Equalizing the In-Ear Acoustic Response of Piezoelectric MEMS Loudspeakers Through Inverse Transducer Modeling

Abstract

Micro-Electro-Mechanical Systems (MEMS) loudspeakers are attracting growing interest as alternatives to conventional miniature transducers for in-ear audio applications. However, their practical deployment is often hindered by pronounced resonances in their frequency response, caused by the mechanical and acoustic characteristics of the device structure. To mitigate these limitations, we present a model-based digital signal equalization approach that leverages a circuit equivalent model of the considered MEMS loudspeaker. The method relies on constructing an inverse circuital model based on the nullor, which is implemented in the discrete-time domain using Wave Digital Filters (WDFs). This inverse system is employed to pre-process the input voltage signal, effectively compensating for the transducer frequency response. The experimental results demonstrate that the proposed method significantly flattens the Sound Pressure Level (SPL) over the 100 Hz-10 kHz frequency range, with a maximum deviation from the target flat frequency response of below 5 dB.

Keywords: MEMS loudspeakers; equalization; inverse systems; piezoelectric transducers.

Figure 1

(a) Optical microscope image of the fabricated MEMS loudspeaker showing the PZT stack distribution. The MEMS device has a total footprint of $4.5\times 4.5{\mathrm{mm}}^2$. (b) The considered MEMS loudspeaker mounted into the thermoplastic packaging, with a 1 cm³ back chamber.

Figure 2

Linear equivalent circuit model of the target piezo-actuated MEMS loudspeaker for in-ear applications.

Figure 3

Target-Inverse-Physical Chain processing algorithm.

Figure 4

(a) Ideal opamp schematic symbol. (b) Equivalent nullor-based representation of the same ideal opamp in (a).

Figure 5

Inverse MEMS loudspeaker equivalent circuit model based on a nullor.

Figure 6

Inverse MEMS loudspeaker equivalent circuit model involving the ideal opamp representation of the nullor.

Figure 7

(a) Block diagram of the acoustic measurement setup, featuring a G.R.A.S. RA0402 ear simulator and a G.R.A.S. 46BD 1/4” microphone. An Audio Precision APx525 audio analyzer is used to generate both DC and AC signals to drive the MEMS loudspeaker and to record the microphone signal. The analog signals generated by APx525 are amplified by $10\times$ to reach the desired driving level. (b) Picture of the MEMS loudspeaker connected to the G.R.A.S. RA0402 ear simulator.

Figure 8

Comparison between SPL curves predicted by the proposed linear equivalent circuit model (solid curves) and the experimental measurements (dash-dotted curves) for different input signal amplitudes.

Figure 9

Frequency-domain SPL of the MEMS loudspeaker after $94{\mathrm{dB}}_{\mathrm{SPL}}$ flat equalization. The measured SPL (orange dash-dotted curve) is compared to the target SPL (solid blue curve).

Figure 10

Comparison of frequency-domain SPL curves for different peak-to-peak input voltage levels. (a) Measurements with chirps with increasing ${\mathrm{V}}_{\mathrm{pp}}$ values, without equalization. (b) Measurements with equalized input signals, each rescaled to have a maximum peak-to-peak amplitude matching the corresponding ${\mathrm{V}}_{\mathrm{pp}}$ value.

Figure 11

Comparison of frequency-domain THD ratio curves: THD measurements obtained by driving the MEMS loudspeaker with a $30{\mathrm{V}}_{\mathrm{pp}}$ signal without any equalization (solid blue curve) are compared to THD measurements obtained using an equalized input signal (orange dash-dotted curve), rescaled to have a maximum peak-to-peak amplitude matching the corresponding $30{\mathrm{V}}_{\mathrm{pp}}$.