In this paper an approach for stability analysis of microwave oscillators is proposed. Using the perturbation theory and averaging method, a theorem which relates the oscillation stability to the stability of the periodic average of the circuit's Jacobian is mentioned. Using this theorem, a criterion for oscillation stability is devised. The proposed criterion is applied to the stability analysis of a negative resistance diode oscillators and a Colpitts oscillator. This method is readily applicable to microwave CAD routines.
2. Suarez, A. and A. Quere, Stability Analysis of Nonlinear Microwave Circuit, Artech House, Norwood, 2003.
3. Jackson, R. W, "Rollett proviso in the stability of linear microwave circuits — Atutorial," IEEE Trans. MTT., Vol. 54, No. 3, 993-1000, 2006.
4. Obregon, J., J. Nallatamby, M. Prigent, M. Camiade, and D. Rigaud, RF and Microwave Oscillator Design, Artech House, Norwood, 2002.
5. Shi, Z. G., S. Qiao, and K. S. Chen, "Ambiguity function of direct chaotic radar employing microwave chaotic Colpitz oscillator," Progress In Electromagnetics Research, Vol. 77, 1-14, 2007.
6. Maas, S. A., Nonlinear Microwave and RF Circuits, Artech House, Norwood, 2003.
7. 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.
8. Wu, C. G. and G. X. JiangKung, "Stabilization procedure for time-domain integral equation," J. of Electromagn. Waves and Appl., Vol. 21, No. 11, 1507-1512, 2007.
9. Coddington, E. A. and N. Levinston, Theory of Ordinary Differential Equations, Mc. Graw-Hill Inc., New York, 1983.
10. Kurokawa, K., "Some basic characteristics of broadband negative resistance oscillator circuits," Bell System Technical Journal, 1937-1955, 1969.
11. Rizzoli, V. and A. Lipparini, "General stability analysis of periodic steady state regimes in nonlinear microwave circuits," IEEE Trans. MTT., Vol. MTT 33, 30-37, 1985.
12. Rizzolli, V., A. Lapparini, A. Cotanzo, F. Mastri, C. Cecchetti, A. Neri, and D. Masotti, "State of the art harmonic balance simulation of forced nonlinear microwave circuits by piecewise technique," IEEE Trans. MTT., Vol. 40, No. 1, 12-27, 1992.
13. Rizzoli, V., A. Neri, and D. Masott, "Local stability analysis of microwave oscillators based on Nyquist's theorem," IEEE Trans. Microwave and Guided Wave Letters, Vol. 7, No. 10, 341-343.
14. Makeeva, G. S., O. A. Golovanov, and M. Pardavi-Horvath, "Mathematical modeling of nonlinear waves and oscillations in gryomagnetic structures by bifurcation theory methods," J. of Electromagn. Waves and Appl., Vol. 20, No. 11, 1503-1510, 2006.
15. Suarez, A., S. Jeon, and D. Rutledge, "Stability analysis and stabilization of power amplifiers," IEEE Microwave Magazine, Vol. 7, No. 5, 145-151, 2006.
16. Suares, A., V. Iglesias, J. M. Collantes, J. Jugo, and J. L. Garcia, "Nonlinear stability of microwave circuits using commercial software," IEE Elec. Letter, 1333-1335, 1998.
17. 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 Trans. MTT., Vol. 47, No. 12, 2403-2410, 1999.
18. Sanchez, D. A., Ordinary Differential Equation and Stability Theory, An Introduction, Dover, New York, 1960.
19. Khalil, H., Nonlinear Systems, Printice Hall, N.J., 2002.
20. Sagar, V., Nonlinear Control Systems, Academic Press, New York, 1999.
21. Migulin, V. V., Basic Theory of Oscillation, Mir Publisher, Moscow, 1983.
22. Shi, Z. G. and L. X. Ran, "Microwave chaotic Colpitts oscillator: design, implementation and applications," J. of Electromagn. Waves and Appl., Vol. 20, No. 10, 1335-1349, 2006.
23. Mokari, M. E., S. Ganesan, and B. Blumgold, "Systematic nonlinear model parameter extraction for microwave HBT device," IEE, 1031-1036, 1993.
24. Slotine, J. E. and W. Li, Applied Nonlinear Control, Printice Hall, New Jersey, Englewood Cliffs, 1991.