Pressure reciprocity calibration of a MEMS microphone

Abstract

This article reports the first use of the pressure reciprocity technique to calibrate a MEMS microphone. This standardized primary calibration method is conventionally used to calibrate laboratory standard microphones. Results for the pressure reciprocity calibration of a MEMS microphone and two laboratory standard microphones are presented for the frequency range 100 Hz to 10000 Hz. Because the amplifier in the MEMS microphone package prevents reciprocal operation, this microphone was used only as a receiver of sound. A description of the procedure is presented along with checks of the measurement results, and data regarding the uncertainties of these results.

1. Introduction

Micro-electromechanical systems (MEMS) microphones are small acoustic sensors fabricated on silicon wafers using automated processes similar to those used by the semiconductor industry for manufacturing integrated circuits. These microphones represent a relatively new type of microphone technology that has developed widespread use in consumer products such as smartphones, laptop computers and tablets, mainly due to the level of stability and reliability these microphones provide given their low cost and small size. Because they are also utilized in measurement applications, for example, urban environmental noise monitoring with wireless sensor networks^1–4 and smartphone sound measurements⁵, there is a need for accurate primary calibration methods to benchmark the performance of these microphones. Primary calibration methods determine microphone sensitivities from first principles, and are intrinsically more accurate than comparison methods, which require a previously calibrated acoustic transfer standard. Novel optical techniques, such as photon correlation spectroscopy⁶, show great promise for primary calibration of MEMS microphones.

A variety of transducers can be calibrated with methods utilizing reciprocity. One example is the pressure reciprocity technique that has long served as a primary method for pressure calibration of microphones^7–10. For calibrations of laboratory standard microphones^11,12, this method is standardized^13,14 and utilized at national measurement institutes worldwide¹⁵. The method exploits the fact that a microphone of this type is a reciprocal transducer. This means that the magnitude of its sensitivity is the same whether it is used as a sound receiver or a sound transmitter. The sensitivities of each of a set of three microphones are determined from the results of three independent measurements made with pairs of microphones connected by an acoustic coupler, with no pairwise combinations repeated. Each pair consists of a transmitter and a receiver. Each measurement provides the product of the pressure sensitivities of the pair. The sensitivities of the three individual microphones can be calculated from the three products. Only two microphones of a triad need be reciprocal^13,14 if one microphone is used only as a transmitter, the second is used once as a transmitter and once as a receiver, and the third is used only as a receiver.

To demonstrate the pressure response calibration of a MEMS microphone by reciprocity, a Knowles Model SPQ1410HR5H-B^*, which is a top port MEMS microphone with an analog output, and two Type LS2aP laboratory standard microphones^11,12 were calibrated by reciprocity in the frequency range 100 Hz to 10000 Hz as a triad using a microphone pressure reciprocity calibration system at the National Institute of Standards and Technology (NIST). This calibration system is ordinarily used to determine the pressure sensitivities of three Type LS2aP microphones by implementing a series of measurements done with two different sized acoustic couplers designed to fit two Type LS2aP microphones¹⁶.

2. Adaptation of MEMS microphone

To calibrate the MEMS microphone in the pressure reciprocity calibration system, the microphone is mounted in an adapter that provides a geometry suitable for installation in the ports of the couplers. The combination of the adapter and the connector for the electrical leads of the microphone is mechanically and electrically interchangeable in the calibration system with the combination of a Type LS2aP microphone used as a receiver and its attached preamplifier. The adapter consists of a brass tube with an outer diameter of 12.7 mm, a bore diameter of 8.0 mm, and a length of 102.1 mm chosen to roughly match the corresponding dimensions of the combination of a Type LS2aP condenser microphone and an attached preamplifier. Tape wrapped around one end of the tube increases the outer diameter of that end to 13.2 mm, which is equivalent to that of a Type LS2aP microphone and provides a snug fit in the coupler port. The smaller outer diameter is required for the rest of the tube length to allow the tube to fit through a collar designed for use with a spring system that applies a compressive force between the face of the tube and the coupler surface.

