Frequency Distortion of Second- and Third-Order Phase-Locked Loop Systems Using a Volterra-Series Approximation

In this paper, the frequency distortion for the nonlinear phase-locked loop (PLL) is derived analytically using a Volterra-series approximation. Both first- and second-order filters are considered in the PLL architecture. Theoretical results are then compared to those obtained via simulation. Comparisons are drawn between the two types of PLL with regard to the amount of distortion observed. Convergence of the Volterra-series solution is also discussed with regard to the system parameters.