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ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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Exact Formula for Pull-in Range of Phase-locked Loop with Proportional-integrating Filter and Piecewise-linear Phase Detector Characteristic

Author(s):

Nikolay Vladimirovich Kuznetsov

Doctor of Physical and Mathematical Sciences, Head of the Department
of Applied Cybernetics, St. Petersburg State University,
Head of the Laboratory of Information and Control Systems of the Institute
for Problems of Mechanical Engineering of the Russian Academy of Sciences (IPMash RAS)

nkuznetsov239@mail.ru

Mikhail Yurievich Lobachev

Ph.D., Researcher of the Department of Applied Cybernetics, St. Petersburg State University

Abstract:

The paper develops an efficient approach for accurately determining the pull-in range of a phase-locked loop with a proportional-integrating filter and a continuous piecewise linear phase detector characteristic. This approach makes it possible to derive an analytical formula for determining the pull-in range and obtain explicit conservative estimates and asymptotic values of the pull-in range. Within the framework of the theory of hidden oscillations, this approach provides a complete solution to the problem of determining the boundary of global stability and revealing its hidden parts corresponding to the nonlocal birth of hidden oscillations.

Keywords

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