A directional acoustic array using silicon micromachined ...

A directional acoustic array using silicon micromachined piezoresistive microphonesa) David P. Arnoldb) and Toshikazu Nishida Department of Electrical and Computer Engineering, Interdisciplinary Microsystems Group, University of Florida, Gainesville, Florida 32611-6130

Louis N. Cattafesta and Mark Sheplakc) Department of Mechanical and Aerospace Engineering, Interdisciplinary Microsystems Group, University of Florida, Gainesville, Florida 32611-6250

共Received 14 March 2002; revised 26 September 2002; accepted 13 October 2002兲 The need for noise source localization and characterization has driven the development of advanced sound field measurement techniques using microphone arrays. Unfortunately, the cost and complexity of these systems currently limit their widespread use. Directional acoustic arrays are commonly used in wind tunnel studies of aeroacoustic sources and may consist of hundreds of condenser microphones. A microelectromechanical system 共MEMS兲-based directional acoustic array system is presented to demonstrate key technologies to reduce the cost, increase the mobility, and improve the data processing efficiency versus conventional systems. The system uses 16 hybrid-packaged MEMS silicon piezoresistive microphones that are mounted to a printed circuit board. In addition, a high-speed signal processing system was employed to generate the array response in near real time. Dynamic calibrations of the microphone sensor modules indicate an average sensitivity of 831 ␮V/Pa with matched magnitude 共⫾0.6 dB兲 and phase 共⫾1°兲 responses between devices. The array system was characterized in an anechoic chamber using a monopole source as a function of frequency, sound pressure level, and source location. The performance of the MEMS-based array is comparable to conventional array systems and also benefits from significant cost savings. © 2003 Acoustical Society of America. 关DOI: 10.1121/1.1527960兴 PACS numbers: 43.38.Hz, 43.38.Gy 关SLE兴

I. INTRODUCTION

As aircraft noise regulations become more stringent, the need for modeling and measuring aircraft noise becomes more important. In order to design quieter aircraft, the physical mechanisms of noise generation must be understood and any theoretical model or computational simulation must be experimentally validated. One validation method is the comparison of the farfield acoustic pressures. Typically, single microphone measurements of aeroacoustic sources in wind tunnels are hampered by poor signal-to-noise ratios that arise from microphone wind self-noise, tunnel system drive noise, reverberation, and electromagnetic interference.1 In addition, a single microphone cannot distinguish between pressure contributions from different source locations. The need for more precise noise source characterization and localization has driven the development of advanced sound field measurement techniques. In particular, the development and application of directional microphone arrays has been documented as a means to localize and characterize aeroacoustic sources in the presence of high background noise.1–12 a兲

Portions of this work were presented in ‘‘Technology development for directional acoustic arrays,’’ at the 142nd Meeting of the Acoustical Society of America, Ft. Lauderdale, FL, December 2001 and ‘‘MEMS-based acoustic array technology,’’ at the 40th AIAA Aerospace Sciences Meeting & Exhibit, Reno, NV, January 2002. b兲 Now affiliated with School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250. c兲 Electronic mail: [email protected] J. Acoust. Soc. Am. 113 (1), January 2003

Although knowledge of the acoustic farfield does not uniquely define the noise source,13 the qualitative localization of a source and analyses of the spatial and temporal characteristics of its farfield radiation can provide insight into noise generation mechanisms. Modern acoustic arrays used in wind tunnel studies of airframe noise are typically constructed of large numbers 共tens or hundreds兲 of instrumentation grade condenser microphones, and range in aperture size from several inches to several feet.6 –12 Data collection, followed by extensive post-processing, has been used to implement various beamforming processes, including conventional beamforming, array shading, and shear-layer corrections.6 –12 The resulting data files can exceed 500 GB in size and require significant post-processing time per dataset.7 A greater number of microphones in an array can improve its ability to characterize a sound field. In particular, an increase in the number of microphones enhances the signal to noise ratio of an array, defined as the array gain, given 共in dB兲 by 10 log(M), where M is the number of microphones.14 In addition, a large number of microphones may be used to improve the spatial resolution and extend the frequency range of an array. The spatial resolution of an array is inversely related to the product kD, where k⫽ ␻ /c is the acoustic wave number, ␻ is the radian frequency, c is the speed of sound, and D is the aperture size. Thus, a larger aperture may be needed to maintain sufficient spatial resolution at low frequencies. In contrast, the intersensor spacing must be less than one-half of the smallest wavelength of

