Acquisition and Tracking Performance of a PLL Using a Class of Nonlinear Filters

A class of nonlinear filters was proposed in [1] as an alternative loop filter of a PLL. This paper examines further aspects of the performance of a PLL incorporating such a nonlinear filter. The acquisition performance due to frequency offsets and the steadystate tracking performance in the presence of noise and frequency offsets are analyzed and compared with experimental and simulation results. The noise analysis is based on techniques using the FokkerPlanck equation. The effect of the nonlinearity in the loop filter is approximated using a quasi-linearization approach. A modification to the original nonlinear filter structure is proposed in order to obtain the best noise performance in the presence of frequency offsets. The overall improvement in performance of a PLL with a nonlinear filter is evaluated and compared with a conventional PLL and other methods of improved acquisition performance such as the sweep method. The necessary graphs and formulas are presented for the design of a PLL with a nonlinear filter. The extra available design parameter enables the compromise between acquisition and noise performance to be overcome to a significant degree.