First-Order Discrete Phase-Locked Loop with Applications to Demodulation of Angle-Modulated Carrier

In this paper, a first-order discrete phase-locked loop that tracks the phase of an incoming analog signal at discrete instants of time occurring once per cycle of the carrier is developed. The functional loop components and the operation of the loop are described in detail. The loop model is developed for both the deterministic and noisy case by a nonlinear coupled difference equation with perturbed (or deviating) arguments. The tracking performance for the inputs of the phase step, the phase ramp, and the sinusoidally modulated carrier is determined and the locking conditions for these input transients are derived. Conceptual designs using this first-order digital loop have been given for the demodulation of phase- and frequency-modulated signals.