Free Response of Piezoelectric Crystals in Series and in Parallel

The free response is considered of piezoelectric crystals (lithium niobate) with various polarities (including longitudinal only, shear only, and combined longitudinal and shear), which are stacked (mechanically and electrically in series) or are parallel (electrically parallel and mechanically uncoupled). Measurements of impedance magnitude from an impedance analyzer are compared with results from PSPICE simulations using a Mason model. These PSPICE models may serve as the basis for designing physical transducers from crystal stacks. INTRODUCTION Stacked piezoelectric elements have been used for some time to obtain large displacements, such as for lithotriptors or ultrasonic welders [1]. A stack combining longitudinal and crossed shear layers has been employed for static force measurement [2]. In the present work, the concept for a multi-mode transducer is based upon stacked crystals, each of which has a piezoelectric response to both longitudinal and shear waves, and which utilizes polarization cancellation to separate the two modes. It is common to use electrical circuit equivalent models, such as the KLM or Mason models, as a tool for transducer design [3]. As a preliminary process to the development of a multi-mode transducer, a Mason model, which is implemented using the electric circuit simulation software PSPICE [4], is used to simulate the free response of piezoelectric crystals in series and in parallel. TRANSDUCER CONCEPT Schematic representations of the cross-section of piezoelectric crystals with different voltages applied are presented in Fig. 1. In the figure, electrodes are indicated by a darker gray color, while the piezoelectric polarization is indicated by an arrow. The zerovoltage state is indicated by a dashed line. The figure indicates that with a positive applied voltage, a longitudinal polarized crystal expands, a shear polarized crystal shifts to the right, and the mixed mode crystal both expands and shifts to the right. Under a negative applied voltage, the motion is opposite; the longitudinal crystal contracts, the shear crystal shifts to the left, and the mixed mode crystal both contracts and shifts left.