Analytically calculating membrane displacement and the equivalent circuit model of a circular CMUT cell

A small-signal equivalent circuit model and FEM often guide CMUT design. The small-signal model is usually derived using a combination of numerical and FEM analysis. A strictly analytical approach to CMUT design is desired because it provides design intuition and efficient numerical analysis. In this paper, we show that the mass-spring-damper model used for many MEMS structures accurately captures the behavior of a CMUT with a circular plate. We provide equations for the CMUT´s equivalent mass-spring-damper parameters, pull-in point, and equivalent circuit parameters. Comparison with FEM shows that the model accurately captures the CMUT´s behavior for a wide range of designs. Using this model, we can derive simple design equations, calculate the small-signal model for frequency response simulations,. and simulate the CMUT´s large-signal transient behavior.