TECHNICAL REVIEW
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TECHNICAL REVIEW
Properties and Calibration of Laboratory
Standard Microphones
BV 0054 – 11
ISSN 0007–2621
Uncertainties in Microphone Frequency
Responses
No.1 2001
InsideCovers.fm Page 4 Tuesday, June 26, 2001 9:01 AM
Previously issued numbers of
Brüel & Kjær Technical Review
1 – 2000
1 – 1999
1 – 1998
1 – 1997
2 – 1996
1 – 1996
2 – 1995
1 – 1995
2 – 1994
1 – 1994
2 – 1990
1 – 1990
2 – 1989
1 – 1989
2 – 1988
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4 – 1987
3 – 1987
2 – 1987
Non-stationary STSF
Characteristics of the vold-Kalman Order Tracking Filter
Danish Primary Laboratory of Acoustics (DPLA) as Part of the National
Metrology Organisation
Pressure Reciprocity Calibration – Instrumentation, Results and
Uncertainty
MP.EXE, a Calculation Program for Pressure Reciprocity Calibration of
Microphones
A New Design Principle for Triaxial Piezoelectric Accelerometers
A Simple QC Test for Knock Sensors
Torsional Operational Deflection Shapes (TODS) Measurements
Non-stationary Signal Analysis using Wavelet Transform, Short-time
Fourier Transform and Wigner-Ville Distribution
Calibration Uncertainties & Distortion of Microphones.
Wide Band Intensity Probe. Accelerometer Mounted Resonance Test
Order Tracking Analysis
Use of Spatial Transformation of Sound Fields (STSF) Techniques in the
Automative Industry
The use of Impulse Response Function for Modal Parameter Estimation
Complex Modulus and Damping Measurements using Resonant and
Non-resonant Methods (Damping Part II)
Digital Filter Techniques vs. FFT Techniques for Damping
Measurements (Damping Part I)
Optical Filters and their Use with the Type 1302 & Type 1306
Photoacoustic Gas Monitors
The Brüel & Kjær Photoacoustic Transducer System and its Physical
Properties
STSF — Practical Instrumentation and Application
Digital Filter Analysis: Real-time and Non Real-time Performance
STSF — A Unique Technique for Scan Based Near-Field Acoustic
Holography Without Restrictions on Coherence
Quantifying Draught Risk
Using Experimental Modal Analysis to Simulate Structural Dynamic
Modifications
Use of Operational Deflection Shapes for Noise Control of Discrete
Tones
Windows to FFT Analysis (Part II)
Acoustic Calibrator for Intensity Measurement Systems
Windows to FFT Analysis (Part I)
Recent Developments in Accelerometer Design
Trends in Accelerometer Calibration
(Continued on cover page 3)
bv005411_TOC.fm Page 1 Monday, June 25, 2001 3:15 PM
Technical
Review
No. 1 – 2001
bv005411_TOC.fm Page 2 Monday, June 25, 2001 3:15 PM
Contents
The Influence of Environmental Conditions on the Pressure Sensitivity of
Measurement Microphones .................................................................................. 1
Knud Rasmussen, Danish Technical University
Reduction of Heat Conduction Error in Microphone Pressure
Reciprocity Calibration....................................................................................... 14
Erling Frederiksen
Frequency Response for measurement microphones – a question of
confidence .......................................................................................................... 24
Johan Gramtorp and Erling Frederiksen
Measurement of microphone random-incidence and pressure-field
responses and determination of their uncertainties ..................................... 36
Johan Gramtorp and Erling Frederiksen
Copyright © 2001, Brüel & Kjær Sound & Vibration Measurement A/S
All rights reserved. No part of this publication may be reproduced or distributed in any form, or
by any means, without prior written permission of the publishers. For details, contact:
Brüel & Kjær Sound & Vibration Measurement A/S, DK-2850 Nærum, Denmark.
Editor: Harry K. Zaveri
Influence of environmental conditions.fm Page 1 Monday, June 25, 2001 3:18 PM
The Influence of Environmental
Conditions on the Pressure Sensitivity of
Measurement Microphones
by Knud Rasmussen*
Abstract
The sensitivity of condenser measurement microphones depends on the
environmental conditions, i.e. static pressure, temperature and humidity,
which affect the acoustic properties of the air enclosed between the diaphragm and the back electrode and in the cavity behind the back electrode.
This paper presents normalized values of the complex static pressure and
temperature coefficients for laboratory standard microphone Brüel & Kjær
Types 4160 and 4180, for the old free-field microphone Type 4145 and for
two of the most commonly used new measurement microphones of the Falcon series, Types 4191 and 4192.
Résumé
La sensibilité des microphones à condensateur varie avec les conditions de
mesurage environnantes : la pression statique, la température et l’humidité
relative. Ces variables influent sur les propriétés acoustiques de l'espace
compris entre le diaphragme, l’électrode arrière, et la cavité située derière
celle-ci. Cet article présente les valeurs normalisées des coefficients de température et de pression statique associées aux Microphones standard de
laboratoire 4160 et 4180, à l’ancien Microphone de champ libre 4145 et à deux
des microphones de mesurage les plus couramment utilisés de la série Falcon, les modèles 4191 et 4192.
* Danish Primary Laboratory of Acoustics, DTU Branch, Department of Acoustic Technology,
Danish Technical University
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Zusammenfassung
Die Empfindlichkeit von Kondensator-Meßmikrofonen hängt von den Umgebungsbedingungen ab. Statischer Druck, Temperatur und Feuchte beeinflussen die akustischen Eigenschaften der Luft, die zwischen der Membran und
der Gegenelektrode und im Hohlraum hinter der Gegenelektrode eingeschlossen ist. Dieser Artikel präsentiert normalisierte Werte für die komplexen Druck- und Temperaturkoeffizienten für die Labor-Normalmikrofone Typ
4160 und 4180, für das ältere Freifeld-Mikrofon Typ 4145 und für zwei der am
meisten eingesetzten neuen Meßmikrofone der Falcon-Serie, Typ 4191 und
4192.
Introduction
For a conventional condenser microphone the enclosed air behind the diaphragm is an integral part of the microphone. Because the acoustic properties of the enclosed air depends on the environmental conditions, i.e. static
pressure, temperature and humidity all such microphones will exhibit a sensitivity which depends on these factors. This effect cannot be avoided, only
minimized through proper design of the microphones.
The standard IEC 61094-2 [1] gives general information about environmental effects on LS (laboratory standard) type microphones as well as some
generalized graphs on the frequency dependence. The theoretical background is given in ref. [2], where a lumped parameter model is developed,
separating the various elements, which contribute to the resulting response
of the microphone. From the basic theory of condenser microphones it is
found that the pressure response of the microphone is inversely proportional to the acoustical impedance of the microphone, which can be derived
from the lumped parameter model.
The model discussed is not restricted to LS type microphones but can be
applied to all microphones of the same basic construction. The model considers the relation between the acoustical impedance of the diaphragm itself,
which can be considered independent of the environmental conditions and
the acoustical impedance of the enclosed air, i.e the thin air film between the
diaphragm and backplate, the holes in the backplate and the cavity behind
the backplate all of which depend on one or more of the environmental variables. The resulting static pressure- and temperature coefficients for the
microphones are then determined by the ratio of the acoustical impedances
of the microphone, calculated from the model at reference environmental
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conditions and when the static pressure, and temperature are changed by
1 kPa and 1 K respectively.
While the geometry of the interior microphone housing does not change
for a given type of microphone, both the mass density (thickness) and
mechanical tension of the diaphragm are subject to systematic and individual changes due to production tolerances and adjustments. Hence it is concluded in [2] that for a given type of microphone the static pressure and
temperature coefficients can be expressed by a single function normalized
with respect to resonance frequency of the microphone and low frequency
value of the individual coefficient. Such normalized functions are given as
Tables in ref.[2] for the complex static pressure and temperature coefficients
for Brüel & Kjær Type 4160 and Type 4180 microphones. The measurements
presented in [2] were performed in 1/3-octave steps only. These measurements have been repeated using a higher frequency resolution, which allows
the coefficients to be expressed by a simple polynomial. In addition, other
types of microphones have also been investigated.
