The convergence of a PLL with variable parameters
A phase-locked loop with variable parameters is considered. In such a system it is possible to obtain a short convergence time together with a small bandwidth. It is supposed that the PLL's parameters cannot be switched and there is a restriction on the velocity of the parameter variation. 
 
 
 
An optimal strategy of parameter variation is obtained which gives an improvement in convergence time by a factor of about 30 in comparision to fixed parameter and small-bandwidth PLLs.
Discrete time-varying filter and PLL for synchronous estimation of parameters of a sine signal corrupted by a closely spaced FM interference
Abstract The concept of time-varying filters as applied to the problem of rejection of a sine signal with fast variations of frequency is explored. Using such filters, a method for synchronous (i.e., when frequency is known) estimation of phase and amplitude of a sine wave corrupted by closely spaced sinusoidal interference with fast frequency variations is proposed. It is shown that the coefficients of the time-varying filter can be effectively determined using a Phase Locked Loop. It is proved that the performance of the proposed estimator depends neither on the interference level nor on the speed of frequency variations. Comparison with an adaptive estimator based on a linear time invariant filter shows the superiority of the proposed one where the interference frequency changes rapidly over time.
Large signal analysis of a sampled PLL
A phase-locked loop with a sequential phase detector is analysed. It is assumed that the frequency difference between the reference and VCO frequencies is large. This leads to a nonlinear model of the sequential phase detector. Conditions for fast convergence are given for two particular cases of the loop filter, when a reference frequency is assumed to be constant.