Skip to main content
SpringerLink
Log in

Synchronization of improved chaotic Colpitts oscillators using nonlinear feedback control

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

The model and the normalized state equations of the novel version of the Colpitts oscillator designed to operate in the ultra-high frequency range are presented. The circuit is investigated numerically and simulations demonstrate chaos in the microwave frequency range. Typical phase portrait, Lyapunov exponent and Lyapunov dimension are calculated using a piece-wise linear approximation of nonlinear I–V characteristic of the bipolar junction transistor. In addition, the feedback controller is applied to achieve chaos synchronization for two identical improved chaotic Colpitts oscillators. In the frame the nonlinear function of the system is used as a nonlinear feedback term for the stability of the error dynamics. Finally, numerical simulations show that this control method is feasible for this oscillator.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Wegener, C., Kennedy, M.P.: RF chaotic Colpitts oscillator. In: Proceedings of the Workshop on Nonlinear Dynamics of Electronic Systems, Dublin, Ireland, pp. 255–258 (1995)

  2. Maggio, G.M., Feo, O.D., Kennedy, M.P.: Nonlinear analysis of the Colpitts oscillator and applications to design. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 46, 1118–1130 (1999)

    Article  MATH  Google Scholar 

  3. Maggio, G.M., Kennedy, M.P.: Classification of steady-state behavior in the Colpitts oscillator. In: Proc. of Int. Conf. on Elec. Circuits and Syst., Cyprus, pp. 811–814 (1999)

  4. Feo, O.D., Maggio, G.M., Kennedy, M.P.: The Colpitts oscillator: families of periodic solutions and their bifurcation. Int. J. Bifurc. Chaos 10, 935–958 (2000)

    MATH  Google Scholar 

  5. Panas, A.I., Kyarginsky, B.E., Maximov, N.A.: Single-transistor microwave chaotic oscillator. In: Proc. NOLTA-2000, Dresden, Germany, pp. 445–448 (2000)

  6. Kyarginsky, B.E., Maximov, N.A., Panas, A.I., Starkov, S.O.: Wideband microwave chaotic oscillators. In: 1st IEEE International Conference on Circuits and Systems for Communications, pp. 296–299 (2002)

  7. Shi, Z.G., Ran, L.X.: Design of chaotic Colpitts oscillator with prescribed frequency distribution. Int. J. Nonlinear Sci. Numer. Simul. 5, 89–94 (2004)

    Google Scholar 

  8. Shi, Z.G., Ran, L.X.: Microwave chaotic Colpitts oscillator: design, implementation and applications. J. Electromagn. Waves Appl. 20, 1335–1349 (2006)

    Article  Google Scholar 

  9. Tamasevicius, A., Mykolaitis, G., Bumeliene, S., Cenys, A., Anagnostopoulos, A.N., Lindberg, E.: Two-stage chaotic Colpitts oscillator. Electron. Lett. 37, 549–551 (2001)

    Article  Google Scholar 

  10. Mykolaitis, G., Tamasevicius, A., Bumeliene, S., Lasiene, G., Cenys, A., Lindberg, E.: HF and VHF chaos oscillator. Electron. Electr. Eng. 32, 12–17 (2001)

    Google Scholar 

  11. Mykolaitis, G., Tamasevicius, A., Bumeliene, S.: Experimental demonstration of chaos from the Colpitts oscillator in the VHF and the UHF ranges. Electron. Lett. 40, 91–92 (2004)

    Article  Google Scholar 

  12. Bumeliene, S., Tamasevicius, A., Mykolaitis, G., Baziliauskas, A., Lindberg, E.: Numerical investigation and experimental demonstration of chaos from two-stage Colpitts oscillator in the ultrahigh frequency range. Nonlinear Dyn. 44, 167–172 (2006)

    Article  MATH  Google Scholar 

  13. Mykolaitis, G., Tamasevicius, A., Bumeliene, S., Baziliauskas, A., Lindberg, E.: Two-stage chaotic Colpitts oscillator for the UHF range. Electron. Lett. 37, 549–551 (2001)

    Article  Google Scholar 

  14. Tamasevicius, A., Mykolaitis, G., Bumeliene, S., Baziliauskas, A., Krivickas, R., Lindberg, E.: Chaotic Colpitts oscillator for the ultrahigh frequency range. Nonlinear Dyn. 46, 159–165 (2006)

    Article  Google Scholar 

  15. Bumeliene, S., Tamasevicius, A., Mykolaitis, G., Baziliauskas, A., Lindberg, E.: Hardware prototype of the two-stage chaotic Colpitts oscillator for UHF range. In: Proc. 12th Workshop NDES 2001, Evora, Portugal, pp. 99–102, May 2004

  16. Kennedy, M.P.: Chaos in the Colpitts oscillator. IEEE Trans. Circuit Syst. I 41, 771–774 (1994)

    Article  Google Scholar 

  17. Tamasevicius, A., Bumeliene, S., Lindberg, E.: Improved chaotic Colpitts oscillator for ultrahigh frequencies. Electron. Lett. 40, 1569–1570 (2004)

