volume | PIER Journals

Abstract

We have studied dynamics of a periodic X-band Gunn oscillator (GO) forced by microwave chaotic signals through numerical simulation and by hardware experiment. The chaos used as forcing signal is generated in a periodically driven non-oscillatory GO. Numerical simulation results indicate that the forced periodic GO becomes chaotic for a moderate strength of forcing chaos. The generated chaos in driven GO is found to become phase or general synchronized to the forcing chaos depending on strength of the latter one. Hardware experiments are performed in X-band of microwave frequency. It shows generation of chaos in driven GO due to forcing. Moreover, synchronization between forcing and generated chaos is indirectly verified.

1. Adler, R., "A study of locking phenomena in oscillators," Proceedings of the IEEE, Vol. 61, 1380-1385, 1973.
doi:10.1109/PROC.1973.9292 Google Scholar

2. 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 Google Scholar

3. Jensen, R. V., "Synchronization of driven nonlinear oscillators," American J. Physics, Vol. 70, 607-619, 2002.
doi:10.1119/1.1467909 Google Scholar

4. Rajavi, B., "A study of injection locking and pulling in oscillators," IEEE Journal of Solid State Circuits, Vol. 39, 1415-1424, 2004.
doi:10.1109/JSSC.2004.831608 Google Scholar

5. Li, C. J., C. H. Hsiao, F. K. Wang, T. S. Horng, and K. C. Peng, "A rigorous analysis of a phase locked oscillator under injection," IEEE Transactions on Microwave Theory and Techniques, Vol. 58, No. 5, 1391-1400, 2010.
doi:10.1109/TMTT.2010.2042898 Google Scholar

6. Pikovsky, A., M. Rosenblum, and J. Kurth, Synchronization: A Universal Concept in Nonlinear Sciences, Cambridge University Press, Cambridge, 2003.

7. Stogartz, S. H., Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering, Levant Books, Kolkata, India, (Indian Edition), 2007.

8. Kurokawa, K., "Injection locking of microwave solid state oscillator," Proceedings of the IEEE, Vol. 61, 1386-1410, 1973.
doi:10.1109/PROC.1973.9293 Google Scholar

9. Alekseev, Y. I., "Determination of basic characteristics of synchronization of Gunn self-excited oscillators," Instruments and Experimental Techniques, Vol. 50, 241-243, 2007.
doi:10.1134/S0020441207020133 Google Scholar

10. Main, E. and D. Coffing, "FM demodulation using an injection locked oscillator," IEEE MTT-S International Microwave Symposium Digest, Vol. 1, 135-138, 2000. Google Scholar

11. Ko, D. S., S. J. Lee, T. J. Baek, S. G. Choi, M. Han, H. C. Park, J. K. Rhee, J. H. Jung, and Y. W. Park, "New tuning method for 94GHz waveguide voltage controlled oscillator," IEEE Microwave and Wireless Components Letters,, Vol. 21, 2011. Google Scholar

12. Bates, R. S. and S. Feeney, "Novel varactor tuned millimeter wave Gunn oscillator," Electronics Letters, Vol. 23, 714-715, 1987.
doi:10.1049/el:19870507 Google Scholar

13. 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 Google Scholar

14. Mosekilde, E., et al. "Mode locking and spatio-temporal chaos in periodically driven Gunn diode," Physical Review B, Vol. 41, 2298-2306, 1990.
doi:10.1103/PhysRevB.41.2298 Google Scholar

15. Zongfu, J. and M. Benkun, "Period doubling and chaos in the Gunn effect," Physical Review B, Vol. 44, 11072–4, 1991. Google Scholar

16. Chakraborty, J., T. Banerjee, R. Ghatak, A. Bose, and B. C. Sarkar, "Generating chaos in injection-synchronized Gunn oscillator: An experimental approach," IETE Journal of Research, Vol. 55, 106-111, 2009.
doi:10.4103/0377-2063.54894 Google Scholar

