 1 +
K 'F
)( Ri + rbb' + RE )2
f
Noise Calculations
NOISE OF THE BJT IN AN EMITTER COUPLED PAIR CONFIGURATION
The circuit of an emitter coupled pair is shown in Fig. A3.7. The 1:1 element in
top of the circuit represents an ideal current mirror.
Fig. A3.7: A emitter coupled pair with an ideal current source an current mirror.
The small signal equivalent of the emitter coupled pair is given below (Fig. ).
Fig. A3.8: the small signal equivalent of Fig. A3. shown with only one noise source
δiB
To calculate the δui2 an ideal current mirror is used to subtract both collector currents
and creates a pure differential output. The transfer function is given by:
Adifferential =
iout
uin ,differential
iout = 2α fe ib
Adifferential =
(A3.16)
α fe
rbb' + R +
α fe
s
Acomm. = 0 ;
165
AIII Noise Calculations
The equivalent input noise is given by eq. (A3.17):
δui2 ≈
2

 8 kT  r + TR R + 8( rbb' + R ) kT + 4qI (rbb' + R) + 4qI
∫   bb' T 
α fe
α fe
α 2fe
Bw 

K' 
U2 
 1 + F  (rbb' + R)2 + 4q T  ⋅ df
f 
I 

Assuming αFE ≈ αfe >> 1 and solving the integral, eq. (A3.18):

 ( r + R )2
T
f
U2


δui2 ≈ 8 kT  rbb' + R R Bw + 4qI  bb'
Bw + K 'F ln max  + 4q T Bw

T 
α fe
f min 
I

As can be seen in (A3.18) the total equivalent input noise is dependant of the bias
current and the inverse of the bias current. An optimum can be found.
Ioptimal =
UT
(A3.19)
f
K 'F ln max
( rbb' + R )2
f min
+
Bw
α fe
Substituting eq. (A3.19) in eq. (A3.18) becomes eq. (A3.20):
δui2
I C = I optimal
T


= 8 kT  rbb' + R R Bw + 8qU T Bw

T 
2
 rbb' + R 
K'
f

 + F ln max
 α

Bw
f min

fe 
Neglecting the 1/f noise, eq. (A3.21):
δui2 K ' = 0
F
I C = I optimal
 r + R
T


 Bw ≈ 8 kT  rbb' + TR R Bw
= 8 kT  rbb' + R R Bw + 8 kT  bb'
 α



T 
T 
fe 

As can be seen in eq. (A3.21) if R >> rbb’ only the noise of R contributes.
SIGNAL TO NOISE RATIO OF THE WHEATSTONE BRIDGE
The differential output of a Wheatstone bridge is maximal if al resistors are the same:
The transfer function of one branch is given by:
U1 =
R( t )
E
R1 ( t ) + R3
The maximal sensitivity of this transfer function is given by:
166
Noise Calculations
∂U1
1
 −2 R1( t )

=
+
E = 0
∂R1 R3  ( R1 ( t ) + R3 )3 ( R1( t ) + R3 )2 
Eq. is valid for R1=R3. The transfer function of the Wheatstone bridge in
combination with a differential amplifier is given by:
 R1 + ∆R1
R2 + ∆R2 
−
∆U out = U1 − U 2 = 
E
 R1 + ∆R1 + R3 R2 + ∆R2 + R4 
to obtain a maximal sensitivity R1,0=R2,0=R1=R2=R is chosen. For differential
resistor variations (∆R=∆R1=-∆R2) the transfer function is given by:
∆R
R
∆U out =
IR
E=
2
2
2
4 R − ∆R
R
∆ 
1− 

 2R 
2 R∆R
The Thévenin equivalent of a Wheatstone bridge is given by:
Fig. A3.9: Equivalent circuit of the Wheatstone bridge.
2
δuWheatstone
= 4 kTaverage R ⋅ Bw
∆f
(A3.22)
The signal to noise of the Wheatstone bridge now is given by:
S
=
N
∆R
R
4kTaverage R ⋅ Bw
IR
167
AIII Noise Calculations
NOISE OF THE GADGET
At last noise of The Gadget will be derived. The noise models of the common
emitter configuration and the noise of the BJT in forward biased diode configuration
will be used. The noise sources are of The Gadget presented in Fig. A3.10.
Fig. A3.10: Noise sources of The Basic Gadget.
The noise models of the diode are given by eq. (A3.13). The noise of The Basic
Gadget will be, using the noise models of the common emitter configuration and the
proper substitutions made:
1
i
A = out =
2 R + rbb' 1
uin
+ +R
α fe
s
2
δuGadget
∆f
= 4 k (Ts R + Trbb' ) + δui
α fe + 1
 (α fe + 1)

