Numerical Solution of the Fokker-Planck Equation for the First Order Phase-Locked Loop.

Abstract

The transient behavior of the phase error probability density function of a first-order phase-locked loop in the presence of additive white Gaussian noise is determined using numerical techniques. In addition, the modulo-2pi probability density function and the cycle slipping density function are found. The algorithm used in these analyses involves numerical integration of a normalized and factored Fokker-Planck equation. Results are shown for cases involving various signal-to-noise ratios and initial conditions. (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1972
Accession Number
AD0754355

Entities

People

  • Allan Rutherford

Organizations

  • Naval Postgraduate School

Tags

DTIC Thesaurus Topics

  • Additives (Chemicals)
  • Algorithms
  • Equations
  • Fokker Planck Equations
  • Gaussian Noise
  • Mathematical Analysis
  • Mathematics
  • Noise
  • Numerical Integration
  • Probability
  • Probability Density Functions

Fields of Study

  • Mathematics
  • Physics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Control Systems Engineering.
  • Fluid Dynamics.