Radiation Impedance of Rectangular CMUTs

TL;DR

This paper introduces a fast, polynomial-based method to accurately estimate the radiation impedance of rectangular CMUTs, improving design efficiency over traditional numerical approaches.

Contribution

It develops a tractable polynomial velocity profile model for rapid radiation impedance calculation of rectangular CMUTs, validated against finite element simulations.

Findings

Radiation resistance is accurately modeled across aspect ratios.

Initial reactance model works well for low aspect ratios.

Alternative shape model improves reactance accuracy at high aspect ratios.

Abstract

Recently, capacitive micromachined ultrasound transducers (CMUTs) with long rectangular membranes have demonstrated performance advantages over conventional piezoelectric transducers; however, modeling these CMUT geometries has been limited to computationally burdensome numerical methods. Improved fast modeling methods such as equivalent circuit models could help achieve designs with even better performance. The primary obstacle in developing such methods is the lack of tractable methods for computing the radiation impedance of clamped rectangular radiators. This paper presents a method which approximates the velocity profile using a polynomial shape model to rapidly and accurately estimate radiation impedance. The validity of the approximate velocity profile and corresponding radiation impedance calculation was assessed using finite element simulations for a variety of membrane aspect ratios and bias voltages. Our method was evaluated for rectangular radiators with width:length ratios from 1:1 up to 1:25. At all aspect ratios, the radiation resistance was closely modeled. However, when calculating the radiation reactance, our initial approach was only accurate for low aspect ratios. This motivated us to consider an alternative shape model for high aspect ratios, which was more accurate when compared with FEM. To facilitate development of future rectangular CMUTs, we provide a MATLAB script which quickly calculates radiation impedance using both methods.