Measurement Technique
The measurement method used for determining the static pressure and temperature coefficients is the same as used in ref.[2], i.e a complete reciprocity
calibration in a short closed plane-wave coupler has been conducted in
accordance with IEC 61094-2 [1]. The measurement setup is identical to the
earlier setup except that the signal generator and the precision voltmeter
were substituted by a Brüel & Kjær Audioanalyzer Type 2012. The measurements were performed by sweeping through the frequency range 200 Hz to
20 or 40 kHz in 1/12-octave steps in order to increase the frequency resolution. However, the major improvement arises from the very short measurement time, about 5 minutes, for the critical part viz. the measurement of the
generated sound pressure. In particular for the temperature coefficient
measurements, this method has resulted in much better repeatability and
more consistent results.
The reciprocity calibrations were conducted at five static pressures in the
range 90 kPa to 110 kPa in steps of 5 kPa and at four temperatures from 15°C
to 30°C in steps of 5°C. The measurements were performed by placing the
coupler and microphones in a pressure vessel and in a climatic chamber
respectively, and the above mentioned coefficients then determined at each
frequency by a conventional straight-line regression analysis of the calculated sensitivities.
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Measurement Results
The measurements have been performed on a number of five different types
of microphones shown in the Table.
Brüel & Kjær
Microphone Type
Number of microphones
4160
4145
4180
4191
4192
18
6
30
6
9
As an example, Fig. 1 shows the measured modulus of the static pressure
coefficient δp for the 18 Type 4160 microphones. In order to derive a single
expression valid for this type of microphones, the results for each microphone are first normalized with the low-frequency value and next the frequency axis is normalized with the resonance frequency of the individual
microphone. The result of such normalization for the very same measurements is shown in Fig. 2. Due to the high number of measurement frequencies a numerical smoothing can be performed followed by a polynomial
approximation. It has turned out that a ninth-order polynomial gives an adequate approximation to the measurement results for all microphones.
0.02
BK 4160
p dB/kPa
0
-0.02
-0.04
-0.06
100
1000
Hz
10000
100000
000303
Fig. 1. Measured modulus of static pressure coefficient of 18 microphones Type Brüel & Kjær
4160
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0.02
BK 4160
p/a0
dB/kPa
0.01
0
-0.01
-0.02
-0.03
1
f/f0
0.1
10
000304
Fig. 2. Measured modulus of static pressure coefficient as shown in Fig. 1 but normalized with
respect to resonance frequency and low-frequency value
This procedure has been applied to modulus and phase for both static
pressure and temperature coefficients for all five type of microphones and
the resulting polynomial constants a 0 – a 9 are given in Tables 1 and 2. The
relevant coefficients δp and δt are then calculated from
2
δ = a 0 + a 1 ⋅ x + a 2 ⋅ x + ..... + a 9 ⋅ x
9
(1)
where x = f/f0 is the frequency normalized by the resonance frequency of the
individual microphone. The constant a 0 will be zero for the phase
responses but represents the individual low-frequency value of the modulus
of the relevant coefficient. In the tables the value of a 0 is given as the average value for the microphones used in the measurements but if available,
individual values for the actual microphone should be used.
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Type 4160
Constants
Modulus
Type 4145
Phase
Modulus
Type 4180
Phase
Modulus
Type 4191
Phase
Modulus
Type 4192
Phase
Modulus
Phase
a0
−0.0152
0
−0.0153
0
−0.00519
0
−0.0054
0
−0.0042
0
a1
−0.00584
0.0176
−0.0107
0.184
−0.0304
0.17
−0.0204
0.0274
−0.0104
0.0499
a2
0.132
0.924
0.428
1.527
0.5976
−2.267
1.469
3.16
0.308
−1.494
a3
−0.596
−6.14
−1.128
−21.76
−3.912
12.03
−8.27
−88.2
−2.029
12.74
a4
1.763
20.1
−0.329
81.26
14.139
−31.245
16.11
464.0
8.44
−55.56
a5
−2.491
−38.31
5.534
−160.52
−27.561
34.22
−17.17
−1212.5
−19.537
117.15
a6
1.581
40.26
−10.212
190.23
29.574
−11.936
21.22
1894
24.765
−137.12
a7
−0.358
−22.937
9.046
−135.88
−17.6325
−4.988
−29.97
−1808
−17.459
93.09
a8
−0.0364
6.665
−4.087
53.91
5.4997
4.632
23.62
969.7
6.4922
−34.45
a9
0.01894
−0.7758
0.756
−9.11
−0.7017
−0.912
−7.046
−222.5
−0.9987
5.359
Table 1. Polynomium constants for the complex static pressure coefficient δp
Type 4160
Constants
Modulus
Phase
Type 4145
Modulus
Type 4180
Phase
Modulus
Phase
Type 4191
Modulus
Phase
Modulus
Phase
a0
−0.0020
0
−0.0034
0
−0.0012
0
−0.0032
0
−0.0053
0
a1
0.00913
−0.107
0.00513
−0.355
0.00633
−0.172
−0.00162
−0.374
0.00849
−0.0598
a2
−0.245
0.0283
−0.2835
1.805
−0.242
1.001
−0.423
0.91
−0.327
0.559
a3
1.673
1.248
0.367
−9.576
1.656
−5.10
−0.914
23.29
3.168
−4.92
a4
−6.058
−7.746
2.598
54.25
−6.1833
11.445
21.0
−124.7
−15.895
24.94
a5
11.766
20.725
−10.478
−166.55
11.81
−7.042
−70.78
282.9
43.32
−65.43
a6
−13.11
−26.957
17.557
276.69
−12.1366
−5.937
87.28
−366.5
−67.277
99.7
a7
8.5138
18.664
−15.654
−254.87
6.875
9.773
−6.41
293.3
59.788
−88.94
a8
−3.0016
−6.78
7.265
122.92
−2.0324
−4.547
−68.78
−137.46
−28.316
42.69
a9
0.4426
1.032
−1.3787
−24.233
0.2457
0.7284
39.49
28.68
5.535
−8.464
*) Valid only for the new improved version having serial numbers higher than 1933099
Table 2. Polynomial constants for the complex temperature coefficientδ t
6
Type 4192 *)
Influence of environmental conditions.fm Page 7 Monday, June 25, 2001 3:18 PM
Due to the high order of the polynomial Eqn.(1), the calculations at high
frequencies are quite sensitive to the constants and the values given in the
tables should not be rounded or otherwise changed. Also the results are only
valid in a limited frequency range which depends on the type of microphone.
Table 3 gives the limitations on the usable frequency range for the coefficients which should not be exceeded.
Brüel & Kjær
Microphone Type
4160
4145
4180
4191
4192
Static pressure coefficient δ p
14
15
35
28
31.5
Temperature coefficient δ t
14
15
35
28
28
Table 3. Maximum recommended frequency in kHz for using Tables 1 and 2
The normalized coefficients are shown in a graphical form in Figs. 3 – 6.
The general response is the same for the three pressure type microphones
while the two free-field Types (4145 and 4191) are significantly different due
to the much higher losses (3 times higher loss factor).
0.02
p (mag)
dB/kPa
0.00
-0.02
-0.04
-0.06
0.01
0.1
4160
f/f0
4145
4180
1
4192
10
4191
000305
Fig. 3. Modulus of normalized static pressure coefficient in dB/kPa
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p (phase) Degrees/kPa
0.1
0
-0.1
-0.2
-0.3
0.01
0.1
1
10
f/f0
4160
4145
4180
4192
4191
000306
Fig. 4. Phase of normalized static pressure coefficient in degrees/kPa
t (mag)
dB/K
0.02
0.00
-0.02
-0.04
0.01
0.1
4160
f/f0
4145
4180
1
4192
10
4191
000307
Fig. 5. Modulus of normalized temperature coefficient in dB/K
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Degrees / K
0.1
t (phase)
0.2
0
-0.1
0.01
1
0.1
4160
10
f/f0
4145
4180
4192
4191
000308
Fig. 6. Phase of normalized temperature coefficient in degrees/K
Practical Applications
When a microphone is used at a certain static pressure ps and temperature t
while the calibration values of the pressure sensitivity level Mp,ref refer to
other conditions, p s ,ref and t ref, the pressure sensitivity level M p in dB re
1V/Pa at the actual conditions can be calculated from
M p = M p, ref + δ p ( p s – p s, ref ) + δ t ( t – t ref ) dB re 1V/Pa
(2)
where the coefficients δp and δt are calculated from Eqn.(1) and Tables 1 and 2.
