Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 18609, 17 pages
Research Article

Models for Master-Slave Clock Distribution Networks with Third-Order Phase-Locked Loops

José Roberto Castilho Piqueira and Marcela de Carvalho Freschi

Escola Politécnica, Universidade de São Paulo, Avenida Prof. Luciano Gualberto, travessa 3, no. 158, São Paulo 05508-900, SP, Brazil

Received 9 September 2006; Accepted 16 February 2007

Academic Editor: José Manoel Balthazar

Copyright © 2007 José Roberto Castilho Piqueira and Marcela de Carvalho Freschi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The purpose of this work is to study the processing and transmission of clock signals in networks of geographically distributed nodes, in order to derive conditions for frequency and phase synchronization between the nodes. The focus is on the master-slave architecture, which presents a priority scheme of clock distribution. One-way master-slave (OWMS ) and two-way master-slave (TWMS) chains are studied, considering that the slave nodes are third-order phase-locked loops (PLLs). Third-order PLLs are chosen to improve the transient response but, if their parameters are not well adjusted, stability problems and chaotic behaviors appear, restricting the lock-in range of the network. Lock-in range for third-order PLLs with Sallen-Key filter is determined and it is verified whether this range is reduced when the PLLs are connected to a network. Numerical experiments show how chain size changes the lock-in ranges and the acquisition times.