Performance of First-order Loops Incorporating Time Delay

Abstract

The influence of time delay on the statistical behavior of the first-order phase-locked-loop is investigated in VHF and UHF synchronous communication systems. The Fokker-Plank equation has been proposed to estimate the probability density function (pdf) of phase fluctuations as well as the average time to Loss lock in the presence of noise. The result reveal that the degradation in the loop performance occurs under various conditions of detuning when the inherent time delay is present.