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Calibration of the pressure sensitivity of microphones by a free-field method at frequencies up to 80 kHz

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A free-field (FF) substitution method for calibrating the pressure sensitivity of microphones at frequencies up to 80 kHz is demonstrated with both grazing and normal-incidence geometries. The substitution-based method, as opposed to a simultaneous method, avoids problems associated with the nonuniformity of the sound field and, as applied here, uses a 1/4-in. air-condenser pressure microphone as a known reference. Best results were obtained with a centrifugal fan, which is used as a random, broadband sound source. A broadband source minimizes reflection-related interferences that can plague FF measurements. Calibrations were performed on 1/4-in. FF air-condenser, electret, and microelectromechanical systems (MEMS) microphones in an anechoic chamber. The uncertainty of this FF method is estimated by comparing the pressure sensitivity of an air-condenser FF microphone, as derived from the FF measurement, with that of an electrostatic actuator calibration. The root-mean-square difference is found to be +/- 0.3 dB over the range 1-80 kHz, and the combined standard uncertainty of the FF method, including other significant contributions, is +/- 0.41 dB.
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Calibration of the pressure sensitivity of microphones
by a free-field method at frequencies up to 80 kHz
Allan J. Zuckerwar
a
and G. C. Herring
b
NASA Langley Research Center, Hampton, Virginia 23681
Brian R. Elbing
University of Michigan, Ann Arbor, Michigan 48109
Received 14 April 2005; revised 2 November 2005; accepted 3 November 2005
A free-field FF substitution method for calibrating the pressure sensitivity of microphones at
frequencies up to 80 kHz is demonstrated with both grazing and normal-incidence geometries. The
substitution-based method, as opposed to a simultaneous method, avoids problems associated with
the nonuniformity of the sound field and, as applied here, uses a
1
4
-in. air-condenser pressure
microphone as a known reference. Best results were obtained with a centrifugal fan, which is used
as a random, broadband sound source. A broadband source minimizes reflection-related
interferences that can plague FF measurements. Calibrations were performed on
1
4
-in. FF
air-condenser, electret, and microelectromechanical systems MEMS microphones in an anechoic
chamber. The uncertainty of this FF method is estimated by comparing the pressure sensitivity of an
air-condenser FF microphone, as derived from the FF measurement, with that of an electrostatic
actuator calibration. The root-mean-square difference is found to be ±0.3 dB over the range
180 kHz, and the combined standard uncertainty of the FF method, including other significant
contributions, is ±0.41 dB. DOI: 10.1121/1.2141360
PACS numbers: 43.58.Vb, 43.38.Kb NHF Pages: 320–329
I. INTRODUCTION
Society has an interest
1,2
in noise reduction for those
airports that are in or near metropolitan areas. The frequency
range 15 kHz is of key importance when considering the
reduction of the public annoyance due to commercial air
traffic. Furthermore, a significant fraction of noise-reduction
research is done by means of wind tunnel testing, rather than
more expensive field testing. The acoustic wavelength will
scale as a function of r, a characteristic scale length, and the
dependence on r can vary considerably, depending on spe-
cific conditions. Confident interpretation of wind-tunnel data
is possible only if the dependence on r is known and ac-
counted for in the transformation between full-scale flight
conditions and scaled-down facility conditions. For the par-
ticular example of linear scaling
3
invariant Strouhal num-
ber and a 1/20-scale model, the 1 5 kHz region is trans-
formed to the 20100 kHz region. Thus the acoustic
frequency range 20100 kHz becomes important for noise
reduction work carried out with small-scale models in wind
tunnels. Microphones used in these studies must be cali-
brated at these ultrasonic frequencies before they can be used
to measure unknown sound sources. Historically, an electro-
static actuator EA has been used to calibrate air-condenser
microphones at these high frequencies.
If imaging of unknown acoustic sources is also of inter-
est, then the microphone cost becomes an issue. A typical
acoustic array may use 100 or more microphones at a sub-
stantial cost per microphone channel. To address the cost
issue, low-cost Panasonic WM-60A electret microphones
have recently been considered
4
for acoustic arrays. The pres-
sure sensitivity is appropriate for this type of application.
However, these electret microphones are not adaptable to the
EA. In addition, other technologies such as microelectrome-
chanical systems MEMS microphones, which would allow
higher packing densities in microphone arrays, are also not
adaptable to the EA. Thus the need arises for high-frequency
calibration techniques for microphone types that are not
compatible with the venerable EA. In this paper, a
substitution-based, free-field FF calibration method is dem-
onstrated to derive the pressure sensitivity of the amplitude
response of various microphones out to frequencies of
80 kHz. A standard air-condenser pressure microphone is
used as the known reference. Two sound sources, a centrifu-
gal fan and a tweeter driven by either frequency sweeps or
random noise, were used. FF calibration design issues, pro-
cedures, results, and uncertainties for several of the above-
mentioned microphones are discussed.
