Performance Analysis of a Cost-Effective Electret Condenser Microphone Directional Array

22 Pages·2003·4 MB·English

by  Humphreys, William M., Jr.

AIAA 2003-3195
Performance Analysis of a Cost-Effective
Electret Condenser Microphone
Directional Array
William M. Humphreys, Jr.
Carl H. Gerhold
Allan J. Zuckerwar
Gregory C. Herring
Scott M. Bartram
NASA Langley Research Center
Hampton, VA 23681-0001
9th AIAA/CEAS Aeroacoustics
Conference & Exhibit
12-14 May 2003 / Hilton Head, SC
For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics
1801 Alexander Bell Drive, Suite 500, Reston, Virginia 20191
PERFORMANCE ANALYSIS OF A COST-EFFECTIVE
ELECTRET CONDENSER MICROPHONE DIRECTIONAL ARRAY
William M. Humphreys, Jr.*
Carl H. Gerhold†
Allan J. Zuckerwar‡
Gregory C. Herring§
Scott M. Bartram¶
Aerodynamics, Aerothermodynamics, and Acoustics Competency
NASA Langley Research Center
Hampton, Virginia 23681-0001
Abstract microphones via laboratory testing and
calibration, (2) evaluate the beamforming
Microphone directional array technology capability of the electret-based LADA using a
continues to be a critical part of the overall series of independently controlled point sources
instrumentation suite for experimental in an anechoic environment, and (3) demonstrate
aeroacoustics. Unfortunately, high sensor cost the utility of an electret-based directional array in
remains one of the limiting factors in the a real-world application, in this case a cold flow
construction of very high-density arrays (i.e., jet operating at high subsonic velocities. The
arrays containing several hundred channels or results of the investigation revealed a
more) which could be used to implement microphone frequency response suitable for
advanced beamforming algorithms. In an effort directional array use over a range of
to reduce the implementation cost of such arrays, 250 Hz - 40 kHz, a successful beamforming
the authors have undertaken a systematic evaluation using the electret-populated LADA to
performance analysis of a prototype measure simple point sources at frequencies up
35-microphone array populated with commercial to 20 kHz, and a successful demonstration using
electret condenser microphones. An ensemble of the array to measure noise generated by the cold
microphones coupling commercially available flow jet. This paper presents an overview of the
electret cartridges with passive signal tests conducted along with sample data obtained
conditioning circuitry was fabricated for use with from those tests.
the Langley Large Aperture Directional Array
(LADA). A performance analysis consisting of Nomenclature
three phases was then performed:
(1) characterize the acoustic response of the
D free expansion jet nozzle
j
________________ diameter, ft
*Research Engineer, Advanced Measurement and eˆ array steering vector,
Diagnostics Branch, Senior Member AIAA.
see eqn. (4)
†Senior Research Scientist, Aeroacoustics Branch,
f frequency, Hz
Member AIAA.
‡Senior Research Scientist, Advanced Measurement Gˆ cross spectral matrix
and Diagnostics Branch.
k acoustic wave number, ft-1
§Research Scientist, Advanced Measurement and
K number of steering locations
Diagnostics Branch.
¶Engineering Technician, Advanced Measurement M total number of array
and Diagnostics Branch. microphones
This material is declared a work of the U.S. N number of data blocks
Government and is not subject to copyright
protection in the United States.
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P(eˆ) array output power for steering potential of this technology. For instance, the
next generation of array processing algorithms
vector eˆ, see eqn. (5)
being developed will potentially require the
P RMS pressure of fundamental
F acquisition of significantly more acoustic
plus harmonic frequencies, Pa
information than is presently done, in some cases
P RMS pressure of harmonic
H requiring acquisition of acoustic boundary
frequencies, Pa
conditions over the entire sphere of source
St Strouhal number
& directivity. DA systems involved in these types
ro,ro distance from source to x of tests will employ hundreds or thousands of
m c
and mth microphone, ft individual microphones. Traditional array
hardware, typically composed of externally-
r,r distance from steering location
m & biased condenser microphone / preamplifier /
to x and mth microphone, ft power supply combinations for a number of
c
R normalized array output of acquisition channels, is in many instances too
k
reference LADA at kth expensive to implement a high-density
steering location microphone system. Therefore, it is desirable to
THD total harmonic distortion, identify devices and hardware which can be used
percent, see eqn. (1) to implement a system exhibiting measurement
T normalized array output of performance comparable to the current
k
ECM LADA at kth generation of arrays, but at much lower cost.
