Total harmonic distortion estimation in piezoelectric micro-electro-mechanical-system loudspeakers via a FEM-assisted reduced-order-model

Piezoelectric micro-electro-mechanical-system (MEMS) loudspeakers are attracting growing research interest in the last years due to the increasing interest towards miniaturization required by new wireless audio devices. Finite Element Models (FEM) and Lumped Element Models (LEM) able to accurately simulate their linear response have been recently proposed in the literature. However, a nonlinear model suitable to predict the Total Harmonic Distortion (THD) of these devices is to date still missing. In this work, we present a FEM-assisted lumped-parameters equivalent circuit for THD estimation which accounts for geometric nonlinearities and piezoelectric hysteresis. The loudspeaker nonlinear electro-mechanical domain is simulated through a Reduced Order Model (ROM) which considers as basis function the pre-stressed undamped actuated mode of the device computed via FEM, to account for loudspeaker diaphragms of arbitrarily complex geometry. Parameters of the acoustical circuit are computed through analytical formulas. The good matching between numerical predictions and experimental results, carried out on a piezoelectric MEMS loudspeaker prototype for in-ear condition, demonstrates the accuracy of the proposed tool.