Synchronisation in Noisy PLL Networks: Time Domain Model and its Analysis

In this paper we consider a PLL network described by an array of interconnected noisy phase oscillators. We define optimal conditions where the entire array synchronises with the reference signal by interacting only between nearest neighbours. We develop a continuous-time model of the PLL network and analyse synchronisation of the system numerically for different architectures of coupling and variations of control parameters. We show that the bidirectional topology significantly outperforms the unidirectional topology in terms of the overall phase noise of the network.