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High frequency Colpitts’ oscillator: A simple configuration for chaos generation

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  • Wafo Tekam, Raoul Blaise
  • Kengne, Jacques
  • Djuidje Kenmoe, Germaine

Abstract

This paper introduces a novel four-component-based high frequency chaotic circuit. The proposed circuit is an implicit common-emitter Colpitts oscillator; hitherto the simplest in the realm of bipolar junction transistor based LC (inductor-capacitor) autonomous chaotic circuits. It consists of a single voltage source in series with a resistor, one bipolar junction transistor, an inductor and a single grounded capacitor. Design procedure takes advantage of an intrinsic capacitance of the transistor to complete the resonant tank. The circuit is mathematically modelled with a three-dimensional autonomous system; theoretical analysis of circuit’s model is presented along with numerical and experimental outcomes. Bifurcation diagrams, Lyapunov exponents, phase portraits and time series revealed that the proposed oscillator is capable of generating striking behaviors such as quasi-sinusoidal orbits, limit cycles and chaos. Overall, a good accordance is found between practice and theory. Comparison between the original Colpitts oscillator and the novel one is done to highlight benefits of the latter. The fact that circuit’s parsimony does not impair chaotic features is of particular interest. Beside well known applications of Colpitts oscillators, this parsimonious version is a good candidate for experimental investigations on networked oscillators and academic purposes owing to its simplicity, low-cost and ease offered in implementation.

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  • Wafo Tekam, Raoul Blaise & Kengne, Jacques & Djuidje Kenmoe, Germaine, 2019. "High frequency Colpitts’ oscillator: A simple configuration for chaos generation," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 351-360.
    • Handle: RePEc:eee:chsofr:v:126:y:2019:i:c:p:351-360
    DOI: 10.1016/j.chaos.2019.07.020
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    References listed on IDEAS

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    Cited by:

    1. Jiri Petrzela, 2022. "Chaos in Analog Electronic Circuits: Comprehensive Review, Solved Problems, Open Topics and Small Example," Mathematics, MDPI, vol. 10(21), pages 1-28, November.
    2. Minati, Ludovico & Innocenti, Giacomo & Mijatovic, Gorana & Ito, Hiroyuki & Frasca, Mattia, 2022. "Mechanisms of chaos generation in an atypical single-transistor oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Ling Zhou & Zhenzhen You & Xiaolin Liang & Xiaowu Li, 2022. "A Memristor-Based Colpitts Oscillator Circuit," Mathematics, MDPI, vol. 10(24), pages 1-16, December.

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