II. MICROPHONE CALIBRATION METHODS
Over the years, several methods have been developed
for microphone calibration. A summary of the more common
methods is presented in Table I. The pressure sensitivity of a
microphone is the voltage per unit sound pressure that the
microphone will produce when a completely uniform pres-
sure is incident on the microphone diaphragm. This is the
appropriate sensitivity, for example, when the microphone is
installed in a small cavity compared to the acoustical wave-
length or is flush-mounted in a large baffle. In contrast, the
a
Present address: Analytical Services and Materials, Inc., Hampton, Virginia
23666.
b
Electronic mail: g.c.herring@larc.nasa.gov
320 J. Acoust. Soc. Am. 119 1, January 2006 0001-4966/2006/1191/320/10/$22.50
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FF sensitivity of a microphone is the voltage per unit sound
pressure produced when a traveling wave incident on the
diaphragm is isolated from boundaries. This FF sensitivity is
different from the pressure sensitivity because of diffraction
of the incident wave, which leads to a spatially varying re-
sultant sound field over the face of the diaphragm. If the
microphone is mounted in free space with minimal mounting
hardware, it exhibits its diffraction-related FF sensitivity. The
difference between a microphone’s FF and pressure re-
sponses is shown in Fig. 1. Thus measurements in the FF
require a frequency-dependent correction C to yield the pres-
sure response.
Table I also lists the limitations of each method.
Coupler-based methods are confined to relatively low fre-
quencies because of the increasing spectral density of cavity
modes with increasing frequency.
5
In the example shown in
Fig. 2, calibration of a microphone would become problem-
atic at frequencies approaching 30 kHz or higher. A piston-
phone provides a constant and known volume velocity to a
microphone inserted in a coupler at a variety of fixed fre-
quencies over the audio range, but again is limited to low
frequencies. For higher frequencies, the EA has long been
used to calibrate air-condenser microphones up to frequen-
cies exceeding 100 kHz, but requires an accessible, conduc-
tive diaphragm. Many newer microphone types fail to meet
this requirement and thus are not compatible with the EA.
This is the appropriate situation for the FF technique to
be considered for high-frequency calibration. Specific
precautions to minimize or eliminate the diffraction
problem are discussed in more detail in a later section of this
article.
Both the coupler and FF methods can both be executed
using reciprocity, simultaneous, or substitution procedures,
each encumbered with its own particular difficulty. The reci-
procity method requires a reciprocal transducer that operates
efficiently as both a transmitter and a receiver at high fre-
quencies, especially in the FF. The simultaneous method,
whereby both the known reference and unknown test micro-
phones are tested at the same time, requires the sound field to
be spatially uniform at all frequencies. The substitution
method, whereby the two microphones are tested sequen-
tially in the same location to avoid the spatial nonuniformity
problem, requires a temporally stable sound source since the
two measurements are no longer made simultaneously. Since
this was deemed the least problematic requirement to fulfill,
substitution was chosen as the preferred high-frequency cali-
bration method in this study.
Time selective techniques have been demonstrated to re-
move the reflections from the time response and thus elimi-
nate the attendant contribution to the measurement
uncertainty.
6,7
These, however, have not been applied to cali-
bration of the microphone pressure sensitivity nor to mea-
surements above 30 kHz.
III. CALIBRATION STANDARDS AND KEY
SPECIFICATIONS
Upon close inspection of existing standards
8,9
for micro-
phone calibration, it is apparent that all are written with low-
frequency calibrations or FF sensitivity in mind. Thus there
is no published national or international standard for micro-
phone pressure-sensitivity calibration in the 20100 kHz
frequency range other than the EA.
10
In this section, several
parameters that will affect the quality of a high-frequency,
FF microphone calibration are discussed.
TABLE I. Common methods of microphone calibration.
Method
Sensitivity
type Frequencies Limitations
Coupler Pressure Low-frequency Cavity modes
Reciprocity
a
Substitution
Simultaneous
Pistonphone Pressure Low-frequency Limited No. of frequencies,
SPLs
Electrostatic
actuator
Pressure Wideband Accessible, conductive
diaphragm
Free-field Free-field Wideband Diffraction/reflections
Reciprocity High-frequency reciprocal
transducer
Substitution Source stability
Simultaneous Uniformity of pressure
field
a
Primary calibration method.
FIG. 1. Typical pressure sensitivity P and free-field sensitivity FF of an
air-condenser microphone. The correction C is the frequency-dependent dif-
ference between the two sensitivities. It depends on the microphone diam-
eter and is shown here for a
1
2
in. microphone at normal incidence.
FIG. 2. Mode locations of a cylindrical cavity having a diameter of
6.35 mmheight of 2.14 mm. The modal designations ijk refer to the
axial, radial, and azimuthal modes, respectively.
J. Acoust. Soc. Am., Vol. 119, No. 1, January 2006 Zuckerwar, Herring, and Elbing: Calibration of pressure sensitivity 321
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One important problem that arises in a typical FF cali-
bration is a frequency-dependent systematic error that gener-
ates an oscillatory pattern on the microphone response spec-
trum. An example of this oscillatory systematic error is
shown in Fig. 3 for a FF calibration of a Panasonic WM60A
electret microphone. A distinct modulation of the sensitivity
is seen at frequencies of 10 kHz and higher. In this study,
five possible different frequency-dependent causes were con-
sidered as origins for this sensitivity variation: 1 interfer-
ence from room resonances; 2 reflections from nearby
mounting structure and subsequent interference between the
incident and reflected acoustic waves; 3 modal breakup
11
in
the diaphragm of the sound source; 4 difference in
diffraction
12
between the unknown test and the known refer-
ence microphones; 5 differences in the acoustic center
location
13
and acoustic impedance between the unknown test
and the known reference microphones. It was determined in
this study that item 2, reflections and subsequent interfer-
ence, was the primary reason for the occurrence of the oscil-
latory systematic errors that can occur.
