COMPUTER OPTIMIZATION OF TRANSDUCER TRANSFER-FUNCTIONS USING CONSTRAINTS ON BANDWIDTH, RIPPLE, AND LOSS

Transducers, having one piezoelectric layer near its half-wave resonan ce and N quarter-wave layers, are designed using computer optimization to adjust the thicknesses and impedances of the various layers so as to fit the resulting transfer function to a target function. An augmen ted Mason model is used to evaluate the transducer. Optimization of fi t is by a steepest descent algorithm, Essentially error-free fits are achieved for target functions that match the underlying dynamics, By a pplying classical filter theory to a lumped-element transducer model, the transducers dynamics are identified as all-pole filters, which are characterized by polynomials of order N to N + 1, The design methodol ogy is tested by designing a series of low-loss transducers that explo re fractional bandwidths from 45 to 116%, From these studies there app ears to be constraints on the minimum Q of the poles, and other proper ties. Typical power transfer efficiencies of -1 dB are achieved by imp edance scale matching, Using a second-order Fano bound, it is shown th at the matching layers function as an optimal compensation network for low-loss hat bandpass transducers. Finally, by the inclusion of loss, lower Q pales are demonstrated with a Bessel transducer.