Stability of synchronized states in one dimensional networks of second order PLLS

Hisa Aki Tanaka, Maria De Sousa Vieira, Allan J. Lichtenberg, Michael A. Lieberman, Shinichi Oishi

    Research output: Contribution to journalArticle

    Abstract

    Synchronous distributed timing clocks are the basic building blocks in digital communication systems. Conventional systems mainly employ a tree-like network of cascaded timing clocks for synchronous clocking. On the other hand, decentralized synchronous networks of timing clocks, which have been proposed from a very early stage of the digital communication, are gaining attention in the consumer communication networks and also recently in large, high-performance digital systems (such as multiprocessors) clocking. In this paper, we present a theoretical study of synchronous networks of timing clocks consisting of locally connected second order phase-locked loops (PLLs). We find a close connection between the stability properties of the first and second order networks. The particular examples of one way and two way nearest neighbor coupling, with a lag-lead filter and a triangular phase detector (PD) are analyzed in detail. Both the synchronized in-phase solution and the wave-like "mode-lock" solution are examined. A criterion is found for the stability of the one-way coupled network while the two-way coupled network is found to be always stable.

    Original languageEnglish
    Pages (from-to)681-690
    Number of pages10
    JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
    Volume7
    Issue number3
    Publication statusPublished - 1997 Mar

    Fingerprint

    Clocks
    Timing
    Digital communication systems
    Phase locked loops
    Telecommunication networks
    Phase-locked Loop
    Locally Connected
    Lead
    Multiprocessor
    Detectors
    Communication Networks
    Building Blocks
    Decentralized
    Communication Systems
    Triangular
    Nearest Neighbor
    Communication
    High Performance
    Detector
    Filter

    ASJC Scopus subject areas

    • General
    • Applied Mathematics

    Cite this

    Stability of synchronized states in one dimensional networks of second order PLLS. / Tanaka, Hisa Aki; De Sousa Vieira, Maria; Lichtenberg, Allan J.; Lieberman, Michael A.; Oishi, Shinichi.

    In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 7, No. 3, 03.1997, p. 681-690.

    Research output: Contribution to journalArticle

    Tanaka, Hisa Aki ; De Sousa Vieira, Maria ; Lichtenberg, Allan J. ; Lieberman, Michael A. ; Oishi, Shinichi. / Stability of synchronized states in one dimensional networks of second order PLLS. In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. 1997 ; Vol. 7, No. 3. pp. 681-690.
    @article{e70add65c0154b2cabd51e194fdc616e,
    title = "Stability of synchronized states in one dimensional networks of second order PLLS",
    abstract = "Synchronous distributed timing clocks are the basic building blocks in digital communication systems. Conventional systems mainly employ a tree-like network of cascaded timing clocks for synchronous clocking. On the other hand, decentralized synchronous networks of timing clocks, which have been proposed from a very early stage of the digital communication, are gaining attention in the consumer communication networks and also recently in large, high-performance digital systems (such as multiprocessors) clocking. In this paper, we present a theoretical study of synchronous networks of timing clocks consisting of locally connected second order phase-locked loops (PLLs). We find a close connection between the stability properties of the first and second order networks. The particular examples of one way and two way nearest neighbor coupling, with a lag-lead filter and a triangular phase detector (PD) are analyzed in detail. Both the synchronized in-phase solution and the wave-like {"}mode-lock{"} solution are examined. A criterion is found for the stability of the one-way coupled network while the two-way coupled network is found to be always stable.",
    author = "Tanaka, {Hisa Aki} and {De Sousa Vieira}, Maria and Lichtenberg, {Allan J.} and Lieberman, {Michael A.} and Shinichi Oishi",
    year = "1997",
    month = "3",
    language = "English",
    volume = "7",
    pages = "681--690",
    journal = "International Journal of Bifurcation and Chaos",
    issn = "0218-1274",
    publisher = "World Scientific Publishing Co. Pte Ltd",
    number = "3",

    }

    TY - JOUR

    T1 - Stability of synchronized states in one dimensional networks of second order PLLS

    AU - Tanaka, Hisa Aki

    AU - De Sousa Vieira, Maria

    AU - Lichtenberg, Allan J.

    AU - Lieberman, Michael A.

    AU - Oishi, Shinichi

    PY - 1997/3

    Y1 - 1997/3

    N2 - Synchronous distributed timing clocks are the basic building blocks in digital communication systems. Conventional systems mainly employ a tree-like network of cascaded timing clocks for synchronous clocking. On the other hand, decentralized synchronous networks of timing clocks, which have been proposed from a very early stage of the digital communication, are gaining attention in the consumer communication networks and also recently in large, high-performance digital systems (such as multiprocessors) clocking. In this paper, we present a theoretical study of synchronous networks of timing clocks consisting of locally connected second order phase-locked loops (PLLs). We find a close connection between the stability properties of the first and second order networks. The particular examples of one way and two way nearest neighbor coupling, with a lag-lead filter and a triangular phase detector (PD) are analyzed in detail. Both the synchronized in-phase solution and the wave-like "mode-lock" solution are examined. A criterion is found for the stability of the one-way coupled network while the two-way coupled network is found to be always stable.

    AB - Synchronous distributed timing clocks are the basic building blocks in digital communication systems. Conventional systems mainly employ a tree-like network of cascaded timing clocks for synchronous clocking. On the other hand, decentralized synchronous networks of timing clocks, which have been proposed from a very early stage of the digital communication, are gaining attention in the consumer communication networks and also recently in large, high-performance digital systems (such as multiprocessors) clocking. In this paper, we present a theoretical study of synchronous networks of timing clocks consisting of locally connected second order phase-locked loops (PLLs). We find a close connection between the stability properties of the first and second order networks. The particular examples of one way and two way nearest neighbor coupling, with a lag-lead filter and a triangular phase detector (PD) are analyzed in detail. Both the synchronized in-phase solution and the wave-like "mode-lock" solution are examined. A criterion is found for the stability of the one-way coupled network while the two-way coupled network is found to be always stable.

    UR - http://www.scopus.com/inward/record.url?scp=0031089348&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0031089348&partnerID=8YFLogxK

    M3 - Article

    VL - 7

    SP - 681

    EP - 690

    JO - International Journal of Bifurcation and Chaos

    JF - International Journal of Bifurcation and Chaos

    SN - 0218-1274

    IS - 3

    ER -