0001-4966/2003/113(1)/289/10/$19.00

© 2003 Acoustical Society of America

289

interest to avoid spatial aliasing.14 The feasibility of scaling the current technology to multiple arrays with larger numbers 共hundreds or thousands兲 of microphones is limited by the cost per channel 共microphone, amplifier, data acquisition兲, data handling efficiency 共acquisition capabilities, signal processing complexity, storage requirements兲, and array mobility 共size, weight, cabling兲. In addition, experiments performed in large wind tunnels are costly and require extensive setup.15 Therefore, an array system that provides near realtime output in a cost-effective manner would be advantageous. Our goal in this paper is to present the design and initial results of a high-speed, reduced-cost acoustic array system designed for aeroacoustic measurements. To address these scaling issues, MEMS microphones and novel packaging techniques were used to build a compact, modular printed circuit board 共PCB兲 array. Batch-fabricated MEMS microphones offer a substantial cost reduction and the potential for improved amplitude and phase matching relative to the commercial condenser microphones used in conventional acoustic arrays. Implementation of the microphone array on the PCB allows for signal conditioning and amplification to be collocated at the array. It also offers the potential of using on-board digital signal processing 共DSP兲 hardware to execute beamforming algorithms without having to transfer the data to remote processors. However, a separate high-speed data acquisition and signal processing system was used in this study.

II. BACKGROUND

An acoustic array is a collection of spatially distributed microphones used to measure an acoustic field. The signals from each microphone are selectively weighted and phase shifted through a signal processing technique known as beamforming in order to focus the array at a region in space. This provides the array with an electronically steerable, directional response. In this section we review the conventional beamforming equations used to generate the array output. An in-depth treatment of spatial arrays and beamforming theory can be found in Johnson and Dudgeon.14 Consider a collection of M omnidirectional microphones in unbounded free space with the origin of a coordinate system located at the array center. Let xជ m denote the location of the mth microphone and consider a point monopole at position xជ ⬘ as shown in Fig. 1. Let y m (t) denote the continuous time signal detected by the mth microphone. The classical continuous time, ‘‘delay-and-sum’’ beamforming equation is given as a weighted linear sum of time shifted signals, M

z共 t 兲⬅

兺

m⫽1

w m y m 共 t⫺⌬ m 兲 ,

共1兲

where w m is a weighting factor and ⌬ m is a time shift applied to the mth microphone.14 By selecting appropriate delays, the acoustic signals from a chosen finite region in the field are coherently amplified while signals emanating from other areas are attenuated. 290

J. Acoust. Soc. Am., Vol. 113, No. 1, January 2003

FIG. 1. Array configuration depicting a point monopole source and an array of five microphones.

Assuming an ideal point monopole source at an arbitrary array focus location, xជ , the time shift and weight for the mth microphone are ⌬ m⫽

r⫺r m c

共2兲

w m⫽

rm , r

共3兲

and

where r and r m are the radial distances from the focus location to the array center and the mth microphone, respectively. The time shift synchronizes each of the measured signals to the signal at the array center. The weight is assigned to compensate for the geometric attenuation of spherically spreading waves. Modification of these coefficients is the basis of more advanced beamforming techniques such as shading and shear layer corrections.7 If the focus location coincides with the actual location of the source, the signals from the microphones are coherently summed and the beamformer output is maximized. This beamforming process is premised on the assumption that ideal pressure measurements are made in the farfield of a distribution of compact, spatially distinct, mutually independent point monopoles. The presence of coherent, closely spaced, or continuously distributed sources, as well as higher order dipoles or quadrupoles, all limit the accuracy of the array measurement.16 Thus, the results obtained from an acoustic array must be interpreted within the assumptions made of the sources, which are not usually known a priori. Additionally, the measurement of the farfield does not uniquely define the source.13 For these reasons, array measurements can only be considered qualitative with regards to source characterization. Frequency-domain beamforming offers several benefits over time–domain methods. These include techniques for reducing side lobes and narrowing the main lobe in the array pattern, as well as reducing noise and reflection effects.5 Using standard Fourier transform pairs, the beamforming expression from Eq. 共1兲 can be transformed into the frequency domain, Arnold et al.: Directional acoustic array using silicon microphones

M

Z共 ␻ 兲⫽

兺 w mY m共 ␻ 兲 e ⫺ j ␻⌬ m⫽1

m

共4兲

,

where Y m ( ␻ ) and Z( ␻ ) are the Fourier transforms of y m (t) and z(t), respectively. Equations 共2兲 and 共3兲 still hold, but ⌬ m now represents a phase shift. A data acquisition system is used to discretely sample data from the microphones at a fixed sampling frequency, f s . The time record for each channel, denoted y m 关 n 兴 , is divided into L blocks, each block consisting of N points, and an N-point fast Fourier transform17 共FFT兲 is applied to each block of data. Equation 共4兲 can be rewritten to define the discrete frequency–domain array response at the kth frequency bin as

