  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.