Five different countermeasures can be used to help mini-
mize or eliminate the systematic error due to these interfer-
ence effects: 1 to perform the calibrations in a suitable
anechoic chamber and cover the mounting structure with an
absorbing foam to minimize reflections; 2 to keep all
mounting hardware far away from, or behind, the test micro-
phone to minimize significant reflections; 3 to choose the
source-microphone separation distance L such that d
2
/L
1, where d = source size and = acoustic wavelength, to
ensure placement of the test microphone beyond the Fresnel
region of the source; 4 to use a broadband source that ex-
hibits minimal phase coherence at all frequencies of interest,
in order to suppress the build-up of standing waves, and to
minimize interference between any reflected and incident
waves near the microphone diaphragm; 5 if a phase-
coherent tonal source must be used to achieve a large enough
signal-to-noise ratio SNR, then to use a grazing-angle,
rather than a normal-angle, incidence to minimize interfer-
ence effects in the vicinity of the microphone diaphragm.
Thus key specifications for any FF calibration procedure
should include the geometry i.e., normal or grazing inci-
dence, the bandwidth characteristics of the source, SNR,
and the source-microphone separation distance. Because the
microphone response to grazing incidence more closely
matches the pressure response, the correction from FF to
pressure sensitivity is accordingly smaller than the correction
for normal incidence.
IV. PRINCIPLE OF THE FF SUBSTITUTION METHOD
Figure 4 illustrates the principle of the substitution
method. The calibrations are performed in an anechoic
chamber with a sound source, the test and reference micro-
phones, and a signal analyzer. The reference and test micro-
phones are tested sequentially. The symbols in the figure are
defined as follows:
P the acoustic pressure in the undisturbed
sound field;
S
R
FF
,S
X
FF
the FF sensitivity of the reference and test
microphones, in mV/Pa;
V
R
,V
X
the output voltage of the reference and test
microphones;
S
R
o
,S
X
o
the sensitivity of the reference and test mi-
crophones at a reference frequency, as deter-
mined for example by a pistonphone at
250 Hz;
P
R
, P
X
the pressure reading for the reference and
test microphones as displayed by the
analyzer.
Then it follows:
P
R
=
V
R
S
R
o
=
S
R
FF
P
S
R
o
=
CS
R
P
P
S
R
o
, 1
P
X
=
V
X
S
X
o
=
S
X
FF
P
S
X
o
=
CS
X
P
P
S
X
o
, 2
where C is the correction factor for converting from FF to
pressure sensitivity. Upon taking ratios, and expressing the
result in dB, one finds the pressure sensitivity M
X
P
of the test
microphone the M’s are the microphone sensitivities in dB
re 1 mV/ Pa,
M
X
P
= L
X
L
R
+ M
R
P
+ M
X
o
M
R
o
, 3
where
L
R
,L
X
the measured FF pressure levels P
R
, P
X
,in
dB re 20
Pa;
FIG. 3. Free-field measurement of the pressure sensitivity of an electret
condenser microphone using a tweeter excited at discrete frequencies. Open
circle: datum point at a discrete frequency.
FIG. 4. Principle of the free-field substitution method.
322 J. Acoust. Soc. Am., Vol. 119, No. 1, January 2006 Zuckerwar, Herring, and Elbing: Calibration of pressure sensitivity
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M
R
P
the known pressure sensitivity of the refer-
ence microphone, as determined by the elec-
trostatic actuator.
The validity of Eq. 3 rests upon two assumptions: first, that
the sound pressure is the same at the reference and test mi-
crophone diaphragms. This implies that the microphone-
diaphragm distance and diaphragm height is matched for the
two microphone measurements as closely as possible; that
the source and microphone are fixed firmly to the chamber
floor or to a common base plate to make their separation
immune to displacement by foot traffic; and finally that the
source remain sufficiently stable between the two measure-
ments so as not to cause significant measurement error. It is
imperative that the measurements on the reference and test
microphones take place with minimum delay after the ex-
change of microphones.
The second assumption is that the correction factor C for
diffraction be the same for both microphones. Since diffrac-
tion is primarily a geometric effect, this implies that both
microphones must present the same surface geometry to the
sound field. If the test and reference microphones are of dis-
similar geometries, then one or both of the microphone
mounts must be modified e.g., encased in an adapter to
match each other in size and shape. Further, it is important
that the size of the microphone holder and stand be mini-
mized as much as practical.
An advantage of the substitution method is that the fre-
quency calibration does not depend upon the frequency spec-
trum of the source, for frequency-dependent variations in
amplitude are expected to cancel. However, if the source
spectrum has structure, as may be expected of a pistonlike
source e.g., loudspeaker, then the error related to source
stability is most sensitive in the regions where structure is
most prominent. A disadvantage of the substitution method is
that the sound source and detector must be very stable and
repeatable over the time period between testing of the test
and reference microphones.
V. EXPERIMENTAL SETUP
In the experimental setup for the FF calibration method,
indicated schematically in Fig. 4, two sound sources were
used for testing: a centrifugal fan Campanella Associates
RSS-10U and a tweeter Motorola KSN1078. A signal ana-
lyzer B&K 2035, remotely located in a control room, was
used to record the data. This performs a fast Fourier trans-
form on the signal, which allows for the data to be recorded
in the frequency domain on a 3.5 in. floppy disk for subse-
quent processing on a spreadsheet. All calibrations were per-
formed in a 2.1 2.53.7-m anechoic chamber, having a
cutoff frequency of 210 Hz and an A-weighted ambient noise
level of 15 dB.
A. Sound sources
The centrifugal fan is a wideband noise source that pro-
duces approximately random noise. A wideband source mini-
mizes the chance of interference between the incident wave
and unwanted reflected waves, and allows for data to be
collected simultaneously over the entire frequency range.
