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.

翻译：近年来，具有长矩形膜片的电容式微机械超声换能器（CMUTs）已展现出优于传统压电换能器的性能优势；然而，对此类CMUT几何结构的建模一直局限于计算负担沉重的数值方法。改进的快速建模方法（如等效电路模型）有助于实现性能更优的设计。开发此类方法的主要障碍在于缺乏可处理的计算夹持矩形辐射体辐射阻抗的方法。本文提出一种方法，利用多项式形状模型近似速度分布，以快速准确地估算辐射阻抗。针对多种膜片纵横比和偏置电压，通过有限元仿真评估了近似速度分布及相应辐射阻抗计算的有效性。我们对宽长比从1:1至1:25的矩形辐射体进行了方法评估。在所有纵横比下，辐射电阻均得到了精确建模。然而，在计算辐射电抗时，我们的初始方法仅对低纵横比情况准确。这促使我们针对高纵横比情况考虑一种替代形状模型，该模型与有限元法（FEM）对比显示出更高的准确性。为促进未来矩形CMUT的开发，我们提供了一个MATLAB脚本，可快速使用两种方法计算辐射阻抗。