Nonlinear analysis of correlative tracking systems using renewal process theory

The theory of renewal Markov processes is used to develop a method for analyzing correlative tracking systems having either periodic or nonperiodic nonlinearities. It is shown that the stationary probability density function, the mean time between two cycles of the phase process, and the average number of cycles to the right or left for an (N+1)-order loop can be obtained by solving a single Fokker-Planck equation of the renewal process. The method is applied to phase-locked loop (PLL) systems.