Precision method for phase match of microphones

Precision method for phase match of microphones George S. K. Wong Institute for National Measurement Standards, National Research Council Canada, Ottawa, Ontario K1A OR6, Canada

(Received 21 January 1991; accepted for publication 28 May 1991 )

This paper describes a precision method for phase match of microphones. The coupler method consists of an acoustical driver that excites two test microphones simultaneously in a small cavity. The phase response contribution of the associated preamplifiers and amplifiers is eliminated with an interchange procedure, which enables the relative phase of a pair of microphones to be assessed accurately. The uncertainty of the method is dependent upon the uncertainty of the phase meter or phase measuring system. Over a frequency range from 63 Hz to 2 kHz and with a commercial phase meter that has an uncertainty of ñ 0.02 deg, the uncertainty of this coupler method for phase comparison is approximately ñ 0.05 deg. The coupler is useful over a frequency range from 10 Hz to 6.3 kHz.

PACS numbers: 43.88.Kb, 43.85.Mt, 43.85.Fm

INTRODUCTION

With the advent of a sound intensity measurement that requires the precise phase match of two microphones, it is necessary to develop a reliable and precise method for the assessment of the phase response of these microphones. It has been shown1'2 that an error of 6 dB can be expected in sound intensity measurements at a relatively low frequency of 63 Hz for a microphone spacing of 6 mm if the phase mismatch between the microphones were to be 0.3 ø. For national laboratories, a direct method is preferred. There are less time consuming signal processing techniques 3 with various uncertainties and various computational algorithms that are capable of measuring the phase response of microphones. However, for high-precision measurement, it is relatively difficult for national laboratories to verify or to sub- stantiate the uncertainty of phase measuring techniques that involve inaccessible computational algorithms such as those in many fast-Fourier-transform (FFT) analyzers. One of the requirements in phase response measurements of microphones is to separate the phase response of the microphones from that of the associated electronic systems, such as amplifiers, filters, and analyzers. In general, phase match of con- denser microphones can be implemented without sophisti- cated instrumentation. When it is necessary to measure the phase response very accurately, e.g., with an uncertainty of a small fraction of a degree, or to ascertain the small phase differences between a pair of microphones, the measurement method requires special attention; and to date, standards for measuring the phase response of microphones are still under development?

The theory 5 on precision phase match of microphones with a coupler is presented here together with experimental data. The uncertainty of the method apparently depends mainly on the uncertainty of the phase measuring instrument, and theoretically one may achieve an uncertainty of less than 0.01 deg with the interchange reference method 6 for the absolute phase measurement of sinusoidal signals.

I. THEORY

The theory for phase match of microphones with a coupler is very similar to the frequency response comparison method with the three-port two-microphone cavity 7 that requires the exchange of microphones with respect to the measuring channels and coupler ports. The measurement procedure is described as follows.

The schematic diagram of the measuring arrangement is shown in Fig. 1. The phase difference between the two channels is

(I)12 = ((I) 1 -•- (I)pl -•- (I)ml) -- ((I) 2 -•- (I)p2 -•- (I)m2), (1) where (I) 1 and •2 are the phases of microphones 1 and 2, respectively, (I)pl and •p2 are the phases of preamplifiers 1 and 2, respectively, (I)ml and (I)m2 are the phases of measuring amplifiers 1 and 2, respectively, and V1 and V2 are the output signals from the two channels.

When microphones 1 and 2 are exchanged, such that microphone 1 is with channel 2 and is inserted into port B, and microphone 2 is with channel 1 and is inserted into port A, and repeating the measurement,

AMPLIFIER (I)

•ml

-•..V I

• •• m2 •V2 AMPLIFIER (2)

FIG. 1. Schematic arrangement of the coupler method.