G i j k ⫽E 关 Y i k Y *j 兴 ,

共11兲

k

where 共•兲* denotes the complex conjugate. The M ⫻M cross-spectral matrix contains the relative magnitude and phase relations between all pairs of microphones and therefore captures all of the information needed to compute the signal location.14 For stationary data, averaging is used to reduce random noise in the measurements.17 Averaging the cross-spectral matrix yields a robust measurement because the relative phase information between microphones is assumed to be precisely known.14 An estimate for the expected value of the cross spectral matrix is given as an average over L blocks of data,

M

Z k⫽

兺

m⫽1

w mY mke ⫺ j ␻k⌬m,

共5兲

where Y mk represents the kth FFT coefficient of the mth channel and ␻ k ⫽k2 ␲ f s /N is the corresponding radian frequency. This can be expressed in matrix form as Z k ⫽eH k Yk ,

共6兲

where (•) H denotes the Hermitian transpose. The steering vector, ek , contains the weights and phase shifts to be applied to the system and is given by

冋

册

w 1e j ␻k⌬1 ] . ek ⫽ w M e j ␻k⌬ M

共7兲

The term Yk contains the kth FFT coefficients for all M channels,

冋册 Y 1k

Yk ⫽

] . Y Mk

共8兲

The N discrete terms of Z represent the discrete frequency spectrum of the beamformer output. If desired, an inverse Fourier transform could be used to convert back to a time– domain representation. More commonly, the array power response is used, representing a time-averaged power spectrum.14 The array power response at the kth frequency bin is given by H P k ⫽eH k E 关 Yk Yk 兴 ek ,

共9兲

where E 关 • 兴 denotes the expected value. The term P k is a real-valued scalar having units of power (Pa2 ). The inner term,

Rk ⬅E 关 Yk YH k 兴⫽

冋

G 11k

G 12k

G 21k

G 22k

] G M 1k

¯

G 1M k ]

¯

GMMk

册

兺

,

共10兲

共12兲

and thus the estimated array power response is given by ˆ Pˆ k ⫽eH k Rk ek .

共13兲

If desired, a corresponding value known as the array pressure response 共having units of Pa兲 can be computed by taking the square root of the array power response. From Eqs. 共12兲 and 共13兲, it is noted that the timeaveraged cross-spectral matrix needs only to be computed once; only the steering vector changes in the computation of the array response at various focus locations. This leads to a computational efficiency when the array response is desired over a region of space, as is the case for spatial mapping applications. In addition, since the cross-spectral matrix contains all of the relevant field information, it can be saved rather than the raw time signals if the spectral analysis parameters 共block size, number of averages, etc.兲 are fixed. This can offer significant reductions in the data storage requirements. In the same manner that linear time-invariant systems are characterized by examining the frequency response, the array pattern corresponds to the wave number–frequency response of a spatiotemporal filter.14 Physically, it represents the array response to an acoustic point source in the same way that the impulse response function represents the response of a linear system to an impulse function. The array pattern is a function of frequency, array focus location, and actual source location, and is given by14 M

W 共 ␻ ,xជ ,xជ ⬘ 兲 ⫽

is known as the spatial correlation matrix or cross-spectral matrix and forms the basis of more advanced beamforming algorithms.14 Each term in the matrix represents a complex valued cross-spectral coefficient given by J. Acoust. Soc. Am., Vol. 113, No. 1, January 2003

L

ˆ ⫽1 R Y YH , k L l⫽1 kl kl

兺 m⫽1

再冋

⬘ ⫺r m 兲共 r ⬘ ⫺r 兲 ⫺ 共 r m rm r⬘ exp j ␻ r rm c ⬘

册冎

. 共14兲

The focus location, xជ , determines r and r m , the radial distances from the focus location to the array center and mth microphone, respectively. The source location, xជ ⬘ , deter⬘ , the radial distances from the source to the mines r ⬘ and r m array center and mth microphone, respectively. The array pattern is generally plotted at a particular frequency for a fixed source location. Arnold et al.: Directional acoustic array using silicon microphones

291

FIG. 2. Circuit schematic of hybrid package. R 0 ⬇600 ⍀, R⫽147 k⍀, C ⫽0.68 ␮ F, G⫽500, V b ⫽3 V, V s ⫽⫾10 V.

