An equivalent circuit model for transmitting capacitive micromachined ultrasonic transducers in collapse mode

The collapse mode of operation of capacitive micromachined ultrasonic transducers (CMUTs) was shown to be a very effective way to achieve high output pressures. However, no accurate analytical or equivalent circuit model exists for understanding the mechanics and limits of the collapse mode. In this work, we develop an equivalent nonlinear electrical circuit that can accurately simulate the mechanical behavior of a CMUT with given dimensions and mechanical parameters under any large or small signal electrical excitation, including the collapse mode. The static and dynamic deflections of a plate predicted from the model are compared with finite element simulations. The equivalent circuit model can estimate the static deflection and transient behavior of a CMUT plate to within 5% accuracy. The circuit model is in good agreement with experimental results of pulse excitation applied to fabricated CMUTs. The model is suitable as a powerful design and optimization tool for collapsed and uncollapsed CMUTs.