Improved phase-locked loop performance via nonlinear loop filters

A new structure for the loop filter of a PLL which consists of a conventional linear first order filter connected in a feedback arrangement with a static nonlinearity is analyzed. In the absence of noise, the steady state operating conditions (i.e., equilibrium points) are independent of the parameters of the nonlinearity, and asymptotic stability of the PLL for sufficiently small frequency detuning is established independent of the initial conditions of the VCO. Due to the nonlinearity, the resulting performance of the PLL during the acquisition node is greatly improved with little resulting loss in the narrow-band filtering capability of the loop. Using Volterra methods, an explicit expression for the variance of the phase error for a cubic nonlinearity is developed which compares favorably with simulation studies.