steering location Several alternate microphone devices have been
U free expansion jet exit velocity, described in the literature which exhibit
j
ft/sec characteristics suitable for DA use and at
& &
economical cost. Among these are MEMS-
W(k,x,xo) ideal array response,
based devices described by Sheplak8, Saini9, and
see eqn. (7) Arnold10, and thin-film electret devices described
W&s hamming window weighting by Hsieh et.al.11
x& Cartesian coordinate, ft Over the last few years, the rapid pace of
x array phase center, ft micro-fabrication technology development has
c
X (f) kth FFT data block for ith yielded several promising new commercial
ik microphones. Given the increasing interest at
microphone, see eqn. (3a)
&(cid:2)
Langley Research Center and elsewhere in
(cid:2)x(cid:2)m distance vector from steering
building higher density array systems, the
location to mth microphone, ft
authors initiated a systematic search for a
ε
weighted RMS array response suitable low-cost commercial off-the-shelf
RMS
error (COTS) microphone which could be used for
ω angular frequency ( = 2πf ), this purpose. After examining several types of
radians / second microphones currently available (including
externally biased condenser, MEMS, and electret
condenser devices), the authors chose to conduct
Introduction
a detailed performance analysis of a prototype
DA system populated with COTS Electret
Aeroacoustic testing capability in both
Condenser Microphones (ECM’s). The
anechoic and hard-walled facilities has grown
objectives of the performance analysis were
tremendously over the last several years, with
threefold:
successful collection of noise source location and
directivity data in a variety of experiments. One
1. Characterize the acoustic response of a
of the reasons for the success of these
suitable ECM via laboratory testing and
measurements has been the development of both
calibration,
microphone directional array (DA)
2. Evaluate the beamforming capability of an
instrumentation and associated robust data
ECM-based directional array using a series
processing algorithms applied in the analysis of
of independently controlled point sources in
the acquired data.1-7 While the gain in test
an anechoic environment, and
productivity resulting from the use of DA
3. Demonstrate the utility of an ECM-based
systems has been significant, several challenges
directional array in a real-world application.
remain to be overcome before fully realizing the
The authors chose as a demonstration to
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apply the ECM array to measurement of driver on the output stage and can operate at a
source strength and directivity in a cold flow maximum supply voltage of +10V, with a
jet at high subsonic and low supersonic maximum current draw of 0.5 mA. The nominal
velocities. sensitivity of a raw WM-60A cartridge when
driven by a +5V source through an 8.2 kΩ load
Note that the cost and performance of the resistor is 15 mV/Pa. Figure 1b illustrates the
sensors chosen to implement high-density DA typical response of the microphones, which are
systems are critical parameters determining the designed to exhibit a flat magnitude response
viability of such arrays, but they are not the only over the audio frequency range of 20 Hz – 20
parameters to consider when designing such kHz.
systems. Microphone package size, data Equalizing Circuit / Packaging: While a typical
handling efficiency (i.e., efficiency of the data WM-60A cartridge operates with a flat response
acquisition system), and array mobility (i.e., over the audio frequency range, its use in
number and size of cables, power connections, aeroacoustic testing requires that the bandwidth
array mounting hardware, etc.) also determine of the device be extended to a significantly
the ultimate success of the system. While higher value. Above 20 kHz the microphone
microphone package size and construction are exhibits a first order sensitivity roll-off of
discussed subsequently, array data handling and approximately 6 dB per octave relative to its
mobility are beyond the scope of this paper - audio range sensitivity. To compensate for this
reference 10 provides a more detailed discussion roll-off, the authors designed a passive circuit to
of these issues. Rather, it is the purpose of this equalize the broadband frequency response of
paper to present an overview of the performance the microphone, in essence trading sensitivity for
analysis conducted on the prototype ECM-based bandwidth. Figure 2 shows a schematic of the
array constructed for this study. The authors ECM cartridge with the equalizing circuit. The
believe this DA system represents a “small circuit was fabricated using surface mount
scale” version of what can be achieved using devices on a small printed circuit board and
economical microphones. mounted along with the ECM cartridge in a
0.32-inch outside diameter aluminum cylinder
Microphone Construction approximately 2 inches in length. An 84-inch,
four-conductor cable was attached to the rear of
the cylinder via a gold-plated screw connector.
