Tapered-thickness piezoelectric ceramics: Models and characteristics

Tapered-thickness piezoelectrics have been studied for use in novel devices and imaging techniques, such as wideband transducers and frequency-controlled beam translation. However, no adequate theoretical model exists. In this work, a staircase model is developed in which the thickness gradient is represented as discrete steps. Each step is modeled as a constant-thickness section, which contributes to the net response. This approach allows the results and techniques developed for conventional devices to be readily applied to those with tapered thickness; it emphasizes important similarities and differences, and provides physical insight into the dynamics of tapered piezoelectrics. The model shows that the distributed half-wavelength resonances dominate its response. In addition, however, a taper-dependent, transverse interaction exists among steps, which adds to the primary response. A coupled oscillator approach is used to model this transverse cross talk with an acoustic transmission line. The theoretical electric input impedance, spectral content, pulse, and continuous-wave pressure profile responses obtained with the model are shown to be in close agreement with the measured responses from several tapered piezoelectric transducers.