Lumped-parameter modeling of MEMS hydrophone for different diaphragm geometries

Abstract

The geometry of hydrophone elements significantly influences array structure fill-factor and overall hydrophone performance. This study introduces an enhanced theoretical model for Microelectromechanical Systems (MEMS) piezoelectric hydrophone elements, comprehensively characterizing their performance across various geometries. Utilizing the Ritz method, our model provides a generalized solution for approximating mode shape functions of hydrophone elements with diverse shapes and boundary conditions. We derive electromechanical equivalent circuits through modal orthogonality, providing a new mathematical insight into the derivation process, while maintaining equivalence to traditional energy-based methods. The static receiving sensitivity expression is then obtained by analyzing the equivalent circuit’s system function. Our proposed model demonstrates satisfactory accuracy with significantly reduced computational demands compared to finite element method (FEM) based numerical models. This comprehensive theoretical framework offers valuable insights for optimizing element dimensions in MEMS hydrophones and piezoelectric micromachined ultrasonic transducers (PMUTs), potentially advancing the design and enhancing the performance of piezoelectric hydrophones.