On the Gardner Problem for Phase-Locked Loops

This paper shows the possibilities of solving the Gardner problem of determining the lock-in range for multidimensional phase-locked loop models. Analytical estimates of the lock-in range for a third-order system are obtained for the first time by developing analogues of classical stability criteria...

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Bibliographic Details
Published in:Doklady. Mathematics 2019-11, Vol.100 (3), p.568-570
Main Authors: Kuznetsov, N. V., Lobachev, M. Y., Yuldashev, M. V., Yuldashev, R. V.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Phase locked loops
Stability criteria
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Summary:This paper shows the possibilities of solving the Gardner problem of determining the lock-in range for multidimensional phase-locked loop models. Analytical estimates of the lock-in range for a third-order system are obtained for the first time by developing analogues of classical stability criteria for the cylindrical phase space.
ISSN:1064-5624
1531-8362
DOI:10.1134/S1064562419060218