III. ARRAY SYSTEM DESIGN AND CONSTRUCTION

The design and fabrication of the MEMS-based array system are presented in this section. Details of the construction of the hybrid package and printed circuit board array are included. This is followed by a discussion of the data acquisition and signal processing system used to generate the array pressure response. Full details of the array system are reported by Arnold.18 A. Hybrid microphone-amplifier packages

The hybrid microphone-amplifier package combines a micromachined piezoresistive silicon microphone19 and an Analog Devices AD624 low-noise differential amplifier20 into a 16-pin, 1.5 cm diameter TO-8 semiconductor package. The differential outputs of the microphone Wheatstone bridge are AC-coupled to the inputs of the amplifier via two resistor-capacitor 共RC兲 pairs, as shown in Fig. 2, with a corner frequency given by f c ⫽1/(2 ␲ RC)⫽1.6 Hz. This hybrid package provides a small, self-contained microphone module with an amplified, low-impedance output. The sensor packages are fitted into sockets on a printed circuit board array, permitting external calibration and interchangeability.

FIG. 3. Diagram of the hybrid microphone-amplifier packaging scheme. 292


FIG. 4. Plot of array layout 共inches兲.

The construction of the hybrid package consists of four layers, as shown in Fig. 3: the package body or ‘‘header,’’ a silicon substrate, the component layer, and a protective lid. A TO-8 package serves as the primary structural element. A silicon substrate is bonded to the header using conductive silver epoxy. The substrate, passivated with silicon dioxide, provides metal bond pads and interconnecting traces for the devices. The components are bonded to the exposed bond pads of the silicon substrate using conductive silver epoxy. Gold wire bonds are used to make additional electrical connections between the chip bond pads and package pins. A slotted lid provides protection against physical damage while permitting acoustic waves to pass. The TO-8 header and lid are connected to the circuit ground for additional electromagnetic shielding.

B. Printed circuit board array

The performance of an array 共spatial selectivity, influence of sidelobes, array gain, etc.兲 is directly influenced by the quantity and geometry of the sensors. Our goal in the research was to validate the concept of a MEMS-based array, not to optimize a particular array geometry. Thus, a layout similar to Cluster 3 in NASA’s small aperture directional array 共SADA兲7 was selected, allowing for a comparison to previously published results. The configuration is identical with the exception that the center microphone has been omitted due to the limitation of 16 channels in the data acquisition system used for testing. As shown in Fig. 4, the planar layout consists of four concentric rings with radii 1.80, 1.94, 3.60, and 3.89 in., each having four microphones. The array is constructed from a double-sided copper clad PCB that serves as the electrical interface and mechanical structure. The top surface of the PCB contains the 16 microphone packages and a laser diode to permit accurate aiming of the array. The bottom surface contains small 共SMB-type兲 connectors for the coaxial cabling. Four layers of Garolite are milled and throughbolted to the circuit board array to provide additional rigidity, as shown in Fig. 5. The theoretical array patterns, obtained using Eq. 共14兲, are shown in Figs. 6 – 8 at 2, 6, and 10 kHz for a 48 in.⫻48 in. scan plane that is parallel to the array face and centered on the z axis for a source at a distance of 36 in. These plots indicate Arnold et al.: Directional acoustic array using silicon microphones

FIG. 5. Diagram of array construction depicting circuit board array and Garolite stiffening layers.

the spatial selectivity of the array, illustrating a narrowing primary lobe 共improved spatial resolution兲 and increasing side lobes with increasing frequency. C. Signal processing

The signal processing consists of continuously sampling data from the array, computing the fast Fourier transform 共FFT兲 on blocks of data, and using conventional frequency– domain beamforming methods as outlined in Sec. II to obtain the array pressure response over a scanned region in space. An Agilent E1432A VXI-based digitizer is used to acquire the signals from the array. The digitizer is interfaced to a host computer 共866 MHz Pentium III, 256 MB RAM兲 via a National Instruments MXI-2 interface bus. The host controls

FIG. 7. Theoretical array pattern and contour plot 共0.5, 1, 3, 6, and 9 dB兲 at 6 kHz for 48 in.⫻48 in. scan plane at 36 in.


