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2007-11-29
Nonlinear Stability Analysis of an Oscillator with Distributed Element Resonator
By
Progress In Electromagnetics Research, Vol. 80, 241-252, 2008
Abstract
In this paper a complete analysis to the stability of a microwave oscillator with distributed element resonator is presented. In this type of oscillators, the circuit description changes form ordinary differential equations to partial deferential equations. In this paper a Gunn diode oscillator with distributed elements resonator is analyzed. The instability condition of the startup phase and the stability condition of the steady state oscillation is investigated.
Citation
Hamid Vahdati Abdolali Abdipour , "Nonlinear Stability Analysis of an Oscillator with Distributed Element Resonator," Progress In Electromagnetics Research, Vol. 80, 241-252, 2008.
doi:10.2528/PIER07111701
http://www.jpier.org/PIER/pier.php?paper=07111701
References

1. Giannini, F. and G. Leuzzi, Nonlinear Microwave Circuit Design, John Wiley, New York, 2004.

2. Coddington, E. A. and N. Levinston, Theory of Ordinary Differential Equations, Mc. Graw-Hill Inc., New York, 1983.

3. Suarez, A. and A. Quere, Stability Analysis of Nonlinear Microwave Circuit, Artech House, Norwood, 2003.

4. Shi, Z. G. and L. X. Ran, "Microwave chaotic Colpitts oscillator: design, implementation and applications," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 10, 1335-1349, 2006.
doi:10.1163/156939306779276802

5. Shi, Z. G. and S. Qiao, "Ambiguity function of direct chaotic radar employing microwave chaotic Colpitts oscillator," Progress In Electromagnetics Research, Vol. 77, 1-14, 2007.
doi:10.2528/PIER07072001

6. Qiao, S., T. Jiang, L. Ran, and K. Chen, "Ultra wide band noise signal radar utilizing microwave chaotic signals and chaos synchronization," PIERS Online, Vol. 3, No. 8, 1326-1329, 2007.
doi:10.2529/PIERS070417101142

7. Jackson, R. W., "Rollett proviso in the stability of linear microwave circuits—Atutorial," IEEE Transaction of Microwave Theory and Technique, Vol. 54, No. 3, 993-1000, 2006.
doi:10.1109/TMTT.2006.869719

8. Sanchez, D. A., Ordinary Differential Equation and Stability Theory, An Introduction, Dover, New York, 1960.

9. Rizzoli, V. and A. Lipparini, "General stability analysis of periodic steady state regimes in nonlinear microwave circuits," IEEE Transaction of Microwave Theory and Technique, Vol. MTT 33, 30-37, 1985.
doi:10.1109/TMTT.1985.1132934

10. Makeeva, G. S., O. A. Golovanov, and M. Pardavi-Horvath, "Mathematical modeling of nonlinear waves and oscillations in gryomagnetic structures by bifurcation theory methods," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 11, 1503-1510, 2006.
doi:10.1163/156939306779274363

11. Suarez, A., S. Jeon, and D. Rutledge, "Stability analysis and stabilization of power amplifiers," IEEE Microwave Magazine, Vol. 7, No. 5, 145-151, 2006.
doi:10.1109/MW-M.2006.247915

12. Mons, S., J. C. Nallatamby, R. Quere, P. Savary, and J. Obregon, "Unified approach for the linear and nonlinear stability analysis of microwave circuits using available tools," IEEE Transaction of Microwave Theory and Technique, Vol. 47, No. 12, 2403-2410, 1999.
doi:10.1109/22.808987

13. Vahdati, H. and A. Abdipour, "Nonlinear stability analysis of microwave oscillators using the periodic averaging method," Progress In Electromagnetics Research, Vol. 79, 179-193, 2008.
doi:10.2528/PIER07100101

14. Kryzing, E., Advance Engineering Mathematics, Printics Hall, N.J., 2002.

15. Makeeva G. S., O. A. Golovanov, and M. Pardavi Horvath, Numerical simulation of nonlinear and parametric oscillations in a semiconductor resonator structure, Progress In Electromagnetics Research Symposium, 2006.

16. Kumar, P., T. Chakravarty, G. Singh, S. Bhooshan, and S. K. Khah, "Numerical computation of resonant frequency of gap coupled circular microstrip antenna," J. of Electromagn. Waves and Appl., Vol. 21, No. 10, 1303-1311, 2007.
doi:10.1163/156939307783239465

17. Geyi, W., "Time-domain theory of metal cavity resonator," Progress In Electromagnetics Research, Vol. 78, 219-253, 2008.
doi:10.2528/PIER07090605

18. Psarros, I. and G. Fikioris, "Two term theory for infinite linear array and application to study of resonances," J. of Electromagn. Waves and Appl., Vol. 20, No. 5, 623-645, 2006.
doi:10.1163/156939306776137809

19. Migulin, V. V., Basic Theory of Oscillation, Mir Publisher, Moscow, 1983.

20. Kung, F. and H. T. Chuah, "Stability of classical finite diference time domain (FDTD) formulation with nonlinear element — Anew perspective," Progress In Electromagnetics Research, Vol. 42, 49-89, 2003.
doi:10.2528/PIER03010901

21. Wu, C. G. and G. X. JiangKung, "Stabilization procedure for time-domain integral equation," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 11, 1507-1512, 2007.

22. Tang, M. and J. F. Mao, "Transient analysis of lossy nonuniform transmission lines using time step integration method," Progress In Electromagnetics Research, Vol. 69, 257-266, 2007.
doi:10.2528/PIER06123001

23. Afrooz, K., A. Abdipour, A. Tavakoli, and M. Movahhediu, "Time domain analysis of active transmission lines using FDTD technique (application to microwave/mm-wave transistors)," Progress In Electromagnetics Research, Vol. 77, 309-328, 2007.
doi:10.2528/PIER07081401

24. Khalil, H., Nonlinear Systems, Printice Hall, N.J., 2002.

25. Peidaee and A. R. Baghai-Wadji, "On the calculation of polynomially perturbed harmonic oscillators," PIERS Online, Vol. 3, No. 4, 486-489, 2007.
doi:10.2529/PIERS061202155000