On the Solution of a Fokker-Planck Equation in the Presence of Correlated Noise.
Abstract
The Fokker-Planck equation corresponding to the first-order phase-locked loop in the presence of exponentially correlated noise is studied. For the case of zero signal-to-noise ratio and aero initial detuning an analytical solution is obtained for the Fokker-Planck equation, reduced modulo 2 pi. The solution is the transition probability density function (p.d.f.) and gives explicit relationships between loop parameters and the transient behavior of the phase error process. From the transition p.d.f. the transition cumulative distribution function and the time-dependent variance of phase error are easily obtained. At sufficiently small values of Dt, where D is the diffusion constant and t is the time, the transition p.d.f. provides a good approximation to the probability of loss of lock in the loop. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 29, 1982
- Accession Number
- ADA124114
Entities
People
- Henry N. Ho
- Roger H. Lang
Organizations
- United States Naval Research Laboratory