the operation of the digitizer, runs the beamforming algorithms, and displays and saves the results using MATLAB v.6.0. In operation, the digitizer samples all 16 channels with 16-bit resolution at a sampling rate of 25.6 kHz. The Agilent E1432A provides the capability to perform real-time fast Fourier transforms 共FFTs兲 on the incoming data, significantly reducing the computational load on the host computer. A Hanning window is used in computing 1024-point FFTs, yielding a frequency resolution of 25 Hz. The digitizer internally compensates for the power lost in the windowing operation by scaling the output by the Hanning window weighting factor of 冑8/3. 17 Typically, 400 nonoverlapping blocks are used, corresponding to 16 s of time data. The cross-spectral matrices for all 512 bin frequencies are computed in real time for each successive block of FFT data that is transferred to the PC host. The time-averaged cross-spectral matrices are obtained by Eq. 共12兲 and the data is converted to units of pressure squared (Pa2 ) by dividing by the square of the microphone sensitivity. The array power response is obtained using Eqs. 共2兲, 共3兲, 共7兲, and 共13兲 and then dividing by the number of microphones squared (M 2 ) to normalize the array output to that of a single microphone. The pressure response is given by the square root of this result. For most of the measurements made in calibrating the array, a 48 in.⫻48 in. grid of regularly spaced 共1 in. increments兲 focal locations are used in a scan plane parallel to the array face at a distance of 36 in. along the z axis. The computation time required to obtain the pressure response over the scan plane for a single frequency bin is under 4 s. If


Arnold et al.: Directional acoustic array using silicon microphones

293

FIG. 9. Magnitude and phase response of 16 hybrid packages at ⬃110 dB.


needed, the power responses from multiple bins can be summed to obtain the power over a wider frequency bin 共e.g., octave analysis兲. The required computation time is increased by approximately 4 s for each additional frequency bin included in the power response analysis. The timeaveraged cross-spectral matrices for all 512 frequency bins are stored to disk, resulting in a file size of 2 MB.

IV. EXPERIMENTAL RESULTS

The experimental methodologies and results for calibrations of the hybrid package and array system are discussed in this section. The frequency responses of the hybrid microphone packages are obtained using a plane wave tube 共PWT兲 acoustic calibrator. The characterization of the array system is performed using an acoustic point source in the University of Florida’s Anechoic Aeroacoustic Test Facility. A. Hybrid package characterization

Each hybrid microphone package is tested individually for amplitude and phase using a 2.54 cm⫻2.54 cm square cross section, normal incidence PWT designed to support plane waves up to 6.7 kHz.18,19 The microphone package and a 1/8 in. Bru¨el and Kjær 共B&K兲 4138 reference microphone are flush mounted at the terminating end of the tube and subjected to normally incident plane waves. The frequency response of the hybrid package is determined with respect to the B&K microphone. 294


The measured responses of the 16 hybrid packages are shown in Fig. 9 over the frequency range of 1– 6.5 kHz at sound pressure levels of approximately 110 dB 共Ref. 20 ␮Pa兲. The average sensitivity of each hybrid package is seen to vary from 780 to 855 ␮V/Pa with a mean of 831 ␮V/Pa over the range tested. A linear trend is noted in the phase response, which could be a phase variation, but may be attributed to a mounting misalignment in the PWT calibration.19 An offset in the axial location of the reference and test microphones will result in a linear bias in the phase measurement. An offset of only 1 mm would result in a phase bias error of 6.25° at 6 kHz. Although the PWT is limited to a maximum frequency of 6.7 kHz, the microphones have demonstrated a flat response to 20 kHz and possess a predicted resonant frequency of 131 kHz.19 For the purposes of array signal processing, as can be seen from Eqs. 共2兲 and 共3兲, matching of the magnitudes and phases between sensor packages is important to minimize uncertainty. The frequency response data are reformatted and shown in Fig. 10 as a relative sensitivity and phase with respect to microphone number one. The magnitude responses of all microphones are shown to match within ⫾0.6 dB, and the phase responses are matched within ⫾1° over the frequency range tested. Mosher et al.21 states that phase matching within ⫾10° is sufficient for obtaining reasonable results without the need for phase corrections. Therefore, the hybrid microphone packages are considered acceptable for use in the array and all the presented data are from uncorrected, raw measurements. B. Array characterization

A method for extensively characterizing an acoustic array has been reported by Mosher et al.21 However, for this Arnold et al.: Directional acoustic array using silicon microphones

FIG. 10. Relative magnitude and phase of 16 hybrid packages with respect to microphone number one.