rbb' +
+ 2R

s
 α fe

+2qI C 

α fe + 1
 rbb' +

+
(
2
+
α
)
R
fe


s


2
 rbb' 1



+
+
R
α

s
 fe



K F'   1 (α fe + 1)
  +


2
+ 2qI B 1 +
r
+
R
'
bb
s

α
f



fe
2
(A3.23)
2
The noise models of the BJT in forward biased diode configuration included and under
the condition that αfe >> 1 eq. (A3.23) becomes:
168
Noise Calculations
2
δuGadget
∆f

T
= 4 kT  s 2 R + 2rbb' 

T
2
2

 1 rbb'  
1 2R 

 +  +

+2qIC ⋅  +
  s α fe 
s α fe  



(A3.24)
2
2

K'    1
1
 

+ 2qI B  1 + F  ⋅   + 2 R +  − rbb'  
s
 

f   s

So the noise produced at the output of The Basic Gadget will be eq. (A3.25):
δiout
=
∆f
2
2

2
2
 1 rbb  

K'   1
1 2R 
1
 Ts


'




 1 + F  ⋅   + 2 R +  − rbb'  
qI
+
+
4 kT  2 R + 2rbb'  + 2qIC ⋅   +
+
2
B
s α  
T


s
 
s α fe 
f    s


fe  

2 R + rbb' 1
+ +R
s
α fe
The noise is dependant of the bias current I. Rewriting eq. (A3.25) to get I explicit
and reminding s=I/UT, eq. (A3.26):
δiout
=
∆f
2
2


2
2
U
r 
K'   U
U
2 R + rbb' 
1 
  T r  I U
 +  T + bb'  +
 1 + F  ⋅   T + rbb' + 2 R +  T − rbb'    
8qU T  s + bb'  + ⋅   T +

 I
   
R  R  I
α fe 
α fe 
α FE 
f    I
 T
 I



2 R + rbb' UT
+
+ R
α fe R
I R
Looking closer to the bias current fraction, eq. (A3.27):
2
2

 U T rbb' 
1
I   U T 2 R + rbb' 
 +
 +
+
+
Noise( I , R ) = ⋅  



α fe 
α fe 
α FE
R  I
 I

Reorganising, UR=IR and
2
2 

K'   U
U
 1 + F  ⋅   T + rbb' + 2 R +  T − rbb'   

 I
  
f    I


α fe
≈ 1 , α 2fe >> α fe eq. simplifies in, eq. (A3.28):
α FE
2
 UT 
rbb' K 'F  U R 
K 'F   
rbb'  
 +
 2 +
+
1 +
 ⋅ 1 + 1 +
+

R
f  2α fe 
f   
R  
 α fe 
The total noise at the output of The Basic Gadget is given by:
1 U2 
K 'F
Noise( I , R )U = IR =  T   1 +
R
2  U R   α FE f
8q
δiout =
∫
Bw
  Ts rbb' 