17. Sarkar, B. C., C. Koley, A. K. Guin, and S. Sarkar, "Some numerical and experimental observations on the growth of oscillations in an X-band Gunn oscillator," Progress In Electromagnetics Research B, Vol. 40, 325-341, 2012.
doi:10.2528/PIERB12032804 Google Scholar

18. Siewe, M. S., H. Cao, and M. A. F. Sanjuan, "Effect of nonlinear dissipation on the basin boundaries of a driven two-well rayleigh-duffing oscillator," Chaos, Solitons and Fractals, Vol. 39, 1092-1099, 2009.
doi:10.1016/j.chaos.2007.05.007 Google Scholar

19. Musielak, D. E., Z. E. Musielak, and J. W. Banner, "Chaos and route to chaos in coupled duffing oscillators with multiple degree of freedom," Chaos, Solitons and Fractals, Vol. 24, No. 4, 907-922, 2005.
doi:10.1016/j.chaos.2004.09.119 Google Scholar

20. 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 Google Scholar

21. 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 Google Scholar

22. Sarkar, B. C., D. Sarkar, S. Sarkar, and J. Chakraborty, "Studies on the dynamics of bilaterally coupled X-band Gunn oscillators," Progress In Electromagnetics Research B, Vol. 32, 149-167, 2011.
doi:10.2528/PIERB11052201 Google Scholar

23. Ram, R. J., R. Sporer, H. R. Blank, and R. A. York, "Chaotic dynamics in coupled microwave oscillators," IEEE Transactions on Microwave Theory and Techniques, Vol. 48, 1909-1916, 2000. Google Scholar

24. Chakravorty, J., S. Sarkar, and B. C. Sarkar, "Studies on the dynamics of driven bilaterally coupled Gunn oscillator," Indian Journal of Science and Technology, Vol. 7, 916-923, 2014. Google Scholar

25. 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, 187-192, 2008. Google Scholar

26. Zhigang, Z., X. Wang, and M. C. Cross, "Transition from partial to complete generalized synchronization in bilaterally coupled chaotic oscillators," Physical Review E, Vol. 65, 056211, 2002. Google Scholar

27. Sarkar, B. C., "Nonlinear dynamics of Gunn oscillator,” (Book chapter)," New Research Trends in Nonlinear Circuits: Design, Chaotic Phenomena and Applications, Chapter 2, Nova Publishers, 2014. Google Scholar

28. Sarkar, B. C., S. Sarkar, C. Koley, A. K. Guin, and T. Banerjee, "Effects of unilateral coupling between two chaotic X-band Gunn oscillators," International Journal of Bifurcation and Chaos, Vol. 23, 1350185-1-1350185-23, 2013. Google Scholar

29. Wolf, A., J. B. Swift, H. Swinney, and J. A. Vastano, "Determining Lyapunov exponents from a time series," Physica D, Vol. 16, 285-317, 1985.
doi:10.1016/0167-2789(85)90011-9 Google Scholar

30. Romano, M. C., M. Theil, J. Kurths, Z. I. Kiss, and J. L. Hudson, "Detection of synchronization for non phase coherent and non stationary data," Europhysics Letters, Vol. 71, 462-472, 2005. Google Scholar

31. Marwan, N., M. Romano, M. Thiel, and J. Kurths, "Recurrence plots for the analysis of complex system," Physics Reports, Vol. 438, 237-329, 2007.
doi:10.1016/j.physrep.2006.11.001 Google Scholar

32. Rulkov, N. F., M. M. Sushchik, L. S. Tsimring, and H. D. I. Abarbanel, "Generalized synchronization of chaos in directionally coupled chaotic systems," Physical Review E, Vol. 51, 980-994, 1995.
doi:10.1103/PhysRevE.51.980 Google Scholar

33. Abarbanel, H. D. I., N. F. Rulkov, and M. M. Sushchik, "Generalized synchronization of chaos: The auxiliary system approach," Physical Review E, Vol. 53, 4528-4535, 1996.
doi:10.1103/PhysRevE.53.4528 Google Scholar

34. 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. Google Scholar

Dr. Bishnu Charan Sarkar

Ms. Suvra Sarkar

Dr. Arun Kanti Guin

Dr. Chaitali Koley