Pull-In Performance of a Piecewise Linear Phase-Locked Loop

This is part of a study concerned with the analysis of phase-locked loops (PLL's). The broad objective throughout this work is to improve upon our general understanding in this important area. More particularly, ly, we are seeking quantitative results indicative of the pull-in behavior of PLL's. In the present paper, we point out some results in foreign publications and focus attention on a paper by Kapranov [1] which is devoted to the study of the pull-in frequency of second-order PLL's with a symmetric phase comparator. We apply the same approach and present results, in closed form, in the more general case where the phase comparator possesses an asymmetric triangular characteristic. Special cases of this phase comparator are the sawtooth and symmetric triangular comparators. It can also be viewed as an approximation to the Tanlock phase comparator. The RC filter case is treated.