Total harmonic distortion estimation in piezoelectric micro-electro-mechanical-system loudspeakers via a lumped elements approach

In the context of the increasing trend towards miniaturization required by new wireless audio devices, piezoelectric micro-electro-mechanical-system (MEMS) loudspeakers are getting extensive attention. Finite Element Methods (FEM) and Lumped Element Methods (LEM) models able to accurately predict their linear response have been recently proposed in the literature. However, a nonlinear model able to predict the Total Harmonic Distortion (THD) of theses types of devices is to date not available. In this paper we present a FEM- assisted lumped-parameters equivalent circuit accounting for piezoelectric hysteresis which demonstrates good agreement with experimental THD results carried out on piezoelectric MEMS loudspeakers prototypes fabricated by STMicroelectronics. The 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 simulate loudspeaker diaphragms of arbitrarily complex geometry. The parameters of the acoustical circuit are instead derived through analytical formulas.