TABLE OF CONTENTS Piezoelectric transformers for raising or lowering electric voltage are widely used in various electronic equipment. In a piezoelectric transformer energy converts twice: from electrical to mechanical and then back to electrical. The basic behavior of a piezoelectric transformer is governed by the linear theory of piezoelectricity.
As a simple example, consider a transformer consisting of two piezoelectric ceramic plates poled in the thickness direction. It has two traction-free surfaces and an interface, which are all electroded (see Fig. 12.1.1) [116].
The driving portion 0 ? x 3 ? h 1 is poled in the positive x 3 direction and the receiving portion ?h 2 ? x 3 ?0 is poled in the negative x 3 direction. Under a time-harmonic driving voltage V 1 (t) with a proper frequency, the transformer can be driven into thickness-stretch vibration and produce an output voltage V 2 (t). The output electrodes are connected by a circuit whose impedance per unit area is denoted by Z L. Since the transformer is inhomogeneous with ceramics poled in different directions, we need to model each layer separately with interface continuity conditions. The plates are thin and edge effects are neglected.
For the driving portion the governing equations for thickness-stretch vibrations are
The boundary conditions at the top surface are
The current density per unit area flowing out of the driving electrode at x