The disadvantage of this sound source is that the SNR is
small compared to a typical tonal source. This ratio can be
increased by moving the microphone closer to the centrifugal
fan. The manufacturers specifications state that a micro-
phone should not be used within 0.5 m of the fan to prevent
systematic errors due to windage from the fan. Calibrations
were typically much better when moved inside of the half-
meter separation because the SNR was larger. Figure 5
shows a typical experimental setup for an air condenser mi-
crophone. Figure 6a shows the emission spectrum of the
centrifugal fan, which reveals no structure except for a small
region near 10 kHz. A “1-over-R test was performed to
verify that the centrifugal fan behaves as a point source.
Figure 6b shows the results of the “1-over-R test. The
results show that the centrifugal fan still acts as a point
FIG. 5. Calibration setup using the centrifugal fan right and microphone
left in an anechoic chamber. The centrifugal fan platform and microphone
stand are attached rigidly to a base-plate not shown on the floor.
FIG. 6. Properties of the centrifugal fan Campanella Associates Reference
Sound Source RSS-101U: a acoustical emission spectrum calibrated by
the manufacturer with a Larson-Davis type 2520 microphone at a distance of
0.5 m; b sound pressure versus reciprocal distance from the fan at frequen-
cies of 10, 30, and 50 kHz. Circles: in-house measurement. Lines: best fit.
J. Acoust. Soc. Am., Vol. 119, No. 1, January 2006 Zuckerwar, Herring, and Elbing: Calibration of pressure sensitivity 323
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source with a separation of 0.4 m, which is less than the
separations used for all calibrations presented here.
The response of the tweeter was inconsistent below
1 kHz, but had exceptional performance above 1 kHz until
the output rolled off at about 60 kHz; it could still be used at
80 kHz. Two types of electrical input were used to excite the
tweeter: swept tones and random noise. With tones, testing
could be done with either a frequency-sweep function or
temporally-fixed tones. Sweeping of the tones is superior be-
cause the time interval required to complete the calibration is
significantly reduced when compared with using fixed tones.
The reduced time is an advantage because heating of the
voice coil affects the input impedance and hence the acous-
tic output of the tweeter. The only advantage to using fixed
tones is that it allows the maximum SNR, which, for ex-
ample, is important for the calibrating low-sensitivity pi-
ezoresistive microphones. The disadvantage of using fixed
tones is that the chance of generating interference effects on
the response profile, as in Fig. 3, is increased.
The random-noise input signal has the advantage of be-
ing able to complete the calibration faster than sweeping
tones, but the accuracy of the calibration is reduced due to
the lower SNR of the acoustic input.
B. Microphones and their mounting
An air-condenser
1
4
-in. pressure microphone B&K type
4136, with the protective grid removed, was used as the
reference microphone for every calibration. The dual-
channel microphone power supply B&K type 2807 was
turned on at least 24 h prior to a calibration. The second
channel was used for the calibration of other air-condenser
microphones.
For the nonair condenser microphones MEMS & elec-
trets an alternative setup was used. These microphones were
powered from a dc power supply Agilent E3630A, located
in the anechoic chamber. The output signal from the micro-
phone was then fed into a single channel instrumentation
amplifier Pacific Instruments SA1A, having a very low out-
put impedance, and from there to the signal analyzer.
The setup for the tweeter was the same for both the
white noise and tone signals, with the exception of the input-
signal generator. The white-noise signal generator was a
multifunction synthesizer Agilent 8904A and the tonal sig-
nal generator was a function generator HP 3314A. The
driver-signal was amplified with a wideband power amplifier
B&K 2713.
Mounting of the microphone is a critical step in the FF
calibration method. One of the primary assumptions is that
both the reference and test microphones encounter the same
pressure field. Two factors dictate the validity of this as-
sumption: temporal stability of the sound source and repeat-
able positioning of the microphone. The positioning of the
microphones entails both the orientation to the sound source
and the geometry of the microphone.
The orientation of the microphone to the sound source
has to be carefully implemented because variations in posi-
tion between tests can have significant effects on the results.
To improve the ability for the microphones to be accurately
positioned, both the sound source and the microphone stand
were fixed to a baseboard. This kept the setup rigidly fixed in
place throughout testing. Even with the sound source stand
and the microphone stand fixed in place, careful measure-
ments still had to be made when mounting the microphones.
The height from the ground to the microphone, distance from
the microphone diaphragm to the source and to the mounting
post, were all adjustable. The height from the ground to the
microphone diaphragm center was fixed at 1.25 m, which
also corresponds to the center of the sound source. The dis-
tances between the microphone diaphragm and source and
between the microphone diaphragm and the mounting post
are summarized in Table II. With the distances listed in Table
II, typical sound SPLs 128 Hz band generated at the micro-
phone diaphragm were the following: centrifugal fan,
55 60 dB at 10 kHz and 3338 dB at 80 kHz; tweeter,
75 80 dB at 10 kHz and 6068 dB at 80 kHz, sweep being
slightly higher than white noise excitation.
The other aspect of proper microphone mounting is the
geometry of the microphone mount. Since the pressure sen-
sitivity was determined here by FF measurements, the geom-
etry associated with the test and reference microphones had
to be nearly identical. Through experience it was determined
that there are two key considerations when considering the
geometry of the microphone mount. First is the shape and
size of the microphone diaphragm surface. Testing was done
with both
1
4
-in. microphones as well as with varied dia-
phragm arrangements. These variations included a recessed
diaphragm electret and a rectangular shaped surface with
the diaphragm mounted in the middle MEMS. The varia-
tions produced good results when careful consideration was
given to replication of the shape and size. The second key
consideration for the microphone mount is the presence of
reflecting surfaces near the microphone diaphragm. In prac-
tice any solid surface, like the microphone stand, should be
placed at least 10 diaphragm diameters behind the
microphone.