The ECM’s employed for this work were
The other end of the cable terminated in a quick
“hybrid” devices composed of COTS
disconnect coupler which was attached to a
microphone cartridges coupled with passive
power and signal distribution patch panel. A
signal conditioning circuitry and packaged to
total of 38 microphones were fabricated in this
enable easy integration into a DA system. The
fashion, at an average cost per microphone of
details of the packaging are described below.
approximately $40. Figure 3 shows a
representative finished microphone.
ECM Cartridge: Several commercially-available
ECM’s were investigated for use in construction
ECM Calibration
of the prototype array system. After considering
candidate devices, the authors chose to use
Four different types of calibration data were
Panasonic WM-60A ECM cartridges as the
sensing element.* Figure 1a illustrates the obtained – the 250-Hz sensitivity of each
packaged microphone (raw cartridge coupled
construction of the ECM cartridge, which houses
with equalizer), the broadband frequency
a recessed 0.25-inch diaphragm protected by a
response (magnitude and phase) of each
cap containing a central access hole
packaged microphone, the background noise
approximately 0.13 inches in diameter. The
level for a sample of raw ECM cartridges, and
microphone incorporates a field-effect transistor
the total harmonic distortion for a sample of raw
cartridges. The various calibration procedures
__________________
and representative data obtain from them are
* Specific manufacturer’s names are explicitly
described subsequently.
mentioned only to accurately describe the research
performed. The use of manufacturer’s names does
not imply an endorsement by the U.S. Government Sensitivity: Figure 4 shows a histogram of the
nor does it imply that the specified equipment is the 250-Hz sensitivity distribution for the ensemble
best available. of 38 packaged microphones used in this study.
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The sensitivity of each microphone was representative microphones. The magnitude
determined using a calibrated pistonphone response of each device is referenced to its
generating a regulated Sound Pressure Level baseline 250-Hz sensitivity. As can be seen in
(SPL) of 94 dB (relative to a reference pressure the figure, the ensemble of magnitude responses
of 20 µPa). The sensitivity of an individual (with one exception) matched to within ±5 dB at
microphone is defined here as the calibration any one particular frequency while the phase
value (specified in units of mV/Pa) which when responses matched to within ±10 degrees at a
applied to the output of the excited microphone particular frequency over the range of 250 Hz
allows it to indicate an SPL of exactly 94 dB at through 16 kHz. The matching of phases within
250 Hz. As can be seen in Figure 4, the the range shown in Figure 5 implies that a
sensitivities show a partial bimodal distribution directional array populated with these
centered around 6.25 and 7.75 mV/Pa, with a microphones should yield accurate beamformed
6.5 mV/Pa average sensitivity exhibited for the estimates of noise strength without the need for a
entire ensemble of microphones. The decrease phase correction. The limits over which array
in the sensitivity of the packaged microphones phase matching needs to be performed are
versus the raw WM-60A cartridges is due to the discussed at length by Mosher13.
