On the limit behavior of second-order analog phase-locked loops

The study of limit behavior of a dynamical system is necessary for nonlinear analysis and computation of the exact boundary of global stability in the parameters’ space. For phase-locked loops (PLLs), a problem of its global stability is equal to a problem of a pull-in range calculation, which is one of the key stability characteristics of a PLL. In this paper, we consider a model of a second-order analog PLL and show that it can exhibit a wide range of limit behavior, including cycles and polycycles of the first and second kind.