Derivation and Design of In-Loop Filters in Phase-Locked Loop Systems

This paper addresses the concept of in-loop filters in phase-locked loop (PLL) systems. The in-loop filters are derived from an optimization perspective, and an analytical method to design the controlling parameters of a PLL with in-loop filters is also presented. Such filters can also be selected as conventional window functions in which case they can be tuned to reject certain frequency components similar to the discrete Fourier transform. In this paper, a rigorous method to introduce the concept of in-loop filters and window functions into PLL systems is presented. This method enables smoother estimation of the signal parameters such as phase angle, frequency, and amplitude in the presence of noise and harmonics. The in-loop filters can be adjusted to completely remove specific harmonics. The method is first developed for a single-phase enhanced PLL system and is then extended to three-phase PLLs including the well-known synchronous-reference-frame PLL. Simulation and experimental results are also included.