681.586

mathematical model, piezotransformer, piezoelectric element, MicroCAP.

The mathematical model of a piezoelectric transformer of the transverse-transverse type and describes the method of its construction has been presented. Although mathematical modeling programs for piezoelectric devices can achieve any predetermined modeling accuracy, the simulation results cannot be directly used in the development of electronic equipment, because the programs are not integrated with CADs, for this reason most often in calculations and in modeling circuits based on piezotransformers, the simplest equivalent circuit is used. But its adequately reflects currents and voltages in the piezotransformer circuit only in the vicinity of the operating resonant frequency. The proposed model is based on a one-dimensional approximation of the equations of state and dynamics of the piezoelectric medium for flat plates of constant thickness and width, which is obtained from a three-dimensional system of equations by averaging the width and thickness. While the usual approximate model often allows to model a piezotransformer with two pairs of electrodes and only in the vicinity of one resonant frequency, the model constructed in the article allows to take into account the presence of several electrodes on piezotransformer surfaces and their different relative positions on the upper and lower surfaces. 'esoplastin. Compared with the usual, the proposed model is more convenient for modeling by means of circuit modeling systems. In the developed model, the piezotransformer is represented as a set of interconnected sections that carry one pair or several pairs of electrodes on the surfaces. Also, in contrast to the usual, the proposed model allows to take into account the presence of several resonant frequencies of the piezotransformer, which allows more adequate modeling of electronic equipment that uses in its structure a piezoelectric transformer of the transverse type. On the basis of the mathematical model the scheme of substitution of separate sections of the piezoelectric transformer is constructed and formulas for calculation of parameters of elements of the scheme are given. In in the article as example the implementation of the developed model in the computer-aided design system MicroCAP has been showed.

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   Doi: 10.1143/jjap.47.2182.
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11. Shine-Tzong Ho. (2007). Modeling and analysis on ring-type piezoelectric transformers. IEEE Transactions on Ultrasonics. Ferroelectrics and Frequency Control. 54 (11). P. 2376–2384.
    Doi: 10.1109/tuffc.2007.542 
12. Pulpan P., Erhart J., & Štípek O. (2007). Analytical Modeling of Piezoelectric Transformers. Ferroelectrics. 351 (1). P. 204–215. Doi: 10.1080/00150190701354299.

1. Katz H. W. Solid state magnetic and dielectric devices/ edited by H. W. Katz New York: Wiley, 1959.
   542 p.
2. Lavrinenko V. V. Piezoelectric transformers. M.: Energy, 1975. 112 р.
3. Harris, John W., Horst Stöcker Handbook of mathematics and computational science. Springer Science & Business Media, 1998. 1056 p. DOI: 10.1007/978-1-4612-5317-4.
4. Yerofeyev A. A. P'yezoyelektronnyye ustroystva avtomatiki. L. ZH Mashinostroyeniye, L otd., 1982.
   212 р.
5. Yerofieev А. А., Danov G. А., Frolov V. N. Piezoelectric transformers and their applications. М.: Radio and communication, 1988. 128 p.
6. Piezoelectric Transformer and Experimental Verification. LiMMS/CNRS, The University of Tokio. 2001.
7. Yu. Е. Paerand, candidate of technical sciences, D. А. Kryvoshei. = Research of characteristics of piezoelectric transformers. Scientific and technical collection “Electronics and communication”. Thematic issue “Electronics and nanotechnologies”. No. 5. 2010. P. 28–34.
8. Piezoelectric Transformer Characterization and Application of Electronic Ballast/Ray-Lee Lin. Dissertation submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirement for the degree of Doctor of Philosophy in Electrical Engineering Blacksburg, Virginia. 2001. 171 p.
9. Yang Y.-J., Chen C.-C., Kuo C.-W., & Lee C.-K. (2008). Thermo-Piezoelectric Finite Element Modeling for Piezoelectric Transformers. Japanese Journal of Applied Physics. 47 (4). P. 2182–2188.
   Doi: 10.1143/jjap.47.2182.
10. Yang Y. J., Chen C. C., Chen Y. M., & Lee C. K. (2008). Modeling of piezoelectric transformers using finite-element technique. Journal of the Chinese Institute of Engineers. 31 (6).P. 925–932.
11. Shine-Tzong Ho. (2007). Modeling and analysis on ring-type piezoelectric transformers. IEEE Transactions on Ultrasonics. Ferroelectrics and Frequency Control. 54 (11). P. 2376–2384.
    Doi: 10.1109/tuffc.2007.542 
12. Pulpan P., Erhart J., & Štípek O. (2007). Analytical Modeling of Piezoelectric Transformers. Ferroelectrics. 351 (1). P. 204–215. Doi: 10.1080/00150190701354299.