Electrical Impedance Mathematical Modeling of Piezoceramic Disc Oscillating in Wide Frequency Range (Part 3. High Frequencies)

This paper discusses the results of mathematical modelling the electrical impedance of a piezoceramic disk oscillating in a wide range of high frequencies. The study aimed to create a mathematical model that would incorporate geometric, physical, and mechanical characteristics of the material to assess the behavior of the disk under conditions of electromechanical resonance and antiresonance. The research particularly focused on the influence of radial and axial displacements of material particles on the frequency dependence of the mechanical quality factor and electrical impedance of the disk. Even more closely, this research scrutinizes specific effects characteristic of the high-frequency mode, in order to increase the accuracy of modeling and ensure optimal technical characteristics of the devices. The mathematical model developed in this paper serves as a tool to obtain estimates for the frequency dependence of the mechanical quality factor and the dynamic electrical capacitance in real conditions, in particular, by including energy losses due to viscous friction into the calculations. Numerical calculations confirm the high correlation between theoretical and experimental data (with the discrepancy lower than 3.10-3), which proves the model usable for designing piezoelectric devices. In particular, it was found that the frequencies of electromechanical resonance and antiresonance are virtually independent of the radial displacements of material particles and are determined by the axial components solely. In addition, the calculation model provides the ability to assess the electrical impedance in the high-frequency range with an accuracy that meets modern requirements for the design of functional piezoelectric devices. The results obtained have practical significance for developing precision elements for military equipment, high-precision sensors, ultrasonic generators, medical diagnostic devices, and other technological systems that function with piezoelectric materials.