Circuit theory based modeling and analysis of CMUT arrays

Abstract

Many ultrasonic technology applications require capacitive micromachined ultrasonic transducers (CMUTs) to be used in the form of large arrays to attain better performance in terms of powerful, broadband and beam-formed radiated acoustic signals. To entirely benefit from its important characteristics, it is necessary to use analysis tools that are capable of handling multiple CMUT cells. In this regard, finite element analysis (FEA) tools become unfit for use because in arrays with large number of cells it is computationally very cumbersome and often practically impossible. Although, some simplification had been done by assuming long 1-D CMUT array elements as infinitely long, the results of these FEA simulations are misleading. In these models only a single periodic portion is modeled and rigid boundary conditions are applied at the symmetry planes. All the cells are assumed to be electrically driven in phase with the rest of the cells and the solution obtained for this portion is extended over the entire element. However, these simple models are not exact, because they exclude the important effects of mutual acoustic interactions between the cells. In this work, we developed an accurate nonlinear equivalent circuit model for circular uncollapsed CMUT cells. We investigated the effects of mutual acoustic interactions in uncollapsed CMUT arrays and showed that the performance of the array is highly influenced with this phenomenon. These mutual acoustic interactions rise through the immersion medium caused by the pressure field generated by each cell acting upon the others. To study its effects, we connected each cell in the array to a radiation impedance matrix that contains the mutual radiation impedance between every pair of cells, in addition to their self radiation impedances. Hence, analysis of the performance of a large array became a circuit theory problem and can be scrutinized with circuit simulators Surface micromachining technology enables batch fabrication of large CMUT arrays, which resolves cost issues and many physical limitations. Designers have to consider a great number of different array configurations. For nearly two decades, the lack of appropriate design and analysis tools prevented the investigation of array performance. By using the proposed model, one can very rapidly obtain the linear frequency and nonlinear transient responses of arrays with a large number of uncollapsed CMUT cells. Although, we use rapid circuit theory techniques, efficient analysis of very large arrays is still challenging, since a typical CMUT array may contain many tens of elements with hundreds of cells in each, which makes it computationally cumbersome. To partition the problem, we electrically drive a small number of elements in the array and keep the rest undriven but biased and with their electrical ports terminated with a load. The radiation impedance matrix can be partitioned and rearranged to represent these loads in a reduced form. In this way, only the driven elements can be simulated by coupling their cells through this reduced radiation impedance matrix. Under small signal regime, the separately calculated responses of element clusters can be added by using the superposition principle to find the total response. This method considerably reduces the number of cells and the size of the actual radiation impedance matrix, at the expense of calculating the inverse of a large complex symmetric matrix.