15
C. Procedure
A requirement for the FF method described here is that a
reference microphone be selected that can be calibrated using
the EA method. Reliance of the FF method upon the EA is
acceptable since the purpose of the FF method is to calibrate
“special microphones” that cannot be mated to the EA. This
requires that the reference microphone has a flat, conducting
TABLE II. Typical distances meters: diaphragm-source and diaphragm-
mounting post.
Source
Normal incidence Grazing incidence
Diaphragm-
source
Diaphragm-
mounting post
Diaphragm-
source
Diaphragm-
mounting post
Centrifugal fan 0.406
a
0.102
b
0.508 Not applicable
Tweeter 0.406 0.089
b
0.495 Not applicable
a
Measured to center of fan.
b
For the SiSonic microphone SP0101Z the diaphragm-mounting post dis-
tance was 0.051 m.
324 J. Acoust. Soc. Am., Vol. 119, No. 1, January 2006 Zuckerwar, Herring, and Elbing: Calibration of pressure sensitivity
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diaphragm. Once the reference microphone has been prop-
erly calibrated with the EA, the FF calibration can be per-
formed on the test microphone.
Before the FF calibration, both the reference and test
microphones were calibrated with a fixed pistonphone B&K
type 4228 at 250 Hz. The test microphone was flush
mounted in a holder, designed to retain the correct coupler
volume of the pistonphone. These pistonphone measure-
ments were taken immediately prior to the FF calibration.
Measurements of the chamber environment were also re-
corded. The main environmental parameters are temperature,
atmospheric pressure, and relative humidity. These data are
used to make small corrections to the calibration and in the
uncertainty analysis.
The method for the start up of the sound source varies
based on the source. If the centrifugal fan was used, then the
fan was left on for approximately 5 min to allow the source
to reach an equilibrium state. The tweeter was used shortly
after being turned on. It is important to note that the tweeter
should be employed in a regular routine. Since the output can
vary over time as a result of an increase in temperature of the
tweeter, the accuracy of the calibration will depend on the
time duration from start to finish. Thus if the time delay
between starting the tweeter and data acquisition is repeat-
able and if there is adequate time for the tweeter to cool
down in between runs, the calibration will be more accurate.
Four data runs are required for a calibration of the test
microphone. The first two runs are performed with the test
microphone, first with the sound source on and second with
the sound source turned off. The latter two runs are per-
formed similarly for the reference microphone. Then the
acoustic pressure P
R
for the reference microphone in Eq. 1
is corrected to
P
R
=
P
R
2
meas P
R
2
bg,
where meas and bg refer to the runs with and without the
source turned on. The acoustic pressure P
X
for the test mi-
crophone in Eq. 2 is corrected similarly. In this work, the
background subtraction was always carried out, even if the
signal was more than 20 dB above the background.
After the FF data had been collected for all four test runs
a second pistonphone reading was taken for each micro-
phone. The first pistonphone reading and this later reading
were used for an average sensitivity at a fixed frequency of
250 Hz. Thus the absolute sensitivity over the entire spec-
trum is fixed to the pistonphone reading. In addition to the
pistonphone measurements, the environmental conditions
temperature, pressure, relative humidity were also repeated.
An independent calibration is desirable for additional
confidence and validation of the FF method. The calibrator
used here, B&K type 4226 Multifunction Acoustic Calibrator
MAC, operates over the range of 31.5 Hz to 16 kHz at oc-
tave intervals except for an intermediate frequency at
12.5 kHz. The FF method did produce some calibrations
that were stable down to 1 kHz i.e., agree with the MAC,
but the 1 kHz endpoint could not be consistently obtained
with the FF method.
VI. RESULTS
This section is organized into two parts: A proof of the
FF calibration concept, whereby the FF calibration method is
tested on a microphone for which the electrostatic actuator
EA calibration is known; and B FF calibrations on micro-
phones having geometries unsuited to an EA calibration. The
signal analyzer was operated in the “Autospectrum” mode
over the frequency range 0 102.4 kHz with a frequency
resolution of 128 Hz. Typical test conditions were 20.5 ° C,
101 900 Pa, and 54% for the temperature, pressure, and rela-
tive humidity. Despite small variations in these parameters,
the difference in air absorption at 80 kHz between the refer-
ence and test microphone measurements never exceeded
0.088 dB over the source-microphone path.
9
A. Proof of the free-field calibration concept
To prove the concept, a series of calibrations was per-
formed on a test microphone for which the wideband pres-
sure sensitivity by the EA method is known, namely a
1
4
-in.
FF air-condenser microphone B&K type 4939. The first test
was performed with the centrifugal fan at normal incidence,
in accord with the specification of prior standards.
8–10
The
result is shown in Fig. 7a. Agreement between the FF and
EA spectra is excellent, the difference not exceeding
±0.5 dB. The difference is greatest in the vicinity of 10 kHz,
where the emission spectrum reveals structure Fig. 6a兲兴.
