Statistical Characteristics of a Two-Ring Discrete Phase Locking System Excited by Combined Random Signals

摘要

A two-ring phase locking system with unidirectional ring coupling that operates in the presence of an input additive mixture of a signal with a randomly changing frequency and Gaussian white noise is considered. The probability distribution density (PDD) of the phase coordinates of the system is studied using the apparatus of Markovian processes. A technique for derivation and numerical solution of the vector Chapman-Kolmogorov equation is proposed. The output phase error variances for one- and two-ring locking systems are compared.