Statistical Behavior of Second-Order Phase-Locked Loops in the Presence of a Mixture of Impulsive and Gaussian Noise

An equation is found for the steady-state probability density function of the modulo-2π-reduced phase error of a secondorder phase-locked loop (PLL) with a proportional-proportional-plus-integral control type filter. The equation involves a certain conditional expectation which has been evaluated in an approximate way following the same approach used by previous authors in the case of sole Gaussian noise. With this approximation the equation becomes of the same type as that pertinent to a first-order system and therefore it can be solved with a method described by Ohlson in [3]. Theoretical results obtained in this way are complemented by experimental observations gathered by simulating the PPL on a digital computer.