Small-Signal Equivalent Circuit Model of Long Rectangular CMUT Membranes

Capacitive micromachined ultrasound transducers (CMUTs) are typically designed with many small membranes per linear array element. However, these membranes can operate out of phase or collapse at different voltages, leading to suboptimal transmit performance and unreliable operation. To avoid these problems, we recently proposed a CMUT architecture with a single large rectangular membrane per element and novel insulated electrode post structures. These single-membrane CMUTs outperformed comparable piezoelectric transducers by almost 3-fold in terms of output pressure and demonstrated electromechanical efficiency values as high as 0.95. In this paper, we present an analytical model which can be used to simulate and optimize single-membrane rectangular CMUTs with or without post structures. Our approach relies on a polynomial deflection model, which was used to derive lumped element model parameters. Using this method, we developed expressions to model both electrostatic and pre-collapse small-signal dynamic CMUT behavior. This modeling framework was incorporated into a MATLAB program. We validated our approach using finite element method (FEM) simulations and experimental results in both air and immersion media. Model predictions for collapse voltage and operating frequency are within 4% of FEM results in both air and immersion. However, the runtime of our MATLAB program was 6 orders of magnitude faster than the corresponding FEM simulations. Compared with experiment, collapse voltage predictions were within 8%, and operating frequency predictions were within 5% in air and 18% in soybean oil. Our results indicate that that rectangular CMUTs may be optimized much further, potentially enabling even greater improvements over piezoelectric transducers.