Pseudo-linear operation of second-order phase-locked loops

Abstract

This paper defines a region of operation, calling it the pseudo-linear region, where a phase-locked loop (p.l.l.), behaves essentially in a linear manner. The results obtained for a loop with an active second-order filter suggest a very simple empirical definition for this region as a function of the parameters of the loop (ζ, and ωn), and classifies the regions of operation of the p.l.l., linear, pseudo-linear, non-linear and cycle slipping.