Nonlinear Analysis of Colpitts Oscillator using on Differential Transform Method

Ghomi Taheri, A.R.; Setoudeh, F.; Tavakoli, M. B.

doi:10.22061/jecei.2020.7543.402

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	Nonlinear Analysis of Colpitts Oscillator using on Differential Transform Method
Journal of Electrical and Computer Engineering Innovations (JECEI)
مقاله 1، دوره 9، شماره 2، مهر 2021، صفحه 127-142 اصل مقاله (1.89 M)
نوع مقاله: Original Research Paper
شناسه دیجیتال (DOI): 10.22061/jecei.2020.7543.402
نویسندگان
A.R. Ghomi Taheri¹؛ F. Setoudeh^* ²؛ M. B. Tavakoli¹
¹Electrical Engineering Department, Engineering Faculty, Islamic Azad University, Arak Branch, Arak, Iran.
²Engineering Faculty, Arak University of Technology, Arak, Iran.
تاریخ دریافت: 02 تیر 1399، تاریخ بازنگری: 06 آبان 1399، تاریخ پذیرش: 06 دی 1399
چکیده
Background and Objectives: The Differential transform method (DTM) is used in the analysis of ordinary, partial, and high-order differential equations. Recently, the DTM is used in the nonlinear analysis of physical nonlinear dynamic systems. Methods: The DTM method is used to analyze and analytically solve the nonlinear mathematical model of bias current-controlled Colpitts oscillator with variable coefficients. Intervals of the validity of the proposed method are evaluated by using the fourth order Runge-Kutta method (RK4M). In this note, the Lyapunov exponent (LE) can be used to analyze the Colpitts oscillator. By using DTM, the LEs are calculated analytically with unknown parameters in a short interval of time t[0, 3 Sec]. Results: In this paper, intervals of the validity of the proposed method are evaluated using RK4M. In addition, LEs are calculated using analytical and numerical methods based on DTM technique and Wolf method, respectively. LEs of the proposed system are presented as a function of the control parameter to confirm the applied technique’s usefulness. Conclusion: By comparing these two methods, the proposed DTM analytical technique is relatively more precise. Simulation results confirmed the impact of different parameters on LEs with two different initial conditions. The results show good accuracy of the DTM in short time intervals t[0, 3 Sec].
کلیدواژه‌ها
Differential Transform Method؛ Nonlinear Analysis؛ Runge-Kutta؛ Lyapunov Exponent؛ Analytically

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Nonlinear Analysis of Colpitts Oscillator using on Differential Transform Method