Phase-locked loops and sampling

Phase-locked loops (PLLs) are properly to be regarded as a class of sampled control systems; they can be treated as continuous systems when the control range and all perturbation frequencies of interest are much smaller than the sampling rate. Thus in the general case, PLLs must be analyzed by the Laplace transform for sequences ("z transform") rather than for continuous signals. Stability limits are presented for some sampled PLLs of practical importance, and the methods of analysis are compared critically with a common approach.