A 1-D lumped theoretical model for CMUT

It is always difficult to optimize parameters of capacitive micromachined ultrasonic transducers (CMUT) because of high computational time cost of finite element method (FEM) analysis and economic cost of prototype manufacturing. Thus a theoretical model is required in designing a CMUT. This paper presents such a 1-D lumped model. A transfer function between output sound pressure and input AC voltage has been deduced based on control theory. This model makes it easier to optimize the parameters of a CMUT with respect to output sound pressure and bandwidth and to understand the influence of each parameter. To derive the proposed 1-D model, transition from a 3-D CMUT device to 1-D lumped model is performed by FEM analysis. Finally a typical example is given for verification. The result obtained by the proposed 1-D lumped model is compared to that by 3-D FEM simulation. It shows that our proposed 1-D lumped model can be used to study the behavior of CMUT at much lower computational cost without losing accuracy.