 + Noise( I , R ) ⋅ df
U T  +


T
R 
 2

2r
U

+ bb' + T + 1 R
 α fe α fe R U R

(A3.29)
169
AIII Noise Calculations
R EFERENCES
[A3.1]Gray and Mayer, Analysis and design of analogue integrated circuits, 1993, New York.
[A3.2]J. Davidse, Ruisarm ontwerpen in de elektronica en communicatietechniek: een postacademische
cursus van de TU-Delft, Kluwer Technische Boeken, 1988.
170
A comparison based on noise
APPENDIX 4: MICROPHONES,
A COMPARISON BASED ON NOISE
The noise output of a transducer is observed compared to a signal output. The
noise of pressure microphones is commonly measured as a r.m.s. voltage after filtering
with a so called “A” weighting filter, see Eq. 6.2. The signal is measured at 1kHz and
94dB SPL, which equals 1 Pa.
In case of a particle velocity sensor, the signal is measured at 94dB PVL
(2.5mm/s) and also at 1kHz. The noise is measured the same way.
In chapter 6 the microflown has been compared to the best performing (1 inch)
B&K condenser microphone. In this appendix it will be compared to a half inch
pressure microphone and a matched pair of half inch pressure microphones that are used
for sound intensity measurements (p-p probe, see Fig. 2.8).
Measurements have shown that the noise of the microflown is purely thermal, see
Eq. 4.19. The sensitivity, and thus the performance of the microflown has increased
over 17dB since February ‘97. The sensitivity now (mid-1997) reaches the 0.22 s/m.
This means that a differential resistor variation of 22% can be expected due to 1 m/s
particle velocity.
To calculate the performance (see Eq. 4.21) the absolute temperature has to be
known. This can be calculated by using the power curve (see Fig. 4.15) and the
temperature coefficient of resistivity. The temperature, at optimal sensitivity is in the
order of 500K. The power dissipation at optimal sensitivity has been measured to be
20mW per sensor (total power dissipation 40mW). The performance then equals 22dB.
The corner frequency is measured 1kHz. The noise factor can be found in Fig. 6.4.
For 20kHz bandwidth the “A” weighed noise factor is 61dB and for 3.4kHz bandwidth
(speech purposes) the “A” weighed noise factor is 46dB.
The selfnoise can be calculated by using Eq. 6.4: Selfnoise equals Noise Factor
minus Performance. The selfnoise for 20kHz bandwidth equals 38dB and the selfnoise
for 3.4kHz equals 23dB. The latter is at 40mW of total power dissipation. For
telecommunication purposes the total power dissipation have to be 10mW at maximum:
the performance will drop approximately 8dB due to the reduced power dissipation. The
selfnoise therefore will increase this 8dB.
171
AIV A comparison based on noise
SIGNAL AND NOISE LEVELS
The signal and noise levels will be given for a pressure microphone, a pressure
difference (pressure gradient) microphone and a microflown.
A microflown has a corner frequency of 1kHz and a performance of 22dB
(Rmicroflown (hot)=400Ω, S=0.22 s/m, Popt=20 mW per sensor (Isensors=7.1mA), Ts=500 K,
see also chapter 4). The preamplifier is based on a half Wheatstone bridge in
combination of a CE configuration and compensates for the low pass behaviour of the
microflown, see appendix 6. The preamplifier has been designed in such a way that the
noise contribution is negligible compared to the noise of the microflown.
In 1Hz bandwidth the noise of the microflown can be calculated, see Eq. A3.1.
unoise ,1Hz = 4kTR = 2.3nV . The signal (vbase) due to 94dB PVL can be calculated
using Eq. 3.44: vbase=1.56mV. The signal to noise ratio at 1kHz in 1Hz bandwidth can
be calculated: 20 Log10
(
)
156
. mV
= 116dB . The gain of the preamplifier will not be taken
2.3nV
into account here; signal and noise will be observed at the input. Since the microflown
has got a low pass behaviour with a corner frequency of 1kHz it has to be compensated:
the noise density therefore will increase with 6dB/oct after 1kHz. See Fig. A4.1.
A half inch pressure microphone usually has a sensitivity of 12.5mV/Pa, see Table
6.2. 94dB SPL equals 1Pa thus an output voltage of 12.5mV will be the result. The
selfnoise of such microphone is listed as 22dB(A) which means that 3µV “A” weighed
noise is measured. This equals 26nV in one Hertz bandwidth at 1kHz (see Eq. 6.2A). At