The MEMS microphone with three American Wire Gauge 30 insulated leads (power, signal, ground) is cast into an epoxy cylinder 4.8 mm in diameter and 6.0 mm long. Isolated 3.1 V DC power for the MEMS microphone is provided by a voltage regulator circuit and a 9 V battery. Battery voltage measurements made before and after each measurement series indicated that this voltage was always well above the minimum required by the voltage regulator circuit. A 2.0 mm thick synthetic rubber grommet is placed at the end of the cylinder furthest inside the bore. This grommet is custom made to locate the cylinder off-center in the bore, so that the desired radial location of the MEMS microphone port relative to the center of the bore can be achieved by rotating the cylinder in the grommet. Figure 1 illustrates the arrangement. The cylinder and grommet are fixed in place by a self-leveling room-temperature-vulcanizing silicone adhesive, which also provides an acoustic seal and fills in the volume of the tube around the cylinder and grommet. This provisional arrangement allows the MEMS microphone to be removed and reinstalled with its port at different radial locations relative to the center of the bore, within the constraints imposed by the location of the microphone port inside the cylinder. Figure 2 shows the microphone port at the three different radial locations used for the measurements, which are 0.45r, 0.28r, and 0.09 r, where r is the 4.0 mm radius of the bore.

Fig. 1.

Arrangement for installing the MEMS microphone port at different locations in the adapter.

Fig. 2.

The MEMS microphone fixed in the adapter with the sound port at the three radial locations: 0.45r (left photo), 0.28r (center photo), and 0.09r (right photo), where r is the 4.0 mm bore radius.

3. Measurement procedure

Data for the microphone triad consisting of the MEMS microphone and two Type LS2aP microphones were acquired at eighteen frequencies in the range 100 Hz to 10000 Hz using the NIST calibration system and procedures ordinarily used for calibrating three Type LS2aP microphones in a single series of measurements¹⁶. Each measurement is done with a pair of microphones, the transmitter and the receiver, installed in the ports of a cylindrical air-filled plane-wave coupler with a diameter equivalent to that of a Type LS2aP microphone diaphragm. For each given pair, the transmitter is electrically driven to produce sound that results in an output voltage from the receiver. At each frequency, the ratio of the receiver voltage to the voltage across a capacitor in series with the transmitter is determined from voltage measurements. Also measured are the temperature, relative humidity and barometric pressure, which is adjusted to 101.325 kPa, the reference static pressure^13,14.

To describe the measurement series completed to calibrate the MEMS microphone, the two Type LS2aP microphones of the triad will be designated LS2aP-1 and LS2aP-2. The series comprises six measurements, the first three done at frequencies in the range 100 Hz to 2000 Hz using a long coupler that has a length of 9.4 mm, and the final three done at all eighteen frequencies in the range 100 Hz to 10000 Hz using a short coupler that has a length of 4.7 mm. For each coupler, LS2aP-1 is the transmitter and LS2aP-2 is the receiver in the first measurement, LS2aP-1 is the transmitter and the MEMS microphone is the receiver in the second measurement, and finally, LS2aP-2 is the transmitter and the MEMS microphone is the receiver in the third measurement. The series is completed without the need to use the MEMS microphone as the transmitter in any of the six measurements. For each of the three radial locations of the MEMS microphone port, six trials of the measurement series were completed for a total of eighteen trials at each frequency.

4. Data reduction and experimental results

The frequency-dependent sensitivity of each microphone in the triad was determined using the calculation method previously described for triads consisting exclusively of Type LS2aP microphones¹⁶. The moduli of the pressure sensitivities (V/Pa) of the three microphones |M_p,1|, |M_p,2|, and |M_p,3|, are given by the following equations.

$$\left|M_{p,1}\right|={\left|\frac{R_{12}\cdot R_{13}}{R_{23}}\cdot \frac{V_{O,12}\cdot V_{O,13}}{V_{O,23}}\cdot \frac{P_{S,23}}{P_{S,12}\cdot P_{S,13}}\cdot \frac{{\kappa }_{23}}{{\kappa }_{12}\cdot {\kappa }_{13}}\cdot \frac{Co{r}_{HW,12}\cdot Co{r}_{HW,13}}{Co{r}_{HW,23}}\cdot \frac{1}{C}\right|}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$$ (1)

$$\left|M_{p,2}\right|={\left|\frac{R_{12}\cdot R_{23}}{R_{13}}\cdot \frac{V_{O,12}\cdot V_{O,23}}{V_{O,13}}\cdot \frac{P_{S,13}}{P_{S,12}\cdot P_{S,23}}\cdot \frac{{\kappa }_{13}}{{\kappa }_{12}\cdot {\kappa }_{23}}\cdot \frac{Co{r}_{HW,12}\cdot Co{r}_{HW,23}}{Co{r}_{HW,13}}\cdot \frac{1}{C}\right|}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$$ (2)

