DOI: https://doi.org/10.15588/1607-3274-2018-4-1

### PRINCIPLES AND METHODS OF THE CALCULATION OF TRANSFER CHARACTERISTICS OF DISK PIEZOELECTRIC TRANSFORMERS

C. V. Bazilo

#### Abstract

Context. Thanks to its unique properties piezoceramics has applications in various fields of engineering and technology. Disk piezoelectric devices are widely used in the elements of information systems. Research has shown that piezoelectric transformers can compete with traditional electromagnetic transformers on both efficiency and power density. The final goal of mathematical modeling of the vibrating piezoelectric elements physical condition is a qualitative and quantitative description of characteristics and
parameters of existing electrical and elastic fields.
Objective. The purpose of this paper is to set out the principles of mathematical models construction that are sufficiently adequate to real devices and occurring physical processes using the simplest example of axially symmetric radial oscillations of the piezoelectric disk.
Method. Mathematical models of piezoelectric transformers working with axially symmetric radial oscillations of piezoceramic disks are constructed with a minimal number of assumptions simplifying the real situation. This allows us to state that the proposed construction scheme delivers mathematical models that are sufficiently adequate to the real objects and physical processes that exist in them.
Results. Main results of this work can be formulated as follows: mathematical model of piezoelectric transformer with ring electrode in the primary electrical circuit is constructed; high sensitivity of frequency characteristic of piezoelectric transformer to the values of the output impedance of the electrical signal source in the primary electrical circuit is demonstrated.
Conclusions. As a result of research of real device’s mathematical model a set of geometrical, physical and mechanical and electrical parameters of a real object can be determined which provides realization of technical parameters of piezoelectric functional element specified in technical specifications. The cost of the saved resources is the commercial price of the mathematical model. Prospects for further research can be to build a mathematical model of a piezoelectric transformer with sector electrodes.

#### Keywords

piezoelectric transformer; axially symmetric oscillations; physical processes; mathematical model.

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#### References

Varadan V., Vinoy K. and Dzhoze K. VCh MEMS i ikh

primenenie. Mosсow, Tekhnosfera, 2004, 528 p.

Bove T., Wolny W., Ringgaard E., and Breboel K. New type

of piezoelectric transformer with very high power density.

Applications of Ferroelectrics, 2000, Vol. 1, pp. 321–324.

DOI: 10.1109/ISAF.2000.941564

Flynn A. M. and Sanders S. R. Fundamental limits on

energy transfer and circuit considerations for piezoelectric

transformers, IEEE Transactions on Power Electronics,

, Vol. 17, pp. 8–14. DOI: 10.1109/63.988662

Shao W., Chen L., Pan C., Liu Y., and Feng Z. Power

density of piezoelectric transformers improved using a

contact heat transfer structure, IEEE Transactions on

Ultrasonics, Ferroelectrics and Frequency Control, 2012,

Vol. 59, pp. 73-81. DOI: 10.1109/TUFFC.2012.2157

Andersen T., Andersen M. A. E., Thomsen O. C. Simulation

of Piezoelectric Transformers with COMSOL. Proceedings

of the 2012 COMSOL Conference in Milan. URL:

aper.pdf

Ivensky G., Shvartsas M., and Ben-Yaakov S. Analysis and

Modeling of a Piezoelectric Transformer in High Output

Voltage Applications. URL:

http://cbucc.com/glecture_file/2002060132032.pdf

DOI: 10.1109/APEC.2000.822822

Huang Y.-T., Wu W.-J., Wang Y.-C., Lee C.-K. Multilayer

Modal Actuator-Based Piezoelectric Transformers, IEEE

Transactions on Ultrasonics, Ferroelectrics, and Frequency

Control, 2007, Vol. 54, No. 2.

DOI: 10.1109/TUFFC.2007.249

Lavrinenko V. V. P’ezoe’lektricheskie transformatory.

Moscow, E’nergiya, 1975, 112 p.

Matematicheskaya e’nciklopediya. Tom 2: D – Koo. –

Moscow, Sovetskaya e’nciklopediya, 1979, pp. 951–952.

Karlash V. L. Longitudinal and lateral vibrations of a plate

piezoceramic transformer. Ukr. J. Phys., 2006, Vol. 51,

No. 10, pp. 986–992.

