Analysis of free processes in time varying circuit by means of generalized characteristic equations method
Developing methods of analysis of free processes in time varying circuit is important both for time varying and nonlinear radio circuits. The principle of linear connection brings together processes in time varying and nonlinear circuits. It is of special interest to extend the existing methods developed for radio circuits with stable parameters to time varying circuits. This article is devoted to one of such methods—the method of characteristic equations for differential equations with fixed factor.
A. A. Andronov, G. S. Gorelik, N. D. Papaleksi, and S. M. Pyzhov, “Some Researches in Field of Nonlinear Oscillations, Carried Out in USSR, Beginning from 1935,” Proceedings of Science Academy of USSR (Izdat. AN SSSR, Moscow, 1948), pp. 357–374 [in Russian].
B. F. Bylov, R. E. Vinograd, D. M. Grobman, and V. V. Nemytskii, Theory of Lyapunov’s Factors and its Application to Stability Problem (Nauka, Moscow, 1966) [in Russian].
V. V. Beloglazov, N. D. Biryuk, and V. V. Yurgelas, “Analysis, properties and potential performance capabilities of a parametric circuit. Resonance,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 50(6), 39 (2007) [Radioelectron. Commun. Syst. 50(6), 315 (2007)].
V. V. Beloglazov, N. D. Biryuk, and V. V. Yurgelas, “Stability analysis of a parametric loop by the Lyapunov-Chetaev method,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 51(3), 27 (2008) [Radioelectron. Commun. Syst. 51(3), 134 (2008)].
Yu. G. Kuleshov, Non-Linear Time Varying Circuits (Vyssh. Shkola, Kyiv, 1970) [in Russian].
V. A. Taft, Spectral Method for Calculation of Non-Stationery Circuits and Systems (Energiya, Moscow, 1978) [in Russian].
G. Schmidt, Parametererregte Schwingungen (Verlag Wissenschaft, Deutsch, 1975) [in German]; Parametric Oscillations (Mir, Moscow, 1978) [in Russian].
S. L. Chechurin, Parametrical Oscillations and Stability of Periodic Movement (Izdat. LGU, Leningrad, 1983) [in Russian].
F. A. Mikhaylov, Analysis and Synthesis of Non-Stationery Linear Systems (Mashinostroyeniye, Moscow, 1977) [in Russian].
V. F. Zaytsev and A. D. Polyanin, Ordinary Differential Equations. Handbook (Faktorial, Moscow, 1997) [in Russian].