Improved equivalent circuit and finite element method modeling of capacitive micromachined ultrasonic transducers

Equivalent circuit model has been widely used to predict the bandwidth of capacitive micromachined ultrasonic transducers (CMUTs). According to this model, the lower cutoff of the bandwidth is determined by the time constant of the parallel RC where R is dictated by the radiation and C is determined by the electrical capacitance of the transducer. The higher cutoff, on the other hand, is determined by the membrane's anti-resonance. In the mechanical part of the model, the radiation impedance is simply added to the membrane, impedance assuming that the membrane impedance does not change when it operates in the immersion medium. Therefore, the mass loading effect of the medium is neglected. Our finite element method calculations showed that the mass loading on the membrane impedance drastically lowers the membrane anti-resonance frequency degrading the bandwidth. In this paper, we present results of equivalent circuit modeling combined with finite element analysis. We constructed a 3D finite element model for one element of a ID array. The element has 7 hexagonal membranes in the width dimension and it is assumed that the membranes are replicated in the length dimension infinitely by using symmetry boundary conditions. By combining membrane impedance with equivalent circuit model, we found that the center frequency of operation is 11 MHz and the bandwidth is 12.5 MHz close to the collapse voltage. We also investigated the effect of the DC bias on the center frequency. Decreasing the bias voltage increased the center frequency without affecting the bandwidth assuming the source impedance is zero.