19 th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, 2-7 SEPTEMBER 2007 AN INITIAL INVESTIGATION ON SIMULTANEOUS MEASUREMENT OF THE FREE-FIELD AND DIFFUSE-FIELD SENSITIVITY OF MICROPHONES PACS: 43.38.Kb Barrera-Figueroa, Salvador 1 ; Rasmussen, Knud 1 ; Jacobsen, Finn 2 1 Danish Primary Laboratory of Acoustics, Danish Fundamental Metrology Ltd., Matematiktorvet B307, 2800 Kgs. Lyngby, Denmark; [email protected]. 2 Acoustic Technology, Ørsted•DTU, Technical University of Denmark, Ørsteds Plads B352, 2800 Kgs. Lyngby, Denmark. ABSTRACT During a reciprocity calibration in a diffuse field, a microphone is used as sound source. In such a case, the sound field at the position of the receiver microphone is a combination of the direct sound wave and the reverberant field. Thus, it is in principle possible to separate the direct impulse response and the reverberant response using a time-selective technique. A reciprocity calibration set-up has been used for measuring the electrical transfer impedance between a pair of microphones placed within a scale model of a reverberation room. The transfer function between the microphones was measured with FFT analysis using pseudo-random noise. Survey measurements showed that measuring the transfer function between microphones using a resolution of 0.5 Hz makes it possible to obtain an impulse response that is sufficiently long to include the reverberant response. A Fourier transform-based, time-selective technique, that has been previously used in free-field calibration of microphones for removing reflections and other acoustical interferences, was used for separating the direct wave between microphones from the reverberant response. INTRODUCTION The sensitivity of a microphone depends significantly on the type of the sound field in which it is immersed. Today practically all microphones are calibrated using pressure-field methods, although more than 90 percent of all microphones are used under diffuse-field or free-field conditions. The diffuse-field sensitivity is in practice calculated from the measured pressure sensitivity using empirical corrections that depend on the type and geometry of the microphone. The disadvantage of this method is that it gives rise to long delays when new transducers are introduced, because it takes time for such corrections to be recognised internationally. Another problem is that some transducers simply cannot be pressure calibrated. A method of free-field reciprocity calibration of unique accuracy has recently been developed to a stage where it can be applied in practical calibrations without the use of costly anechoic rooms [1, 2]. The purpose of this initial investigation is to develop a method and establish a set-up for reciprocity calibration of condenser microphones under diffuse-field conditions, and to demonstrate that diffuse-field reciprocity calibration is possible with high precision. The reciprocity technique for microphone calibration under pressure-field conditions (in closed couplers) was introduced in the 1940s [3-5], and since then has developed to a level of very high accuracy. The reciprocity technique yields the absolute sensitivity, and thus it is used in primary calibration [6]. The free-field reciprocity technique was also introduced in the 1940s [3, 4], but it took much longer time to develop this method to a high level of accuracy [7], partly because of the extreme difference in signal levels (if the transmitter microphone is driven with 10 V the response from the receiver microphone will typically be less than 1 μV), and partly because reflections from the walls of the in practice less than perfect anechoic room have a serious influence. More recently, time selective techniques based on advanced signal processing have been developed [1-2, 10]. Application of the time selective techniques implies the possibility of doing free-field calibrations under non-anechoic conditions.
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19th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, 2-7 SEPTEMBER 2007
AN INITIAL INVESTIGATION ON SIMULTANEOUS MEASUREMENT OF THE FREE-FIELD AND DIFFUSE-FIELD SENSITIVITY OF MICROPHONES
1Danish Primary Laboratory of Acoustics, Danish Fundamental Metrology Ltd., Matematiktorvet B307, 2800 Kgs. Lyngby, Denmark; [email protected] Technology, Ørsted•DTU, Technical University of Denmark, Ørsteds Plads B352, 2800 Kgs. Lyngby, Denmark.
ABSTRACTDuring a reciprocity calibration in a diffuse field, a microphone is used as sound source. In such a case, the sound field at the position of the receiver microphone is a combination of the direct sound wave and the reverberant field. Thus, it is in principle possible to separate the direct impulse response and the reverberant response using a time-selective technique. A reciprocity calibration set-up has been used for measuring the electrical transfer impedance between a pair of microphones placed within a scale model of a reverberation room. The transfer function between the microphones was measured with FFT analysis using pseudo-random noise. Survey measurements showed that measuring the transfer function between microphones using a resolution of 0.5 Hz makes it possible to obtain an impulse response that is sufficiently long to include the reverberant response. A Fourier transform-based, time-selective technique, that has been previously used in free-field calibration of microphones for removing reflections and other acoustical interferences, was used for separating the direct wave between microphones from the reverberant response.
INTRODUCTIONThe sensitivity of a microphone depends significantly on the type of the sound field in which it is immersed. Today practically all microphones are calibrated using pressure-field methods, although more than 90 percent of all microphones are used under diffuse-field or free-field conditions. The diffuse-field sensitivity is in practice calculated from the measured pressure sensitivity using empirical corrections that depend on the type and geometry of the microphone. The disadvantage of this method is that it gives rise to long delays when new transducers are introduced, because it takes time for such corrections to be recognised internationally. Another problem is that some transducers simply cannot be pressure calibrated.