$$\left|M_{p,3}\right|={\left|\frac{R_{13}\cdot R_{23}}{R_{12}}\cdot \frac{V_{O,13}\cdot V_{O,23}}{V_{O,12}}\cdot \frac{P_{S,12}}{P_{S,13}\cdot P_{S,23}}\cdot \frac{{\kappa }_{12}}{{\kappa }_{13}\cdot {\kappa }_{23}}\cdot \frac{Co{r}_{HW,13}\cdot Co{r}_{HW,23}}{Co{r}_{HW,12}}\cdot \frac{1}{C}\right|}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$$ (3)

where the subscript x identifies the transmitter, and the subscript y identifies the receiver, R_xy is the ratio of the receiver voltage to the capacitor voltage, V_o,xy is the sum of the geometrical cavity volume and the low frequency equivalent diaphragm volumes of the microphones, P_s,xy is the barometric pressure, κ_xy is the ratio of specific heats of the air in the cavity, C is the capacitance of the capacitor in series with the transmitter, and Cor_HW,xy is a frequency-dependent parameter that accounts for heat conduction at the walls of the cavity and wave motion along its length, as well as the equivalent diaphragm volumes.

Table 1 lists the mean sensitivity level (dB re 1V/Pa) as a function of frequency calculated for the MEMS microphone from the sensitivities determined for all eighteen trials along with the expanded uncertainty (coverage factor, k = 2) of these measurement results. As part of the calculation method, a two-step iterative fitting procedure is utilized to determine the front cavity volume of each microphone. This fitting procedure minimizes the average absolute difference between the sensitivities obtained with the short coupler and the long coupler in the frequency range 200 Hz to 2000 Hz for each microphone.

Table 1.

MEMS microphone sensitivity level (dB re 1V/Pa) with expanded (k = 2) uncertainty.

Frequency (Hz)	Sensitivity level (dB re 1 V/Pa)	Expanded (k=2) uncertainty (dB)
100	−42.41	0.12
200	−41.96	0.12
250	−41.93	0.12
315	−41.95	0.12
500	−42.04	0.12
700	−42.14	0.12
1000	−42.23	0.12
1500	−42.30	0.12
2000	−42.31	0.12
2500	−42.29	0.13
3000	−42.24	0.13
4000	−42.06	0.13
5000	−41.81	0.14
6000	−41.47	0.15
7000	−41.06	0.16
8000	−40.56	0.17
9000	−39.97	0.18
10000	−39.28	0.20

For the MEMS microphone, the initial value of 0.0 mm³ for the adapter front cavity volume was varied by increments of 2.0 mm³ in the first step. In the second step, the result from the first step was varied by increments of 0.2 mm³ to determine the best fit result. The absolute differences in measured sensitivities between the long and short couplers were averaged over all eighteen trials for the frequencies of the fit. To assess the accuracy of this procedure, the expanded uncertainties of Table 1 were recalculated with the average absolute differences included. The differences, the expanded uncertainties, and the increase in expanded uncertainties are shown in Table 2. For all frequencies, the increase in expanded uncertainties is negligible compared to the 0.12 dB expanded uncertainty.

Table 2.

Average absolute differences with associated increases in expanded uncertainties.

Frequency (Hz)	Average absolute difference (dB)	Expanded (k=2) Uncertainty (dB)	Increase in Expanded (k=2) Uncertainty (dB)
200	0.012	0.12	0.0025
250	0.010	0.12	0.0016
315	0.007	0.12	0.0007
500	0.001	0.12	0.0000
700	0.002	0.12	0.0001
1000	0.004	0.12	0.0003
1500	0.005	0.12	0.0004
2000	0.003	0.12	0.0001

Figure 3 shows the MEMS microphone sensitivity data expressed as a frequency response normalized to the mean sensitivity level for 1000 Hz, and the typical free field response specified by the microphone manufacturer¹⁷. This figure is presented for comparison of the trends in the two responses. Because of the small package size of this microphone, in the applicable frequency range relatively small differences are expected between the pressure response and the free field response. The measured response tracks the typical response closely. In the frequency range 100 Hz to 3000 Hz, the response is relatively flat with a slight low-frequency roll-off. Above 3000 Hz, the response rises gradually to a value of 3 dB at 10000 Hz. In addition, when rounded to the nearest decibel, the measured value for the mean sensitivity level at 1000 Hz is −42 dB and matches the specified typical value. For this frequency, the sensitivity level range specified for 100 % testing is −45 dB to −39 dB.

