A lumped circuit model for the radiation impedance of a 2D CMUT array element

Abstract

Elements of a 2D array used for 3D acoustic imaging have dimensions smaller than half of the acoustic wavelength due to the Nyquist criteria for spatial sampling. Therefore, analyses involving circuit models for the array elements have to account for the reactive part of the radiation impedance of the array element. In this paper, we introduce a lumped circuit model for the complex radiation impedance of a 2D CMUT array element. Using the finite element method (FEM) we first show that the radiation impedance of the array element is identical to that of a plane piston transducer of comparable dimensions. Then, we show that the complex radiation impedance of the 2D array element can be represented by a simple resonant circuit placed parallel to the real radiation impedance in the Mason's equivalent circuit. The component values of the reactive lumped elements forming the resonant circuit were determined by fitting the impedance of overall equivalent circuit to the FEM results using the Nelder-Mead minimization algorithm.