Probability Distribution for the Phase Jitter in Self-Timed Reconstructive Repeaters for PCM

Over the past several years the problem of maintaining pulse spacing within very close bounds in PCM transmission has received considerable attention both theoretically and experimentally. The effects of timing jitter in degrading repeater performance, in introducing distortion in 503 504 T H E BELL SYSTEM T E C H N I C A L J O U R N A L , MARCH 1902 the decoded analog signal, and in enhancing the difficulty of dropping or adding several pulse trains in time have been documented. 1 " 8 Sources of mistiming in a self-timed reconstructive repeater are well catalogued and include: noise, crosstalk, mistiming, finite pulse width effects, and amplitude to phase conversion in nonlinear devices. The first four of these sources have been considered in various analyses of timing jitter in self-timed and separately-timed P C M repeaters. Amplitude to phase conversion in nonlinear circuits has received attention primarily from the experimental viewpoint. The majority of the theoretical work to date has been concerned with timing errors in self-timed repeaters when the timing-wave extractor is a simple tuned circuit. For a random pulse train exciting the tuned circuit in the presence of noise and mistiming, results have been obtained for the mean displacement and the standard deviation of the zero crossings from their ideal location. This analysis is appropriate to repeaters employing complete retiming. These time displacements can also be considered as phase errors and we will use this terminology in what follows.