introduction of the equalizing circuitry. Note
that the ensemble distribution is dominated by Broadband Frequency Response – Ultrasonic
variations in the sensitivities of individual raw Spectrum: Magnitude and phase responses for
ECM cartridges only. Given the low-cost of each microphone for frequencies above the audio
these cartridges, if one desires a matched spectrum (16 – 40 kHz) were obtained using a
response among the microphones incorporated substitution method freefield calibration. This
into a DA system, it is a simple matter to calibration method conformed with the
measure the sensitivities of a large sample of International Electrotechnical Commission (IEC)
cartridges and then choose those with similar standard for calibration of microphone
characteristics. However, this step was not equipment.14 Each fabricated electret
performed for this study. Rather, the individual microphone was mounted in an 8-foot by 12-foot
measured sensitivities of the packaged by 6-foot high anechoic chamber directly in line
microphones were accounted for during analysis with a series of 1.0-inch diameter ultrasonic
of all collected data. ceramic transducers, as shown in the sketch in
Figure 6. Each transducer was positioned
Broadband Frequency Response – Audio 74 inches from the microphone. The shortest
Spectrum: The broadband pressure response of microphone to chamber wedge-tip distance was
each packaged microphone covering the audio approximately 24 inches. A custom mounting
frequency spectrum (250 Hz to 16000 Hz) was bracket with attached guide bar, shown in
obtained using a standards-traceable Bruel and Figure 7, allowed correct alignment of each
Kjaer 4226 multifunction calibrator which had microphone in the chamber such that all
been modified to allow access to the transducer diaphragms occupied as closely as possible the
driving signal. A special nylon coupler was same axial location with respect to the source.
fabricated to allow insertion of the microphones Freefield calibration data were obtained at
into the calibrator with minimal acoustic loss. frequencies of 23.176, 29.976, and 39.576 kHz
The calibrator generated a constant SPL of 94 dB by operating each of three different ceramic
and was driven by an external precision signal transducers at its resonant frequency (to
generator operated over the range of 250 Hz – eliminate higher-order source diaphragm
16 kHz in 250-Hz steps. The driving signal from vibration modes). The transducer driving signal
the generator and the microphone output signal and the microphone output signal were recorded
were recorded by a two-channel, PC-based by the same two-channel PC-based transient data
transient data recorder with a per-channel recorder used for the audio spectrum calibration,
sampling rate of 100 ksamples/sec. To obtain at a per-channel sampling rate of
the magnitude and phase response of each 100 ksamples/sec. Upon completion of
microphone, the transfer function between the acquisition of calibration data using the three
driving signal and microphone output were ceramic transducers, the electret microphone was
computed using Welch’s averaged periodogram replaced with a standards-traceable Bruel and
method.12 Kjaer 4136 reference microphone and a repeat
Figure 5 shows the pressure responses set of calibration data was acquired using the
obtained using the calibrator for 10 three transducers. The freefield magnitude and
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phase response of the electret microphone at the was applied when using these devices in a DA
resonant frequency of each transducer was system at frequencies above 20 kHz. Given that
obtained using Welch’s method in a similar only three freefield calibration frequencies were
manner to the audio spectrum calibration. acquired (due to the limited availability of
One challenge encountered during the ceramic transducers at ultrasonic frequencies
freefield calibration process concerned the below 40 kHz), a linear interpolation procedure
determination of the proper corrections to apply was employed to provide the narrowband phase
to the freefield phase response. Such corrections correction at frequencies other than the resonant
were required to account for offsets introduced in ceramic ones.
the line of sight distance between the ceramic
transducer and the microphone when installing Background Noise Measurement: The
different devices in the anechoic chamber, since background noise level of a raw ECM cartridge
the guide bar on the mounting bracket shown in was determined using a vacuum-isolation
Figure 7 provided a necessary, but not sufficient chamber mounted on a vibration-damped table.15
alignment. The preferred method for computing The vacuum-isolation chamber consisted of an
the phase correction was to generate a very short inner chamber maintained at ambient conditions
duration resonant frequency chirp using the into which the cartridge was placed. The inner
ceramic transducer and then measure the time for chamber was then suspended within a vacuum
the sound wave to travel from the source to each chamber to provide a high degree of acoustic
reference or test microphone. Unfortunately, the isolation from the surrounding environment.
ceramic transducers employed for the test did not Figure 9 illustrates the background noise
produce a chirp signature suitable for accurately autospectrum for a typical cartridge for three
determining the transit time. Thus, an alternate different vacuum pressures. As can be seen in
procedure was developed to obtain the phase the figure, classic 1/f noise dominates the
corrections using a high frequency paper-cone response at the lower end of the frequency
tweeter in place of the ceramic transducers. The spectrum. The background noise characteristic
tweeter provided a much cleaner chirp signature exhibited in Figure 9 is typical for electret-type
for determining small transit time variations, and microphones.
