A LOCK-ON PROBABILITY ANALYSIS FOR THE INITIAL SYNCHRONIZATION OF PHASE-LOCKED LOOPS,
Abstract
This report presents a general method for the calculation of the lock-on time as a function of the initial phase (angular) error and initial frequency (angular velocity) error, in the absence of noise, with particular reference to the specially-important phase-locked-loop characterized by a nonlinear differential equation. As a result of the presence of saddle-points in the phasespace of the differential equations of phase-locked loops, it is shown that for any value of the initial frequency error, the lock-on time will be indefinitely large for a value of the initial phase error sufficiently close to a saddle-point separatrix, and that the lock-on time varies as the negative logarithm of the distance of the initial point from the separatrix when this distance is sufficiently small. An explicit formula is given for the equation for the phase-lockedloop. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 03, 1963
- Accession Number
- AD0433698
Entities
People
- Robert J. Mclaughlin
Organizations
- Harvard University