1253 J. Acoust. Soc. Am. 90 (3), September 1991 0001-4966/91/091253-03500.80 1253

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(I)21 = ((I) 2 -•- (I)pl -•- (I)ml) -- ((I) 1 -•- (I)p2 -•- (I)m2). (2) The phase difference of the microphones is obtained

from Eq. ( 1 ) minus Eq. (2):

(I) 1 -- (I) 2 = ((I)12 -- (I)21)/2. (3)

The phase difference of the measuring system is obtained by adding Eqs. ( 1 ) and (2):

((I)pl -[- (I)ml) -- ((I)p2 '•- (I)m2) = ((I)12 '•- (I)21)/2. (4) From Eqs. (3) and (4), the phase difference between

the microphones and the phase difference between the instruments, such as preamplifiers and amplifiers, of the two channels can be deduced. For experimental verification of the above theory, the instrument phase difference between the two channels can be measured with conventional electri-

cal methods, and the results can then be compared with those obtained with the above coupler method.

II. EXPERIMENTAL RESULTS

The arrangement of the coupler is shown in Fig. 2. The microphones and the preamplifiers were inserted into adapt- ors and were mounted face to face in the coupler. The spacing between the protective grids of the microphones was 7.5 mm. The driver unit (Beyer DT880) was connected to the coupler by a tube (3 mm internal diameter, 117 mm long) that provides an approximate plane-wave excitation to the coupler. Two preamplifiers (Briiel and Kjaer 2639) and two measuring amplifiers (Briiel and Kjaer 2636) each with one- third octave filters (Briiel and Kjaer 1617) constituted the instrumentation channels for electrical phase difference assessment.

ADAPTOR FOR MICROPHONE PREAMPLIFIER

DRIVER UNIT

FIG. 2. General arrangement of the coupler for phase match of microphones.

The phase difference between the two channels, without the microphones, can be measured very precisely by a direct electrical method, using a common sinusoidal signal applied to both channels simultaneously. In our case, the phase difference between the microphones was measured with a precision phase meter (Krohn-Hite model 6620). The signal source for the experiment was a Krohn-Hite type 4025A oscillator. The amplitude of the sinusoidal signal from the oscillator was adjusted for full-scale output from the measuring amplifiers.

A. Measurement procedure

With the coupler, two Briiel and Kjaer type 4133 (half- inch) microphones were measured according to the procedure given in Eqs. ( 1 )-(4), at one-third octave frequencies from 10 Hz to 8 kHz. The microphones and preamplifiers were removed from the coupler, and direct electrical measurement of the phase difference between the instruments of the two channels was performed immediately by applying a common sinusoidal signal to both preamplifiers. In both the coupler method and the direct electrical method, the same gain settings for the measuring amplifiers were used.

Table I shows the tabulated data of the phase difference between the two instrument channels measured with the di-

rect electrical method and the corresponding measurement obtained with the coupler. For the data obtained with the

TABLE I. Phase difference between electronic instrument channels deter-

mined by phase measurement with the three-port coupler and by direct electrical phase measurement. Microphones were inserted into the coupler with protective grids.

(A) (B) Difference Frequency Direct measurement Three-port method (B) -- (A)

(Hz) (deg) (deg) (deg)

10 2.35 2.25 --0.10

12.5 0.88 0.76 --0.12

16 2.53 2.42 --0.11

20 0.70 0.62 -- 0.08

25 2.23 2.14 -- 0.09

31.5 1.20 1.13 -- 0.07

40 2.29 2.22 -- 0.07

50 1.20 1.14 -- 0.06 63 2.41 2.39 --0.02 80 1.56 1.51 -- 0.05

100 2.35 2.31 --0.04

125 1.50 1.48 --0.02

160 2.46 2.44 --0.02

200 1.30 1.31 0.01

250 4.49 4.49 0.0

315 -- 0.02 -- 0.05 -- 0.03

400 4.48 4.48 0.0

500 -- 0.04 - 0.06 -- 0.02

630 4.60 4.63 0.03

800 0.27 0.27 0.0 1000 4.46 4.51 0.05

1250 0.16 0.15 --0.01

2000 -- 0.04 -- 0.04 0.0

2500 4.15 4.23 0.08

3150 0.31 0.30 -- 0.01

4000 4.03 3.99 --0.04

5000 0.18 0.26 0.08

6300 4.27 4.30 0.03 8000 0.60 -- 2.09 -- 2.69

1254 J. Acaust. Sac. Am., Vol. 90, No. 3, September 1991 George S. K. Wang: Precision method/phase-match of microphones 1254


TABLE II. Difference in phase response of two Briiel and Kjaer microphones (type 4133 St. No. 591884 and 1517798 ) with protective grids, measured with the three-port coupler.

