Transient analysis of phase-locked loops in the presence of noise
Abstract
Transient or time-dependent behavior was studied of phase-locked 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 (lag-filter) PLL's in the presence of white Gaussian noise are considered. For each of the two PLL models above, the corresponding Fokker-Planck equation for the transition probability density of phase error is formulated. In the region of low signal-to-noise ratio perturbation techniques were used to obtain approximate modulo-2pi solutions to the Fokker-Planck 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;
- Fokker-Planck Equation;
- Signal To Noise Ratios;
- Tables (Data);
- Transition Probabilities;
- Electronics and Electrical Engineering