On first cycle slip time of phase-locked loops in cascade

Precise measurement and spacecraft tracking are obtained by using phase-locked loops in cascade in two-way communications links. Statistics on cycle slip time are of vital importance in system planning and design. This paper presents: (1) results of a computer simulation study of the mean time to first cycle slip of cascade phase-locked loops preceded by bandpass limiters, and (2) the determination of probability distributions of cycle slip. Numerical results are obtained for a typical coherent communication system.