# Mathematical Modelling of Rod-Type Piezo-Electric Transducers for Acoustoelectronic Devices

## DOI:

https://doi.org/10.20535/RADAP.2021.86.58-67## Keywords:

piezoelectric transducer, acoustoelectronics, mathematical model, electrical signal generator## Abstract

The work is devoted to the peculiarities of the construction and study of mathematical models of rod-type piezoelectric transducers, which are widely used in various acoustoelectronic devices (hydroacoustic means of target detection, ultrasonic non-destructive testing, medical diagnostics, etc.). In contrast to the existing mathematical models of piezoelectric transducers (based on amplitude-phase dependences, resonant piezoelectric transducers, equivalent circuits, etc.), the proposed mathematical model makes it possible to establish a dependence, which is a mathematical description of the acoustic coupling that exists in a solid piezoceramic rod between wave fields on its various areas.

An algorithm for calculating a mathematical model of rod-type piezoelectric transducers is presented and based on the determination of the transformation ratio, which occurs when the inverse piezoelectric effect. Analytical dependencies, which make it possible to determine the electrical impedance and the amplitude value of the potential in the electrical circuit of the piezoelectric transducer, are obtained. It is shown that these dependencies underlie the expression for determining the transformation ratio К(ω, П), which is a mathematical model of a rod piezoelectric transducer. At the same time, the principle of operation of such a transducer provides for the use of longitudinal vibrations in a prismatic rod.

The results of the mathematical modelling are presented on the example of a rod transducer with a square cross-section made of piezoelectric ceramics of the PZT type. The performed comparisons of the calculated and experimentally obtained values of the frequency dependence of the modulus of the transformation ratio of the piezoceramic transducer showed a high convergence between them (the discrepancy between the results of mathematical modelling and the experimentally obtained data for the same value of the operating frequency does not exceed 8.5%).

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*Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia*, (86), pp. 58-67. doi: 10.20535/RADAP.2021.86.58-67.

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