1kHz the signal to noise ratio is 20 Log10
(
)
12.5mV
= 113dB . The noise density will
26nV
increase under the 500Hz due to 1/f noise. See Fig. A4.1.
Now let’s focus on the (self) noise of a p-p probe. An example of a high quality
matched pair is the Brüel & Kjær sound intensity microphone pair B&K 4181. One of
the ½ inch matched microphones has a selfnoise of 20dB(A) and a sensitivity of 11.2
mV/Pa (at 1kHz). It will be convenient to express noise values in voltages and in one
Hertz bandwidth. The latter corresponds to: Unoise=19nV in 1 Hz bandwidth at 1 kHz.
Microphones such as the B&K type 4148 do have a 1/f noise behaviour that will be
dominant under frequencies under the 500Hz.
Because the differential pressure is measured to determine the particle velocity,
two microphones are used, the total noise will increase a factor √2.
172
A comparison based on noise
The previous is depicted in Fig A4.1. A plane wave with a sound intensity level
of 94dB is submitted to the p-p probe. The signal is caused by the subtraction of both
pressure microphone outputs, this signal is used to calculate the particle velocity. Due
to a mismatch in both microphones for lower frequencies the arithmetical error in the
prediction of the particle velocity will increase. This effect increases as the sound field
becomes more reactive.
As can be seen in Fig. A4.1, if the frequency decreases the signal decreases and
the noise increases; the signal to noise ratio decreases rapidly for frequencies lower
than 500Hz. The signal will be integrated, see Eq. (2.38) and therefore the frequency
response will be flat, the noise however will also be integrated: the signal to noise
ratio therefore will not be altered.
The results which are depicted in Fig. A4.1 will be discussed now. As can be
seen the signal to noise ratio of a microflown up to 1kHz is similar to the signal to
noise ratio of a ½” microphone of frequencies above the 500Hz. However the human
ear is most sensitive for frequencies around the 3kHz. Therefore for audio purposes a
½” microphone will perform better. In other words the “A” weighted noise of a
microphone is lower than the “A” weighed noise of the microflown.
For measurement purposes the microflown should be compared to the p-p probe
since this probe is designed to measure the particle velocity. As can be seen the signal
to noise ratio of a microflown is better up to approximately 3kHz. From 3kHz to
8kHz the p-p probe performs better. The pressure gradient approximation of a p-p
probe is not valid for frequencies above the 8kHz for 8.5mm spacing.
In a reactive field up to 500 Hz the particle velocity is measured correctly by
using a microflown and not by using a p-p probe.
173
AIV A comparison based on noise
Fig. A4.1: Noise output voltage in 1 Hz bandwidth and signals due to 94dB SIL in a
plane wave.
174
Pictures of Probes
APPENDIX 5: PICTURES OF PROBES
Fig. A5.1: First realisation of a microflown for speech purposes.
175
AV Pictures of Probes
Fig. A5.2: Microflown mounted in a m5 bolt for measurements in an impedance tube.
176
Pictures of Probes
Fig. A5.3: A p-u probe: a ½’’ B&K microphone and a packaged Microflown facing it.
177
AV Pictures of Probes
Fig. A5.4: Detail of a P-U probe a ½’’ B&K microphone and a packaged Microflown
facing it.
178
AVI Electronic Circuits
APPENDIX 6:ELECTRONIC CIRCUIT
Fig A6.1: Preamplifier for telecommunications applications.
This realisation is designed for a 20Hz-3400Hz signal band. The microflown
used has a corner frequency of 300Hz.
The aim of the first stage (transistor T1) of the preamplifier is amplification of
the microflown signal. For signal to noise reasons the base series resistance has to be
much lower than the half of the hot microflown sensor resistance and the bias current
has to be calculated, see eq. 3.46. The combination Re1 and Ce1 shows a high pass
filter (HPF) character and the combination Rc1 and Cc1 a low pass filter (LPF
character. The corner frequencies are chosen fHPF=20Hz and fLPF=3400. It is
important to connect the capacitor Ce1 to the ground (GND) to reject noise of the
power supply (VCC).
The combination Cf1 and Rb1 parallel to Rb2 will act as the compensation