care was taken to not move the tweeter when
installing different devices in the mounting Total Harmonic Distortion: The total harmonic
fixture. Using an acquisition sampling rate of distortion (THD) for a series of raw ECM
300 ksamples/sec, sufficient to resolve ≈3 µsec cartridges was determined using an externally
time increments, the distance offset for each of driven Whittaker PC-125 acoustic calibrator
the 38 microphones when installed into the excited at a frequency of 1 kHz for a range of
anechoic chamber was adequately determined sound pressure levels spanning 100 – 140 dB.
via a time series cross covariance analysis. Note The THD for a microphone is defined as the root
that this process assumed that the reinstallation mean square (RMS) value of the total harmonics
of a microphone into the mounting bracket using of a measured calibration signal, divided by the
the guide bar resulted in an additional offset of RMS value of the fundamental plus harmonics of
no more than a few thousandths of an inch, the signal. This can be expressed in percentage
corresponding to sub-microsecond travel time form as
adjustments. As will be seen in the phase data
shown subsequently, this correction procedure P
worked very well in practice. THD= H x100% (1)
P
Figure 8 shows the freefield responses for ten
F
representative packaged microphones obtained
using the procedure described above. The where P and P are defined as
H F
freefield data (converted to pressure response) is
overlaid with the Figure 5 audio spectrum
pressure response data. As can be seen in the P = P2 + P2 +(cid:22)+ P2 (2a)
H 2 3 n
figure, the ultrasonic magnitude responses were
matched to within ±5 dB at a given frequency
while the phase responses were matched to P = P2 + P2 + P2 +(cid:22)+ P2 (2b)
F 1 2 3 n
within ±25 degrees. Since the high frequency
phase response deviation between microphones
greatly exceeded ±10 degrees, a phase correction
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measured over the first n harmonics. It was the “reference LADA”), and (2) fabricated and
determined empirically that the fundamental and packaged electret microphones (hereafter
first three harmonics were sufficient to obtain an referred to as the “ECM LADA”). The reference
accurate estimate of the THD for the ECM LADA microphones were powered by a bank of
cartridges tested. regulated DC supplies, one for each microphone.
Figure 10 shows the THD measured on ten The ECM LADA was powered by a single
representative cartridges. Indicated on the plot is regulated DC power supply, since the current
the average SPL level at which the THD reaches draw from each electret microphone was no
four percent. Sound pressure levels encountered more than 0.3 mA using a supply voltage of
during aeroacoustic testing in ground facilities +5 V and a load resistor of 8.2 kΩ. In all cases
(anechoic chambers, treated wind tunnels, etc.) the output signals from each microphone were
typically do not exceed 120 dB; therefore, the conditioned using high-pass elliptic filters at a
maximum expected THD when using these frequency of 300 Hz. Although not required, the
microphones in a DA application is electret microphone outputs were additionally
approximately 1-2%. amplified by a factor of 10 after filtering.
Directional Array Evaluation System Data Acquisition: The data acquisition system
consisted of a 64-channel transient data recorder
Array Construction: The performance analysis controlled by a PC. All data channels were
objective of testing the packaged electret simultaneously recorded with a 16-bit dynamic
microphones in a prototype DA was facilitated range at a sampling rate of 100 kHz. The analog
by utilizing an existing array mounting system. bandwidth of the system at this sampling rate
For this purpose, the authors chose to utilize the was 40 kHz based on the settings of the
Langley Large Aperture Directional Array anti-aliasing filters. Typical acquisition run
(LADA).16 A photograph of the LADA is shown times ranged from 5 to 10 seconds with the data
in Figure 11. A four-foot diameter fiberglass stored in raw binary format on the PC hard drive.
