Dynamical properties and chaos synchronization of improved Colpitts oscillators

In this paper, the dynamics and synchronization of improved Colpitts oscillators designed to operate in ultrahigh frequency range are considered. The model is described by a continuous time four-dimensional autonomous system with an exponential nonlinearity. The system is integrated numerically and various bifurcation diagrams and corresponding graphs of largest 1D Lyapunov exponent are plotted to summarize different scenarios leading to chaos. It is found that the oscillator moves from the state of fixed point motion to chaos via the usual paths of period-doubling, intermittency and interior crisis routes when monitoring the bias (i.e. power supply) in tiny ranges. In order to promote chaos-based synchronization designs of this type of oscillators, a synchronization strategy based upon the design of a nonlinear state observer is successfully adapted. The suggested approach enables synchronization to be achieved via a scalar transmitted signal which represents a suitable feature for communication applications. Numerical simulations are performed to demonstrate the effectiveness and feasibility of the proposed technique.

[1]  A. Pugh.  The art of electronics. 2nd edn: By Paul Horowitz and Winfield Hill. Pp. 1125. Cambridge University Presss. 1989. £29.95, US$49.50 , 1990 .

[2]  Li Guo-Hui.  Synchronization and anti-synchronization of Colpitts oscillators using active control , 2005 .

[3]  张超,et al.  Synchronization between two different chaotic systems with nonlinear feedback control , 2007 .

[4]  Kyandoghere Kyamakya,et al.  Stability and Bifurcation Analysis of Electronic Oscillators: Theory and some Experiments , 2009 .

[5]  G. Mykolaitis,et al.  Numerical Investigation and Experimental Demonstration of Chaos from Two-Stage Colpitts Oscillator in the Ultrahigh Frequency Range , 2006 .

[6]  Mehdi Roopaei,et al.  Review article on adaptive synchronization of chaotic systems with unknown parameters , 2011 .

[7]  A. Tamasevicius,et al.  Improved chaotic Colpitts oscillator for ultrahigh frequencies , 2004 .

[8]  A. Tamasevicius,et al.  Experimental demonstration of chaos from Colpitts oscillator in VHF and UHF ranges , 2004 .

[9]  Michael Peter Kennedy,et al.  Nonlinear analysis of the Colpitts oscillator and applications to design , 1999 .

[10]  B. Z. Essimbi,et al.  Synchronization of improved chaotic Colpitts oscillators using nonlinear feedback control , 2009 .

[11]  Erik Lindberg,et al.  Towards Threshold Frequency in Chaotic Colpitts oscillator , 2007, Int. J. Bifurc. Chaos.

[12]  C. Wu,et al.  A Universal Circuit for Studying and Generating Chaos-Part I: Routes , 1993 .

[13]  Parlitz,et al.  Synchronization-based parameter estimation from time series. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  S. Mascolo,et al.  Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal , 1997 .

[15]  Paul Horowitz,et al.  The Art of Electronics , 1980 .

[16]  Almudena Suarez,et al.  Stability Analysis of Nonlinear Microwave Circuits , 2003 .

[17]  J. M. Ngundam,et al.  Synchronization of Colpitts oscillators with different orders , 2009 .

[18]  Wuneng Zhou,et al.  Adaptive bidirectionally coupled synchronization of chaotic systems with unknown parameters , 2011 .

[19]  S. Bowong.  Stability analysis for the synchronization of chaotic systems with different order: application to secure communications , 2004 .

[20]  G. Mykolaitis,et al.  Chaotic Colpitts Oscillator for the Ultrahigh Frequency Range , 2006 .

[21]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[22]  A. Tamaševičius,et al.  Coupled Chaotic Colpitts Oscillators: Identical and Mismatched Cases , 2006 .

[23]  Jamal Daafouz,et al.  Adaptive synchronization of uncertain chaotic colpitts oscillators based on parameter identification , 2005 .

[24]  R. Ostojic,et al.  Synchronization of chaotic Colpitts oscillators with applications to binary communications , 1999, ICECS'99. Proceedings of ICECS '99. 6th IEEE International Conference on Electronics, Circuits and Systems (Cat. No.99EX357).

[25]  S. Mascolo,et al.  A system theory approach for designing cryptosystems based on hyperchaos , 1999 .

[26]  Michael Peter Kennedy.  Chaos in the Colpitts oscillator , 1994 .

[27]  S. Mascolo,et al.  Synchronisation of hyperchaotic oscillators using a scalar signal , 1998 .

[28]  A. M. Young,et al.  Introduction to chaos-based communications and signal processing , 2000, 2000 IEEE Aerospace Conference. Proceedings (Cat. No.00TH8484).

[29]  Xiaodong Chen,et al.  Loop Gain and its Relation to Nonlinear Behavior and Chaos in a Transformer-Coupled oscillator , 2004, Int. J. Bifurc. Chaos.

[30]  Stephen A. Maas,et al.  Nonlinear Microwave and RF Circuits , 2003 .

[31]  Antanas Cenys,et al.  Two-stage chaotic Colpitts oscillator , 2001 .

[32]  A. Tamasevicius,et al.  Synchronization of VHF chaotic Colpitts oscillators , 2001 .