Transient Behavior of a Phase-Locked Loop in the Presence of Noise

Transient behavior of the first-order phase-locked loop in the presence of noise is investigated. Numerical integration is used to obtain solutions for the Fokker-Planck equation which represents loop dynamics, Results illustrate quantitative behavior of the time-varying probability density function of phase error when the input is a constant frequency sinusoid in the presence of additive white Gaussian noise. Several selected values of signal-to-noise ratio (SNR) are considered.