An Electromechanical Model for Clamped-Edge Bimorph Disk Type Piezoelectric Transformer Utilizing Kirchhoff Thin Plate Theory

In this paper, an analytical solution for a clamped-edge bimorph disk-type piezoelectric transformer with Kirchhoff thin plate theory is proposed. The electromechanical equations for transient motions are first derived, and coupled expressions for mechanical response and voltage output are obtained. For the case of excitation around the first resonant frequency, the resulting equations are further simplified. There are analytical solutions for a mechanical response, voltage, current, and power outputs. According to the analytical model, the output voltage is affected by the inner radius of the input and output electrodes, the radius of the piezoelectric transformer (PT), and the thickness ratio between the lead zirconate titanate (PZT) layer and the substrate. When the inner radius of the input electrode approaches zero (electrode becomes circular shape), it achieves maximum output voltage at the first resonance frequency excitation. On the contrary, when the inner radius of the output electrode approaches zero, the output voltage reaches its minimum value. Voltage ratios remain constant as the disk radius changes, and the first resonance frequency is inversely proportional to the square of the disk radius. The voltage ratio is fixed even with the miniaturization of the PT.