panel provided a flat surface to flush mount all
microphones. The panel was attached to a pan- Data Reduction: Post processing of acquired
tilt unit secured to a rigid tripod support. This
LADA data began with the computation of an
allowed precise alignment changes in the
M x M cross-spectral matrix for each ensemble
elevation and azimuth of the face of the array.& A of data, where M is the total number of
small laser diode pointer was place at x , microphones in the array. The computation of
c
corresponding to the phase center of the array (in the individual matrix elements was performed
this case the center of the fiber glass panel), to using Fast Fourier Transforms (FFT) of the
aid in array alignment. The LADA incorporated original data ensemble. This was done after
35, 0.32-inch diameter microphone mounting converting the raw data to engineering units. The
holes arranged in a two-dimensional pattern time data were segmented into a series of non-
consisting of logarithmic spirals. This overlapping blocks each containing 4096 sam-
microphone layout, shown in Figure 12, was ples. Using a Hamming window, each of these
based on a design by Underbrink et.al. at Boeing blocks of data was Fourier transformed into the
(see chapter 3 in reference 7). It consisted of frequency domain with a frequency resolution of
five spirals of seven microphones each with the 24.4 Hz. The individual cross spectrum for
inner-most microphones lying on a 1-inch radius microphones i and j was computed via
and the outer-most on a 17-inch radius. This
design resulted in acceptable beamwidth and G (f)= 1 ∑N[X*(f)X (f)] (3a)
minimal sidelobe height over an operational ij NWs k=1 ik jk
frequency range of 2 - 30 kHz. The micr&ophone
mounting coordinates, referenced to x , are
c
listed in Table I. where Ws is the Hamming window weighting
constant, N is the number of blocks of data, and
Array Population: The LADA was populated
X is an FFT data block. The full matrix was
with either of two types of sensors –
formed as
(1) commercial, standards-traceable, 0.25-inch
externally-biased Bruel and Kjaer 4136
condenser microphones (hereafter referred to as
6
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where the superscript T denotes a complex
( )
transpose of the matrix, and Peˆ is a mean-
G G (cid:22) G 
 11 12 1M  squared-pressure quantity. The division by M2
G (cid:23) serves to reference the array output level to an
Gˆ =  22 . (3b) equivalent single microphone output level.
 (cid:25) (cid:23) 
References (16) and (17) provide greater detail
 
 G  concerning additional processing performed on
MM
the LADA data.
The lower triangular elements of this Hermitian ECM LADA Evaluation
matrix were computed by taking the complex
conjugates of the upper triangular elements. All
Test Configuration: The beamforming capability
cross spectral matrix elements were employed in
of the ECM LADA was evaluated in the Langley
subsequent processing, with no modification of
Anechoic Noise Research Facility (ANRF). The
the diagonal terms. Note that for in-flow
ANRF is an anechoic chamber measuring 27.5 ft
applications of the array, the diagonal terms can
x 27.5 ft x 25.6 ft in which static or wind tunnel
be removed to improve the spectral dynamic
testing can be performed. The facility is
range by subtracting off self-noise dominated
primarily employed for engine nacelle noise
auto-spectra during the beamforming process
studies. To assess the capability of the ECM
(see chapter 1 of reference 7). However, this
LADA to identify discrete incoherent noise
additional step was not required for the data
sources, independently controlled speakers were
acquired as part of this study.
installed in the facility. These speakers were
A classical delay and sum beamforming
attached to mounting platforms positioned at
approach was used for the analysis of the array
various locations with respect to the center of the
data. This approach assumed distributions of
array. Figure 13 illustrates one such
monopoles for the measured sources. In delay
configuration where a single source (consisting
and sum beamforming, the array is electronically
of a piezo-electric cone tweeter) was located
“steered” to a series of chosen source locations.
8 feet directly in front of the array. Both pure
For each selected steering location, a steering
tone and white noise signals were recorded by
vector eˆ containing a retarded time phase the array microphones and processed using the
adjustment for each microphone in the array was data analysis procedures described previously.
defined as All calibrations performed on the ECM LADA
were repeated for the reference LADA, using the
& same calibration frequencies, source strengths,
 r & 
 1 exp[j(k ⋅x )] and source locations.
