Accession Number:

AD0266951

Title:

A THRESHOLD THEORY FOR PHASE-LOCKED LOOPS

Descriptive Note:

Corporate Author:

MASSACHUSETTS INST OF TECH LEXINGTON LINCOLN LAB

Personal Author(s):

Report Date:

1961-08-22

Pagination or Media Count:

1.0

Abstract:

A model of a phase-locked loop has been developed which is valid for all signal-to-noise ratios. The model is in the form of a nonlinear feedback sy tem ith randomly time-varying par meters. The analysis considers two operating regions. In low signal-to-noise ra io regio s, the important consideration is stability. We want to study the asymptotic stability in the mean of a nonlinear system. It follows directly that a necessary condition for asymptotic stability of any nonlinear system is that a linearized model about some equilibrium point be asymptotically stable. By considering all possible equilibrium points, we can find an upper bound on the value of noise density which makes the system unstable. This upper bound represents a threshold value for system operation. In high signal-to-noise ratio regions, our results provide an exact statistical description of system behavior. Therefore, knowledge of the spectrum of the signal and noise may be used to optimize the syste configuration. Author

Subject Categories:

Distribution Statement:

APPROVED FOR PUBLIC RELEASE