A Nonlinear Lumped Equivalent Circuit Model for a Single Uncollapsed Square CMUT Cell

An accurate nonlinear lumped equivalent circuit model is used for modeling of capacitive micromachined ultrasonic transducers (CMUTs). Finite-element analysis (FEA) is a powerful tool for the analysis of CMUT arrays with a small number of cells while with the harmonic balance (HB) analysis of the lumped equivalent circuit model, the entire behavior of a large-scale arbitrary CMUT array can be modeled in a very short time. Recently, an accurate nonlinear equivalent circuit model for uncollapsed single circular CMUT cells has been developed. However, the need for an accurate large-signal circuit model for CMUT cells with square membranes motivated us to produce a new nonlinear large-signal equivalent circuit model for uncollapsed CMUT cells. In this paper, using analytical calculations and FEA as the tuning tool, a precise large signal equivalent circuit model of square CMUT dynamics was developed and showed excellent agreement with finite-element modeling (FEM) results. Then, different CMUT single cells with square and circular membranes were fabricated using a standard sacrificial release process. Model predictions of resonance frequencies and displacements closely matched experimental vibrometer measurements. The framework presented here may prove valuable for future design and modeling of CMUT arrays with square membranes for ultrasound imaging and therapy applications.