Parametric linear modeling of circular cMUT membranes in vacuum.

We present a lumped element parametric model for the clamped circular membrane of a capacitive micromachined ultrasonic transducer (cMUT). The model incorporates an electrical port and two sets of acoustic ports, through which the cMUT couples to the medium. The modeling approach is based on matching a lumped element model and the mechanical impedance of the cMUT membrane at the resonance frequencies in vacuum. Very good agreement between finite element simulation results and model impedance is obtained. Equivalent circuit model parameters can be found from material properties and membrane dimensions without a need for finite element simulation.