Lumped element modeling of circular CMUT in collopsed mode

Capacitive micromachined ultrasonic transducer is a microelectromechanical device, which serves as an acoustic signal source or sensor, in a variety of applications including medical ultrasound imaging, ultrasound therapy, airborne applications. It has a suspended membrane with an electrode inside, and at the underlying substrate there is another electrode, so that the membrane can be deflected by the electrical field formed between the electrodes. Similarly, any mechanical disturbance on the membrane can be sensed as a change in the capacitance of the two electrodes. CMUT is a nonlinear device which has a distributed mechanical operation. Although, it is a mass-spring system basically, the nonlinear electrical force and the radiation force makes it impossible to solve CMUT through analytical equations. In order to predict its behavior, and design a CMUT towards the needs of a specific application, either finite element analysis or equivalent electrical circuit modeling should be utilized. Finite element analysis (FEA) can predict the distributed CMUT operation with high accuracy, but its usage is limited to designs employing low number of CMUTs because of the computation cost. Recently, advances in equivalent circuit modeling, made it possible to simulate arrays employing very high number of CMUTs, with high accuracy. These models assume uncollapsed mode operation and except collapsed mode operation as it is highly nonlinear. This thesis focuses on obtaining an accurate equivalent circuit model for a circular CMUT in collapsed mode. The outcome is a parametric circuit model, that can simulate a CMUT of any physical and material parameters, under an arbitrary electrical or mechanical excitation. In collapsed mode, the compliance of the membrane is no longer constant as in uncollapsed mode, and it increases with increasing contact radius. Similarly, the capacitance, the electrical force and the radiation impedance all have new behavior regarding the contact radius. As there is no analytical solution for those parameters, we perform numerical calculations and extract expressions for each of them. First, we calculate the collapsed membrane deflection, utilizing the exact electrical force distribution in the analytical formulation of membrane deflection. Then we use the deflection profile to calculate the capacitance, electrical force, and compliance. Performing a set of calculations for different CMUT dimensions, different pressure and voltage levels, we obtain dependencies of those parameters on rms deflection. Then we develop a lumped element model of collapsed membrane operation, expressing the parameters as functions of rms deflection. The radiation impedance for the collapsed mode is also included in the model. The model is then merged with the uncollapsed mode model to obtain a simulation tool that handles all CMUT behavior, in transmit or receive. Large- and smallsignal operation of a single CMUT can be fully simulated for any excitation regime. The results are in good agreement with FEM simulations.