A time-selective technique for free-field reciprocity calibration of condenser microphones

Abstract

In normal practice, microphones are calibrated in a closed coupler where the sound pressure is uniformly distributed over the diaphragm. Alternatively, microphones can be placed in a free field, although in that case the distribution of sound pressure over the diaphragm will change as a result of the diffraction of the body of the microphone, and thus, its sensitivity will change. In the two cases, a technique based on the reciprocity theorem can be applied for obtaining the absolute sensitivity either under uniform pressure or free-field conditions. In this paper, signal-processing techniques are considered that improve the accuracy of the free-field calibration method. In particular, a fast Fourier transform ͑FFT͒-based time-selective technique for removing undesired reflections from the walls of the measurement chamber has been developed and applied to the electric transfer impedance function between two microphones. The acoustic centers of the microphones have been determined from the ''cleaned'' transfer impedance values. Then, the complex free-field sensitivities of the microphones have been calculated. The resulting complex sensitivities and acoustic centers have proved to be in good agreement with previously published data, and this confirms the reliability of the time-selective technique, even in nonanechoic environments. Furthermore, the obtained results give a new reference for further comparisons, because they cover a frequency range with an accuracy that has not been obtained by previously published data.

The acoustic center of laboratory standard microphones

“…21. The measurement system consists of a homemade reciprocity apparatus which is connected to a Brüel & Kjaer PULSE ͑B&K͒ analyzer; the receiver and transmitter microphone are connected to the reciprocity apparatus.…”

“…The nature of these unwanted effects has been analyzed using statistical methods, 7 and using time-selective procedures. 8 Although time-selective methods can eliminate the unwanted contaminations, application of such methods may affect the accuracy of the estimated acoustic center. In this paper the time-selective technique described in Ref.…”

“…In this paper the time-selective technique described in Ref. 8 has been used for removing the unwanted reflections and interference between the microphones. The effect of the time-selective technique on the electrical transfer impedances used for determining the acoustic center is analyzed.…”

A note on determination of the diffuse-field sensitivity of microphones using the reciprocity technique

“…10. The procedure applied in this case was as follows: ͑a͒ The transfer function between the signals of two microphones was measured; ͑b͒ at low and high frequencies this frequency response was taken smoothly to zero by applying a bandpass filter; ͑c͒ an inverse discrete Fourier transform was calculated; ͑d͒ a timeselective window was applied to the resulting impulse response in order to separate the direct and the reverberant response; and ͑e͒ a discrete Fourier transform was applied to the reverberant part of the impulse response.…”

“…More recently, time-selective techniques based on advanced signal processing have been developed. 10 Application of the time-selective techniques implies the possibility of doing free-field calibrations under nonanechoic conditions. Only a little has been published on diffuse-field calibration of microphones.…”