Numerical Solution of the Fokker-Planck Equation for the First Order Phase-Locked Loop.
NAVAL POSTGRADUATE SCHOOL MONTEREY CALIF
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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