Cycle Slips in Phase-Locked Loops: A Tutorial Survey

Cycle slips in phase-locked loops are statistical, nonlinear phenomena. This makes a mathematical analysis extremely difficult. As a consequence, the results of such an analysis are not easily accessible to the practicing engineer. It is the purpose of this survey paper to present a self-contained discussion of cycle slips in phase-locked loop avoiding advanced mathematical tools. Based on the results of an extensive experimental study we explain the underlying principle of the complex interaction between nonlinearity and noise. The results are complemented by simple, approximate analysis which agrees well with the experimental findings. In addition, we present a new and complete set of diagrams on cycle slip statistics not presently available in the literature.