Mean time to lose lock for a second-order extended tracking range delay-locked loop

The delay-locked loop (DLL) is an appropriate device to guarantee fine synchronization for direct-sequence spread spectrum systems. For the performance analysis at low signal to noise ratios the mean time to lose lock (MTLL) represents the most important criterion. The MTLL of the second-order extended tracking range DLL is investigated. A coherent loop with a passive loop filter is considered. The MTLL is approximated by an explicit expression for the leading order term based on results by Kramers (1940). The investigations show significant differences for the MTLL of different loop structures. Furthermore, design considerations and optimal loop parameters are given