Stability and Bifurcation Analysis of Electronic Oscillators: Theory and some Experiments

Abstract:
We consider the electronic structure of a shunt-fed Colpitts oscillator. This oscillator is a feedback circuit built with a single bipolar junction transistor which is responsible of the nonlinear behavior of the complete circuit. The interest of investigating the dynamics of this circuit is justified by its multiple potential applications in the field of engineering and also by the striking/tremendous and very complex behavior the oscillator can exhibit, leading to periodic, multi-periodic and chaotic motions. We discuss some potential applications of the shunt-fed Colpitts oscillator. The modeling process leads to the derivation of mathematical equations (ODEs) to describe the behavior of the shunt-fed Colpitts oscillator. Using these equations, the stability and bifurcation analyzes are carried out and basins of attraction of stable solutions are obtained as well as some bifurcation diagrams showing the extreme sensitivity of the system to tiny changes in the values of the electronic circuit components. Analytical, numerical and experimental methods/approaches are considered to get full insight of the dynamical behavior of the proposed oscillator. Analytical and numerical results are validated by the results obtained from a real physical implementation (Hardware implementation) of the oscillator.