network. The corner frequency is chosen 3400Hz. While for frequencies lower than
300Hz no compensation is needed the resistor Rf1 in combination is chosen to have a
corner frequency of 300Hz. The capacitor Cf2 is used as DC-decoupling.
The values Rb1 and Rb2 are chosen equally large while then the second stage
can be designed the same as the first stage.
The aim of the third stage is to create a low output resistance. The capacitor C01
is used for the DC-decoupling.
179
Bibliography
BIBLIOGRAPHY
J. van Kuijk, T.S.J. Lammerink, H.-E. de Bree, M. Elwenspoek, J.H.J. Fluitman,
Multi-parameter detection in fluid flows, Sensors and Actuators A 46-47 (1995) pp.
369-372.
H-E. de Bree, P.J. Leussink, M.T. Korthorst, H.V. Jansen, T. Lammerink, M.
Elwenspoek, The microflown, a novel device measuring acoustical flows, Sensors and
Actuators A, Sensors and Actuators: A. Physical, volume SNA 054/1-3, pp. 552-557,
(1996).
H-E. de Bree, P.J. Leussink, M.T. Korthorst, Y. Backlund, H.V. Jansen, The
Wheatstone gadget, a simple circuit measuring differential resistance variations,
proceedings MME 1995, Denmark, pp. 201-204.
H. Schurer, P. Annema, H-E. de Bree, C.H. Slump, O. Hermann, Comparison of
two methods for measurement of horn input impedance, presented at the 100th
convention AES, 1996 may 11-14 Copenhagen.
H-E. de Bree, P.J. Leussink, M.T. Korthorst, M. Elwenspoek, The Two Sensor
Microflown, an improved flow sensing principle, proceedings Eurosensors X,
Leuven, 1996.
H-E. de Bree, P.J. Leussink, M.T. Korthorst, H.V. Jansen, M. Elwenspoek, A
method to measure apparent acoustic pressure, flow gradient and acoustic intensity,
proceedings Eurosensors X, Leuven, 1996.
H-E. de Bree, M.T. Korthorst, P.J. Leussink, H. v. d. Weyer, M. Elwenspoek, The
µ-flown, A true particle velocity microphone, to be published.
180
Bibliography
H-E. de Bree, H. Schurer, M.T. Korthorst, P.J. Leussink, T. Veenstra, T.
Lammerink, A direct method to measure acoustical impedance using a micro
machined flow microphone, Calibration & measurements, to be published.
H-E. de Bree, M. Elwenspoek, T. Lammerink, J. Fluitman, “use of a fluid flow
measuring device as a microphone and system comprising such a microphone”,
PCT/NL95/00220, International patent (pending).
H-E. de Bree, C.P. Roodenburg, M.T. Korthorst, H.V. Jansen, M. Elwenspoek,
“inrichting en werkwijze ter bepaling van de akoestische geluidintensiteit”, Dutch
patent (pending).
181
LEVENSLOOP
Hans-Elias de Bree is geboren op 11 januari 1969 te Soest. Omdat op de lagere
school het lezen en schrijven wat achter bleef bij de rest leek het nog hele klus om de
MAVO te halen. Dat viel gelukkig erg mee maar het truukje “schrijven” blijft een groot
probleem. Hierna was het de beurt aan de MTS hetgeen niet geheel aan zijn
verwachtingen voldeed. Na de eerste dag kwam hij dan ook enigszins teleurgesteld terug
maar volgens zijn moeder was het nog maar vier jaar dus “nog maar eventjes doorzetten
jongen”. Na drie jaar hield hij de MTS toch maar voor gezien en startte aan de HTS
Electrotechniek Hilversum. Al vanaf de kleuterschool moest dan Pa, dan Ma “brandjes
blussen” op school als een en ander weer eens ontspoord was. Vanaf de HTS ging het
aanmerkelijk beter, maar ook daar kon hij z’n draai niet echt vinden. Het besluit om naar
een jaar deze school te verlaten voor de Universiteit Twente bleek een gouden greep. Na
de propaedeuse heeft hij tijdens zijn studie vele bestuursfuncties en student-assistentschappen vervuld. Van de opbrengsten hiervan is hij een half jaar naar Indonesië
vertrokken voor zijn eerste sabbatical leave. Hierna ontving hij zijn bul in januari 1995.
Wat sport betreft houdt hij van volleyballen, snookeren, golfen, wandelen en zeilen
maar om hem een sportmens te noemen gaat te ver. Verder speelt hij redelijk hoorn en
een beetje saxofoon. Alles waar “ste” achter staat heeft zijn voorliefde.
Zoals al wel duidelijk zal zijn is het onderwerp van zijn promotie de microflown.
Net voor dat hij naar Indonesië vertrok heeft hij deze zo’n beetje per toeval uitgevonden.
Het idee was zo leuk dat er meteen een patent op aangevraagd werd. Als alles normaal
zou zijn verlopen, dan zou de stichting die het patent in eerste instantie financierde ook
