Fast time-domain modeling of fluid-coupled cMUT cells: from the single cell to the 1-D linear array element

We report a fast time-domain model of fluid-coupled cMUTs developed to predict the transient response-i.e., the impulse pressure response-of an element of a linear 1-D array. Mechanical equations of the cMUT diaphragm are solved with 2-D finite-difference schemes. The time-domain solving method is a fourth-order Runge-Kutta algorithm. The model takes into account the electrostatic nonlinearity and the contact with the bottom electrode when the membrane is collapsed. Mutual acoustic coupling between cells is introduced through the numerical implementation of analytical solutions of the impulse diffraction theory established in the case of acoustic sources with rectangular geometry. Processing times are very short: they vary from a few minutes for a single cell to a maximum of 30 min for one element of an array. After a description of the model, the impact of the nonlinearity and the pull-in/pull-out phenomena on the dynamic behavior of the cMUT diaphragm is discussed. Experimental results of mechanical displacements obtained by interferometric measurements and the acoustic pressure field are compared with simulations. Different excitation signals-high-frequency bandwidth pulses and toneburst excitations of varying central frequency-were chosen to compare theory with experimental results.