Self and Mutual Radiation Impedances for Modeling of Multi-Frequency CMUT Arrays

Multi-frequency capacitive micromachined ultrasonic transducers (CMUTs) consist of interlaced large and small membranes for multiband operation. In modeling these devices, accurate and computationally efficient methods are required for computing self- and mutual-acoustic-radiation impedances. However, most previous works considered mutual-acoustic impedance between radiators of identical size. A need was thus found to revisit the fundamental framework for mutual-acoustic impedance for its applicability to radiators, especially flexural disks, of differing size. The Bouwkamp integral method is used to achieve infinite series expressions for self- and mutual-acoustic radiation impedances. Polynomial-fitting-based approximate relations of the mutual-acoustic impedance are developed for arbitrary array geometries and are in good agreement with exact expressions. The derived mutual-acoustic impedance is incorporated into equivalent circuit models of multi-frequency CMUTs showing excellent agreement with finite element modeling. The results demonstrate that mutual-acoustic interactions significantly impact device performance. The framework presented here may prove valuable for future design of multi-frequency arrays for novel multiscale imaging, superharmonic contrast imaging, and image therapy applications.