POSSIBILITY OF APPLYING METHODS OF ANALYSIS AND SYNTHESIS OF LINEAR ELECTRICAL CIRCUITS TO SOME NONLINEAR CIRCUITS

Authors

Qudrat Gayratovich Abidov, Tashkent State Technical University, Tashkent city, Republic of Uzbekistan, DSc, professor, abidoff@rambler.ru, https://orcid.org/0000-0001-8315-0351;Follow
Anvar Ismatullaevich Rahmatullaev, Tashkent State Technical University, Tashkent city, Republic of Uzbekistan, Research Associate,anvarrahmatullayev@gmail.uz, https://orcid.org/0000-0003-2419-0366;Follow
Mexrnoz Odiljonovna Gafurova, Tashkent State Technical University, Tashkent city, Republic of Uzbekistan, Research Associate, gafurova.mexrnoz@mail.ru, https://orcid.org/0009-0006-7612-8221.Follow

Abstract

This article discusses the possibility of applying the analysis and calculation methods used in linear electric circuits to certain nonlinear circuits. It is shown that if we abandon the quantitative criteria for the analysis and synthesis of nonlinear circuits using linear principles, some problems in nonlinear electrical engineering can be correctly solved based on linear theory. As an example, the simplest ferroresonant voltage stabilizer is considered, using the method of superposition and the equivalence of ferroresonant circuits in series and parallel connections. The electrical diagram is shown, and a formula for the stabilization coefficient is derived, representing a complex nonlinear function dependent on both linear and nonlinear circuit parameters. Under certain conditions, a simplified formula for calculating the output voltage stabilization coefficient is provided.

In a circuit where Kirchhoff’s laws strictly apply, the method of superposition, which pertains to the analysis of linear circuits, can also be applied to circuits with nonlinear elements. The stabilization of the output voltage of a simple single-phase ferroresonant voltage stabilizer and the characteristics of two ferroresonant circuits with parallel and series connections of passive elements are also presented. Basic calculation formulas are provided as well.

First Page

61

Last Page

64

References

1. L.O. Chua, Peng-Ming-Lin. Machine analysis of electronic circuits. Translation from English, M.: Energy, 1980.
2. K.S.Demirchyan, L.R.Neumann, Korovkin N.V., Chechurin V.L. Theoretical bases of electrical engineering. Textbook for High Schools. Volume 1. Peter, 2003. 463 p.
3. Vlah I., Singhal I., Machine methods of analysis and design of electronic circuits: Transl. from English, M.: Radio and Communications, 1988.
4. Tu.Yu. Modern Theory of Control. -M.; Mashinostroenie, 1971. 300 p.
5. Samsonov, I.D.; Tillyakhodzhaev, M.M. .Bazarov, N.H. To determine the structural scheme of an electromagnetic vibrator with amplitude frequency control. ElectrotechnicalIndustry.Elektroproizvod.1981 v.9(98), 8-9 p.
6. Matkhanov P.N., Basics of the electrical circuits analysis. Nonlinear circuits. M,: High school, 1977. 272 p.
7. Tondle A. “Auto oscillation of mechanical systems” M.: Mir, 1979. 429 p.
8. Bessonov L.A. Theoretical fundamentals of electrical engineering. Electrical circuits.
9. M.O.Atajonov, S.J.Nimatov, A.I.Rakhmatullaev, A.B.Sadullaev, AIP Conference Proceedings 2552,050014, (2023), https://doi.org/10.1063/5.0112403
10. Amirov C.F., Yakubov M.S., Jabborov N.G. Theoretical foundations of electrical engineering. (first book) TSTU, 2006 -144 b.
11. Karimov A.S. Theoretical Electrical Engineering. -T.: Teacher, 2003. - 428 p.
12. Amirov SF, Yaqubov MS, Jabborov NG, Sattorov HA, Balgaev N.E. Collection of problems from theoretical bases of electrical engineering. - T: Sparks of Literature, 2015.-420 p.
13. John Bird. "Electrical and Electronic Principles and Technology" LONDON AND NEW YORK, 2014.-455 p.
14. Abidov, K.G.; Rakhmatullaev, A.I. Investigation of an electromagnetic vibration-excitation device with a series-connected capacitor in an electric circuit. - Tashkent: TSTU, 2018 No. 3.58-63 p.
15. Abidov, K.G.; Rakhmatullaev, A.I. Possibility of application of a reciprocity principle at conversions of currents and voltages on the nonlinear four-poles.// TSTU. 2019 No. 1.80-84 p
16. K.G.Abidov, O.O.Zaripov, and others. AIP Conference Proceedings, 2552, 030022, (2022), https://doi.org/10.1063/5.0112384
17. K.Abidov, K.Dadadjanov, S.Sobitov. Static modes of an electromagnetic working shaft (EMWSh) and an electro-electromagnetic working shaft (EEMWSh) with the inclusion of a capacitor in the rotor circuit of the motors. E3S Web of Conferences, 410, 02058, (2023), https://doi.org/10.1051/e3sconf/202341002058
18. R.Karimov, D.Xushvaktov. Analysis of reactive power consumption Denav oil extraction plant. E3S Web of Conferences, 384, 01053, (2023), https://doi.org/10.1051/e3sconf/202338401053
19. N.Khamudkhanova, M.Idriskhodjaeva, K.Kholbutayeva. Construction principle of automatic control system adjustable multi-engine drive water lift pump unit. E3S Web of Conf., 384, 01057, (2023), https://doi.org/10.1051/e3sconf/202338401057
20. K.G.Abidov, K.Dadajanov, U.Absoatov, S.Sabitov. Research for reduction material-capacity of load-lift cranes with multi-engine electric drives on the base electromagnetic work shaft systems. E3S Web of Conferences, 383, 04044, (2023), https://doi.org/10.1051/e3sconf/202338304044
21. M.O.GAFUROVA, K.G.ABIDOV, Electromagnetic field model as a source of water cavitation energy. Technical science and innovation, 1/2024, https://btstu.researchcommons.org/journal/vol2024/iss1/9/

Recommended Citation

Abidov, Qudrat Gayratovich; Rahmatullaev, Anvar Ismatullaevich; and Gafurova, Mexrnoz Odiljonovna (2024) "POSSIBILITY OF APPLYING METHODS OF ANALYSIS AND SYNTHESIS OF LINEAR ELECTRICAL CIRCUITS TO SOME NONLINEAR CIRCUITS," Technical science and innovation: Vol. 2024: Iss. 3, Article 11.
Available at: https://btstu.researchcommons.org/journal/vol2024/iss3/11