A tensile-plate-on-air-spring model (or called TDK model for short) for micromachined electrostatic ultrasonic transducers has been developed based on a thorough investigation of their dynamic mechanism. The mechanical stiffness effects caused by the compressibility of air gaps, bending stiffness of the diaphragm and in-plane tension applied to the diaphragm, together with an electrostatic negative stiffness effect are included completely in the model. Desired particular fundamental frequency and bandwidth can be obtained by only properly tailoring the geometry, dimensions and materials of transducers according to the model, which provides thereby a reliable theoretical basis for the understanding and optimised design of such transducers.
A theoretical model and mathematical description for silicon micromachined elec- trostatic or capacitive ultrasonic imaging transducers have been developed. Ac- cording to the model the basic performance parameters of such a transducer, such as natural frequencies, eigenfunctions, resonance and anti-resonance frequencies, and the mechanical impedance of the diaphragm can be predicted from the ge- ometry of the transducer and property parameters of materials used. The paper reveals that this type of transducers has two basic operation modes, correspond- ing to the resonance of a mass-spring oscillator comprised of the diaphragm and the air cushion, and the first-order bending mode of the diaphragm itself respec- tively, and presents an optimal method for extending the bandwidth by making the two modes coupled, and thereby provides a theoretical basis for the optimal de- sign.