Karlash V. L. Vynuzhdennye e’lektromexanicheskie

kolebaniya pryamougol’nyx p’ezokeramicheskix sterzhnej s

razdelennymi e’lektrodami, Prikladnaya mexanika, 2013,

Tom 49, No. 3, pp. 125–134.

Bogdan A. V., Petrishhev O. N., Yakimenko Yu. I.,

Yanovskaya Yu. Yu. Issledovanie xarakteristik

p’ezoe’lektricheskogo transformatora na osnove radial’nyx

kolebanij v tonkix p’ezokeramicheskix diskax, E’lektronika

i svyaz’, Tematicheskij vypusk «E’lektronika i

nanotexnologii», 2009, P. 1, pp. 269–274.

Bogdan A. V., Petrishhev O. N., Yakimenko Yu. I.,

Yanovskaya Yu. Yu. Matematicheskoe modelirovanie

kolebanij tonkix p’ezokeramicheskix diskov dlya sozdaniya

funkcional’nyx e’lementov p’ezoe’lektroniki, E’lektronika i

svyaz’, Tematicheskij vypusk «E’lektronika i

nanotexnologii», 2009, part. 2, pp. 35–42.

Buchacz A., Placzek M., Wrobel A. Modelling of passive

vibration damping using piezoelectric transducers – the

mathematical model, Maintenance and reliability, 2014,

Vol. 16, No. 2, pp. 301–306.

Livingston D., Kiran Kumar P., Venugopal. N. Modeling

and simulation of multiple piezoelectric transformer

converters, International Journal of Emerging Technology

and Advanced Engineering, 2013, Vol. 3, No. 8, pp. 237–

Paerand Yu., Kryvoshei D. Secondary power supplies with

piezoelectric transformers. Electronics and Nanotechnology.

Kyiv, 2011, pp. 55.

Buchacz A., Wrobel A. Piezoelectric layer modelling by

equivalent circuit and graph method, Journal of

Achievements in Materials and Manufacturing Engineering,

, Vol. 20, No. 1–2, pp. 299–302.

Cheng K. W. E., Ho Y. L., Ho S. L., Kwok K. W., Wang X.

X., Chan H., Xue X. D. Modeling and analysis of

piezoelectric transformer using multi-mesh loop matrix

circuit under square-wave excitation conditions. IAS, 2005,

pp. 2207–2211.

Huang Y., Ling Z. Progress in research on piezoelectric

transformers, Electronic Components & Materials, 2004,

Vol. 23, No. 1, pp. 7–10.

Petrishhev O. N. Garmonicheskie kolebaniya

p’ezokeramicheskix e’lementov. Chast’ 1. Garmonicheskie

kolebaniya p’ezokeramicheskix e’lementov v vakuume i

metod rezonansa – antirezonansa. Kiev, Avers, 2012, 300 p.

Grinchenko V.T., Ulitko A.F., Shul’ga N.A. Mexanika

svyazannyx polej v e’lementax konstrukcij, Vol. 5.

E’lektrouprugost’. Kiev, Naukova dumka, 1989, 280 p.

Dzhagupov R. G., Erofeev A. A. P’ezoe’lektronnye

ustrojstva vychislitel’noj texniki, sistem kontrolya i

upravleniya: Spravochnik. SPb, Politexnika, 1994, 608 p.

Tixonov A. N. Matematicheskaya model’. V kn.

Matematicheskaya e’nciklopediya. Moscow, Sovetskaya

e’nciklopediya, 1982, Vol. 3, Koo – Od., pp. 574–575.

Petrishhev O. N., Bazilo K. V. Principy i metody rascheta

peredatochnyx xarakteristik diskovyx p’ezoe’lektricheskix

transformatorov. Chast’ 2. Metodika rascheta parametrov i

xarakteristik prostejshego diskovogo p’ezoe’lektricheskogo

transformatora. Vіsnik Cherkas’kogo derzhavnogo

texnologіchnogo unіversitetu, 2015, No. 4, pp. 10–23.

Spravochnik po special’nym funkciyam s formulami,

grafikami i matematicheskimi tablicami. Ed. M. Abramovic

and I. Stigan. Moscow, Nauka, 1979, 832 p.

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