Accidental phase modulation in second-order phase-locked loops

The phase-locked loop, essential element for phase synchronization in communications and control, is studied for several types of application. However, some cases urge for more accurate models, mainly regarding to the accidental phase modulation, an unavoidable phenomenon provoked by imperfections of circuits and transmission media, causing oscillations around the synchronous state, even when this state is reached. In this work, this problem is treated by distinguishing two different cases: jitter (high frequency) and wander (low frequency). In addition, the perturbation origins are modeled, dividing the problem into deterministic and random signal perturbations showing how they affect the equilibrium even with the loop operating in the pull-in range.