Derivation of a 1D CMUT model from FEM results for linear and nonlinear equivalent circuit simulation

This paper presents a new method, which derives a 1D model for CMUT arrays from FEM simulations using piston radiator and plate capacitance theory. A few static and harmonic FEM analyses of a single CMUT membrane cell are sufficient to derive the mechanical and electrical parameters of an equivalent piston as the moving part of the cell area. These parameters describe the behavior of the CMUT in air and simplify the investigation of wave propagation within the connecting fluid represented by FEM or transmission line matrix (TLM) models. For an array of parallel driven cells the acoustic parameters are derived as a complex mechanical fluid impedance depending on the membrane shape form. Results from linear and nonlinear 1D model simulations of single cells and CMUT arrays will be presented and compared with FEM and measurement results. All results fit very well for the first membrane mode which is included so far. As a main advantage, the nonlinear behavior of the CMUT can be investigated easier and faster compared to FEM simulations.