Synchronization Failures in a Chain of PLL Synchronizers

In digital transmission systems employing PLL repeaters, timing jitter is produced mostly by intersymbol interference (ISI). Despite the fact that IS1 represents a narrow-band disturbance to the PLL for a long chain of N repeaters, it is responsible for cycle slips of the PLL repeater. It is demonstrated that the cycle slip rate is the key parameter determining the error performance of the system. It is shown that the accumulated jitter for a large chain becomes a narrow-band process, which can be replaced by an equivalent low-pass jitter-noise process, which lends itself to analytical treatment. Numerical results of the cycle slip rate are given, based on the solution of a time-dependent Fokker-Planck equation. The results are useful for a wide range of loop transfer functions and phase-detector characteristics. The theoretical findings are confirmed by experimental results.