Theoretical simulation of the behavior of micromachined electrostatic ultrasonic transducers

A general three-dimensional (M) theoretical model for simulating the behaviour of micromachined electrostatic ultrasonic transducers has been developed. The model takes into account the transducer's geometry, the properties of material used, tension in diaphragm, and bias voltage, and then gives a complete mathematical formulation. Some special cases of it are briefly discussed also. The paper further applies the general model and its simplified varieties to predict natural frequencies of a surface micromachined ultrasonic transducer. The comparison between these theoretical values and measured results indicates that the 3D model gives accurate prediction and is a generalized model for describing the behaviour of various electrostatic audio and ultrasonic transducers.