Equivalent Circuit Models for Large Arrays of Curved and Flat Piezoelectric Micromachined Ultrasonic Transducers

Equivalent circuit models of large arrays of curved (spherical shape) and flat piezoelectric micromachined ultrasonic transducers (pMUTs) have been developed for complex pMUT arrays design and analysis. The exact solutions for circuit parameters in the electromechanical domain, such as mechanical admittance, input electrical impedance, and electromechanical transformer ratio, were analytically derived. By utilizing the array solution methods previously established for the thickness-mode piezoelectric devices and capacitive micromachined ultrasonic transducers (cMUTs), the single pMUT circuit model can be extended to models for array structures. The array model includes both the self- and mutual-acoustic radiation impedances of individual transducers in the acoustic medium. Volumetric displacement, induced piezoelectric current, and pressure field can be derived with respect to the input voltage matrix, material, and geometrical properties of each individual transducer and the array structure. As such, the analytical models presented here can be used as a guideline for analyses and design evaluations of large arrays of curved and flat pMUTs efficiently and can be further generalized to evaluate other pMUT architectures in the form of single devices or arrays.