Accumulation of jitter: A stochastic model

A problem that has been considered extensively in the past is the accumulation of jitter in a chain of regenerative repeaters. For simplicity it is usually assumed that all repeaters in the chain are identical. However, this is not the case in real systems, where considerable differences among the repeaters of a chain have been observed. These random variations are due mainly to manufacturing tolerances, aging effects, temperature changes, etc. In this work, we examine the accumulation of systematic and random jitter along the chain, when the repeater transfer functions are subjected to random variations. We derive expressions for the expected value and variance of the output jitter spectrum in terms of average values of the repeater's jitter transfer function. In addition we find the expected value and the variance of the RMS jitter. Finally we examine two special cases where the timing circuit employs either a phased-locked loop or a surface acoustic wave filter, and derive some asymptotic relations for the power spectral density and root-mean-square value of the accumulated systematic jitter.