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Determination of parameters of elements of the equivalent circuit of a piezoelectric resonator

DOI 10.18127/j00338486-201907(10)-04

Keywords:

B.D. Zaitsev – Professor, Main Research Scientist, Saratov branch of Kotel’nikov IRE of RAS
E-mail: zai-boris@yandex.ru
A.P. Semyonov – Ph.D.(Phys.-Math.), Senior Research Scientist, Saratov branch of Kotel’nikov IRE of RAS
E-mail: alex-sheih@yandex.ru
A.A. Teplykh – Ph.D.(Phys.-Math.), Senior Research Scientist, Saratov branch of Kotel’nikov IRE of RAS
E-mail: teplykhaa@mail.ru
I.A. Borodina – Ph.D.(Phys.-Math.), Leading Research Scientist, Saratov branch of Kotel’nikov IRE of RAS
E-mail: borodinaia@yandex.ru


To calculate the characteristics of piezoelectric resonators, various methods are used, among which the most popular is the method of equivalent circuits. This method is based on the Mason’s equivalent circuit, which includes an electromechanical transformer with an electrical and two mechanical terminals. In most cases, the mechanical part of the circuit is converted into the electrical one, and the number of the required parameters is significantly reduced. With this approach, most researchers consider these parameters to be fixed, i.e. frequency independent. However, this is true only near the resonant frequency and for resonators that have a very small value of the coefficient of electromechanical coupling. In this paper, using the example of two resonators with a longitudinal and lateral electric field, we show a new approach to determining the frequency characteristics of the dynamic elements of an equivalent circuit. For the experiments, two resonators with a longitudinal and lateral electric field were made of PZT 19 piezoceramics. Using the LCR parameter meter, the frequency dependences of the real and imaginary parts of the electrical impedance and admittance were measured. For each resonator, the presence of two resonances was established. The frequency dependences of the real and imaginary parts of the dynamic electrical impedance were calculated from these dependencies. The frequency dependences of the real and imaginary parts of the electrical impedance and admittance constructed from these data exactly coincided with the experimental graphs. Obviously, this scheme can be used to assess the effect of conducting layers on the free side of a resonator with a lateral electric field on its characteristics. The effect of the conductivity of the liquid contacting with such a resonator can also be evaluated.

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