Анализ процессов в параметрическом контуре общего вида

Abstract

In many publications, it is maintained importance of analysis of nonlinear radio circuits. In spite of all this it does not make the principle of linear introduction [1], maintaining that solution of every nonlinear equation may be exactly achieved in specially sorting out linear equation. This principle, formulating for abstract mathematical equations, may be transfer to theory of radio circuits. In this case determination is following: arbitrary process in every nonlinear radio circuit may be exactly achieved in specially sorting out linear radio circuit. The principle of linear introduction raises importance of analysis of linear radio circuits of general aspect for theory of nonlinear circuits. For radio electronics it are interesting linear circuits with periodical varying parameters (capacitances, inductances, resistances). This is complicated problem in general case. In this publication it has been proposed the birst step in this direction exactly it is worked out analysis of time varying circuit. It is supposed that all elements of circuit are positive and change in time according arbitrary continuous periodical functions of time with the same periods. For this purpose it is adapted well-known in theory of circuits with constant parameter method of complex amplitudes. This mathematical method has been worked out inside electrotechics, it does not inscribe in classical mathematics. It is given particular attention to problem of stability of time varying circuit. In the time of solution this problem it is found that it is not given due attention Lyapunov's theory of stability in radio electronics. This it is worked out an application Lyapunov's theory of stability for problem of stability of time varying circuit, just that vary case of use of the first and the second Lyapunov's methods. Besides that it is considered unlyapunov's method of analysis of stability, working out on the basis of method of complex amplitude. Although proposing this analysis is limited with linear object (time varying circuit), it bears a relation to nonlinear circuit through principle of linear introduction.

• the principle of linear introduction
• forcing oscillations
• free process
• theory of stability
• analogy with time varying and usual circuit

For citation

References

1. Былов Б. Ф. Теория показателей Ляпунова и ее приложения к вопросам устойчивости / Б. Ф. Былов, Р. Э. Виноград, Д. М. Гробман, В. В. Немыцкий.-М.:Наука,1966.-575с.
2. Величко Ю. Т. Теоретичнi основи радiотехнiчних мереж / Ю. Т. Величко.-Львiв: Видавництво ЛДУ, 1966.-340с.
3. Канторович Л. В. Приближенные методы высшего анализа / Л. В. Канторович, В. И. Крылов.-М.-Л.:Госфизматиздат,1962.-708с.
4. Каган В. Ф. Основания теории определителей / В. Ф. Каган.-Одесса,1922.-521с.
5. Бирюк Н. Д. Основы теории параметрических радиоцепей / Н. Д. Бирюк, В. В. Юргелас.- Воронеж: Издательско-полиграфический центр ВГУ, 2012.-345с.
6. Ляпунов А. М. Собрание сочинений. Т.2 / А. М. Ляпунов.-М.: Изд. АНСССР,1956.-470с.
7. Якубович В. А. Линейные дифференциальные уравнения с периодическими коэффициентами и их приложения / В. А. Якубович, В. М. Старжинский.-М.:Наука,1972.-718с.
8. Зайцев В. Ф. Справочник по линейным обыкновенным дифференциальным уравнениям / В. Ф. Зайцев, А. Д. Полянин.-М.:Факториал,1997.-304с.
9. Демидович Б. П. Лекции по математической теории устойчивости / Б. П. Демидович.-М.:Наука,1967.-472с.
10. Гантмахер Ф. Р. Теория матриц / Ф. Р. Гантмахер.-М.:Наука,1988.-548с.