The FF spectrum follows the inflection point at about
20 kHz, the sensitivity minimum at 50 kHz, and in this case
appears to remain well-behaved at frequencies down to
1 kHz. The discrete calibration points triangles obtained
FIG. 7. Pressure sensitivity of a B&K type 4939
1
4
-in. free-field microphone
as calibrated by the free-field method heavy line,EAlight line, and
Multifunction Acoustic Calibrator B&K type 4226, triangles. Source: cen-
trifugal fan. Incidence: a normal, b grazing.
J. Acoust. Soc. Am., Vol. 119, No. 1, January 2006 Zuckerwar, Herring, and Elbing: Calibration of pressure sensitivity 325
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with the MAC also reveals excellent consistency with the
other two calibration methods. Figure 7b shows the results
for grazing incidence. Here agreement between the FF and
EA spectra lies within ±0.5 dB only within the interval
350 kHz.
For some test microphones it is desirable to increase the
SPL to ensure adequate SNR. Here the use of a tweeter will
prove useful. However, there will be some sacrifice in accu-
racy because the tweeter response shows structure across the
frequency spectrum. In Fig. 8 the tweeter is excited by white
noise. The FF pressure sensitivity of the microphone at a
normal and b grazing incidence shows agreement with the
EA to ±1 dB, except in a small region near 80 kHz. A small
oscillatory pattern is evident, especially in the normal re-
sponse.
Alternatively, one can drive the tweeter with a frequency
sweep, which improves the SPL especially at the higher fre-
quencies. In Figs. 9a and 9b the sweep frequency ranges
from 5 to 102.4 kHz linearly over a sweep time of 120 s.
The responses are similar to those obtained from white noise.
They may be somewhat better in the low-kHz range, but
show spikes at the upper end of the spectrum. Otherwise,
agreement with the EA appears to lie also within ±1 dB.
B. Free-field calibrations on microphones unsuited to
an EA calibration
A calibration was performed on an electret condenser
microphone, Panasonic WM-60A. The cartridge is 6 mm in
diameter and contains a small hole 共⬃2mm for acoustic
access to a recessed diaphragm. A felt pad covering the hole
was removed prior to calibration. The unavailability of ac-
cess to the diaphragm precluded the possibility of an EA
calibration. The cartridge was installed in a tube of dimen-
sions 6.35 mm o.d. 50.8 mm length, which contained a cir-
cuit board to accommodate the needed circuit components.
The supply voltage was 5.00 V in series with an 8.2 k
resistor on the circuit board. The assembled microphone was
fitted into a microphone holder, which was tapered on the
microphone end to resemble a conventional
1
4
-in. condenser
microphone adapter, as shown in Fig. 10a.
The results of the calibrations using the centrifugal fan,
tweeter excited by white noise, and tweeter excited by a
frequency sweep, are shown in Figs. 11a–11c, respec-
tively. The heavy and light lines represent normal and graz-
ing incidence in each figure. Results for grazing are for the
most part slightly lower than for normal. Figure 11a shows
the adverse effect of low SNR for grazing incidence as early
as 40 kHz, where nevertheless the sensitivity lies well be-
yond the −3 dB point. Grazing shows slightly better agree-
ment with the MAC the whole way down to 1 kHz. Figures
11b and 11c reveal good agreement between normal and
grazing, as well as with the MAC, at frequencies down to
about 3 kHz. The normal incidence, however, shows an un-
explained spike in the response slightly below 50 kHz. Ex-
cept for the spike, the calibrations from 3 kHz to the fre-
quency where the sensitivity drops 20 dB agrees with each
other to within ±1 dB.
A second microphone is a microelectromechanical sys-
tem MEMS capacitive microphone, SiSonic SP0101Z,
manufactured by Knowles Acoustics. The rectangular car-
tridge has dimensions of 6.50 6.25 2.37 mm. A small
FIG. 8. Pressure sensitivity of a B&K type 4939
1
4
-in. free-field microphone
as calibrated by the free-field method heavy line,EAlight line, and
Multifunction Acoustic Calibrator B&K type 4226, triangles. Source:
tweeter excited by white noise. Incidence: a normal, b grazing.
FIG. 9. Pressure sensitivity of a B&K type 4939
1
4
-in. free-field microphone
as calibrated by the free-field method heavy line,EAlight line, and
Multifunction Acoustic Calibrator B&K type 4226, triangles. Source:
tweeter excited by linear frequency sweep 5 102.4 kHz over a sweep time
of 120 s. Incidence: a normal, b grazing.
326 J. Acoust. Soc. Am., Vol. 119, No. 1, January 2006 Zuckerwar, Herring, and Elbing: Calibration of pressure sensitivity
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hole on one face renders acoustic access to the recessed dia-
phragm, an arrangement unsuited to an EA calibration, while
the opposite face contains four solder pads for electrical con-
tacts. A cylindrical adapter, 12.7 mm 1/2 in. in diameter,
was fabricated with a rectangular recess to seat the cartridge
flush with the surface, and provided with spring-loaded con-
tacts to make electrical contacts through an access hole in the
adapter see Fig. 10b兲兴. Finally a sleeve pressing against the
corners of the cartridge provided enough tension to hold the
cartridge in place. The adapter was designed to permit cali-
bration with the MAC; but an unfavorable length-to-diameter
ratio did not appear to have an adverse influence on the FF
calibration, at least by the centrifugal fan. A matching cylin-
drical adapter was made for the
1
4
-in. reference microphone.
The results are shown for the centrifugal fan and tweeter
in Figs. 12a and 12b. The centrifugal fan yields excellent
agreement among normal incidence, grazing incidence, and
the MAC, all within ±1 dB of each other. The calibration
reveals diaphragm resonances near 15 and 35 kHz. The
tweeter calibrations meet the ±1 dB uncertainty specification
only from 3 kHz to just over the first peak at about 18 kHz.
