Periodic Small Signal Analysis of a Wide Class of Type-II Phase Locked Loops Through an Exhaustive Variational Model

Phase-locked loops are important building blocks for several different applications. Modern design and implementation of these circuits is largely advantaged by a mixed analog/digital simulation approach since phase locked loops are stiff systems and a full analog representation is in general too large to simulate in reasonable time. Even though current algorithms, based on a mixed analog/digital representation, lead to models characterized by outstanding properties, they do not allow efficient simulations of important periodic and small signal features such as modulation/demodulation or noise effects. In this paper a novel, reliable and efficient method is proposed that overcomes those limitations and makes possible to evaluate both modulation/demodulation and noise effects in the widely adopted class of type-II phase-locked loop circuits based on a digital three-state phase-frequency detector.