zijn promotie betalen. Helaas is dat niet gelukt. Het karakter van de promotie veranderde
hierdoor aanzienlijk, omdat de verantwoordelijkheid van de financiering van het promotie
project en het patent nu bij hem zelf lagen. Als je aan de ondernemende universiteit
promoveert, ligt het natuurlijk voor de hand om met een goed idee een eigen bedrijf te
starten. Dat is dan ook waar hij, samen met twee collega’s, na zijn promotie aan wil
beginnen.
DANKWOORD
In ruim twee jaar promoveren en ook nog de microflown vercommercialiseren dat
kan alleen maar met een heleboel steun en hulp. Nu het promoveren erop zit is het tijd
om de mensen die mij zo geholpen hebben hiervoor te bedanken.
Allereerst wil ik natuurlijk Inez van de Wolfshaar bedanken die mij de afgelopen
jaren volledig gesteund heeft. Verder mijn vader en moeder voor hun steun en positieve
instelling. Mijn vriend voor het leven Bert Burger voor zijn relativerende humor ‘tobben,
tobben, tobben’, Steven de Graaf ‘ik wordt al moedeloos als ik dat proefschrift zie’, Bert
Jansen ‘is die deal nou nog niet rond?’.
De reden waardoor ik zeker wist dat promoveren een juiste keuze was ontdekte ik
in Pisa. Samen met Miko Elwenspoek, Henri Jansen, Vincent Spiering en Ylva Backlund
hebben we een zeer goede conferentie (wetenschappelijke term voor feest) gehad. Het
kan dan ook geen toeval zijn dat Miko mijn promotor is, Henri mijn kamergenoot werd
en dat ik samen met Ylva een belangrijk (ahum) wetenschappelijk artikel heb geschreven.
Wie een tijd bij MicMec zit, valt in slaap bij ‘Goede Tijden Slechte Tijden’. Meer
soap dan bij MicMec is nergens te vinden. Centrum van de actie is natuurlijk de
koffiehoek en hoofdrolspeler aldaar is Dick Ekkelkamp. Mijn kamer heeft maar één
(verse?) luchttoevoer en die is aangesloten op kamer van Erwin Berenschot en Meint de
Boer. Dank voor alles wat ik met jullie heb mogen delen.
De microflown uitvinden is leuk maar wat je met het idee gaat doen is pas echt van
belang. Een grote groep studenten heeft er met een zeer groot enthousiasme aan
gewerkt. Hiervan verdienen uiteraard PELE Leussink en Twan Korthorst de meeste
dank. Zij zijn er vanaf het prilste begin bij geweest en hebben mij door dik en dun
gesteund. Verder wil ik de D-studenten Theo Veenstra, Martin van Es, Niels Olij, KeChun Ma en Hanneke Vreugdenhil bedanken. Uiteraard wil ik Pedro Roodenburg met
wie het allemaal begon, Arnoud van der Wel, Sjoerd Oosterbaan, Jeroen Kruiver, Oene
van der Vegt, Wilfred Beckers, Edwin Potman, Albert Wessel, Vincent Pol, Huy van
Nguyen, Daniël den Arend, Lude Bakema en Niels Mosely ook bedanken.
Vooral in de begintijd hebben Gert-Jan Burger en Henri Jansen het Microflown
Team erg geholpen, volgens mij heeft Henri het woord ‘microflown’ zelfs verzonnen.
Gert-Jan komt zo nu en dan nog steeds met goede tips langs.
Om de microflown beter te leren begrijpen moet je haar gebruiken. Samen met
Hans Schurer hebben we een leuke toepassing uitgewerkt en een artikel geschreven. Met
Bert Wolbert van de faculteit werktuigbouwkunde werken we het laatste half jaar ook
prettig samen. Van de firma Sennheiser wil ik graag de heren Dr. Ing. W. H. Niehoff en
Dr. Ing. V. Gorelik bedanken voor hun inzet en vertrouwen in het microflown project.
Het poppodium Atak wil ik graag bedanken voor de enthousiaste medewerking en
samenwerking.
Verder wil ik Frans van den Beemt en Arie Phillipo bedanken dat hoewel de STW
formeel de zaak “microflown” twee maal gesloten heeft ze toch door zijn gegaan met
hun ondersteuning.
Hans van de Weyer wil ik graag bedanken voor zijn inhoudelijke hulp. De
financiële adviezen van collega ing. Vraets heb ik zeer op prijs gesteld. Verder heb ik
veel aan de strategische adviezen van dhr. Krijgsman gehad.
Als laatste wil ik graag meneer van den Hul bedanken. Dankzij zijn motiverende en
inspirerende begeleiding en financiële bijdrage heeft de microflown nu een kans van
slagen als een product. Hij heeft ons (ook Pele en Twan) de eerste stappen in het
ondernemer zijn geleerd en hopelijk kunnen we nog lang op zijn steun rekenen.
-------------------------------------------------Hans-Elias de Bree
Graio at University of Twente
A Proud member of the Microflown Team
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