An Improved Lumped Element Model for Circular-Shape pMUTs

This paper presents an improved lumped element model for clamped, circular-shape, piezoelectric micromachined ultrasonic transducers (pMUTs). A small signal equivalent circuit is developed to include electrical, mechanical, and acoustic domains, which are analyzed separately and combined with the associated couplings. For the first time, a two-term mode shape approach is adapted to reveal intrinsic and extrinsic properties of a pMUT, such as equivalent circuit parameters, input impedance, velocity, displacement, bandwidth, quality factor, directivity, and the on-axis pressure in the near and far field. These properties are compared with prior reports in the literature and exact solutions, as well as Finite Element Method (FEM) simulations. The errors relative to exact solution for all these properties are below 0.5%. These improvements in error are from 5x to about 3 orders of magnitude better than those of prior works. As such, the improved model could be helpful in design and simulation tools for pMUTs.