The Effect of Phase Jitter on the Performance of a First-Order Phase-Locked Loop

A filterless phase-locked loop is considered with an arbitrary periodic phase comparator. The loop has a jittered input and is perturbed by thermal noise. Under such conditions the loop skips cycles from time to time. A study is made of the statistical behavior of the loop and emphasis is placed on the determination of the average time of skipping cycles. This problem is related to the first passage time problem of mathematical statistics and has been studied by a number of authors [1], [2], [3], [15]. The specific interest in the present paper is the study of the effect of timing jitter on the "spilling" of stores in a digital transmission system. A comparison of the average frequency of "spilling\´ the stores is made for a sawtooth, sinusoidal, and an "inscribed in" and "circumscribed about" triangular phase comparator. Examples using numbers typical of a digital transmission system show that the average frequency of "spilling" the stores in the time division multiplex should be exceedingly small.