A two-dimensional model of the multi-element piezoelectric transducer

A two-dimensional model of the piezoelectric transducer for acoustic imaging applications is described. The single piezoelectric element is described, in the frequency domain, by a 5×5 matrix computed by the two-dimensional piezoelectric plate model. In order to simulate the total array, the same model is used to compute a 4×4 matrix describing the inactive material which usually fills the gap between the elements. To predict the behavior of the overall transducer, an algorithm is developed which, using these two matrices, builds the overall matrix of the array. This algorithm has been numerically checked to verify its results. The model easily takes into account the backing and the matching plates. In order to verify its results, a simple array was built, and the measured electrical impedance was compared with the computed one, yielding good agreement