Acoustic matching network synthesis using discrete space Fourier transforms

A method used to analyze and synthesize acoustic plane wave matching structures between a transducer and a medium is described. The analysis is applicable to multilayer structures with periodic discontinuities in characteristic impedance. It is shown that the frequency response of such structures is approximately equal to the discrete-time Fourier transform of the individual-layer reflection coefficients. The synthesis procedure uses the inverse transform to generate a sequence of layer characteristic impedances. Using this method, high transformation ratios over wide bandwidths can be obtained. A numerical example, using PZT-5A and water, is presented. The matching layer impedances generated by the Fourier synthesis procedure are then analyzed using an ideal transmission line model. The results of the analysis agree well with the predicted results of the synthesis procedure, indicating the validity of the approximations used to arrive at this method