paper, only a preliminary characterization was performed in order to verify proper operation of the MEMS-based system. The array response to an acoustic point source was measured in an anechoic chamber, having a 100 Hz cutoff frequency, as a function of source frequency, source amplitude, and source location. Each measured response was compared to the theoretical response 共array pattern兲 given by Eq. 共14兲. The acoustic point source consists of a JBL 2426Jcompression driver mated to a 53 cm long, 1.9 cm diameter metal pipe. The pressure field generated by the device is modeled as a piston at the end of a pipe and performs suitably as a point monopole for frequencies below 11.5 kHz.18 Several metrics were used to quantify the differences between the measured and theoretical responses. For this analysis, the measured array response is normalized by its peak value for a direct comparison to the normalized array pattern. The first metric is a comparison of the beamwidths of the mainlobe at 0.5, 1, 3, 6, and 9 dB down from the peak values.7 Because the main lobe does not have perfect cylindrical symmetry, an equivalent beamwidth is used. It is obtained by computing the diameter of a circle having the same area as enclosed by the respective contour curve. The second metric is to compute a weighted root mean squared 共rms兲 error for the measured response. It provides an estimate of the total relative error over J scan locations and is expressed as weightedគerrorrms⫽

冑

兺 Jj⫽1 M j 共 T j ⫺M j 兲 2

J

,

共15兲

where T j and M j represent the normalized theoretical and measured responses at the jth scan location, respectively. The J. Acoust. Soc. Am., Vol. 113, No. 1, January 2003

FIG. 11. Measured array pressure response and contour plot 共0.5, 1, 3, 6, and 9 dB兲 at 2 kHz and ⬃100 dB for a 48 in.⫻48 in. scan plane at 36 in.

error is weighted by the measured response M j to account for the relative effect the errors would have in the total measured response. A third metric is a comparison of the location of the measured peak response to the actual source location. 1. Array response versus frequency

The array response was first examined as a function of frequency for a point source positioned at a distance of 36 in. on the z axis of the array. Discrete tones were used to achieve an average sound pressure level of approximately 100 dB at the array microphones. The measured array pressure responses are shown at 2, 6, and 10 kHz in Figs. 11–13. These measured responses closely match the corresponding theoretical array patterns, shown in Figs. 6 – 8. The equivalent 3 dB main lobe beamwidth is shown in Fig. 14 for frequencies from 1 to 10 kHz. This data is representative of the results obtained for the equivalent 0.5, 1, 6, and 9 dB beamwidths. The measured beamwidths are shown to closely match the theoretical values for frequencies of 3 kHz and higher. Due to the relatively small aperture size, errors are expected at the lower frequencies. Verification of the main lobe beamwidth is important from a spatial resolution standpoint, but it does not validate the total response, particularly the effect of side lobes. A measure of the total error is given by the weighted rms errors as shown in Fig. 15. It is important to note that unlike the theoretical response, the acoustic array interacts with the incident sound field, resulting in scattering. Thus, the measured response includes these scattering effects, which are unaccounted for Arnold et al.: Directional acoustic array using silicon microphones

295



in the theoretical response. The error remains below 5% up to 8 kHz before increasing to a maximum of 9% at 10 kHz. One possible explanation is that diffraction effects from the microphone package may become important at higher frequencies. If the package is crudely modeled as the end of a rigid cylinder, it is known that diffraction effects become significant for values of kd larger than 2, where k is the acoustic wave number and d is the radius of the cylinder.13 It is noted that for the 1.5 cm package, kd⫽2 at approximately 7.2 kHz.

Figure 16 shows the average microphone pressure and the peak array pressure versus the free-field pressure measured by the single B&K microphone. For a strong, tonal point source, the free-field pressure, the average microphone pressure, and the peak array pressure should all be equal. At higher sound pressure levels, the average microphone pressure and peak array pressure converge to within 1 dB, but there is an offset of approximately 5 dB between these values and the free-field value. A 3 dB increase could be explained as a pressure doubling due to a sound hard boundary condition at the face of the array. The additional amplification may be due to diffraction effects. Regardless of the absolute levels, the lower end of the curve illustrates the existence of the array gain. As the incident sound pressure level decreases, the average microphone response asymptotes to 69.1 dB

2. Array response versus sound pressure

One benefit of an acoustic array is its improvement in the signal to noise ratio of the measured signal, referred to as the array gain. The use of multiple microphones enables the measurement of source signals that are below the noise floor of any one particular microphone. Thus, an important characteristic of an array is its performance as a function of incident sound pressure, or equivalently the signal-to-noise ratio of the microphones. For this experiment, the point source is fixed along the z axis of the array at a distance of 36 in. and the array response to a 6 kHz tone is measured at various sound pressure levels. As a reference, the array was removed and a single B&K 4138 microphone was used to measure the free-field sound pressure level at the location of the array origin for several sinusoidal voltage amplitudes supplied to the speaker. The array was then reinstalled and the responses were measured using the calibrated speaker voltage inputs. 296


FIG. 14. Theoretical and measured 3 dB beamwidths as a function of frequency at ⬃100 dB for source at 36 in. Arnold et al.: Directional acoustic array using silicon microphones

