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.
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.
| № | Author name | position | Name of organisation |
|---|---|---|---|
| 1 | Abidov Qudrat Gayratovich Q.G. | DSc, professor | Tashkent State Technical University |
| 2 | Rahmatullaev A.I. | Research Associate | Tashkent State Technical University |
| 3 | Gafurova M.O. | Research Associate | Tashkent State Technical University |
| № | Name of reference |
|---|---|
| 1 | 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. |
| 2 | 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. |
| 3 | 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. |
| 4 | 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 |
| 5 | 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 |
| 6 | 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 |
| 7 | 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/ |