Phase-jitter dynamics of digital phase-locked loops

Recent work on the subject of digital phase-locked loops (DPLL's) has examined the unwanted phase jitter that occurs in such systems due to frequency quantization in a number-controlled oscillator. In this paper, we show that the theory of nonlinear dynamics can provide an analytical explanation of this phase jitter, along with other features of the system behavior. In particular, we will describe the phase-jitter dynamics mathematically in terms of the well-known circle rotation map and area-preserving twist map.