A Two-Dimensional Equivalent Circuit for the Tall Thin Piezoelectric Bar

Abstract

An equivalent circuit is derived for the tall thin bar based on the piezoelectric constitutive relations. The model has two sections, a z-direction (thickness) and an x-direction (lateral). The z-direction section resembles the equivalent circuit for a thickness mode transducer, while the x-direction section resembles the circuit for a side electroded length expander. The two sections are coupled through capacitors which model mechanical compliance. The model consists of two transmission lines, two transformers and five capacitors. circuit approach is the ability to apply circuit theory to the analysis and design of linear array elements. This includes simulation of quarter wave layers, electronic drivers, backing impedances, electrical matching networks and lateral loading. The equivalent circuit was simulated on SPICE. Theoretical time and frequency responses were generated for experimental elements and compared with laboratory observations. The principal advantage of the equivalent