Transient analysis of phaselocked loops in the presence of noise
Abstract
Transient or timedependent behavior was studied of phaselocked loops (PLL's) in the presence of noise. The cases of the first order PLL's in the presence of exponentially correlated noise and the second order (lagfilter) PLL's in the presence of white Gaussian noise are considered. For each of the two PLL models above, the corresponding FokkerPlanck equation for the transition probability density of phase error is formulated. In the region of low signaltonoise ratio perturbation techniques were used to obtain approximate modulo2pi solutions to the FokkerPlanck equation. These approximate solutions are then used to determine the transition cumulative distribution function, the time dependent mean, and the time dependent variance of phase error. Numerical results which show the transient behavior of the PLL as a function of various loop parameters of interest are presented as tables and figures.
 Publication:

Ph.D. Thesis
 Pub Date:
 December 1975
 Bibcode:
 1975PhDT........61H
 Keywords:

 Phase Locked Systems;
 Random Noise;
 Time Dependence;
 White Noise;
 Distribution Functions;
 FokkerPlanck Equation;
 Signal To Noise Ratios;
 Tables (Data);
 Transition Probabilities;
 Electronics and Electrical Engineering