Frequency quantization in first-order digital phase-locked loops with frequency-modulated input

Frequency granularity in a digital phase-locked loop arises from quantization in the number-controlled oscillator which prevents
the loop from locking exactly onto its reference signal and introduces unwanted phase jitter. Based on a nonlinear analysis of trajectories in the phase space, we have recently investigated the effect of frequency
quantization in a first-order loop with a frequency-modulated input signal and have derived useful bounds on the steady-state phase jitter excursion. In this paper, we continue that work and derive the maximum modulation amplitude such that loop cycle slipping is avoided. We also examine in
detail the loop behavior in acquiring phase-lock.