In the absence of individual values for resonance frequency and low-frequency value of the coefficients of the microphones, Table 4 shows the average value for the microphones used in this investigation and the spread in
the values expressed as twice the standard deviation. The repeatability of
the measured low-frequency values of the environmental coefficients given
in Table 4 is about 5% for the individual microphones, while the normalized
response remains essentially the same. It should be recalled that the figures
given for the WS-microphones (Types 4145, 4191 and 4192) are based upon a
small number of specimens representing a limited period of production. Consequently the average values given may be slightly offset and the uncertainty
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Influence of environmental conditions.fm Page 10 Monday, June 25, 2001 3:18 PM
interval heavily underestimated. This will in particular be true for both average value and uncertainty interval for the temperature coefficient.
The low frequency value of the static pressure coefficient is determined by
the ratio of the compliance of the back cavity and the total compliance of the
microphone which is dominated by the diaphragm compliance. Consequently the low frequency value is a function of the microphone sensitivity.
Brüel & Kjær
Microphone Type
4160
4145
4180
4191
4192
8.41
± 0.52
11.96
±1.10
22.34
±1.68
35.17
±1.97
24.22
± 2.20
Low frequency static pressure
coefficient δ p dB/kPa
−0.0152
± 0.0014
−0.0153
± 0.0011
−0.0052
±0.0012
−0.0054
± 0.0015
−0.0042
± 0.0014
Low frequency
temperature coefficient
δ t dB/K
− 0.0020
± 0.0016
−0.0034
± 0.0004
−0.0012
± 0.0023
−0.0032
± 0.0018
− 0.0053*)
± 0.0054
Resonance frequency
kHz
*) Valid only for the improved version having serial numbers higher than 1933099
Table 4. Average values of resonance frequency, static pressure and temperature coefficients
for the investigated microphones
-0.014
dB / kPa
BK 4160
-0.015
-0.016
-0.017
-27.6
-27.4
-27.2
-27.0
-26.8
dB re 1V/Pa (250 Hz)
-26.6
-26.4
000309
Fig. 7. Low frequency value a0 of static pressure coefficient δp as function of the pressure sensitivity level at 250 Hz for 18 microphones Brüel & Kjær Type 4160
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Figs. 7 and 8 show the relations between the measured low-frequency value of
the static pressure coefficients, i.e. the constants a 0 for the static pressure
coefficients and the microphone sensitivity level Mp ,250 Hz at 250 Hz in dB re
1 V/Pa for the Brüel & Kjær microphone Types 4160 and 4180 used in this
investigation.
-0.0045
BK 4180
dB / kPa
-0.0050
-0.0055
-0.0060
-39.5
-39.0
-38.5
-38.0
-37.5
dB re 1V/Pa (250 Hz)
000310
Fig. 8. Low frequency value a0 of static pressure coefficient δp as function of the pressure sensitivity level at 250 Hz for 30 Brüel & Kjær microphones Type 4180
The linear regression line shown on the graphs is given by
and
δp = −0.0739 – 2.164·10–3 · Mp,250 Hz dB/kPa for Brüel & Kjær Type 4160
(3)
δp = –0.02642 – 543·10−6 · Mp,250 Hz dB/kPa for Brüel & Kjær Type 4180
(4)
with an expanded uncertainty (k = 2) of 0,0005 dB/kPa. These figures deviate
slightly from the values reported in ref. [2] mainly due to the larger number
of microphones involved.
A similar relation does not exist for the low frequency value of the temperature coefficients as this value is determined solely by the mechanical construction. The resonance frequency of the microphones too cannot be predicted
from the pressure sensitivity but has to be determined by other means, such
as through measurement of the phase response of the microphone.
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Uncertainty Estimation
The resulting uncertainty when correcting calibration results to reference
environmental conditions and/or deriving the sensitivities at environmental
conditions different from those valid for the calibration data, is determined
by the uncertainty of the individual low frequency value of the above-mentioned coefficients and resonance frequency of the microphones. Table 4
gives an estimate on the uncertainty of the low-frequency value of the coefficients when typical values are applied. For the static pressure coefficient of
LS-microphones a lower uncertainty can be obtained by using the relations
given in Eqns.(3 – 4).
However, at high frequencies the major contribution arises from the uncertainty on the resonance frequency because the slope of all the coefficients
has a maximum around that frequency. If the average values shown in Table 4
are used for the resonance frequency, the spread in the values also given in
Table 4 may be used to estimate the uncertainty of the coefficients.
Additional Remarks
The static pressure only affects the acoustical properties of the enclosed air
and not the properties of the diaphragm. This is why the static pressure
coefficient can be derived by Eqns. 3 and 4 with a fairly low uncertainty.
However, the temperature affects both the acoustical properties of the
enclosed air and the behaviour of the diaphragm due to small dimensional
changes in the microphone. The dimensional changes may result in two
effects, viz a resulting change in diaphragm tension and a change in the distance between diaphragm and back-electrode. Both effects will change the
sensitivity but a change of the diaphragm tension will be at minimum at the
resonance frequency of the microphone. In an optimal design the two effects
are balanced to give a minimum effect on the sensitivity at low frequencies.
The major influence is caused by the air properties which results in the large
values of the temperature coefficient at higher frequencies, see Figs. 5 – 6.
The influence of humidity has not been discussed up to now. It is but fairly
easy to see that humidity affects the acoustic properties of the enclosed air
in the very same way as temperature, and that about 30% change in the relative humidity results in the same changes as 1 degree Celcius. It has therefore not been possible up to now to demonstrate any effect of humidity on
the sensitivity of the microphones used in this investigation. Humidity will
not affect the mechanical part of the microphone either as long as condensa-
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Influence of environmental conditions.fm Page 13 Monday, June 25, 2001 3:18 PM
tion is not present. However, it is possible that the electrical insulation
between diaphragm and backplate may be affected by humidity. If so the
microphone will exhibit an increased noise level and instability, but probably
not a reversible dependence of humidity. The isolators used in the tested
types of microphones are not hygroscopic and only excessive dirt on the isolator may result in a dependence of humidity.
Conclusion
Measurement results are presented showing the influence of static pressure
and temperature as function of frequency on the pressure sensitivity of specific type of microphones, arising mainly from changes in the acoustical
properties of the air enclosed behind the diaphragm.
The determination of the coefficients are based on measurements performed in the intervals 90 – 110 kPa and 15 – 30°C without observing any sign
of non-linearity. Thus it is estimated that Eqn. 2 and the figures given in
Tables 1 and 2 are valid in the ranges of static pressures 70 – 120 kPa and temperatures 0 – 40°C without affecting the stated uncertainty significantly.
References
[1]
IEC Publication 61094 – 2, 1992: “Measurement microphones – Part 2 –
Primary method for pressure calibration of laboratory standard microphones by the reciprocity technique”
[2]
Rasmussen, K., “The static pressure and temperature coefficients of laboratory standard microphones”, Metrologia, 36, pp.265 – 273, 1999
13
Reduction of Heat Conduction.fm Page 14 Monday, June 25, 2001 3:19 PM
Reduction of Heat Conduction Error in
Microphone Pressure Reciprocity
Calibration
by Erling Frederiksen
Abstract
The microphone reciprocity calibration method, which is used for absolute
determination of the sound pressure unit (Pa), is highly refined today. Thus
phenomena having hitherto only minor influence on the calibration results
have today become of greater interest. One such phenomenon is related to
non-regular surface elements of the cavity in front of the diaphragm of the
calibrated standard microphones. These surface elements cause additional
heat-conduction effects, which need to be taken into account in high precision calibrations. This effect, which is generally ignored, even by highly
elaborated sensitivity calibration programs, may cause significant errors,
especially at low frequencies. Examples of errors are calculated and shown
for commonly applied types of microphone and calibration coupler.
Résumé
La méthode d’étalonnage des microphones par réciprocité, utilisée pour
déterminer de manière absolue l’unité de pression acoustique (Pa), a été
grandement corrigée et affinée au fil des années. Par voie de conséquence,
des phénomènes qui n’influaient pratiquement pas jusque là sur les résultats
de l’étalonnage retiennent aujourd’hui l’intérêt. Un de ces phénomènes est
lié à l’irrégularité de surface des éléments de la cavité située devant le
diaphragme des microphones standard étalonnés. Ces éléments induisent un
effet de conduction thermique qui doit être pris en compte pour les étalonnages de haute précision. Cet effet, généralement ignorés par les programmes
avancés d’étalonnage en sensibilité, peut être cause d’erreurs, notamment
aux basses fréquences. Des exemples de calculs erronés sont ici présentés
pour des types de microphones et de coupleurs d’étalonnage courants.