Significant differences occur in the region between the peaks
from 18 to 35 kHz. Below 3 kHz the white noise calibration
dotted line veers far astray. The unfavorable length-to-
diameter ratio of the adapter may be the culprit.
The final microphone unsuited to an EA calibration is
another MEMS microphone, “SiSonic Ultrasonic Prototype,”
having the same size but a greater bandwidth than the above.
The microphone, as delivered, was mounted on a small rect-
angular circuit board, 24.2 mm L . 11.7 mm W. Since the
microphone could not be detached from the circuit board, the
latter was inserted into a rectangular fixture at the end of a
support rod, which provided adequate separation from the
microphone stand. This arrangement is shown in Fig. 10c.
The fixture, 26.8 mm L . 14.2 mm W., served as an acous-
tic baffle. The reference microphone was flush-mounted in a
similar baffle of the same dimensions. The geometry is un-
suited to a MAC calibration. Because the baffle precluded a
FIG. 10. Mounting arrangement of test microphones unsuited to an electro-
static actuator calibration: a Electret condenser microphone Panasonic
WM-60A, b MEMS microphone SiSonic SP0101Z in adapter, c
MEMS microphone SiSonic Ultrasonic Prototype on a circuit board/
adapter.
FIG. 11. Pressure sensitivity of electret condenser microphone Panasonic
WM-60A. Sound sources: a centrifugal fan, b tweeter excited by white
noise, c tweeter excited by swept tones. Triangles: multifunction acoustic
calibrator data B&K type 4226. Light line: grazing incidence. Heavy line:
normal incidence.
J. Acoust. Soc. Am., Vol. 119, No. 1, January 2006 Zuckerwar, Herring, and Elbing: Calibration of pressure sensitivity 327
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conventional pistonphone calibration as well, the sensitivity
of the test microphone at a reference frequency was obtained
by matching FF sound pressures between the test and refer-
ence microphones at 2 kHz. The result is M
X
0
=4.2 mV/Pa.
The best results of the FF calibration were obtained us-
ing the centrifugal fan and tweeter excited by white noise, as
shown in Fig. 13. The fundamental diaphragm resonance is
seen to be shifted to about 30 kHz. Agreement between the
two sound sources is within ±1 dB from 2 to 50 kHz.
VII. ESTIMATE OF THE CALIBRATION UNCERTAINTY
For normal incidence and the FF microphone of Sec. VI
A and Fig. 7, the rms differences between the EA and the FF
methods are ±0.3, ± 0.8, and ±1.0 dB over the 180 kHz
range for the fan, white-noise, and tweeter sweep methods.
Contributions to the combined uncertainty of the FF method
are summarized in Table III. These values might realistically
be considered reasonable estimates for the uncertainty of a
test microphone that is nearly geometrically identical to the
reference microphone. One might cautiously expect that the
nongeometrically-identical microphones of Sec. VI B may
have slightly larger uncertainties due to additional reflection-
related problems.
In Table III, group I contributions are independent of the
acoustic source. The dominant contributions to the EA cali-
bration are “cross-talk” and loading of the microphone dia-
phragm by the radiation impedance. The relative uncertainty
of cross-talk,
14
from one frequency to the next, was deter-
mined through a measurement of the EA response with and
without the polarization voltage over the frequency range
180 kHz. The uncertainty due to radiation loading
10
is
based on theoretical estimates of the ratio of radiation im-
pedance to diaphragm stiffness reactance. It is noted that this
ratio falls off dramatically with decreasing diaphragm diam-
eter, because the equivalent volume varying inversely with
diaphragm stiffness reveals a disproportionate decrease fac-
tor 40 from
1
2
in. to
1
4
in.. The microphone-source separa-
tion uncertainty is 0.001 m out of a separation of 0.5 m. The
uncertainty due to orientation of the microphones is based on
the effect of an angular deviation of upon the FF correc-
tion factor at 50 kHz worst case. The uncertainty due to air
attenuation, based on ambient changes between reference
and test microphone measurements, is evaluated at 80 kHz
worst case according to Annex B of Ref. 15.
Group II contributions depend upon the sound source.
For each source the rms deviation of the FF from the EA
sensitivity of the proof-of-concept condenser microphone
Sec. VI A was computed over the measured frequency
range. This procedure accounts for imperfect cancellation of
effects due to diffraction and acoustic pressure mismatch at
the microphones.
FIG. 12. Pressure sensitivity of MEMS microphone SiSonic SP0101Z.
Sound sources: a centrifugal fan, b tweeter excited by swept tones solid
lines and white noise dotted line, normal incidence. Triangles: Multifunc-
tion Acoustic Calibrator data B&K type 4226. Light line: grazing inci-
dence. Heavy line: normal incidence.
FIG. 13. Pressure sensitivity of MEMS microphone SiSonic Ultrasonic
Prototype. Sound sources: centrifugal fan at normal incidence heavy line,
tweeter excited by white noise at normal incidence light line.
TABLE III. Contributions to the measurement uncertainty.
