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

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.