Equivalent circuit-based analysis of CMUT cell dynamics in arrays

Abstract

Capacitive micromachined ultrasonic transducers (CMUTs) are usually composed of large arrays of closely packed cells. In this work, we use an equivalent circuit model to analyze CMUT arrays with multiple cells. We study the effects of mutual acoustic interactions through the immersion medium caused by the pressure field generated by each cell acting upon the others. To do this, all the cells in the array are coupled through a radiation impedance matrix at their acoustic terminals. An accurate approximation for the mutual radiation impedance is defined between two circular cells, which can be used in large arrays to reduce computational complexity. Hence, a performance analysis of CMUT arrays can be accurately done with a circuit simulator. By using the proposed model, one can very rapidly obtain the linear frequency and nonlinear transient responses of arrays with an arbitrary number of CMUT cells. We performed several finite element method (FEM) simulations for arrays with small numbers of cells and showed that the results are very similar to those obtained by the equivalent circuit model.

Resonances and nonuniformities in CMUT elements or arrays

“…The mechanical ports of the N = n × m cells are connected to an N -port represented by the N × N Z matrix. Diagonal entries of Z matrix represent the self-radiation impedance [4] of the CMUT cells, while the off-diagonal entries [9] show the mutual-radiation impedance between the cells. The array elements are connected to m sinusoidal voltage sources,…”

“…where A = ρ 0 c o πa 2 10 n=0 p n (ka) n [9]. We can simplify the infinite summation using the Mercator series to get an implicit analytic dispersion relation for R-B waves:…”

A Simplified Equivalent Circuit Model of MEMS Electrostatic Actuator

“…The model can be simulated using any circuit simulator capable of simulating SPICE and Verilog-A. There are several equivalent circuit models which have been developed [9][10][11][12][13][14][15][16][17][18][19], however this paper presents a simplified model which is accurate as well as fast and can used for system level simulations [20][21].…”

Parametric nonlinear lumped element model for circular CMUTs in collapsed mode

“…starting from Mason's model for acoustic transducers [11], equivalent circuit modeling has been improving as a powerful alternative to FEM [9], [12]- [15], especially for array modeling [16]- [18]. The studies directed toward understanding and modeling mutual impedance of cMUT arrays [2], [4], [17], [19], [20] have helped to improve the accuracy of lumped element simulations.…”

“…The operation of large cMUT arrays can only be predicted using lumped element modeling, because the computation cost of FEM exponentially increases with increasing cell count. currently, the uncollapsed-mode operation of cMUT arrays is well understood through equivalent circuit model simulations [17]. The mechanical and electrical properties of uncollapsed-mode operation are perfectly adapted to the lumped model [21].…”