volume | PIER Journals

Abstract

A simple electromagnetic system composed by a Schottky barrier diode (SBD) and linear lossless microstrip line is introduced in this paper. The period doubling phenomenon in this circuit system is studied following the train of thought, which is adopted in the field of the driven Resistor-Inductor-Diode (RLD) series circuit. The related phenomenon and its origins have been studied extensively in RLD circuit. However, it will not be able to exhibit period doubling and chaos if SBD is applied in RLD circuit. We show period doubling phenomena in a microwave circuit containing SBD for the first time. This paper reveals that the given circuit can produce cycle period doubling at microwave frequency by means of simulations and experiments. Physical verification and theoretical explanation have been given in this paper.

1. Linsay, P. S., "Period doubling and chaotic behavior in a driven an harmonic oscillator," Phys. Rev. Lett., Vol. 47, No. 19, 1349-1352, 1981.
doi:10.1103/PhysRevLett.47.1349

2. Singh, J. P. and B. K. Roy, "Simplest hyperchaotic system with only one piecewise linear term," Electronics Letters, Vol. 55, No. 7, 378-380, Apr. 2019.
doi:10.1049/el.2018.8078

3. Lai, Q., P. D. K. Kuate, F. Liu, and H. H. Iu, "An extremely simple chaotic system with infifinitely many coexisting attractors," IEEE Trans. Circuits Syst. II, Exp. Briefs, Vol. 67, No. 6, 1129-1133, Jun. 2020.
doi:10.1109/TCSII.2019.2927371

4. Carroll, T. L. and L. M. Pecora, "Parameter ranges for onset of period doubling in the diode resonator," Phys. Rev. E, Vol. 66, 046219-1-046219-8, 2002.

5. Tanaka, S., S. Higuchi, and T. Matsumoto, "Sheet structure in global bifurcations of a driven R-L-diode circuit," Phys. Rev. E, Vol. 54, 6014-6028, 1996.
doi:10.1103/PhysRevE.54.6014

6. De Moraes, R. M. and S. M. Anlage, "Effects of UHF stimulus and negative feedback on nonlinear circuits," IEEE Trans. Circuits Syst. I, Fundamental Theory and Applications, Vol. 51, No. 4, 748-754(7), Apr. 2004.
doi:10.1109/TCSI.2004.826214

7. Lu, L. and Z. W. Du, "Chaos in a simple microwave circuit with a PIN diode," Antennas Propagation and EM Theory (ISAPE), 963-965, 2010.

8. Xu, F. and P. Tan, "Analysis of Period-doubling Bifurcation and Chaos using physics-based SiC diode model," 2015 18th International Conference on Electrical Machines and Systems (ICEMS), 612-615, Oct. 25-28, 2015.

9. Basu, S., S. A. Maas, and T. Itoh, "Quasi-periodic route to chaos in a microwave doubler," IEEE Microwave Guided Wave Lett., Vol. 5, No. 7, 224-6, Jul. 1995.
doi:10.1109/75.392282

10. Rollins, R. W. and E. R. Hunt, "Exactly solvable model of a physical system exhibiting universal chaotic behavior," Phys. Rev. Lett., Vol. 49, 1295, 1982.
doi:10.1103/PhysRevLett.49.1295

11. De Moraes, R. M. and S. M. Anlage, "Unified model and reverse recovery nonlinearities of the driven diode resonator," Phys. Rev. E, Vol. 68, 026201-1-026201-9, 2003.

12. Kim, C. M., C. H. Cho, C. S. Lee, J. H. Yim, J. Kim, and Y. Kim, "Period doubling and bifurcation in an electronic circuit with a fast-recovery diode and square-wave input," Phys. Rev. A, Vol. 38, 1645-1648, 1988.
doi:10.1103/PhysRevA.38.1645

13. Corti, L., L. De Menna, G. Miano, and L. Verolino, "Chaotic dynamics in an infinite-dimensional electromagnetic system," IEEE Trans. Circuits Syst. I, Fundamental Theory and Applications, Vol. 41, No. 11, 730-736, 1994.
doi:10.1109/81.331524

14. Blakely, J. N. and N. J. Corron, "Experimental observation of delay-induced radio frequency chaos in a transmission line oscillator," Chaos, Vol. 14, No. 4, 1035-41, Dec. 2004.
doi:10.1063/1.1804092

15. Demergis, V., A. Glasser, M. Miller, T. M. A. Jr, E. Ott, and S. M. Anlage, "Delayed feed-back and chaos on the driven diode-terminated transmission line,", arXiv:nlin/0605037, May 2006.

16. Sharkovsky, A. N., Y. Maistrenko, P. Deregel, and L. O. Chua, "Dry turbulence from a time delayed Chua's circuit," J. Circuits, Syst. and Comput., Vol. 3, No. 2, 645-668, 1993.
doi:10.1142/S021812669300040X

17. Miano, G. and A. Maffucci, Transmission Lines and Lumped Circuits, Academic Press, 2001.

18. Kawata, J., Y. Nishio, and A. Ushida, "Analysis of Chua's circuit with transmission line," IEEE Trans. Circuits Syst. I, Fundamental Theory and Applications, Vol. 44, No. 6, 556-558, 1997.
doi:10.1109/81.586030

Dr. Yong Xia

Professor Xiao-Wei Shi