Nonlinear Analysis of Jitter Transfer in Charge Pump Phase-Locked loops regarding Channel Length Modulation Effect

Due to the nonlinear behavior caused by the charge pump, charge pump phase-locked loops (CPPLLs) are nonlinear systems. In an ideal charge pump, the applied current is constant; however, in practice, it is not constant due to the transistor's non-ideal effects. In this paper, regarding the transistor's channel length modulation effect (CLM) on charge pump’s current, the non-linear differential equation of the system is obtained and shows that the phase lock loop is a nonlinear system with memory and Voltaire Series expansion can be used to analyze it. As a result, a method for estimating a jitter transfer with a second-order filter is proposed. System level simulation is used to validate the analytical results with particular emphasis on the jitter transfer characteristics. The effect of different loop parameters has also been studied. The experiments all show excellent conformance between analytical equations and simulation results.