Frequency Phase difference ( Hz ) ( deg )

10 3.64

12.5 3.03 16 2.48

20 2.05

25 1.72

31.5 1.39

40 1.15

50 0.94

63 0.78

80 0.62

100 0.52

125 0.44

160 0.34

200 0.28

250 0.23

315 0.18

400 0.14

500 0.11

630 0.07

800 0.05

1000 0.03 1250 0.02

1600 0.00

2000 -- 0.01

2500 0.03 3150 0.12

4000 0.24

5000 0.26

6300 1.06

direct electrical method shown in column marked (A), the phase difference does not follow any obvious order of pro- gression and is considered to be dominated by the phase re- sponses of the one-third octave filters. Column (B) is the corresponding phase information obtained with the coupler method [ see Eq. (4) ]. Over the frequency range from 10 Hz to 6.3 kHz, the maximum difference between the two sets of readings is within _ 0.12 deg in-phase, and over the midband frequencies from 63 Hz to 2 kHz, the maximum difference is within _ 0.05 deg in-phase. Within these limits, the experimental results are consistent with the theoretical pre-

diction for this coupler method. The above measurements were obtained without signal averaging. Both measuring amplifiers were set at fast response, and the signals for the phase meter were derived from the ac output of the measuring amplifiers with an amplitude of approximately 1 V rms. The useful upper frequency limit of the coupler is approximately 6.3 kHz. There were no noticeable changes in the experimental results when the measurements were repeated, and at frequencies higher than 6.3 kHz, the results deviated from the theoretical prediction. This might be due to asym- metry in the coupler as well as limitations due to the internal dimensions of the coupler.

Table II shows the phase difference between two Briiel and Kjaer type 4133 microphones measured with the coupler. It is interesting to see that for the same model of microphones, there is a phase difference of 3.6 deg at 10 Hz.

III. CONCLUSION

The experimental data obtained with this coupler method are consistent with the theoretical prediction for precision phase match of microphones. The upper frequency limit of the existing coupler is approximately 6.3 kHz. The experimental results indicate that, without signal averaging, the uncertainty of the method at midband frequencies is approximately _ 0.05 deg, including the phase meter uncertainty of _ 0.02 deg.

•M. P. Waser and M. J. Crocker, "Introduction to the two-microphone cross-spectral method of determining sound intensity," Noise Control Eng. J. 22, 76-85 (1984).

2S. Gade, "Sound intensity, Part I: Theory," Briiel and Kjaer Instruments, Inc., Technical Review No. 3 (1982), pp. 3-39.

3E. Frederiksen and O. Schultz, "Pressure microphones for intensity measurements with significantly improved phase properties," in Proceedings of 12th International Congress on Acoustics, 1986, paper M2-1.

4V. Nedzelnitsky, "Development of standards for measuring the phase response of microphones," Proceedings of Inter-noise 84, Honolulu, 1984, pp. 1323-1328.

5G. S. K. Wong, "Phase response measurement with the three-port two microprobe coupler," J. Acoust. Soc. Am. Suppl. 1 88, S 114 (1990).

6G. S. K. Wong, "Precise measurement of phase difference and the amplitude ratio of two coherent sinusoidal signals," J. Acoust. Soc. Am. 75, 967- 972 (1984).

7G. S. K. Wong and T. F. W. Embleton, "Three-port two-microphone cavity for acoustical calibrations," J. Acoust. Soc. Am. 71, 1276-1277 (1982).

1255 J. Acoust. Soc. Am., Vol. 90, No. 3, September 1991 George S. K. Wong: Precision method/phase-match of microphones 1255


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Precision method for phase match of microphones