Synchronization limit and chaos onset in mutually coupled phase-locked loops

Hisa Aki Tanaka, Shinichi Oishi, Kazuo Horiuchi

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    A study of the dynamical properties, such as lock-in or lock-out condition, for mutually coupled phase-locked loops (PLLs) incorporating lag filters and triangular phase detectors, is presented. The system is analyzed in the context of nonlinear dynamical system theory. The symmetry of the mutually coupled PLL's system reduces the original fourth-order ordinary differential equation (ODE) that governs the phase dynamics of the voltage-controlled oscillators (VCO) outputs to the third-order ODE, for which the geometric structure of the invariant manifolds provides an understanding as to how and when lock-in can be obtained or out-of-lock behavior persists. In addition, two-parameter diagrams of the one-homoclinic orbit are obtained by solving a set of non-linear (finite dimensional) equations.

    Original languageEnglish
    Title of host publicationIEEE Asia-Pacific Conference on Circuits and Systems - Proceedings
    Place of PublicationPiscataway, NJ, United States
    PublisherIEEE
    Pages317-321
    Number of pages5
    Publication statusPublished - 1994
    EventProceedings of the 1994 IEEE Asia-Pacific Conference on Circuits and Systems - Taipei, Taiwan
    Duration: 1994 Dec 51994 Dec 8

    Other

    OtherProceedings of the 1994 IEEE Asia-Pacific Conference on Circuits and Systems
    CityTaipei, Taiwan
    Period94/12/594/12/8

    Fingerprint

    Phase locked loops
    Ordinary differential equations
    Chaos theory
    Synchronization
    Nonlinear dynamical systems
    Variable frequency oscillators
    System theory
    Orbits
    Detectors

    ASJC Scopus subject areas

    • Electrical and Electronic Engineering

    Cite this

    Tanaka, H. A., Oishi, S., & Horiuchi, K. (1994). Synchronization limit and chaos onset in mutually coupled phase-locked loops. In IEEE Asia-Pacific Conference on Circuits and Systems - Proceedings (pp. 317-321). Piscataway, NJ, United States: IEEE.

    Synchronization limit and chaos onset in mutually coupled phase-locked loops. / Tanaka, Hisa Aki; Oishi, Shinichi; Horiuchi, Kazuo.

    IEEE Asia-Pacific Conference on Circuits and Systems - Proceedings. Piscataway, NJ, United States : IEEE, 1994. p. 317-321.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Tanaka, HA, Oishi, S & Horiuchi, K 1994, Synchronization limit and chaos onset in mutually coupled phase-locked loops. in IEEE Asia-Pacific Conference on Circuits and Systems - Proceedings. IEEE, Piscataway, NJ, United States, pp. 317-321, Proceedings of the 1994 IEEE Asia-Pacific Conference on Circuits and Systems, Taipei, Taiwan, 94/12/5.
    Tanaka HA, Oishi S, Horiuchi K. Synchronization limit and chaos onset in mutually coupled phase-locked loops. In IEEE Asia-Pacific Conference on Circuits and Systems - Proceedings. Piscataway, NJ, United States: IEEE. 1994. p. 317-321
    Tanaka, Hisa Aki ; Oishi, Shinichi ; Horiuchi, Kazuo. / Synchronization limit and chaos onset in mutually coupled phase-locked loops. IEEE Asia-Pacific Conference on Circuits and Systems - Proceedings. Piscataway, NJ, United States : IEEE, 1994. pp. 317-321
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