Fig. 3.

Measured frequency response of the MEMS microphone shown normalized to the sensitivity level for 1000 Hz. The typical free field response specified by the manufacturer is displayed for comparison, also normalized to the sensitivity level for 1000 Hz.

To examine the effect of the MEMS microphone port location on the measured sensitivity, Figure 4 shows the differences between the mean sensitivity level determined for each given location from six trials and the mean sensitivity level determined from all eighteen trials. All these differences are within ±0.07 dB at frequencies equal to or less than 3000 Hz, within ±0.10 dB at frequencies equal to or less than 8000 Hz, and within ±0.13 dB at frequencies equal to or less than 10000 Hz. These differences are attributable to non-uniformities in the sound pressure distribution due to radial wave motion in the coupler. Such non-uniformities are consistent with the observation that these differences increase at the higher frequencies of measurement where smaller wavelengths lead to larger effects. In addition, the magnitudes of these differences are consistent with the recommended specification of ±0.1 dB given in standards^13,14 for sound pressure distribution uniformity over microphone diaphragms in reciprocity calibrations done with these couplers. The range in sensitivities for all eighteen trials was used to determine an uncertainty component that accounts for the effect of the MEMS microphone port location. This component is the dominant contribution to the expanded uncertainty of the reported measurement results for the MEMS microphone.

Fig. 4.

Differences between the mean sensitivity levels determined from all eighteen trials and for the three radial locations: 0.45r, 0.28r, and 0.09r, where r is the 4.0 mm bore radius.

To explore the potential effects of using a MEMS microphone instead of a Type Ls2aP as one of the three microphones in the reciprocity calibration procedure, two other calibration data sets were compared to the reciprocity calibration data obtained using the MEMS microphone. Historical LS2aP-1 and LS2aP-2 reciprocity calibration data determined with only Type LS2aP microphones were compared with mean sensitivity levels of these two microphones determined from the calibration done with the MEMS microphone. The largest difference at any frequency for either of these Type LS2aP microphones is 0.03 dB at 8000 Hz, for which the expanded (k = 2) uncertainty for the calibration of Type LS2aP microphones is 0.06 dB. An additional data set was obtained when the MEMS microphone (with the port located at 0.28r) was calibrated by a different method: comparison in the small coupler by substitution using LSaP-1 and LS2aP-2 as transfer standards, and a third Type LS2aP microphone only as a transmitter. The other three microphones were used only as receivers. Absolute differences were calculated between the sensitivity levels determined from this comparison calibration and the reciprocity calibrations. These differences were 0.01 dB for the frequency range 250 Hz – 4000 Hz, 0.03 dB for 8000 Hz, and 0.04 dB for 10000 Hz. These values are significantly less than those of the corresponding expanded uncertainties of the measurement results.

The standard and expanded (k =2) uncertainties for the MEMS microphone pressure reciprocity calibration results are reported in Table 3. These uncertainties were determined by applying published guidelines for evaluating uncertainties¹⁸. A Type A standard uncertainty was determined by pooling the variances of the results obtained for all three microphone port locations. A Type B standard uncertainty was determined by using the range in the MEMS microphone sensitivities measured for all three microphone port locations to define the width of a rectangular probability distribution. Additional Type B standard uncertainties are included that have been previously described for pressure reciprocity calibrations of Type LS2aP microphones at NIST¹⁶. These Type B standard uncertainties correspond to the terms shown in Eq. (1–3). The standard uncertainties u_P due to the terms denoted P_s,xy are derived from the barometer manufacturer’s specifications. The standard uncertainties u_C due to the C⁻¹ term are derived from the transmitter unit manufacturer’s specifications. The standard uncertainties u_R due to the terms denoted R_xy are derived from the voltmeter manufacturer’s specifications and measurements of the electrical cross-talk, signal-to-noise ratios, and polarizing voltages in the calibration system. The standard uncertainties u_V due to the terms denoted V_o,xy are based on measurements of coupler dimensions and measuring instrument manufacturer’s specifications. The standard uncertainties u_κ and u_Cor due to the terms denoted κ_xy and Cor_HW,xy respectively, are based on the limitations of the models used to determine these terms.