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Reduction of Heat Conduction.fm Page 15 Monday, June 25, 2001 3:19 PM
Zusammenfassung
Die Mikrofonkalibrierung nach dem Reziprozitätsverfahren, das zur absoluten Bestimmung des Schalldrucknormals (Pa) verwendet wird, ist heute
stark verfeinert. Deshalb haben Phänomene, die bisher nur geringen Einfluß
auf die Kalibrierergebnisse hatten, an Interesse gewonnen. Eines dieser
Phäno-mene hängt mit nichtregulären Elementen an der Hohlraumoberfläche vor der Mem-bran kalibrierter Normalmikrofone zusammen. Diese Oberflächenelemente verursachen zusätzliche Wärme-leitungs-effekte, die bei
hochpräzisen Kalibrierungen berücksichtigt werden müssen. Dieser Effekt,
der in der Regel ignoriert wird - selbst bei sehr anspruchsvollen Kalibrierprogrammen - kann bedeutende Fehler verursachen, insbesondere bei tiefen Frequenzen. Es werden Beispiele für Fehler mit gebräuchlichen Mikrofontypen
und Kalibrierkupplern berechnet und gezeigt.
Introduction
The sound pressure unit (Pascal) today is determined by calibrating Laboratory Standard Microphones using the pressure reciprocity calibration technique. This absolute calibration method was invented in the forties by
National Bureau of Standards in USA. Since then the method has been carefully analysed and highly refined. Therefore, the calibration uncertainty of
internationally leading calibration laboratories is now as low as 0,025 dB
(k =2) from say 100 Hz to 5 kHz or to 10 kHz depending on the size and type
of microphone. A consequence of this is that physical phenomena, which
have relatively small influence on the calibration and were previously
ignored, have now become of interest for national and other high-level calibration laboratories. Such a phenomenon is described below. It is related to
heat conduction that occurs at surfaces of the front cavities of standardised one-inch Laboratory Standard Microphones, such as Brüel & Kjær
Types 4160, 4144 and 4145.
Reciprocity Calibration
Microphone reciprocity calibration is generally performed with three microphones (A, B and C) which are acoustically coupled together two by two
(AB, AC and BC); see the international standard IEC 61094-2. One of the two
microphones is driven as a sound source, while the other one receives the
generated sound. The coupling is made by a gas (usually air), which is
15
Reduction of Heat Conduction.fm Page 16 Monday, June 25, 2001 3:19 PM
enclosed in a small cavity formed by the coupler and the two microphones.
For each pair of microphones both the electrical and the acoustic transfer
impedances are determined. The electrical impedance is measured, while
the acoustic impedances is calculated from the gas properties, the cavity
dimensions and the impedance of the microphones.
According to the IEC standard the acoustic transfer impedance is calculated by considering a pure adiabatic compression process in the coupler
and by applying a correction factor for the deviation from this ideal situation.
The deviation is caused by heat conduction between the gas and the walls of
the cavity. The heat conduction correction is a complex factor and a function
of the type of gas (ratio of specific heats) and frequency. The correction
increases with decreasing frequency and with increasing ratio between the
cavity surface area and the volume of the coupler; see IEC 61094 -2, Annex A.
When the electrical and acoustic impedance parameters are measured and
calculated, the pressure sensitivities can be worked out for all three microphones. The formulae below are examples, which define the sensitivity of
microphone ‘A’ and the acoustic transfer impedance of the coupler with the
microphones ‘A’ and ‘B’ inserted:
M p, A =
Z a, BC
Z e, AB ⋅ Z e, AC
------------------------------------- ⋅ -------------------------------------Z e, BC
Z a, AB ⋅ Z a, AC
1
1 - -----------1 -
----------------- =  -----------+
Z
 cosh (γ ⋅ l AB ) +
Z a, AB
Z
a, A
a, B
 S AB ⋅ ∆ H, AB

σ⋅c
1
 ---------------------------------- + ---------------------------------- ⋅ ------------------------------- sinh ( γ ⋅ l AB )
σ
⋅
c
S
⋅
∆
Z
⋅
Z

a, A
a, B
AB
H, AB
where
Mp,A
Ze,AB, Ze,AC , Ze,BC
Za,AB, Za,AC, Za,BC
Za,A, Za,B
γ
lAB
16
Pressure Sensitivity of Microphone ‘A’
Electrical Transfer Impedance with microphones ‘A’,
‘B’ and ‘C’ respectively
Acoustic Transfer Impedance with microphones ‘A’,
‘B’ and ‘C’ respectively
Acoustic Diaphragm Impedance of microphones ‘A’
and ‘B’
Complex sound propagation coefficient (γ =α+jβ)
Length of cavity with microphones ‘A’ and ‘B’
Reduction of Heat Conduction.fm Page 17 Monday, June 25, 2001 3:19 PM
SAB
ρ
c
∆H,AB
Mean cross-sectional area of cavity with microphones
‘A’ and ‘B’
Density of enclosed gas
Speed of sound in enclosed gas
Heat conduction correction for the cavity with microphones ‘A’ and ‘B’
According to IEC 61094 -2 standard the heat-conduction correction can be
applied either to the volume or to the cross-sectional area of the cavity. In the
expression above, which accounts for axial wave-motion and leads to the
lowest calibration uncertainty, the correction is applied to the cross-sectional area.
Calculation of the heat conduction correction and the underlying theory is
quite complex. The subject is described in Annex A of the IEC standard and by
H. Gerber in an article of the Journal of the Acoustical Society of America (JASA,
Vol. 36, 1964).
Microphone Front Cavities
The cavity between the front surface and the diaphragm of a Laboratory
Standard Microphone is called the front cavity. The two front cavities of a
pair of microphones contribute to the surface area and to the volume of that
cavity, which during the pressure reciprocity calibration couples the microphones together. Ideally these front cavities should be cylindrical. However,
the presently available types of one-inch Laboratory Standard Microphone
(IEC 61094 -1, LS1p and LS1f) do have a thread for mounting a diaphragm
protection grid. This thread increases the cavity surface area significantly;
see Fig. 1. The surface area of the thread, which has flanks of 60°, is twice as
large as that of a cylindrical surface, which encloses the same volume of air.
For Type 4160 the threaded length is 1,4 mm, which leads to an additional
surface area of 80,5 mm2; see Fig. 1.
When used for reciprocity calibration the microphones Type 4144 and
Type 4145 are equipped with an Adapter Ring (DB 0111), which forms the
front cavity required by the IEC 61094 -1 standard. This ring has a thread and,
therefore, an extra surface area, which is identical to that of Type 4160. However, the adapter ring and the microphone do also form a narrow ring-shaped
cavity along the edge of the active part of the diaphragm. Both surface and
volume of this cavity contribute significantly to the overall area and volume
of the cavity, which couples the microphones together; see Fig. 2. The volume of the ring-shaped cavity is approx. 35 mm3, while its area is 250 mm2.
17
Reduction of Heat Conduction.fm Page 18 Monday, June 25, 2001 3:19 PM
1.95mm
1.4mm
ø18.8mm
010083
Fig. 1. Front cavity of the Brüel & Kjær Laboratory Standard Microphone Type 4160. The
thread makes the surface area twice as large as that of a corresponding cylindrical surface
The volume and extra surface areas influence the calibration results. The
influence of the latter is caused by the effect of heat-conduction.
1.4mm
1.95mm
DB0111
Sealing Ring
Ring Cavity
ø18.8mm
ø22.0mm
010084
Fig. 2. Front Cavity of Brüel & Kjær Microphones Types 4144/45 equipped with Adapter Ring
(DB0111). Thread and ring-shaped cavity increase front cavity area and volume significantly
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Reduction of Heat Conduction.fm Page 19 Monday, June 25, 2001 3:19 PM
Influence of Heat Conduction on Calibration Results
The influence of heat conduction depends on the ratio of surface area and
volume of the applied coupler and microphones. Basically there are two
types of coupler, which are generally called Large Volume and Plane Wave
Couplers. Today Large Volume Couplers are less frequently used. Most internationally leading calibration laboratories have replaced them by two or
more Plane Wave Couplers with internal diameter identical to that of the diaphragm of the calibrated microphones. These couplers act as essentially
ideal acoustic transmission lines and are treated accordingly, which means
that they cover a much wider frequency range than the large couplers. On
the other hand their smaller volume implies a higher ratio between surface
area and volume, which makes them more sensitive to the effect of heat-conduction that occur between the enclosed gas and the surfaces of the cavity.
