On the pull-in and hold-in ranges of type 1 PLL with piecewise-linear phase detector characteristic

Abstract

In the present work, we consider a special case of a second-order system of ordinary differential equations which describes dynamics of a synchronization circuit called a phase-locked loop (PLL). A lead-lag loop filter and a piecewise-linear phase detector characteristic are considered resulting the final model to be a type 1 PLL. The stability and synchronization properties of the loop are characterized by so-called hold-in range and pull-in range, which describe set of parameters providing local stability of equilibria and global stability of the system, respectively. In this article, we determine the set of loop parameters such that the pull-in and hold-in ranges coincide.