The Frequency Alternation Method Of The Nonlinear Dynamic Circuits

The nonlinear dynamic circuits are applied widely promoted with the development of the modern circuit's theory and the design technology, and the new electronic device and the large integrated circuit are arising unceasingly. The study of the modern analysis method, in particular modern analysis solution method for the nonlinear dynamic circuits will have the great theory meaning and practical value for the development of the modern circuit's theory and the accurate design of the modern circuitBased on the study deeper into the solution methods of the nonlinear dynamic circuits in more detail, this paper in connection with the method of the periodic solution which one of the four formats(the equilibrium point, and periodic solution, and quasi-periodic solution and the chaos solution) for the steady solutions for the nonlinear dynamic circuits the response frequency alternation method of the periodic oscillation solutions for the autonomous and the non-autonomous nonlinear dynamic circuits is produced. The nonlinear time transformation is introduced. The expression of the state variable of the dynamic circuits is shown as the simple harmonic function. The response frequency is solved by using the alternation method. And the undisturbed (intrinsic) frequency is used for the alternation initial value of the response frequency. A series of the differential and integral of the response frequency are involved, and the response frequency determining by this present is shown as the second radical usually. And than the response frequency is expanded as the Taylor expansions. And than the approximate expressions of the state variables, response frequency, response period and the time inverse transformation are calculated analytically. As the applied examples, the LC series circuit, RLC series circuit, Van der Pol's oscillation circuit and the ferro-resonant circuit are solved specifically. The results shown that only taken the second expansion of the response frequency and the second alternation, the results of the present are in good agreement compared with the numerical integral method...