Fast and accurate CMUT modeling using equivalent circuits with lumped parameters

CMUT analysis is often done by equivalent circuits, but available circuits are not well adapted to include off axis steering of an array with several CMUTs per element. Here we show that the theory presented in [1] is well suited to establish equivalent circuits also for this case. The model has high computational efficiency, and is able to include effects of the viscosity of the fluid. The description assumes an infinite periodic array, and is formulated in k-vector space. The main focus is on the interaction between the CMUTs and the fluid, including interactions between different CMUTs through the fluid. We obtain an equivalent circuit of the Mason type for each CMUT vibration mode with parameters that depend both on the frequency and k-vector of the excitation. Two versions of the model are inherent in the theory in [1], but only one is presented here. The model presented allows CMUTs within an element to be different, whereas the elements must be equal and periodic, and on a rectangular grid. The model shows the effect of resonances due to neighbor coupling between CMUTs through the fluid. The CMUT parameters vary with frequency and steering angle, but may be interpolated to obtain fast computation. Computation times for an array with several equal CMUTs per element over a range of 0 to 45 degrees in steering angle and 1 to 12 in relative frequency are on the order of 4 s per included mode in each CMUT when interpolation of the CMUT parameters is used.