We perform a systematic analysis of a system consisting of a two-stage Colpitts oscillator. This well-known chaotic oscillator is a modification of the standard Colpitts oscillator obtained by adding an extra transistor and a capacitor to the basic circuit. The two-stage Colpitts oscillator exhibits better spectral characteristics compared to a classical single-stage Colpitts oscillator. This interesting feature is suitable for chaos-based secure communication applications. We derive a smooth mathematical model (i.e., sets of nonlinear ordinary differential equations) to describe the dynamics of the system. The stability of the equilibrium states is carried out and conditions for the oc-J. Kengne ( ) · V.A. Fono Laboratoire d'Automatique et d'Informatique Appliquée currence of Hopf bifurcations are obtained. The numerical exploration reveals various bifurcation scenarios including period-doubling and interior crisis transitions to chaos. The connection between the system parameters and various dynamical regimes is established with particular emphasis on the role of both bias (i.e., power supply) and damping on the dynamics of the oscillator. Such an approach is particularly interesting as the results obtained are very useful for design engineers. The real physical implementation (i.e., use of electronic components) of the oscillator is considered to validate the theoretical analysis through several comparisons between experimental and numerical results.

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A novel two‐step algorithm to accurately analyze the transmission properties of the transmission lines loaded with electrically small resonators is introduced. The algorithm comprises a set of equations to predict and modify the geometrical parameters of the transmission line when loaded with the electrically small resonators. To verify the algorithm, a comparative study on the performance of a proof of concept compact metamaterial hybrid branch‐line coupler through numerical analysis and laboratory measurement was presented. © 2017 Wiley Periodicals, Inc. Microwave Opt Technol Lett 59:1341–1347, 2017