volume | PIER Journals

Abstract

The dynamics of a system comprising of two bilaterally coupled Gunn oscillators (BCGOs) has been examined using a circuit theoretic model of the Gunn oscillator (GO). The effects of coupling factors (k_ij) between i-th and j-th oscillators on the frequency-range of synchronized operation and the magnitude of common frequency of oscillation have been examined semi-analytically and by numerical solution of the system equations. The occurrence of chaotic oscillations at the verge of synchronization bands is observed in numerical simulation. The experimental response of the BCGO operating in the X-band is obtained and the results are found to be qualitatively similar to the analytical and numerical predictions.

1. Boi, S., I. D. Couzin, N. D. Buono, N. R. Franks, and N. F. Britton, "Coupled oscillators and activity waves in ant colonies," Proceedings Royal Society, 371-378, London, 1998.

2. Glova, A. F., "Phase locking of optically coupled lasers," Quantum Electronics, Vol. 33, No. 4, 283-306, 2003.
doi:10.1070/QE2003v033n04ABEH002415

3. Stori, D. W., et al. "Dynamics of two strongly coupled Van der Pol oscillators," International Journal of Nonlinear Dynamics, Vol. 7, No. 3, 143-152, 1982.
doi:10.1016/0020-7462(82)90014-2

4. Anishchenko, V., S. Astakhov, and T. Vadivasova, "Phase dynamics of two coupled oscillators under external periodic force," Europhysics Letters, Vol. 86, 2009.
doi:10.1209/0295-5075/86/30003

5. Ram, R. J., R. Sporer, H. R. Blank, and R. A. York, "Chaotic dynamics in coupled microwave oscillators," IEEE Trans. Microwave Theory and Technique, Vol. 48, 1909-1916, 2000.

6. Uwate, Y. and Y. Nishio, "Synchronization phenomena in Van der Pol Oscillators coupled by a time varying resistor," International Journal of Bifurcation and Chaos, Vol. 17, No. 10, 3565-3569, 2007.
doi:10.1142/S0218127407019378

7. Volos, C. K., I. M. Kyprianidis, and I. N. Stouboulos, "Experimental synchronization of two resistively coupled duffing type circuits," Nonlinear Phenomena in Complex Systems, Vol. 11, No. 2, 187-192, 2008.

8. Liang, L. and Z. Bo, "A new nonlinear circuit model for GaAs Gunn diode in oscillator," 8th International Symposium on Antennas, Propagation and EM Theory, 1306-1309, 2008.
doi:10.1109/ISAPE.2008.4735465

9. Bates, R. S. and S. Feeney, "Novel varactor tuned millimeter wave Gunn oscillator," Electronics Letters, Vol. 23, No. 14, 714-715, 1987.
doi:10.1049/el:19870507

10. Biswas, B. N., S. Chatterjee, S. Sarkar, A. K. Bhattacharya, and S. K. Ray, "Bias tuned injection locked discriminators," IEEE Trans. on Microwave Theory and Techniques, Vol. 35, No. 9, 812-818, 1987.
doi:10.1109/TMTT.1987.1133757

11. Sarkar, S., T. Banerjee, D. Mondal, and B. C. Sarkar, "Theory and performance of an electrically controlled microwave phase shifter," Indian Journal of Pure and Applied Physics, Vol. 43, 215-220, 2005.

12. Sarkar, S., "Structure and application of a modified lock-in notch filter using solid state microwave oscillator," Indian Journal of Engineering and Material Science, Vol. 1, 149-152, 1994.

13. Kurokawa, K., "Injection locking of microwave solid state oscillator," Proc IEEE, Vol. 61, 1386-1410, 1973.
doi:10.1109/PROC.1973.9293

14. Diakoku, K. and Y. Mizushima, "Properties of injection locking in the non-linear oscillator," International Journal of Electronics, Vol. 31, 279-292, 1971.
doi:10.1080/00207217108938225

15. Zhu, X., Y. Chen, and W. Hong, "Q-band injection-locked Gunn diode oscillator," International Journal of Infrared and Millimeter Waves, Vol. 17, No. 3, 527-533, 1996.
doi:10.1007/BF02088026

16. Alekseev, Y. I., "Determination of basic characteristics of synchronization of Gunn self-excited oscillators," Instruments and Experimental Techniques, Vol. 50, No. 2, 241-243, 2007.
doi:10.1134/S0020441207020133

17. 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

18. Qiao, S., Z.-G. Shi, T. Jiang, and L.-X. Ran, "A new architecture of UWB radar utilizing microwave chaotic signals and chaos synchronization," Progress In Electromagnetics Research, Vol. 75, 22-237, 2007.

19. Jiang, T., S. Qiao, Z.-G. Shi, L. Peng, J. Huangfu, W.-Z. Cui, W. Ma, and L.-X. Ran, "Simulation and experimental evaluation of the radar signal performance of chaotic signals generated from a microwave Colpitts oscillator," Progress In Electromagnetics Research, Vol. 90, 15-30, 2009.
doi:10.2528/PIER08120104

20. Nikishov, A. Y., "Generation of the microwave chaotic oscillations by CMOS structure," PIERS Proceedings, 457-461, Moscow, Russia, Aug. 18--21, 2009.

21. Dmitriev, A. S., A. V. Kletsov, and L. V. Kuzmin, "Experimental generation of chaotic oscillations in microwave band by phase-locked loop," PIERS Proceedings, 1498-1502, Moscow, Russia, Aug. 18--21, 2009.

22. Shi, Z. G., S. H. Hong, and K. S. Chen, "Experimental study on tracking the state of analog Chuas circuit with particle filter for chaos synchronization," Physics Letters A, Vol. 372, 5575-5580, 2008.
doi:10.1016/j.physleta.2008.06.082

23. Jordan, D. W. and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, 4th Ed., Oxford University Press, 2007.

24. Kantz, H. and T. Schreiber, Nonlinear Time Series Analysis, Cambridge University Press, 2004.

25. Hilborn, R. C., Chaos and Nonlinear Dynamics, 2nd Ed., Oxford University Press, 2000.
doi:10.1093/acprof:oso/9780198507239.001.0001

26. Hegger, R., H. Kantz, and T. Schreiber, TISEAN Package, Web-address: http://www.mpipks-dresden.mpg.de/ tisean.

Dr. Bishnu Charan Sarkar

Dr. Debdeep Sarkar

Ms. Suvra Sarkar

Dr. Joydeep Chakraborty