The plane wave couplers are also more sensitive to the equivalent volume
or impedance of the calibrated microphones, which varies between units of
any certain type of microphone. However, today the influence of such variations is (or may be) minimized by calibrating with two or more different couplers and by using a data fitting method for the microphone parameters. The
fitting method is based on the logical assumption that the results of reciprocity calibrations should not depend on the size or length of the
applied coupler.
Therefore, the value, which gives identical results with the different couplers, is taken as the correct value.
Accredited calibrations of one-inch microphones, which are performed by
the Danish Primary Laboratory of Acoustics (DPLA), are made with two couplers of lengths 7,5 mm and 15,0 mm respectively; see Fig. 3 and Table 1 for
further dimensions. As the Brüel & Kjær Reciprocity Calibration System and
several other calibration laboratories use couplers of the same dimensions,
these couplers were taken as examples for demonstrating the influence of
the microphone thread and the ring shaped cavity.
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Reduction of Heat Conduction.fm Page 20 Wednesday, July 4, 2001 1:41 PM
Microphone
Front Cavity
Coupler Cavity
D
L2
L1
Coupler
Coupler
Microphone
010085
Fig. 3. Sketches of long and short Plane Wave Couplers used by many calibration laboratories.
Dimensions are given in Table 1
DPLA and Type 9699
Couplers
Diameter (D)
Length (L1)
without
Microphones
Length (L2)
with
Microphones
Long Coupler Cavity
18,6 mm
15,0 mm
18,9 mm
Short Coupler Cavity
18,6 mm
7,5 mm
11,4 mm
Table 1. Coupler dimensions
Microphones
Type 4160
Types 4144/45
Additional Volume
Additional Surface Area
none
81 mm2
35 mm3
331 mm2
Table 2. Additional ring-cavity volume and surface area of microphones
Volume and surface area of the ring-shaped cavity and of the additional
surface area of thread are given in Table 2 for the Brüel & Kjær microphones
Types 4160, 4144 and 4145. These microphones are commonly calibrated by
the pressure reciprocity method and applied as national standards. The
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Reduction of Heat Conduction.fm Page 21 Monday, June 25, 2001 3:19 PM
0.03
0.02
Coupler Length: 7.5 mm
0.01
Coupler Length: 15 mm
0
-0.01
10
100
1000
10000
010086
Fig. 4. Increase in heat-conduction corrections for microphone Type 4160. Valid for calibrations made with Plane Wave Couplers of 7,5 mm and 15,0 mm length
0.09
0.06
Coupler Length: 7.5 mm
dB
0.03
Coupler Length: 15 mm
0
-0.03
10
100
1000
10000
Hz
010087
Fig. 5. Increase in heat-conduction corrections for microphones Type 4144 and Type 4145.
Valid for calibrations made with Plane Wave Couplers of 7,5 mm and 15,0 mm length
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Reduction of Heat Conduction.fm Page 22 Monday, June 25, 2001 3:19 PM
influence of the listed microphone parameters has been calculated for the
couplers described above. The calculations of transfer impedance and
microphone sensitivity are made in accordance with IEC 61094 -2 by a program written in Mathcad from MathSoft, Inc. This specific program was chosen, because the program (MP.exe from the Danish Technical University),
which is generally used by DPLA, considers cylindrical microphone front
cavities and cannot account for the larger surface areas.
The influence of the additional surfaces, which is calculated for different
combinations of microphones and couplers, are shown in Figs. 4 and 5. It is
presented as the increase in heat-conduction correction caused by the surfaces of the thread and the ring-cavity. Note the different resolutions used on
the scales of the graphs.
0.03
Coupler Length: 7.5 mm
0.02
dB
0.01
Coupler Length: 15 mm
0
Data Fitting
Range
-0.01
10
1000
100
Hz
10000
010088
Fig. 6. Additional heat-conduction corrections for microphone Type 4160. The curves are valid
for calibrations made with Plane Wave Couplers of 7,5 mm and 15 mm length, when the equivalent volume of the microphone diaphragm is fitted based on sensitivity results obtained over
the range from 125 Hz to 2000 Hz
If the data fitting method is applied for microphone diaphragm equivalent volume, the influence of the additional front cavity surfaces is reduced. This is
especially the case within the frequency range of the fitting itself. DPLA optimizes the accuracy at the important calibrator frequencies 250 Hz and 1000 Hz
22
Reduction of Heat Conduction.fm Page 23 Monday, June 25, 2001 3:19 PM
0.09
Coupler Length: 7.5 mm
0.06
dB
0.03
Coupler Length: 15 mm
0
Data Fitting
Range
-0.03
10
100
1000
10000
Hz
010089
Fig. 7. Additional heat-conduction corrections for microphones Type 4144 and Type 4145. The
curves are valid for calibrations made with Plane Wave Couplers of 7,5 mm and 15,0 mm
length, when the equivalent volume of the microphone diaphragm is fitted based on sensitivity
results obtained over the range from 125 Hz to 2000 Hz
by fitting the equivalent volume over the range 125 Hz to 2000 Hz. This means
that the corrections shown in Fig. 6 and Fig. 7 should be applied with the present
versions of the Sensitivity Calculation Program MP.exe, which do not account
for the heat-conduction of the additional front cavity surfaces.
Conclusion
Non-regular and non-desired surface areas related to the front cavity of the
presently available types of Laboratory Standard Microphone (IEC 61094 -1,
LS1p and LS1f) have significant influence on the sensitivity determined by
the pressure reciprocity calibration methods described in IEC61094-2 and in
other standards. Therefore, these additional surface areas must always be
taken into account, when low calibration uncertainty is required. Proper
attention to the surfaces and the related heat-conduction eliminates significant systematic calibration errors. These errors, which decrease with frequency may be as large as –0.08 dB at 20 Hz and –0.02 dB at 250 Hz depending
on the types of microphone and coupler applied for the calibration.
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Frequency_response_for_measurement_microphones.fm Page 24 Monday, June 25, 2001 3:21 PM
Frequency Response for Measurement
Microphones – a Question of Confidence*
by Johan Gramtorp and Erling Frederiksen
Summary
For many applications it is important to know the frequency response of the
measurement microphone. There are a number of methods available for
determination of the frequency response of a microphone. Some of the
methods are described in IEC standards as 61094 − 2 and 61094 − 3. For the
special Laboratory Standard microphones as LS1P and LS2P (described in
IEC 61094 –1) it is possible to have a primary calibration at a national calibration laboratory. Most of the other measurement microphones are normally calibrated using the electrostatic actuator calibration method. The
actuator response is measured and the free-field correction supplied by the
microphone manufacturer is added. From most manufacturers no information about the uncertainty on the determination of the actuator response
and the free-field corrections has been available. A complete set of uncertainty values for actuator responses and free-field corrections for the new
Brüel & Kjær Falcon Range microphones will be presented and discussed.
Résumé
Dans le cadre de nombreuses applications, il est essentiel de connaître la
réponse en fréquence du microphone de mesurage. Pour déterminer ce paramètre, plusieurs méthodes sont utilisables, et certaines sont décrites dans
des textes normatifs tels que CEI 61094 – 2 et 61094 – 3. En ce qui concerne les
microphones standard de laboratoire LS1P et LS2P (décrits dans la
CEI 61094 – 1), un étalonnage primaire est possible auprès d’un centre
d’étalonnage au niveau national. La plupart des autres microphones de
mesurage sont généralement étalonnés au moyen d’une méthode par excitation électrostatique. A la réponse mesurée de l’excitateur sont ajoutées les
* First presented at ASA Conference in December 1996
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Frequency_response_for_measurement_microphones.fm Page 25 Monday, June 25, 2001 3:21 PM
termes correctifs de champ libre fournis par le fabricant. Or, la plupart des
fabricants n’informent ni sur l’incertitude de détermination de la réponse de
l’excitateur ni sur les corrections de champ libre. Un jeu complet des valeurs
relatives à ces deux paramètres est ici présenté et discuté pour les nouveaux
microphones de la gamme Falcon de Brüel & Kjær.
