Accession Number : AD0433698


Title :   A LOCK-ON PROBABILITY ANALYSIS FOR THE INITIAL SYNCHRONIZATION OF PHASE-LOCKED LOOPS,


Corporate Author : HARVARD UNIV CAMBRIDGE MASS CRUFT LAB


Personal Author(s) : McLaughlin,Robert J


Report Date : 03 Feb 1963


Pagination or Media Count : 95


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)


Descriptors :   *OSCILLATORS , SYNCHRONIZATION(ELECTRONICS) , CONTROL SYSTEMS , PROBABILITY , CIRCUITS , INFORMATION THEORY , ERRORS , FREQUENCY ANALYZERS , NETWORKS , NOISE , TIME , STATISTICAL ANALYSIS , STATISTICAL FUNCTIONS , DIFFERENTIAL EQUATIONS , PERTURBATION THEORY


Distribution Statement : APPROVED FOR PUBLIC RELEASE