Estimating the critical number of slave nodes in a single-chain PLL network

The existence and stability conditions for the synchronous state in telecommunication networks with single-chain master-slave clock distribution architecture are determined. The slave nodes are modeled as first-order phase-locked loops (PLLs) and the signal processing and propagation delays are taken into account. We analytically show that if the number of slaves exceeds a critical value, synchronization is unreachable.