IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v126y2019icp351-360.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077919302723
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.07.020?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ren, Guodong & Xue, Yuxiong & Li, Yuwei & Ma, Jun, 2019. "Field coupling benefits signal exchange between Colpitts systems," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 45-54.
    2. Kengne, Romanic & Tchitnga, Robert & Mabekou, Sandrine & Tekam, Blaise Raoul Wafo & Soh, Guy Blondeau & Fomethe, Anaclet, 2018. "On the relay coupling of three fractional-order oscillators with time-delay consideration: Global and cluster synchronizations," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 6-17.
    3. Li, Guo Hui & Zhou, Shi Ping & Yang, Kui, 2007. "Controlling chaos in Colpitts oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 582-587.
    4. Barry, D.A & Parlange, J.-Y & Li, L & Prommer, H & Cunningham, C.J & Stagnitti, F, 2000. "Analytical approximations for real values of the Lambert W-function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 53(1), pages 95-103.
    5. Tchitnga, R. & Mezatio, B.A. & Fozin, T. Fonzin & Kengne, R. & Louodop Fotso, P.H. & Fomethe, A., 2019. "A novel hyperchaotic three-component oscillator operating at high frequency," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 166-180.
    6. Tchitnga, Robert & Fotsin, Hilaire Bertrand & Nana, Bonaventure & Louodop Fotso, Patrick Hervé & Woafo, Paul, 2012. "Hartley’s oscillator: The simplest chaotic two-component circuit," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 306-313.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tchitnga, R. & Mezatio, B.A. & Fozin, T. Fonzin & Kengne, R. & Louodop Fotso, P.H. & Fomethe, A., 2019. "A novel hyperchaotic three-component oscillator operating at high frequency," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 166-180.
    2. Mezatio, Brice Anicet & Motchongom, Marceline Tingue & Wafo Tekam, Blaise Raoul & Kengne, Romanic & Tchitnga, Robert & Fomethe, Anaclet, 2019. "A novel memristive 6D hyperchaotic autonomous system with hidden extreme multistability," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 100-115.
    3. Martínez-Guerra, Rafael & Pasaye, José Juan Rincón, 2009. "Synchronization and anti-synchronization of chaotic systems: A differential and algebraic approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 840-846.
    4. Leutcho, Gervais Dolvis & Kengne, Jacques, 2018. "A unique chaotic snap system with a smoothly adjustable symmetry and nonlinearity: Chaos, offset-boosting, antimonotonicity, and coexisting multiple attractors," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 275-293.
    5. Jiménez, F. & Jodrá, P., 2009. "On the computer generation of the Erlang and negative binomial distributions with shape parameter equal to two," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1636-1640.
    6. Guo, Yeye & Wang, Chunni & Yao, Zhao & Xu, Ying, 2022. "Desynchronization of thermosensitive neurons by using energy pumping," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 602(C).
    7. Zhang, Zhe & Ai, Zhaoyang & Zhang, Jing & Cheng, Fanyong & Liu, Feng & Ding, Can, 2020. "A general stability criterion for multidimensional fractional-order network systems based on whole oscillation principle for small fractional-order operators," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    8. Nepomuceno, Erivelton G. & Lima, Arthur M. & Arias-García, Janier & Perc, Matjaž & Repnik, Robert, 2019. "Minimal digital chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 62-66.
    9. Jose Miguel Riquelme-Dominguez & Sergio Martinez, 2020. "A Photovoltaic Power Curtailment Method for Operation on Both Sides of the Power-Voltage Curve," Energies, MDPI, vol. 13(15), pages 1-17, July.
    10. Venetis, Ioannis A. & Paya, Ivan & Peel, David A., 2007. "Deterministic impulse response in a nonlinear model. An analytical expression," Economics Letters, Elsevier, vol. 95(3), pages 315-319, June.
    11. Lóczi, Lajos, 2022. "Guaranteed- and high-precision evaluation of the Lambert W function," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    12. Liu, Zhilong & Zhou, Ping & Ma, Jun & Hobiny, Aatef & Alzahrani, Faris, 2020. "Autonomic learning via saturation gain method, and synchronization between neurons," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    13. Njitacke, Z.T. & kengne, J. & Kengne, L. Kamdjeu, 2017. "Antimonotonicity, chaos and multiple coexisting attractors in a simple hybrid diode-based jerk circuit," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 77-91.
    14. Kai Han & Yuntian He & Alex X. Liu & Shaojie Tang & He Huang, 2020. "Differentially Private and Budget-Limited Bandit Learning over Matroids," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 790-804, July.
    15. Zhang, Shenghai & Luo, Shaohua & He, Shaobo & Ouakad, Hassen M., 2022. "Analog circuit implementation and adaptive neural backstepping control of a network of four Duffing-type MEMS resonators with mechanical and electrostatic coupling," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    16. Jodrá, P., 2010. "Computer generation of random variables with Lindley or Poisson–Lindley distribution via the Lambert W function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(4), pages 851-859.
    17. Zhang, Yuan & Cao, Jinde & Liu, Lixia & Liu, Haihong & Li, Zhouhong, 2024. "Complex role of time delay in dynamical coordination of neural progenitor fate decisions mediated by Notch pathway," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    18. 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).
    19. Dejan Brkić & Pavel Praks, 2018. "Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright ω-Function," Mathematics, MDPI, vol. 7(1), pages 1-15, December.
    20. Wu, Fuqiang & Guo, Yitong & Ma, Jun & Jin, Wuyin, 2023. "Synchronization of bursting memristive Josephson junctions via resistive and magnetic coupling," Applied Mathematics and Computation, Elsevier, vol. 455(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:126:y:2019:i:c:p:351-360. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.