A simple closed-form model to accurately calculate the electromechanical coupling coefficient of CMUTs

Abstract

Abstract A simple highly accurate closed-form model to calculate the electromechanical coupling coefficient of a capacitive micromachined ultrasonic transducer (CMUT) is presented. The model exploits the electrostatic spring softening phenomenon to derive an expression for the energy converted from electrical to mechanical domain and includes the nonlinear change of the CMUT diaphragm stiffness during large deflections. The model has been validated by comparing the model predicted values with experimental results published elsewhere along with the results predicted by some existing models. The comparison shows that the model predicted values are in excellent agreement with experimental results. The model also enables one to quantify the effects of residual stress, bending, and nonlinear stretching of the diaphragm on the transduction efficiency of CMUTs without any computationally intensive finite element analysis method. The model resolves the ambiguity of the absence of electrostatic spring softening effect in some existing models.