In this paper, we derive linearized discrete-time models of higher order Charge-Pump Phase-Locked Loops (CPPLLs). The behaviour of CP-PLLs in the steady state is analysed
and an important feature is developed. The nonlinear state equations of CP-PLLs are linearized around the equilibrium point. The linearized discrete-time model is finally verified using behavioral simulations in Matlab and PSpice.