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, Shin'ichi Oishi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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
Issue number3
Publication statusPublished - 1997 Mar

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics


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