r 1
 c 
eˆ =  (cid:23)  (4) Performance Metrics: Two quantitative metrics
rm exp[j(k&⋅x& )] were used to assess the accuracy of the
r m  beamformed output when using the ECM LADA
 
c to characterize point sources in the ANRF. The
first metric consisted of computation of a
&(cid:2) &(cid:2) weighted RMS error for the beamformed output
where (cid:2)k(cid:2) is the acoustic wave vector, (cid:2)x(cid:2)m is the of the ECM LADA compared with similar
distance vector from the steering location to each output from the reference LADA. Using an
microphone m, ω is the angular frequency, and expression similar to that presented by Arnold,
the ratio (r /r) is included to normalize the et.al.18, the weighted RMS error summed over all
m c
distance related amplitude to that of the phase steering locations measured by the array can be
center of the array. The output power spectrum expressed as
(or response) of the LADA at the steering
location was obtained from
∑K
T (R −T )2
k k k
P(eˆ)= eˆTGˆeˆ (5) εRMS = k=1 K (6)
M2
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American Institute of Aeronautics and Astronautics
where T is the normalized measured response by very similar between the theoretical response,
k
the ECM LADA, R is the normalized measured ECM LADA output, and reference LADA
k
response by the reference LADA, and K is the output. The lower right portion of each figure
total number of measured steering locations. shows a horizontal slice through each contour
The second performance metric consisted of plot (normalized to the reference LADA output)
comparing the beamformed output of the ECM and further illustrates the uniformity of the
LADA with its theoretical response. Assuming a sidelobe structure when comparing the two
simple monopole source, the LADA ideal array arrays.
response can be expressed as Table II lists the weighted RMS errors for
frequencies spanning the range of
W(k,x&,x&o) ≡ ∑M ro ejk[(ro−r)−(rmo−rm)] (7) 3n1or5m Hazli z- e2d0 kHEzC, Mco-m puatnedd usirnegfe reeqnnc.e -(L6A) DfoAr
ro
m=1 m beamform outputs similar to those shown in
Figures 14 - 16. The error values are plotted in
&
where x is an arbitrary Cartesian location in Figure 17. It is clearly seen in this figure that the
weighted RMS errors are higher for very low
space to which the array is electronically steered,
&
beamform frequencies, but approach a
xois the source location, ro and r oare the
& m frequency-invariant average value of 0.0046
distances from the source to x and the mth above 2500 Hz. This is a remarkable result and
c
indicates that for the data obtained using a single
microphone, respectively, and r and r&m are the
point source in the ANRF, the beamform results
distances from the steering location to x and the
c when using the reference and ECM LADA’s are
microphone, respectively. The response shown
extremely consistent above a frequency of
in eqn. (7) is normally expressed in decibels
& 2500 Hz. Interestingly, this frequency also
referenced to the level obtained at xo : corresponds closely with the theoretical low
frequency limit of the array microphone pattern
& & for the LADA.
&  W(k,x,xo) 
dB(x) = 20log  & &  (8)
10W(k,xo,xo) Cold Flow Jet ECM LADA Demonstration
 
Along with the beamforming evaluation using
Eqn. (8) is plotted as a color cont&our map with distributions of point sources, it was also desired
contour level proportional to dB(x), computed to demonstrate the utility of the ECM LADA in a
over the complete ensemble of measured steering real-world application. The authors chose as a
locations. Color contour maps generated using demonstration to apply the array in a series of
eqn. (8) over a range of beamform frequencies simple measurements of source strength and
were compared with their experimental directivity in a cold flow jet operated at high
counterparts to assess the response fidelity of the subsonic exit velocities in the ANRF. Note that
ECM LADA. it is beyond the scope of this paper to present a
detailed study of jet noise using the array.
Sample Results: Figure 14 illustrates the Rather, the goal of the demonstration was to
theoretical and experimental array responses for apply and evaluate the ECM LADA in a rich
the ECM and reference LADA’s measuring the sound field containing broadband noise and high
5-kHz narrowband component of a generated background levels.
