Research on an alternative LS2P microphone based on a new reciprocity calibration system

. The microphone calibration by the reciprocity technique specified in IEC 61094-2 is used to determine the sensitivity of laboratory standard microphones according to the IEC 61094-1 with the smallest measurement uncertainty for the use as reference microphones. So far, laboratory standard microphones by the manufacturer Brüel & Kjær (Type 4160 and Type 4180) are almost exclusively used as laboratory reference microphones. In order to create an alternative, the initiative has been taken to examine the usability of the ½-inch laboratory microphones G.R.A.S. 40AU-1. Studies were launched to check the microphone parameters, the stability and the reciprocity of the microphones as well as the compatibility with microphones by Brüel & Kjær. Basis for the investigation was a new validated reciprocity calibration system. The realization of the system and the research results are presented and discussed. Additionally, results of comparison measurements with national metrology institutes are shown in shortened fashion.


Introduction
The usual primary method of determining the complex pressure sensitivity of laboratory standard (LS) microphones is the pressure reciprocity calibration method (described in the IEC publication 61094-2 [1]). This method takes advantage of the fact that LS microphones are reciprocal transducers. This means that the microphone works both as sound receiver and sound source (transmitter). During calibration, two out of three microphones are coupled acoustically, one of which acts as receiver, the other acting as transmitter. The microphones are connected by a coupler (a small cylindrical cavity). In order to determine the sensitivity of each of the three microphones the electrical transfer impedance of the paired microphones has to be measured precisely. In addition to the electrical transfer impedance, the acoustic transfer impedance of the enclosed air volume between the microphones has to be modelled accurately. The acoustic transfer impedance is influenced by several factors including the microphone parameters.
In the past, this method has been applied almost exclusively to LS microphones manufactured by Brüel & Kjaer -the 1-inch pressure (LS1P) microphone type 4160 and the ½-inch pressure (LS2P) microphone type 4180 -and the validity of the approach was * maria.enge@spektra-dresden.de approved through high effort of metrological investigation and with a large number of microphones.
Currently, comparable research to evaluate alternative types of microphones has not been published as yet. In this report, the results of a first investigation with LS microphones of the type 40AU-1 manufactured by G.R.A.S determined with a new reciprocity calibration system by SPEKTRA are presented.

Design of the reciprocity calibration system
SPEKTRA developed a new reciprocity calibration system according to the current standard [1]. Figure 1 shows a schematic diagram of the calibration system. It includes four air-filled sapphire plane-wave couplers, a microphone fixture and a pressure chamber (see Figure 2). The microphones are connected to a vibration control system SRS 35 by SPEKTRA via a microphone transmitter unit Brüel & Kjaer ZE0796 and a microphone preamplifier unit Brüel & Kjaer 2673. Furthermore, the software CS18 that controls the SRS 35 and a MATLAB ® script for the calculation of the sensitivities are included. The MATLAB ® script contains all approaches for determining the sensitivities of the standard [1]. It is possible to compare the approaches and to validate the calculation systematically. The MATLAB ® script and the calculation program developed by the Swiss national metrology institute METAS were compared in earlier research. The difference of the calculation is up to 1.3•10 -5 dB (10 -6 dB on the average).
To determine the microphone parameters, SPEKTRA measures the front cavity depth using a laser distance sensor, the reference front cavity diameter value was provided for the manufacturer. Thus the front cavity volume and the equivalent volume have been optimized in a frequency range between 200 Hz and 2 kHz, to minimize the difference between the pressure sensitivities using four couplers according the standard [1]. A reference resonance frequency together with a reference loss factor was determined by a least square fit in a frequency range between 1 kHz and 20 kHz. The determination of the microphone parameters can be performed automatically by the MATLAB ® script.  From these results the short-term stability coefficient of the microphones was approximately calculated. According to the standard [2], it is determined based on the standard deviation of five measurements and must be smaller than 0.02 dB. The average standard deviation for the three measurements is 0.0014 dB in the required frequency range from 250 Hz to 1 kHz.

Initial investigations
Besides the standard microphone combinations, other microphone combinations were measured to estimate the reciprocity of the microphones. Thus the role of the microphones were reversed; the microphone acting as the transmitter in the first step is the receiver in the second step. The deviation between the determined pressure sensitivities should be as small as possible. In this case, the average standard deviation is 0.004 dB.
Furthermore, primary calibrations with one or two G.R.A.S. 40AU-1 and one or two known Brüel & Kjaer 4180 were carried out. These investigations were carried out in cooperation with the Danish Fundamental Metrology DFM, METAS and SPEKTRA. A Brüel & Kjaer 4180 was used as known test standard to verify the calibration method.   According to the standard [2], the long-term stability coefficient has to be smaller than 0.02 dB/year. The average standard deviation between the results of the measurements at the end of 2017 and at the end of 2018 is 0.002 dB in the required frequency range from 250 Hz to 1 kHz.
In the course of these measurements METAS and SPEKTRA also reported the microphone parameters of the G.R.A.S. 40AU-1 285094 (see Table 1). The parameters all lie all in the range expected by the standard [2] and by the reports of comparison measurements with ½-inch LS microphones.

Conclusions
The initial investigations on the G.R.A.S. 40AU-1 with the new reciprocity calibration system by SPEKTRA provided the basis for further research. It could already be shown that the primary calibration of the G.R.A.S. 40AU-1 is reproducible. Furthermore, it could be shown, that the G.R.A.S. 40AU-1 has a very good short-term stability. The results so far also show a good long-term stability of the G.R.A.S. 40AU-1. Therefore it can be assumed with a high confidence that the targeted measuring accuracy can be achieved with the G.R.A.S. 40AU-1.
Nevertheless, further studies should be conducted to determine the influence of static pressure and temperature on the sensitivity of G.R.A.S. 40AU-1, as has been done for Brüel & Kjaer 4160 and 4180 [3]. Furthermore, the applicability of IEC TS 61094-7 [4] to determine the free-field sensitivity levels for G.R.A.S. 40AU-1 based on the pressure sensitivity levels should be re-examined. Finally, the stability of the G.R.A.S. microphones should be monitored over a longer period. For this purpose further comparison measurements with the German National Metrology Institute PTB, DFM and METAS are planned.