A method of free-field reciprocity calibration of unique accuracy has recently been developed to a stage where it can be applied in practical calibrations without the use of costly anechoic rooms [1, 2]. The purpose of this initial investigation is to develop a method and establish a set-up for reciprocity calibration of condenser microphones under diffuse-field conditions, and to demonstrate that diffuse-field reciprocity calibration is possible with high precision.
The reciprocity technique for microphone calibration under pressure-field conditions (in closed couplers) was introduced in the 1940s [3-5], and since then has developed to a level of very high accuracy. The reciprocity technique yields the absolute sensitivity, and thus it is used in primary calibration [6]. The free-field reciprocity technique was also introduced in the 1940s [3, 4], but it took much longer time to develop this method to a high level of accuracy [7], partly because of the extreme difference in signal levels (if the transmitter microphone is driven with 10 V the response from the receiver microphone will typically be less than 1 μV), and partly because reflections from the walls of the in practice less than perfect anechoic room have a serious influence. More recently, time selective techniques based on advanced signal processing have been developed [1-2, 10]. Application of the time selective techniques implies the possibility of doing free-field calibrations under non-anechoic conditions.
Very little has been published on diffuse-field calibration of microphones [8-10]. The only fundamental studies were published more than forty years ago [8], and no standard about the diffuse-field calibration of microphones has ever been developed, undoubtedly because diffuse-field reciprocity calibration of microphones is even more difficult than free-field reciprocity calibration.
In this initial investigation, the transfer function between two Laboratory Standard (LS) microphones was measured using pseudo-random noise and FFT analysis. The measured function is not very reliable at low frequencies because the signal-to-noise ratio is extremely poor. Additionally, the low frequency resonances of the room are well separated from each other and they are still not a part of the diffuse-field. In order to solve this, one has either to extrapolate the transfer function to low frequencies from knowledge of the behaviour of the microphones, or to apply a band-pass frequency filter that eliminates the low frequency and high frequency portions of the frequency response. The first option requires knowledge of the microphone sensitivity under free-field or random-incidence conditions. However, the latter option was followed for this initial investigation. The resulting impulse response can be divided in two by means of a time-selective procedure: The resulting impulse response, “cleaned” of the influence of reflections in the same way as in the time selective method developed for free-field calibration, corresponds to the free-field response. Conversely, instead of “cleaning” the response from reflections one may single out the part of the response that corresponds to the diffuse-field. However, the process does not finish here. Interference effects in the diffuse field will cause fluctuations that depend on the particulars of the experimental arrangement, which means that the diffuse-field frequency response must be smoothed.
EXPERIMENTAL SET-UPMaking the measurements in a large reverberation room requires the microphone cables to be long. This may have an adverse effect on the signal-to-noise ratio. Therefore, the measurements were carried out in a scale model of a reverberation room. The scale model has a volume of approximately 2.5 m3. The reverberation time of the room was measured a number of times. Figure 1 shows a picture of reverberation room. The Schroeder frequency of the room has been estimated to be about 1 kHz. This is perfectly adecquate for microphone calibration because the difference between the diffuse-field sensitivity and the pressure sensitivity of a microphone is very small below 1 kHz.
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Figure 1. Picture of the scale model of the reverberation room.
The measurement set-up was composed of a Brüel & Kjær Reciprocity Apparatus type 5998, a microphone amplifier Brüel & Kjær type NEXUS model 2690, and a Brüel & Kjær PULSE Multi-channel Analyser. The receiver microphone was connected to a preamplifier with a 20 dB built-in amplifier, and to a 20 dB additional amplifier. The preamplifiers were attached to cylindrical rods of the same diameter as the microphones, and sufficiently long as to approximate semi-infinite cylinders in the frequency range of measurement. Figure 2 shows a schematic drawing of the measurement set-up.
The ratio of receiver-transmitter output voltages was measured with FFT analysis using pseudo-random noise. The subsequent determination of the impulse response requires a fine frequency sampling of the frequency response in order to determine the total reverberant response. Thus, it was required to measure the frequency response in frequency steps of ∆f = 0.5 Hz. In order to cover the entire frequency range with such a fine resolution, sequential zooms were performed.
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Figure 2. Schematics of the measurement system used for measuring the transfer impedance in the reverberation room.
Figure 3. Frequency response measured in the scale model of the reverberation room.
The zooms had a bandwidth of 3.2 kHz, and 6400 frequency lines at successive centre frequencies.
