Self-synchronization of second order PLLs in communication networks

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 VLSI 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. The existence of a wave-like state is undesirable in synchronizing networks, but may be removed by its destabilization.