New stability criteria for the nonuniform sampling digital phase-locked loops

Stability criteria for digital nonuniform sampling zero-crossing phase-locked loops are derived. The functional nonlinear discrete-time equation on the S/sup 1/-circle manifold is used to describe the phase error process in a loop of any order. Disturbed N:1 phase entrainment is studied, where the perturbation is either the frequency offset or additional random noise and effects due to quantization. The class of loops with discontinuous characteristic of the phase detector is advocated as they exhibit fast acquisition, no matter what the initial phase error conditions are, for any order of loop. The notion of the covering space from the theory of dynamical systems is used to consider the dynamics of the loop on the S/sup 1/-circle manifold. The approach is extensible to include the fading of the input waveform, AM and PM modulation, and loop filters with variable coefficients.