DISCUSSIONThe determination of the frequency response using such a fine resolution is not free of problems. The frequency response had to be measured sequentially in different segments using zoom FFT. Figure 3 shows the ratio of output voltage on the receiver microphone to the voltage on the terminals of the reference impedance at the transmitter microphone. The microphones are located in front of each other with the diaphragms oriented face to face at a distance of 20 cm between diaphragms. The complex frequency response makes it possible to determine the delays caused by the distance between the microphones and thus to separate the direct and reverberant responses. The value of the frequency response shows a very large variability as a function of frequency. This is the expected behaviour of such a sound field. However, there are two frequency ranges that show a very significant behaviour. Up to 10 kHz, the variability of the frequency response seems to be uniform. However, at frequencies above 10 kHz the variability reduces significantly. This is also clearly visible both in the phase and in the modulus of the frequency response. This is caused by the fact that the microphones are very directional at such frequencies and thus the ratio of direct to reverberant sound fields increases. This is unavoidable when the microphones are being measured in a face-to-face configuration.
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Figure 5. Direct and reverberant impulse responses and the time selective window used for separating them from the total impulse response.
Figure 4. Total impulse response and the direct and reverberant responses.
The impulse response corresponding to the above frequency response is shown in figure 4. The impulse response has two well defined sections: one corresponding to the direct impulse wave between the microphones, and another corresponding to the reverberant portion of the sound field. The direct impulse response is compared with an impulse response of a frequency response measured under free-field conditions. The measurement in free field was made at a distance between microphones of 24 cm, which is slightly larger than the 20 cm used in the reverberant room. However, it can be seen that the shape of the impulse response is very similar in the two cases. This indicates the possibility of determining the free-field sensitivity from measurements in the reverberation room using time-selective procedures.
The next step is to separate the direct impulse response and the reverberant response. In the first case it seems natural to use the procedure described in reference [1]. A slightly modified version of such a procedure can be used for separating the reverberant response. The two responses are separated from the total impulse response by means of a time-selective window. Figure 5 shows the impulse response and the time-selective window used for separating each response from the total response. The time-selective window is a Tukey window. It should be noticed that the time-selective window used for separating the direct impulse response is very short, 2 ms, while the window used for separating the reverberant response is very long, 1 s. This may have a certain influence on the “cleaned” estimate of each particular estimate of the frequency response.
Figure 6 shows the free-field frequency response, the reverberant frequency response and the total frequency response; the last was already shown in figure 3. The free-field response is totally free from any reflection from the room, but the extremes of the frequency response might be distorted by the application of the very short time-selective window. Such a distortion will have the form of a ripple, and its periodicity in the frequency domain will be a function of the duration of the window as described in reference [1]. In order to evaluate the extent of this problem, it will be necessary to find the difference between an ideal frequency response and a “cleaned” frequency response.
On the other hand, it is interesting to note that the reverberant response shows very larger fluctuations in the frequency range where the total response was dominated by the direct response; in other words, the reverberant response is free from any influence from the free-field response. This has two major consequences: on the one hand, it follows more closely the definition of a diffuse field, and on the other hand, it makes it indispensable to use smoothing procedures either spatially, in frequency or in both in order to obtain a smooth estimate of the diffuse-field that could be directly compared to the random-incidence response.
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Figure 6. Frequency responses before and after the application of the time-selective window.
CONCLUSIONSThe possibility of determining the free-field and diffuse-field sensitivities from measurements of the electrical transfer impedance in a reverberation room has been investigated. It seems feasible to separate the direct and reverberant responses using different time-selective windows. The properties of the separated frequency responses are as expected: the free-field response is free from any reflection and may compare well with a frequency response obtained in a free field. The diffuse-field response requires further processing, namely frequency and spatial averaging in order to obtain a smooth estimate that can be compared with the random-incidence response.
References:
[1] S. Barrera-Figueroa: New methods for transducer calibration: Free-field reciprocity calibration of condenser microphones. Acoustic Technology, Ørsted•DTU, Technical University of Denmark, PhD thesis, 2003.[2] S. Barrera-Figueroa, K. Rasmussen and F. Jacobsen: A time-selective technique for free-field reciprocity calibration of condenser microphones, Journal of the Acoustical Society of America 114, 2003, 1467-1476.[3] W. R. MacLean: Absolute measurement of sound without a primary standard. Journal of the Acoustical Society of America 12, 1940, 140-146.[4] A. L. DiMattia and F.M. Wiener: On the absolute pressure calibration of condenser microphones by the reciprocity method. Journal of the Acoustical Society of America 18, 1946, 341-344.[5] W. Wathen-Dunn. On the reciprocity free-field calibration of microphones. Journal of the Acoustical Society of America 21, 1949, 542-546.[6] IEC International Standard 1094-2: Measurement microphones Part 2: Primary method for pressure calibration of laboratory standard microphones by the reciprocity technique, 1995.[7] IEC International Standard 1093-3: Measurement microphone Part 3: Primary method for free-field calibration of laboratory standard microphones by the reciprocity technique, 1995.[8] H. G. Diestel: Reciprocity calibration of microphones in a diffuse sound field. Journal of the Acoustical Society of America 33, 1961, 514-518.[9] T.Nakajima: Reciprocity calibration of laboratory standard microphones in a diffuse sound field, Researches of the Electrotechnical Laboratory, Issue 706, 1970, pp. 1-87, in Japanese.[10] M. Vorländer and H. Bietz: Novel broad-band reciprocity technique for simultaneous free-field and diffuse-field microphone calibration. Acustica 80, 1994, 365-377.
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