Zusammenfassung
Bei vielen Anwendungen ist es wichtig, den Frequenzgang des Meßmikrofons
zu kennen. Der Frequenzgang eines Mikrofons läßt sich mit Hilfe verschiedener Verfahren bestimmen. Einige der Verfahren sind in Normen wie
IEC 61094 –2 und IEC 61094 – 3 beschrieben. Für spezielle Labor-Normalmikrofone wie LS1P und LS2P (beschrieben in IEC 61094 – 1) ist es möglich, eine Primärkalibrierung bei einem nationalen Kalibrierlaboratorium
durchzuführen. Die meisten anderen Meßmikrofone werden normalerweise
mit einem elektrostatischen Kalibriergitter kalibriert. Zu dem mit dem Kalibriergitter aufgenommenen Frequenzgang werden die vom Mikrofonhersteller angegebenen Freifeldkorrekturen addiert. Die meisten Hersteller
machen keine Angaben über die Meßunsicherheit bei der Frequenzgangermittlung mit Kalibriergitter und Bestimmung der Freifeldkorrektur. Es
wird ein kompletter Datensatz mit Meßunsicherheiten für Frequenzgänge
mit Kalibriergitter und Freifeldkorrekturen für die neuen Brüel & Kjær-Mikrofone der Falcon-Serie vorgestellt und diskutiert.
Introduction
In an earlier article, ref. [1] Erling Frederiksen, Johan Gramtorp, “Measurement of Microphone Free-field Corrections and Determination of their
Uncertainties” the determination of the free-field correction (without protection grid) for a Brüel & Kjær Type 4191 microphone was described.
This article covers all the new Brüel & Kjær Falcon Range microphones,
and the influence of the protection grid and the electrostatic actuator calibration is described. This leads to uncertainty values for the resulting individual free-field response calibration (0° incidence).
Description of Free-field Corrections
The free-field correction is the ratio between the free-field response and the
response of the microphone diaphragm system. The correction is dominantly
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Frequency_response_for_measurement_microphones.fm Page 26 Monday, June 25, 2001 3:21 PM
2
Free-field Response
0
-2
Free-field Correction
-4
dB
-6
Actuator Response
-8
-10
-12
100
10000
1000
Hz
100000
980142
Fig. 1. Free-field Frequency Response of a Brüel & Kjær Type 4191 microphone obtained by
adding the free-field correction to an individually measured Actuator Response
determined by sound reflection and refraction caused by the microphone body.
Actually there are two different types of free-field corrections. They refer to the
slightly different pressure-field and electrostatic actuator responses. Both
responses account for the individual properties of the microphone diaphragm
system. The free-field corrections mentioned in this paper all refer to the electrostatic actuator response, Fig. 1. The frequency response calibrations based
on measurement of the individual electrostatic actuator response are especially simple and require no special acoustic facilities.
Determination of Free-field Corrections
The determination of the type specific free-field correction for a microphone
with protection grid includes the following:
1) Free-field response measurement
2) Electrostatic actuator response measurement
3) Determination of free-field correction without protection grid
4) Protection grid correction measurement
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Frequency_response_for_measurement_microphones.fm Page 27 Monday, June 25, 2001 3:21 PM
Free-field Response Measurement
The free-field response were measured using the free-field reciprocity technique described in the international standard IEC 61094 –3.
Three microphones were calibrated together. Pairwise they were mounted
in an anechoic room where one was transmitting sound to the other. Microphone (a) transmitted to receiver (b), (b) to (c), and (c) to (a).
The sensitivity products can be expressed by the following formula (as
described in Ref. [1]):
αd
U R, b
da b
ab
M f, a ⋅ M f, b = – ------------- ⋅ -------------------------------- ⋅ e
2
U T, a ρ ⋅ π ⋅ f ⋅ C
a
UR ,b :
f:
ρ:
UT,a :
Ca :
α:
dab :
Receiver output voltage
Frequency
Air density
Transmitter driving voltage
Transmitter Capacitance
Sound attenuation of air
Distance between acoustic centres of the microphones
For all three pairs of microphone the output voltage of the receiver microphone, the voltage driving the transmitter and the transmitter capacitance
were measured. During the measurement of the receiver voltage, the voltage
across the transmitter was kept constant as a function of frequency.
After determination of the above parameters for the three pairs of microphones the individual free-field sensitivity module were calculated using the
formula below.
M f, a =
α ( d – d + d ) 1
--d a b ⋅ d ca
U T, b
Cb
 U R, a ⋅ U R, c
ab bc
ca 2
1
 ------------------------------- ⋅ ------------------------------- ⋅ ----------------------- ⋅ ------------------ ⋅ --------------------2- ⋅ e

U T, a ⋅ U T, c
Ca ⋅ Cc ρ ⋅ π ⋅ f
U R, b
db c


The resulting uncertainty of the 0°-incidence free-field response was estimated from the uncertainty of the parameters applied for its calculation.
Their uncertainties were separated into groups of random and systematic
errors as their weight in the reciprocity calculations are different. The sys-
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Frequency_response_for_measurement_microphones.fm Page 28 Monday, June 25, 2001 3:21 PM
tematic errors do partly eliminate each other while the non correlated or random errors add up statistically. The relative uncertainty of free-field
response was determined by using the formula below:
∆M f
----------- = A ×
Mf
1
--
2
2
  ∆U R 2  ∆U T 2  ∆C 2  ∆ f 2
∆d 2
∆ρ 2
∆α 2
∆ d 2
+  --------- +  -------- +  αd --------- +  αd --------- 
  ------------ +  ------------ +  -------- +  ----------








2
UT
C
d
ρ
α
d 
 UR
 f 
where the weighting factor “A” equals 1/2 for the systematic and 3 ⁄ 2 for the
random uncertainties respectively.
As can be seen from the formula there are a lot of sources adding to the uncertainty of the free-field response. Some of the systematic errors cancel out during
the reciprocity calculation ( ∆U R ⁄ U R and ∆ U T ⁄ U T ) . The dominant uncertainties ends up being the systematic uncertainties in the measurement of transmitter capacitance and distance between the acoustic centres of the microphones.
Electrostatic Actuator Response Measurement
The actuator responses were measured with the 0.01 dB resolution and with
the same measurement system as that used for the free-field measurements.
This type of measurement is relatively easy to perform.
The response measured with an electrostatic actuator is generally influenced by the radiation impedance which loads the microphone diaphragm.
This influence is dependent of the diaphragm impedance of the microphone
(smallest for microphones with the highest diaphragm impedance). The
influence is for all the microphones less than 0.3 dB below 10 kHz and ranges
to about 0.3 dB at 40 kHz for Type 4191 and 2.0 dB at 20 kHz for Type 4189/90.
As the influence may be modified by the mechanical configuration of the
actuator, the actuator type used for calibration service should be equal to
that used for determination of the free-field corrections.
The actuator response is measured with the same measuring system as the
free-field response. Combined with long measuring times, and correction for
frequency response for the total measurement system, this leads to lower
uncertainty values than normally achieved for electrostatic actuator measurements. Typical U95 values of 0.072 dB at 20 kHz and 0.132 dB at 40 kHz.
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Frequency_response_for_measurement_microphones.fm Page 29 Monday, June 25, 2001 3:21 PM
Determination of Free-field Correction without
Protection Grid
The absolute sensitivity cannot be measured accurately with an electrostatic actuator. Therefore, there is no reason for also spending great efforts
on obtaining an absolute measurement of the free-field response. The division of the free-field response by the actuator response will, anyway, give a
result which contains a significant error. However, as this error makes a constant factor over the entire frequency range, some methods are available for
its elimination.
To verify the measured free-field correction results the microphone and
the sound field were simulated by a mathematical model. Simulation of the
free-field corrections have been made for very detailed models of all the
Brüel & Kjær Falcon Range microphones by the Boundary Element Method.
The simulation accounted for the microphone dimensions, the diaphragm
impedance and the properties of the ambient air. These simulations were
based on the principles described in ref. [4] Peter Juhl, “Numerical Investigation of Standard Condenser Microphones”. This method has proved to be
very accurate at frequencies below the diaphragm resonance frequency. The
1/3 octave calculation results are shown by the points in Fig.2.
