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, Shin'ichi
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.
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U2 - 10.1142/S0218127497000479
DO - 10.1142/S0218127497000479
M3 - Article
AN - SCOPUS:0031089348
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 -