Uncertainty contribution
Standard
uncertainty
dB
I Electrostatic actuator
Cross talk 0.15
Radiation loading 0.07
Pistonphone 0.20
Microphone-source separation 0.017
Microphone orientation 0.10
Air attenuation 0.088
II Pressure measurement
Centrifugal fan 0.30
Tweeter, white noise 0.80
Tweeter, frequency sweep 1.00
III Combined standard uncertainty
Centrifugal fan 0.41
Tweeter, white noise 0.85
Tweeter, frequency sweep 1.04
328 J. Acoust. Soc. Am., Vol. 119, No. 1, January 2006 Zuckerwar, Herring, and Elbing: Calibration of pressure sensitivity
Downloaded 23 Jun 2011 to 128.118.40.79. Redistribution subject to ASA license or copyright; see http://asadl.org/journals/doc/ASALIB-home/info/terms.jsp
The entries under group III are the combined standard
uncertainties for each source, based on summation in quadra-
ture according to the specification of Ref. 16.
VIII. SUMMARY
The free-field substitution method has proved effective
for calibrating microphone pressure sensitivity at frequencies
out to at least 80 kHz and is applicable to microphones un-
suited to an EA calibration. Best results were obtained with a
centrifugal fan at normal incidence. For a microphone with a
relatively low SNR, however, a tweeter excited either by
white noise or a frequency sweep will provide a higher SPL
but the overall accuracy will be reduced.
The selection of specific instruments for testing does not
imply endorsement by the National Aeronautics and Space
Administration.
ACKNOWLEDGMENTS
We are pleased to thank W.R. Noack and R.M. Faison,
Wyle Laboratories, for performing the electrostatic actuator
calibrations, and S.M. Bartram and W.M. Humphreys,
NASA Langley Research Center, for fabricating equipment
used in the anechoic chamber and for helpful comments on
the manuscript.
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J. Acoust. Soc. Am., Vol. 119, No. 1, January 2006 Zuckerwar, Herring, and Elbing: Calibration of pressure sensitivity 329
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This technical note describes the measurement of the free field response of working standard microphones and associated equipment in the frequency range 500 Hz - 25 kHz. The measurements were made in a small anechoic chamber by comparison with a reference microphone having a known free-field response. Repeated measurements have been made in order to investigate the repeatability and the uncertainty of measurement. The results are based on the measurement of the time weighted impulse response. By the use of suitable time windows it is also possible to make the measurements in ordinary untreated rooms. (C) 2004 Institute of Noise Control Engineering.
Conference Paper
Microphone directional array technology continues to be a critical part of the overall instrumentation suite for experimental aeroacoustics. Unfortunately, high sensor cost remains one of the limiting factors in the construction of very high-density arrays (i.e., arrays containing several hundred channels or more) which could be used to implement advanced beamforming algorithms. In an effort to reduce the implementation cost of such arrays, the authors have undertaken a systematic performance analysis of a prototype 35-microphone array populated with commercial electret condenser microphones. An ensemble of microphones coupling commercially available electret cartridges with passive signal conditioning circuitry was fabricated for use with the Langley Large Aperture Directional Array (LADA). A performance analysis consisting of three phases was then performed: (1) characterize the acoustic response of the microphones via laboratory testing and calibration, (2) evaluate the beamforming capability of the electret-based LADA using a series of independently controlled point sources in an anechoic environment, and (3) demonstrate the utility of an electret-based directional array in a real-world application, in this case a cold flow jet operating at high subsonic velocities. The results of the investigation revealed a microphone frequency response suitable for directional array use over a range of 250 Hz - 40 kHz, a successful beamforming evaluation using the electret-populated LADA to measure simple point sources at frequencies up to 20 kHz, and a successful demonstration using the array to measure noise generated by the cold flow jet. This paper presents an overview of the tests conducted along with sample data obtained from those tests.
Article
Current understanding of airframe noise was reviewed as represented by experiment at model and full scale, by theoretical modeling, and by empirical correlation models. The principal component sources are associated with the trailing edges of wing and tail, deflected trailing edge flaps, flap side edges, leading edge flaps or slats, undercarriage gear elements, gear wheel wells, fuselage and wing boundary layers, and panel vibration, together with many minor protrusions like radio antennas and air conditioning intakes which may contribute significantly to perceived noise. There are also possibilities for interactions between the various mechanisms. With current engine technology, the principal airframe noise mechanisms dominate only at low frequencies, typically less than 1 kHz and often much lower, but further reduction of turbomachinery noise in particular may make airframe noise the principal element of approach noise at frequencies in the sensitive range.
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IntroductionOne-Dimensional Standing WavesTwo-Dimensional Standing WavesThree-Dimensional Standing WavesReferences
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IntroductionSound RadiationLoudspeaker System ComponentsDirect-Radiating Loudspeaker SystemsHorn-Loaded LoudspeakersMeasurementsReferences
Article
Principles of the expression of uncertainty in measurements are briefly reviewed and special aspects of the uncertainty quantification in NAA are discussed in detail regarding the relative and k 0-standardization in both modes of the technique, i.e., INAA and RNAA. A survey of uncertainty sources is presented and calculation of the combined uncertainty is demonstrated by an example of manganese determination in biological material by RNAA.
Article
The success of the high bypass ratio turbofan engine in reducing the external noise of civil transport aircraft at take-off and landing, while improving the economics of air travel, has opened up the debate as to how much further it will be possible to reduce aircraft noise by the introduction of new aircraft or existing aircraft retrofitted with new engines. Irrespective of what new technology can offer in respect of further engine noise reduction for no loss of performance, it is now clear that all future aircraft will require airframe noise to be reduced on the approach, since today it is comparable with engine noise. This paper discusses the major components of airframe noise and reviews the present state of airframe noise prediction. Finally, a comparison is made between prediction and experimental data and the prospects for airframe noise reduction.