Mathematical Modeling the Electrical Impedance of the Piezoceramic Disk Oscillating in a Wide Frequency Range (Part 1. Low Frequencies)
DOI:
https://doi.org/10.20535/RADAP.2023.94.41-48Keywords:
piezoelectric transducer, acoustoelectronics, mathematical modeling, impedance, disk elementAbstract
The article presents the results of mathematical modeling and analysis of the electrical impedance of a piezoceramic disk that undergoes oscillations at low frequencies, i.e., when the length of the elastic wave significantly (by an order of magnitude or more) exceeds the radial size of the disk. Thus, the proposed mathematical model of disk-shaped ceramic elements of piezoelectric transducers, which are an important component of modern communication devices, environmental sensors, precision equipment, medical devices, etc. A key characteristic of the mathematical model described in the article is its ability to determine analytical dependencies that allow estimating such fundamental electrical properties of the piezoceramic disk element as electrical impedance and quasi-static electrical capacitance, thereby significantly simplifying the calculation of such an element already at the design stage.
The static dielectric permittivity of a piezoceramic disk vibrating at low frequencies has been investigated. The calculated value of this parameter, based on the physical constants’ characteristic of the piezoceramic of the PZT (lead zirconate titanate) type, is 1.844 times higher compared to the high-frequency (dynamic) dielectric permittivity.
It has been found that in the low-frequency range, when the mechanical stresses in the vibrating piezoceramic disk approach zero and the direct piezoelectric effect is almost negligible, the electrical impedance of such a disk can be described as the reactive resistance of a capacitor with electrical capacitance equivalent to the quasi-stationary capacitance of the disk. This is confirmed by a high degree of convergence between theoretical data and experimental results, with discrepancies not exceeding 6%.
The results obtained in the article can be valuable for scientific research in the fields of precision instrument engineering and radio equipment manufacturing. Additionally, they have practical applications in the development and production of high-tech equipment.
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Copyright (c) 2023 Костянтин Базіло, Руслана Трембовецька, Людмила Усик, Еміль Фауре, Андрій Чорній
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