Table 3.

The standard and expanded (k = 2) uncertainties for the MEMS microphone pressure reciprocity calibration results.

Uncertainties
Frequency (Hz)	Type A (%)	Type B (%)							Expanded (k = 2)
	Pooled variances	Rectangular distribution from MEMS data	uP	uC	uR	uκ	uV	uCor	%	dB
100	0.16	0.63	0.01	0.04	0.05	0.06	0.13	0.11	1.36	0.12
200	0.16	0.65	0.01	0.04	0.05	0.06	0.13	0.10	1.38	0.12
250	0.16	0.66	0.01	0.04	0.04	0.06	0.13	0.10	1.40	0.12
315	0.16	0.66	0.01	0.04	0.04	0.06	0.13	0.10	1.41	0.12
500	0.16	0.67	0.01	0.04	0.04	0.06	0.13	0.10	1.43	0.12
700	0.16	0.67	0.01	0.04	0.04	0.06	0.13	0.10	1.43	0.12
1000	0.16	0.67	0.01	0.04	0.04	0.06	0.13	0.10	1.43	0.12
1500	0.16	0.68	0.01	0.04	0.05	0.06	0.13	0.10	1.44	0.12
2000	0.16	0.68	0.01	0.04	0.05	0.06	0.13	0.10	1.44	0.12
2500	0.16	0.69	0.01	0.04	0.04	0.06	0.13	0.11	1.47	0.13
3000	0.16	0.70	0.01	0.04	0.04	0.06	0.13	0.11	1.49	0.13
4000	0.16	0.73	0.01	0.04	0.04	0.06	0.13	0.11	1.54	0.13
5000	0.17	0.76	0.01	0.04	0.04	0.06	0.23	0.11	1.64	0.14
6000	0.17	0.80	0.01	0.04	0.04	0.06	0.23	0.11	1.71	0.15
7000	0.17	0.85	0.01	0.04	0.04	0.06	0.23	0.12	1.82	0.16
8000	0.17	0.91	0.01	0.04	0.04	0.06	0.23	0.13	1.94	0.17
9000	0.18	0.99	0.01	0.04	0.04	0.06	0.23	0.17	2.10	0.18
10000	0.19	1.09	0.01	0.04	0.04	0.06	0.23	0.21	2.30	0.20

5. Summary

Pressure reciprocity calibration of a MEMS microphone has been accomplished in the frequency range 100 Hz to 10000 Hz by adapting this microphone for measurements in a system ordinarily used to perform such calibrations of sets of three Type LS2aP microphones. Two Type LS2aP microphones were calibrated along with the MEMS microphone used as a sound receiver only. The results are consistent with MEMS microphone specifications provided by the manufacturer. To assess the accuracy of the iterative fitting procedure applied to minimize the differences in sensitivity levels determined with two different sized couplers, the expanded uncertainties were recalculated by including the average absolute differences between couplers derived from the fit results. The increase in the uncertainties due to including these differences in the uncertainty calculations is negligible.

Very good agreement was found between historical LS2aP-1 and LS2aP-2 calibration data and mean sensitivity levels of these two microphones from the calibrations done with the MEMS microphone, as well as between the sensitivity levels for the MEMS microphone determined by pressure reciprocity and comparison by substitution methods. Because of this agreement, the effect of using a MEMS microphone instead of a Type LS2aP as one of the three microphones in the reciprocity calibration procedure is deemed to be insignificant. Reciprocity calibrations completed with the MEMS microphone port located at different radial locations indicate that the largest component in the uncertainty of the results arises from non-uniformities in the sound pressure distribution inside the coupler due to wave motion. Further studies designed to investigate and improve pressure reciprocity calibrations of MEMS microphones should use enhanced methods for spatial sampling, and for adapting these microphones for measurements in the plane-wave couplers. Investigation of such calibrations at higher frequencies should use a MEMS microphone with a much more uniform frequency response above 10000 Hz than that of the microphone used for these measurements. For measurements above 20000 Hz, it would be prudent to use as the propagation medium a gas (e.g., helium or hydrogen) with higher acoustic velocity than air, and/or to use couplers and reciprocal condenser microphones of smaller diameter.