A Lumped circuit model for the mutual radiation impedance of acoustic array elements

Closely spaced transducer elements used in ultrasonic imaging suffer from cross-coupling via the fluid medium. Circuit models for transducer elements in ultrasonic arrays have to account for the coupling effect for an accurate representation of their radiation impedance. In this paper, we present a circuit model for the cross-coupling effects among capacitive micromachined ultrasonic transducer (cMUT) elements. Using the finite element method (FEM) we first show that the mutual radiation impedance of cMUT cells with a physical distance much smaller that the acoustic wavelength obey the analytic results derived for plane piston transducers. Then, we show that this mutual impedance can be modeled by an electrical RLC tank circuit suitable to be used in general circuit simulators. The circuit shows 80% percent accuracy in between 5 to 15 MHz for a cMUT resonant frequency of 11.8 MHz. Found element values for R, L and, C components are 0.268m , 4.156pH and, 49.946´F respectively. We then combine this circuit with a previously proposed model for the self radiation impedance of a cMUT cell to yield an equivalent circuit representation that accounts for the cross-coupling effect. The proposed equivalent circuit proves itself to be useful in the analysis of transceiver front-end integrated circuits where an accurate transducer model is compulsory for optimizing circuit performance.