FIG. 15. Weighted rms error as a function of frequency at ⬃100 dB for a 48 in.⫻48 in. scan plane at 36 in.

while the peak array response asymptotes to 57.5 dB. Thus, the array can effectively detect a source that is 11.6 dB below the noise floor of the individual microphones. The asymptotic values represent the minimum detectable signals for a 25 Hz bin at 6 kHz. The estimated noise floors for a 1 Hz bin at 6 kHz are 55.1 dB for the hybrid packages and 43.5 dB for the array. The microphones possess a linear response to sound pressure levels of at least 160 dB.19

FIG. 17. Absolute spatial error 共in inches兲 in the peak response of the array at 6 kHz and ⬃100 dB.

ment was ⫾0.25 in. Thus, the performance at 6 kHz appears to be independent of the source location. V. CONCLUSIONS AND FUTURE WORK

Perhaps the most useful aspect of a directional array is its capability for source localization. As a one-dimensional verification, a 6 kHz source at a distance of 36 in. is translated in the x direction in 3 in. increments to a distance of 24 in., and the performance of the array was examined. Ideally, the array response should be calibrated over a broad range of locations in space.21 Figure 17 shows the weighted rms error for the array response as a function of the x location. The error remains constant at approximately 2.5% over the range tested. Of greater importance is the ability of the array to accurately locate a source in space. Figure 18 shows the absolute spatial error of the peak array response plotted vs the x location of the source. It should be noted that a finer mesh, using a grid of 0.1 in. in the array response, was used to obtain the measures of spatial error. The error is seen to randomly fluctuate as a function of position, with a mean value of 0.3 in. These values are reasonable considering the accuracy in distance measurements in setting up the experi-

A directional acoustic array has been developed using a MEMS piezoresistive microphone, a hybrid sensor packaging scheme, printed circuit board construction technique, and a VXI-based signal processing system to produce a highspeed, cost-effective, modular, array measurement system. In addition to reducing the cost, the use of a printed circuit board as the array structure allows for the potential integration of the signal conditioning, data acquisition, and/or signal processing hardware. The estimated total cost of the 16channel array, excluding labor and the cost of the data acquisition and signal processing system, is significantly less than a conventional array. The hybrid packages can be interchanged between low-cost printed circuit boards of various geometries, further reducing the costs. The use of high-speed data acquisition and digital signal processors has enabled near real-time computation of the time-averaged crossspectral matrices. This provides the user with almost instant access to array response results and eliminates the need to save large amounts of time-series data. The resulting time savings can reduce the experimental costs, particularly for large wind tunnel studies. The results from calibrations of the hybrid package and array verify the functionality of the system. From plane wave tube calibrations, the hybrid microphone packages show an average sensitivity of 831 ␮V/Pa with matched magnitude 共⫾0.6 dB兲 and phase 共⫾1°兲 responses. From tests conducted

FIG. 16. Average array microphone pressure and peak array response pressure versus free-field pressure at 6 kHz.

FIG. 18. Weighted rms error at 6 kHz and ⬃100 dB as a function of the source x location.

3. Array response versus location



297

in an anechoic chamber, the array shows accurate source localization capabilities of ⫾0.3 in. It has a minimum detectable signal of 47.8 dB for a 1 Hz bin at 6 kHz and a maximum input of 160 dB. For the small-aperture array presented, the usable frequency range is limited to 3– 8 kHz. A larger number of sensors can broaden the frequency range by increasing the overall array size while maintaining small intersensor spacings. The array noise floor was experimentally verified to be 11.6 dB below the noise floor of the individual microphones, as predicted by the theoretical array gain. For this array system, an extensive calibration is needed to quantify the response over a larger parameter space. The calibration should include in situ calibrations of the microphones and a complete analysis of the directivity and accuracy of the array over a broad frequency range.21 An analysis of the scattering effects could provide insight for improvements in accuracy. Additional efforts are aimed at reducing the size and increasing the physical robustness of the hybrid packages, improving the construction techniques used for the array, and integrating the signal conditioning and amplification circuitry at the array. The integration of DSP hardware with the PCB microphone array is currently being undertaken to further increase the system performance. ACKNOWLEDGMENTS

Financial support for this work is provided by a NASA– Langley Research Center Grant #NAG-1-2133, monitored by Dr. William H. Humphreys, Jr. Integration of the DSP hardware with the microphone array for real-time monitoring is supported by National Science Foundation 共NSF兲 Grant No. ECS-0097636. Also, David P. Arnold is supported by a National Science Foundation Graduate Research Fellowship. The authors would also like to thank Dr. Mark Allen at the Georgia Institute of Technology for support in the fabrication of the silicon substrates used in the hybrid package. Appreciation is also extended to David Martin and Dr. Jian Li at the University of Florida. 1

P. T. Soderman and S. C. Noble, ‘‘Directional microphone array for acoustic studies of wind tunnel models,’’ J. Aircr. 12, 168 –173 共1975兲. 2 J. Billingsley and R. Kinns, ‘‘The acoustic telescope,’’ J. Sound Vib. 48, 485–510 共1976兲.

