Table of Contents
Journal of Chaos
Volume 2014, Article ID 945658, 11 pages
http://dx.doi.org/10.1155/2014/945658
Research Article

Complex Dynamical Behavior of a Two-Stage Colpitts Oscillator with Magnetically Coupled Inductors

1Department of Physics, Laboratory of Electronics and Signal Processing (LETS), Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon
2Department of Telecommunication and Network Engineering, IUT-Fotso Victor of Bandjoun, University of Dschang, P.O. Box 134, Bandjoun, Cameroon
3Department of Electrical Engineering, Laboratory of Automation and Applied Computer (LAIA), IUT-Fotso Victor of Bandjoun, University of Dschang, P.O. Box 134, Bandjoun, Cameroon
4Department of Physics, Laboratory of Mechanics and Modelling of Physical Systems (L2MPS), Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon

Received 26 May 2014; Accepted 11 September 2014; Published 21 October 2014

Academic Editor: Uchechukwu E. Vincent

Copyright © 2014 V. Kamdoum Tamba et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A five-dimensional (5D) controlled two-stage Colpitts oscillator is introduced and analyzed. This new electronic oscillator is constructed by considering the well-known two-stage Colpitts oscillator with two further elements (coupled inductors and variable resistor). In contrast to current approaches based on piecewise linear (PWL) model, we propose a smooth mathematical model (with exponential nonlinearity) to investigate the dynamics of the oscillator. Several issues, such as the basic dynamical behaviour, bifurcation diagrams, Lyapunov exponents, and frequency spectra of the oscillator, are investigated theoretically and numerically by varying a single control resistor. It is found that the oscillator moves from the state of fixed point motion to chaos via the usual paths of period-doubling and interior crisis routes as the single control resistor is monitored. Furthermore, an experimental study of controlled Colpitts oscillator is carried out. An appropriate electronic circuit is proposed for the investigations of the complex dynamics behaviour of the system. A very good qualitative agreement is obtained between the theoretical/numerical and experimental results.