10
9
8
7
6
dB
5
4
3
2
1
0
1
10
kHz
100
980143
Fig. 2. Measured (curve) and calculated (points) free-field corrections for Type 4190 (0 ° incidence). The results are valid without protection grid
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Frequency_response_for_measurement_microphones.fm Page 30 Monday, June 25, 2001 3:21 PM
The resulting free-field correction may thus be determined by Boundary
Element Method below 1 kHz. At frequencies above 1 kHz the measured freefield correction (free-field response divided by the electrostatic actuator
response) was adjusted by multiplying a constant to give the best fit to the
calculated low frequency values. The curve shown in Fig. 2 gives the resulting free-field correction determined by the above described method.
The free-field corrections given are valid at 101.3 kPa, 23°C and 50% RH.
The measurements have been performed at temperatures between 20°C and
22°C. This leads to a small systematic uncertainty.
The measurement of the free-field response and the electrostatic actuator
response have been made in series. Changes in the frequency response of the
microphone cartridge between the measurements has to be handled as a systematic uncertainty. The sum of these uncertainties (U95) is below 0.085 dB
at all frequencies.
Protection Grid Correction Measurement
The manufacturing uncertainties and uncertainties related to the combination
of microphone and protection grid are the contributions to the uncertainty of
the influence of the protection grid. The parameters investigated are:
1)
2)
3)
4)
5)
Width of grooves
Length of grooves
Diameter of centre hole
Internal height of protection grid
Slit between the outside of the diaphragm ring and the inside of the
protection grid
The above parameters were varied by several times the production tolerances, in order to have a measurable influence of the variations.
The influence of the protection grid is small at low frequencies, and
increasing for increasing frequencies. At frequencies below 8 kHz the uncertainty (U95) is below 0.1 dB. It is increasing to approximately 0.45 dB at the
highest operating frequency for the microphone (see Fig. 3). The protection
grid account for close to half of the total uncertainty for the free-field
response.
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Frequency_response_for_measurement_microphones.fm Page 31 Monday, June 25, 2001 3:21 PM
0.6
0.5
4188
4189/90
4191
4192
4188 grid
4189/90 grid
4191 grid
4192 grid
0.4
dB 0.3
0.2
0.1
0.0
0.1
1
10
100
kHz
980144
Fig. 3. Total free-field correction uncertainties for Brüel & Kjær Falcon Range microphones
without and with protection grid. (U95 ). The upper group of curves are with protection grid
Electrostatic Actuator Response Calibration
As mentioned earlier the response measured with an electrostatic actuator
is generally influenced by the radiation impedance which loads the microphone diaphragm. The influence may be modified by the mechanical configuration of the actuator, the actuator type used for calibration service should
be equal to that used for determination of the corrections.
The uncertainties used are estimated for “Calibration Services”, and they
are due to systematic uncertainties of the frequency response for the measurement system, random uncertainties caused by acoustical noise and systematic uncertainties caused by differences in mechanical dimensions of the
actuator. Mechanical resonances in the combination of electrostatic actuator, microphone, preamplifier housing and holder for preamplifier add to the
uncertainties at frequencies above 5 kHz.
The resulting uncertainties for the electrostatic actuator calibration are
shown in Fig. 4.
The “Factory Calibration” performed at Brüel & Kjær resulting in a Calibration Chart and a Data Diskette have lower uncertainty values. This is due to
the very low systematic uncertainty on the frequency response of the measuring system.
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Frequency_response_for_measurement_microphones.fm Page 32 Monday, June 25, 2001 3:21 PM
0.6
0.5
0.4
dB 0.3
ACT calib.
0.2
0.1
0.0
100
10
1
0.1
kHz
980145
Fig. 4. Total electrostatic actuator calibration uncertainties for Brüel & Kjær Falcon Range
microphones (U95 )
Free-field Response Uncertainties
The different contributions to the total uncertainty are shown for all
Brüel & Kjær Falcon Range microphones without and with protection grid in
Fig. 5. The electrostatic actuator calibration is the main contributor at low
and medium frequencies. At the highest frequencies the protection grid is
dominant. This picture is typical for all the Falcon Range microphones.
0.6
0.5
4188
4189/90
4191
4192/93
4188 grid
4189/90 grid
4191 grid
4192/93 grid
0.4
dB 0.3
0.2
0.1
0.0
0.1
10
1
100
kHz
980141
Fig. 5. Total uncertainties for Brüel & Kjær Falcon Range microphones without and with protection grid (U95). The upper group of curves are with protection grid
32
Frequency_response_for_measurement_microphones.fm Page 33 Monday, June 25, 2001 3:21 PM
Comments
From the measurement results for the free-field correction some interesting
analysis can be performed. If the free-field corrections for all the 6 Brüel & Kjær
Falcon Range microphones are plotted on the same graph (see Fig. 6) it is seen
that there are noticeable differences already at 2 kHz. The difference is increasing towards higher frequencies. In Fig. 7 the maximum difference is shown both
for the measured and the calculated (BEM) free-field correction. The interesting
thing about these results is that seen from the outside there are no differences
between the microphones without protection grid.
The differences in Fig. 7 are caused by the differences in diaphragm impedance and damping of the diaphragm. For other 1/2″ microphones with different mechanical mechanical configuration around the diaphragm even larger
differences in free-field corrections can be expected.
This leads to the conclusion, that it is very important that the free-field
correction is actually measured for the microphone type for which it is used
during calibration. It is not enough to use the free-field correction of a seemingly similar microphone type.
10
9
8
7
6
dB
5
4
3
2
1
0
1000
10000
100000
Hz
980146
Fig. 6. Free-field correction for 6 different 1/2 ″ Brüel & Kjær Falcon Range microphones without protection grid
33
Frequency_response_for_measurement_microphones.fm Page 34 Monday, June 25, 2001 3:21 PM
2.0
1.5
dB
1.0
0.5
0.0
1
10
kHz
100
980147
Fig. 7. Difference in free-field correction for 6 different 1/2 ″ Brüel & Kjær Falcon Range microphones with exactly the same mechanical configuration around the diaphragm
- - - - Boundary Element Calculation
------- Brüel & Kjær measurements
Conclusion
For each of the Brüel & Kjær Falcon Range microphones uncertainty values
have been presented relating to:
1)
2)
3)
free-field correction
influence of protection grid
electrostatic actuator calibration
The total uncertainty (U 95) of the free-field response for the Brüel & Kjær
Falcon Range microphones with protection grid are typically below 0.1 dB for
frequencies up to 2 kHz, below 0.25 dB up to 10 kHz and increasing to
between 0.35 dB and 0.58 dB at the highest operating frequency.
The uncertainty of the free-field response can be reduced approximately
50% by using the microphone without protection grid.
For other microphones larger uncertainties for the free-field response can
be expected.
As microphone frequency responses are generally not accompanied by the
corresponding uncertainty values, the frequency response for measurement
microphones are a question of confidence.
34
Frequency_response_for_measurement_microphones.fm Page 35 Monday, June 25, 2001 3:21 PM
References
[1]
Erling Frederiksen, Johan Gramtorp, “Measurement of Microphone
Free-field Corrections and Determination of their Uncertainties”,
Brüel & Kjær: Technical Review No. 1 –1996, 9 – 18 (and ICA95, 15th
International Congress on Acoustics, proceedings IV, 209 – 212)
[2]
IEC 61094 – 2, “Primary method for pressure calibration of laboratory
standard microphones by the reciprocity technique”
[3]
IEC 61094 – 3, “Primary method for free-field calibration of laboratory
standard microphones by the reciprocity technique”
[4]
Peter Juhl, “Numerical Investigation of Standard Condenser Microphones”, Journal of Sound and Vibration 1994 Vol. 177 (4), 433 – 446
35
Microphone_random_incidence.fm Page 36 Monday, June 25, 2001 3:23 PM
Measurement of Microphone Randomincidence and Pressure-field Responses
and Determination of their Uncertainties*
by Johan Gramtorp and Erling Frederiksen
Abstract
For many applications it is important to know the frequency response of the
measurement microphone. In two earlier papers [1] & [2] the determination
of the free-field response and the uncertainties of the responses based on
actuator calibration for 1/2″ microphones were discussed. This paper continues by discussing actuator based pressure-field and random-incidence
responses and their uncertainties. From most manufacturers no information
on the uncertainties is available. A complete set of uncertainty values for
pressure-field and random-incidence corrections and responses for the
Brüel & Kjær Falcon Range 1/2″ microphones will be presented and discussed.
