Analysis of Pull-in Range Limit by Charge Pump Mismatch in a Linear Phase-Locked Loop

In this paper, we show the relationship between the pull-in range of a linear phase-locked loop (PLL) and the current mismatch of the charge pump that controls the frequency of the oscillator in the PLL. We evaluate the pull-in range of the PLL based on a nonlinear behavioral model of the pull-in process with three types of phase detectors. We introduce the mismatch error to the charge pump current in the PLL and study the impact of this error on the pull-in range. We also apply the mismatch error to a nonlinear differential equation that describes the loop dynamics of the PLL and calculate the pull-in range under this mismatch condition. We validate the limitations of the pull-in range due to the current mismatch by a numerical simulation with MATLAB.