Discrete-Time Circuital Modeling of Hysteretic Piezo-Actuated MEMS Loudspeakers for In-Ear Applications

Piezoelectrically actuated micro-electromechanical systems (MEMS) loudspeakers have experienced significant advancements in recent years, achieving acoustic performance for in-ear applications comparable with traditional electrodynamic microspeakers. Despite their advantages in compactness, power efficiency, and ease of integration, these devices are limited by nonlinear hysteretic effects inherent to piezoelectric transduction, which often lead to undesirable distortion. Accurate and computationally efficient models are crucial for enabling digital signal processing (DSP) precompensation algorithms to address this challenge. While well-established nonlinear lumped-element models of electrodynamic loudspeakers have supported DSP techniques for equalization and linearization, the lack of analogous models for MEMS loudspeakers has constrained their broader application. This article presents a nonlinear discrete-time circuital model for a piezo-actuated MEMS loudspeaker designed for in-ear applications. The proposed model integrates two key processing components: a neural network (NN)-based block that accurately captures the nonlinear hysteretic behavior of piezoelectric transduction, and a linear circuit-equivalent block that represents the loudspeaker's vibration and acoustic environment. The discrete-time implementation of the model, including a wave digital filter (WDF) realization of the circuit-equivalent block, enables efficient and accurate simulation of nonlinear hysteretic dynamics under arbitrary input signals. Validation against experimental data-including time-domain pressure waveforms, frequency-domain sound pressure level (SPL), and total harmonic distortion (THD)-demonstrates the model's accuracy and effectiveness across a wide range of operating conditions.