Résumé
Il est important, dans de nombreuses applications, de connaître la réponse en
fréquence du microphone de mesurage. Dans deux articles précédents [1] & [2],
la détermination de la réponse en champ libre et l’incertitude des réponses
basées sur le calibrage des microphones de 1/2″ ont été discutées. Le présent
article poursuit ce thème en discutant réponses et incertitudes en champ de
pression et incidence aléatoire. La plupart des constructeurs ne fournissent
aucune information sur ces incertitudes. Cet article présente et discute un
ensemble de valeurs d’incertitude pour les réponses et corrections des mesures
en champ de pression et avec incidence aléatoire pour les Microphones 1/2″ de
la gamme Falcon Brüel & Kjær.
* First presented at ICA 1998
36
Microphone_random_incidence.fm Page 37 Monday, June 25, 2001 3:23 PM
Zusammenfassung
Bei vielen Anwendungen ist es wichtig, den Frequenzgang des Meßmikrofons
zu kennen. In zwei früheren Beiträgen ([1] und [2]) wurde die Ermittlung
des Freifeld-Frequenzgangs und der damit verbundenen Unsicherheiten
anhand der Kalibrierung von ½″-Mikrofonen mit Kalibrier-gittern diskutiert. Dieser Beitrag setzt die Betrachtungen mit einer Diskussion des
Druck- und Diffusfeld-Frequenzgangs und der Unsicherheiten auf der Basis
von Kalibriergittern fort. Die meisten Hersteller machen keine Angaben
über die Meßunsicherheit. Es wird ein kompletter Datensatz mit Meßunsicherheiten für Druck- und Diffusfeldkorrekturen und Frequenzgänge für
die neuen ½″-Mikrofone der Falcon-Serie von Brüel & Kjær vorgestellt und
diskutiert.
Pressure-field Response
Until now most of the pressure-field responses for “Working Standard”
microphones presented on calibration charts, have actually been electrostatic actuator responses. They differ slightly from the true pressure-field
response due to the radiation impedance of the microphone diaphragm.
The Brüel & Kjær Falcon Range 1/2″ microphones can, due to the very
robust diaphragm clamping technique, fit directly into reciprocity calibration couplers. Based on pressure-field reciprocity measurements performed
in different couplers and the corresponding electrostatic actuator response,
it is thereby possible to determine a type specific pressure-field correction as
shown in Fig. 1.
3
2
dB 1
0
-1
1
100
10
kHz
4189
4190
4191
4192/93
010094
Fig. 1. Pressure-field corrections for Brüel & Kjær Falcon Range 1/2 ″ microphones based on
pressure-field reciprocity measurements
37
Microphone_random_incidence.fm Page 38 Monday, June 25, 2001 3:23 PM
The individual pressure-field response for any of these microphones can now
be determined by adding the type specific pressure-field correction to the individually measured electrostatic actuator response. The uncertainties for the
pressure-field corrections are dominated by the uncertainties from the pressure-field reciprocity measurement. The total uncertainties shown in Table 1 are
dominated by the uncertainties from the electrostatic actuator calibration.
Microphone
Type
0.25kHz 0.5 kHz
1 kHz
2 kHz
4 kHz
8 kHz
16 kHz
20 kHz
4189 – 93
0 dB
0.07 dB
0.07 dB
0.11 dB
0.16 dB
0.25 dB
0.27 dB
0.07 dB
Table 1. Pressure-field response uncertainties U95 for Brüel & Kjær Falcon Range 1/2ð microphones based on actuator calibration
Random-Incidence Response
The random-incidence responses presented on the calibration charts are
based on a large number of free-field measurements with different angles of incidence increased in small steps, and calculated as a weighted sum according to
IEC 60651 or 61183, combined with electrostatic actuator calibration. Until now
most of the random-incidence responses, have been calculated from measurements performed in 30° angle steps according to IEC 651 (now IEC 60651).
The Brüel & Kjær Falcon Range 1/2″ microphones has been measured in 5°
angle steps and calculated according to IEC 61183. These measurements are
normalised with the 0°-incidence free-field reciprocity response for the microphone.
3
2
dB 1
0
-1
1
100
10
kHz
30 deg.
10 deg.
5 deg.
010095
Fig. 2. Random-incidence correction for Brüel & Kjær Type 4191 microphone calculated from
free-field corrections in different angle steps
38
Microphone_random_incidence.fm Page 39 Monday, June 25, 2001 3:23 PM
When the random-incidence correction is calculated in different angle steps
on the same measurement data, the differences are very small up to 15 kHz as
shown on Fig. 2. Above 15 kHz the differences increase to approximately 0.4 dB
at 40 kHz. The uncertainties for the random-incidence corrections (calculated in
5° angle steps) are dominated by the differences in the measurements for + and
− angles and the uncertainties from the influence of the protection grid.
The total uncertainties on the random-incidence responses, shown in Table 2,
have almost equal contributions from the random-incidence correction and the
electrostatic actuator calibration below 8 kHz. Above 8 kHz the uncertainties on
the random-incidence correction becomes dominating.
Microphone Type
0.25 kHz
0.5–
2 kHz
4 kHz
8 kHz
16 kHz
4188 with DZ 9566
0 dB
0.14 dB
0.17 dB
0.23 dB
0.44 dB
4189/90
0 dB
0.10 dB
0.15 dB
0.19 dB
0.55 dB
0.63 dB
4191
0 dB
0.10 dB
0.15 dB
0.19 dB
0.34 dB
0.37 dB
4192/93
0 dB
0.10 dB
0.15 dB
0.19 dB
0.34 dB
0.37 dB
20 kHz
32 kHz
40 kHz
0.75 dB
0.99 dB
Table 2. Random-incidence response uncertainties U95 for Brüel & Kjær Falcon Range 1/2 ″
microphones based on actuator calibration
Conclusion
We have come from pressure-field responses, that were actually electrostatic
actuator responses to closed coupler pressure-field responses, and from random-incidence responses based on measurements performed in 30° angle
steps to measurements performed in 5° angle steps. The responses can now be
accompanied by the corresponding uncertainties instead of only being a thin
line on the calibration chart.
References
[1]
Gramtorp, J and Frederiksen, E, “Frequency response for measurement
microphones: a question of confidence”, Honolulu, ASA December 1996
[2]
Frederiksen, E and Gramtorp, J, Brüel & Kjær: Technical Review No.1 1996, “Measurement of Microphone Free-field Corrections and Determination of their Uncertainties”, 9 – 18 (and proceedings of ICA95 15th
International Congress on Acoustics, Trondheim, Norway, IV 209 –212,
1995)
39
InsideCovers.fm Page 5 Tuesday, June 26, 2001 9:01 AM
Previously issued numbers of
Brüel & Kjær Technical Review
(Continued from cover page 2)
1 – 1987 Vibration Monitoring of Machines
4 – 1986 Field Measurements of Sound Insulation with a Battery-Operated
Intensity Analyzer
Pressure Microphones for Intensity Measurements with Significantly
Improved Phase Properties
Measurement of Acoustical Distance between Intensity Probe
Microphones
Wind and Turbulence Noise of Turbulence Screen, Nose Cone and
Sound Intensity Probe with Wind Screen
3 – 1986 A Method of Determining the Modal Frequencies of Structures with
Coupled Modes
Improvement to Monoreference Modal Data by Adding an Oblique
Degree of Freedom for the Reference
2 – 1986 Quality in Spectral Match of Photometric Transducers
Guide to Lighting of Urban Areas
1 – 1986 Environmental Noise Measurements
4 – 1985 Validity of Intensity Measurements in Partially Diffuse Sound Field
Influence of Tripods and Microphone Clips on the Frequency Response
of Microphones
3 – 1985 The Modulation Transfer Function in Room Acoustics
RASTI: A Tool for Evaluating Auditoria
2 – 1985 Heat Stress
A New Thermal Anemometer Probe for Indoor Air Velocity
Measurements
Special technical literature
Brüel & Kjær publishes a variety of technical literature which can be obtained
from your local Brüel & Kjær representative.
The following literature is presently available:
❍ Catalogues (several languages)
❍ Product Data Sheets (English, German, French,)
Furthermore, back copies of the Technical Review can be supplied as shown in
the list above. Older issues may be obtained provided they are still in stock.
03-09-01
13:55
Page 1
BV 0054 – 11
ISSN 0007–2621
BV0054-11_omslag.qxd
HEADQUARTERS: DK-2850 Nærum · Denmark
Telephone: +45 45 80 05 00 · Fax: +45 45 80 14 05
Internet: http://www.bksv.com · e-mail: [email protected]
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