LTP Modeling of Single-Phase $T/4$ Delay-Based PLLs

A large number of single-phase phase-locked loops (PLLs) require generating a 90° phase-shifted version of their single-phase input signal. Among the wide variety of options, using a quarter-cycle transfer delay is particularly popular. In recent years, several single-phase transfer delay-based PLLs (TD-PLLs) have been proposed in the literature. The major difference between different TD-PLLs lies in the way they have adapted to frequency changes. Regardless of this structural difference, a common trend in investigating TD-PLLs is obtaining a linear time-invariant (LTI) model and analyzing it. Obtaining such a model, however, is often based on neglecting the input signal amplitude variations and double-frequency oscillations in the transient behavior of TD-PLLs, which results in some inaccuracies. To deal with this problem, the linear time-periodic (LTP) modeling of TD-PLLs is presented in this letter. It is demonstrated that the LTP model does not have the limitations of the LTI one and can provide much higher accuracy, but at the cost of a higher model complexity.