Analytically calculating membrane displacement and the equivalent circuit model of a circular CMUT cell

An improved lumped element nonlinear circuit model for a circular CMUT cell

“…In [1, Eq. (10)], if the derivative had been taken with respect to x P , similar to the approach in [2], rather than x, there would have been an additional (1 − r 2 /a 2 ) 2 term inside the integral and the two results would have been identical.…”

An equivalent circuit for collapse operation mode of CMUTs

“…For the uncollapsed case, the displacement profile, x(r), as a function of applied uniform pressure is given by [4] or [5]. For the collapsed case, on the other hand, the displacement profile under uniform pressure is given by [2].…”

“…For the collapsed case, on the other hand, the displacement profile under uniform pressure is given by [2]. Although the electrostatic force on a CMUT membrane is not uniformly distributed in the case of an applied potential, we assume that any deflection profile caused by the applied voltage can be approximated by the deflection caused by a uniform pressure as in [4]. This is a good assumption when the membrane has an electrode covering its full surface.…”

“…2. Additionally, the electrical force generated by a voltage can be determined by using the deflection profiles in [2] and the equations in [4] or [5] as a function of the rms displacement. The resulting electrical force curves with respect to the rms displacement are plotted for different voltages in …”

“…Electrical equivalent circuit models, on the other hand, are based on Mason's linear equivalent circuit model for the uncollapsed mode, which are inadequate to predict the collapse state. In recent years, the efforts for modelling the nonlinear behavior of CMUTs [4], [5] have increased. However, all those models are valid for the uncollapsed mode, as well.…”