white noise source. The tweeter source (shown The jet which was chosen for the
in Figure 13), was located with respect to the demonstration was a 2-inch diameter, Mach 1.0
center of the LADA at (0.0, 0.0, 96.0) inches. contour convergent nozzle which had been
The theoretical response was computed using previously used for measurements of mean
eqns. (7) and (8), while the experimental pressure and farfield acoustics.19 Figure 18
beamformed output of the LADA was obtained shows a photo of the nozzle mounted in the
using eqn. (5). Figures 15 and 16 illustrate ANRF with the ECM LADA shown in the
similar responses for the 10-kHz and 20-kHz background. The majority of the nozzle shown in
narrowband component of the white noise the photo was covered with acoustic foam to
spectrum, respectively. As can be seen in these prevent sound reflections. The jet was operated
figures, the spatial distribution of sidelobes is at high subsonic exit velocities spanning Mach
8
American Institute of Aeronautics and Astronautics
numbers from 0.50 to 0.99 to provide generated Panasonic WM-60A electret cartridge were
noise which was then measured by the array. fabricated for use with the Langley Large
Noise data were acquired at several orientations Aperture Directional Array. The results of the
of the array with respect to the jet exit plane (i.e., investigation revealed a fabricated microphone
various azimuth angles with respect to the jet frequency response suitable for directional array
axis) to obtain a measure of the jet directivity. use, with minimal magnitude and phase response
Figure 19 shows a sample noise location map for variations in the audio frequency spectrum and
a narrowband frequency of 5 kHz obtained with moderate variations at higher frequencies. Also,
the LADA positioned 8 feet from the center of the results using an ECM-populated LADA to
the nozzle, pointing directly at the exit plane measure point source noise in the Langley
(azimuth angle = 90 degrees). ANRF revealed excellent agreement between
One useful characteristic of a DA system reference array data, theoretical array response,
when measuring free jet flow noise is the array’s and the LADA beamformed output. Finally, a
ability to extract from the beamformed data the successful demonstration was conducted using
variation of the axial location of the jet peak the ECM LADA to measure properties of the
source strength as a function of frequency. As noise field generated by a cold flow jet. Thus,
discussed by Lilley20, the axial location data economical COTS electret microphones show
should collapse to single curve when the great promise for array work, especially for
frequency parameter is expressed as the Strouhal lower-frequency applications such as the jet
number noise demonstration presented here. Additional
fD studies similar to this one are planned for COTS
St = j (9) MEMS microphones which have recently
U
become available.
j
where f is the acoustic frequency, D is the jet Acknowledgments
j
diameter, and U is the jet exit velocity.
j
Figure 20 shows the axial location of the jet peak The authors gratefully acknowledge the
source strength as measured by the ECM LADA contributions of Mick Hartzheim of the
for three different jet exit velocities spanning Raytheon Company in the construction of the
Mach numbers from 0.5 to 0.99. Also shown in packaged electret microphones, and of Beverly
the figure are two theoretical curves presented by Anderson of the NASA Langley Aeroacoustics
Lilley in reference 20 which were obtained from and Hypersonics Propulsion Support Section in
calculations based on Lighthill’s acoustic the construction, installation, and operation of
analogy. The lower curve is based on the the cold flow jet.
assumption of a zero initial thickness for the jet
mixing region. The upper curve is based on the References
assumption that the mixing region becomes fully
turbulent a defined distance downstream from 1. Gramann, R.A., and Mocio, J.W.,
the jet exit. These two curves bracket the ECM “Aeroacoustic Measurements in Wind
LADA results, indicating a good ability of the Tunnels Using Adaptive Beamforming
array to extract useful information from the jet Methods”, Journal of the Acoustical Society
noise data. of America, Vol. 97, Number 6, pp. 694-
701, 1995.
Summary
2. Watts, M.E., Mosher, M., and Barnes, M.J.,
Directional array technology will continue to “The Microphone Array Phased Processing
be an integral part of experimental aeroacoustics. System (MAPPS)”, AIAA Paper 96-1714,
However, cost remains a limiting factor in the 2nd AIAA/CEAS Aeroacoustics Conference,
construction of future high-density array systems State College, PA, 1996.
which will be needed to implement advanced
beamforming algorithms. In an effort to reduce 3. Meadows, K.R., Brooks, T.F., Humphreys,
the construction costs of future arrays, the W.M., Jr., Hunter, W.W., Jr., and Gerhold,
authors have undertaken a systematic C.H., “Aeroacoustic Measurements of a
investigation of one class of economical sensing Wing-Flap Configuration”, AIAA Paper 97-
device, the electret condenser microphone. A 1595, 3rd AIAA/CEAS Aeroacoustics
series of customized microphones based on the Conference, Atlanta, GA, 1997.
9
American Institute of Aeronautics and Astronautics