Cycle slips in synchronizers subject to smooth narrow-band loop noise

The cycle slipping in synchronizers subject to smooth narrowband loop noise is discussed. Such loop noise is shown to occur in repeater chains and in ring local area networks. The average rate of cycle slips and of bursts of cycle slips is evaluated, and closely approximated by a very simple expression that clearly indicates the influence of the loop noise bandwidth and the phase-detector characteristic. A comparison to the case of white loop noise reveals that, for most phase-detector characteristics, the slip rate caused by smooth narrowband loop noise is larger by several orders of magnitude than for white loop noise