298


3

T. F. Brooks, M. A. Marcolini, and D. S. Pope, ‘‘A directional array approach for the measurement of rotor noise source distributions with controlled spatial resolution,’’ J. Sound Vib. 112, 192–197 共1987兲. 4 J. R. Underbrink and R. P. Dougherty, ‘‘Array design for non-intrusive measurement of noise sources,’’ Noise-Con 96 Proceedings, Seattle, Washington, September 1996, pp. 757–762. 5 M. Mosher, ‘‘Phased arrays for aeroacoustic testing: theoretical development,’’ 2nd AIAA/CEAS Aeroacoustics Conference, AIAA Paper 96-1713, State College, PA, May 1996. 6 M. E. Watts, M. Mosher, and M. Barnes, ‘‘The microphone array phased processing system 共MAPPS兲,’’ in Ref. 5, AIAA Paper 96-1714, May 1996. 7 W. H. Humphreys, T. F. Brooks, W. W. Hunter, and K. R. Meadows, ‘‘Design and use of microphone directional arrays for aeroacoustic measurements,’’ 36th Aerospace Sciences Meeting & Exhibit, Reno, NV, AIAA Paper 98-0471, January 1998. 8 W. H. Herkes and W. H. Stoker, ‘‘Wind tunnel measurements of airframe noise of a high-speed civil transport,’’ in Ref. 7, AIAA Paper 98-0472. 9 R. W. Stoker and R. Sen, ‘‘An experimental investigation of airframe noise using a model-scale Boeing 777,’’ 39th AIAA Aerospace Sciences Meeting & Exhibit, Reno, NV, AIAA Paper 2001-0987, January 2001. 10 J. F. Piet and G. Elias, ‘‘Airframe noise source localization using a microphone array,’’ 3rd AIAA/CEAS Aeroacoustics Conference, Atlanta, GA, AIAA Paper 97-1643, May 1997. 11 R. Davy and H. Remy, ‘‘Aiframe noise characteristics of a 1/11 scale Airbus model,’’ 4th AIAA/CEAS Aeroacoustics Conference, Toulouse, France, AIAA Paper 98-2335, June 1998. 12 P. Sijtsma and H. Holthusen, ‘‘Source location by phased array measurements in closed wind tunnel test sections,’’ 5th AIAA/CEAS Aeroacoustics Conference, Bellevue, WA, AIAA Paper 99-1814, May 1999. 13 A. P. Dowling and J. E. Ffowcs Williams, Sound and Sources of Sound 共Ellis Horwood Limited, Chichester, England, 1983兲, Chap. 7. 14 D. H. Johnson and D. E. Dudgeon, Array Signal Processing 共Prentice– Hall, Englewood Cliffs, NJ, 1993兲, Chaps. 1– 4. 15 J. Kegelman, ‘‘Accelerating ground-test cycle time: the six-minute model change and other visions for the 21st century,’’ in Ref. 7, AIAA Paper 98-0142. 16 T. F. Brooks and W. M. Humphreys, ‘‘Effect of directional array size on the measurement of airframe noise components,’’ in Ref. 12, AIAA Paper 99-1958. 17 J. S. Bendat and A. G. Piersol, Random Data Analysis and Measurement Procedures, 3rd ed. 共Wiley, New York, 2000兲, Chaps. 1, 11. 18 D. P. Arnold, ‘‘A MEMS-based directional acoustic array for aeroacoustic measurements,’’ Master’s thesis, University of Florida, Gainesville, FL, 2001. 19 D. P. Arnold, S. Bhardwaj, S. Gururaj, T. Nishida, and M. Sheplak, ‘‘A piezoresistive microphone for aeroacoustic measurements,’’ Proceedings of ASME IMECE 2001, New York, NY, November 2001. 20 ‘‘AD624 precision instrumentation amplifier,’’ Product Data Sheet, Rev. C, Analog Devices, May 2001. 21 M. Mosher, M. E. Watts, S. M. Jaeger, and S. Jovic, ‘‘Calibration of microphone arrays for phased array processing,’’ in Ref. 10, AIAA Paper 97-1678.