    Article  Google Scholar 

  18. Uchida, A., Kawano, M., Yoshomori, S.: Dual synchronization of chaos in Colpitts electronic oscillators and its applications for communications. Phys. Rev. E 68, 056207 (2003)

    Article  Google Scholar 

  19. Qiao, S., Shi, Z.G., Chen, K.S., Cui, W.Z., Ma, W., Jiang, T., Ran, L.X.: A new architecture of UWB radar utilizing microwave chaotic signals and chaos synchronization. Prog. Electromagn. Res. 75, 225–237 (2007)

    Article  Google Scholar 

  20. Burykin, V.A., Panas, A.I.: Chaotic synchronization of RF generators. In: Proceedings of the 5th International Specialist Workshop on Nonlinear Dynamics of Electronic Systems NDES’97, Moscow, Russia, pp. 548–553 (1997)

  21. Tamasevicius, A., Mykolaitis, G., Bumeliene, S., Cenys, A., Lindberg, E.: Synchronization of VHF chaotic Colpitts oscillator. In: Proceedings of the Ninth Workshop on Nonlinear Dynamics of Electronic Systems NDES’97, Delft, The Netherlands, pp. 223–226 (2001)

  22. Rubezic, V., Ostojic, R.: Synchronisation of chaotic Colpitts oscillator with applications to binary communications. In: Proceedings of the 6th IEEE International Conference on Electronics, Circuits and Systems ICECS’99, Paphos, Cyprus, pp. 153–156 (1999)

  23. Li, G.H.: Synchronization and anti-synchronization of Colpitts oscillators using active control. Chaos Solitons Fractals 26, 87–93 (2005)

    Article  MATH  Google Scholar 

  24. Fotsin, H.B., Daafouz, J.: Adaptive synchronization of uncertain chaotic Colpitts oscillators based on parameter identification. Phys. Lett. A 339, 304–315 (2005)

    Article  MATH  Google Scholar 

  25. Baziliauskas, A., Krivickas, R., Tamasevicius, A.: Coupled chaotic Colpitts oscillator: Identical and mismatched cases. Nonlinear Dyn. 44, 151–158 (2006)

    Article  MATH  Google Scholar 

  26. Cenys, A., Tamasevicius, A., Mykolaitis, G.: Hyperchaos and synchronization in mean field coupled chaotic oscillator. In: Proc. Int. Symp. on Nonlinear Theory and its Applications NOLTA’98, Crans-Montana, Switzerland, pp. 519–540 (1998)

  27. Effa, J.Y., Essimbi, B.Z., Ngundam Mucho, J.: Synchronization of Colpitts oscillators with different orders. Commun. Nonlinear Sci. Numer. Simul. 14, 1590–1597 (2009)

    Article  MathSciNet  Google Scholar 

  28. Lü, L., Guo, Z.A., Zhang, C.: Synchronization between two different chaotic systems with nonlinear feedback control. Chin. Phys. 16, 1603–1607 (2007)

    Article  Google Scholar 

  29. Mykolaitis, G., Tamasevicius, A., Bumeliene, S., Lasiene, G., Cenys, A., Anagnostopoulos, A.N., Lindberg, E.: Towards microwave chaos with two-stage Colpitts oscillator. In: Proceedings of the Ninth Workshop on Nonlinear Dynamics of Electronic Systems NDES’97, Delft, The Netherlands, pp. 97–100 (2001)

  30. Giannakopoulos, K., Deliyannis, T.A.: Comparison of five methods for studying a hyperchaotic circuit. Int. J. Electron. 92, 143–159 (2005)

    Article  Google Scholar 

  31. Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov exponents from a time series. Physica D 16, 285–317 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  32. Frederickson, P., Kaplan, J.L., Yorke, E.D., York, J.A.: The Lyapunov dimension of strange attractors. J. Differ. Equ. 49, 185–207 (1983)

    Article  MATH  Google Scholar 

  33. Feki, M., Robert, B.: Observer-based chaotic synchronization in the presence of unknown input. Chaos Solitons Fractals 15, 831–840 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  34. Liao, T.L., Huang, N.S.: An observer-based approach for chaotic synchronization with applications to secure communications. IEEE Trans. Circuits Syst. I 46, 1144–1150 (1999)

    Article  MATH  Google Scholar 

  35. Myneni, K., Thomas, T.A.: New method for the control of fast chaotic oscillations. Phys. Rev. Lett. 83, 2175–2178 (1999)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département de Physique, Faculté des Sciences, Université de Yaoundé 1, B.P. 812, Yaoundé, Cameroon

    J. Y. Effa & B. Z. Essimbi

  2. Département des Génies Electrique et Télécommunication, ENSP, Université de Yaoundé 1, B.P. 8390, Yaoundé, Cameroon

    J. Mucho Ngundam

Authors
  1. J. Y. Effa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. Z. Essimbi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Mucho Ngundam
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Y. Effa.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Effa, J.Y., Essimbi, B.Z. & Mucho Ngundam, J. Synchronization of improved chaotic Colpitts oscillators using nonlinear feedback control. Nonlinear Dyn 58, 39–47 (2009). https://doi.org/10.1007/s11071-008-9459-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-008-9459-7

Keywords

Search

Navigation