The Gardner Problem and Cycle Slipping Bifurcation for Type-2 Phase-Locked Loops-Reference-Cited by-同舟云学术

The Gardner Problem and Cycle Slipping Bifurcation for Type-2 Phase-Locked Loops

Published:2022-07 Issue:09 Volume:32 Page:
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Kuznetsov Nikolay V.¹²³⁴^ORCID,Arseniev Dmitry G.⁴⁵,Blagov Mikhail V.¹²,Lobachev Mikhail Y.¹⁶,Wei Zhouchao⁷,Yuldashev Marat V.¹,Yuldashev Renat V.¹

Affiliation:

1. Faculty of Mathematics and Mechanics, Saint Petersburg State University, Russia

2. Faculty of Information Technology, University of Jyväskylä, Finland

3. Institute for Problems in Mechanical Engineering, of the Russian Academy of Sciences, Russia

4. Peter the Great Saint Petersburg Polytechnic University, Russia

5. Saint Petersburg State University, Russia

6. Industrial Management Department, LUT University, Finland

7. School of Mathematics and Physics, China University of Geosciences, China

Abstract

In the present work, a second-order type-2 phase-locked loop (PLL) with a piecewise-linear phase detector characteristic is analyzed. An exact solution to the Gardner problem on the lock-in range is obtained for the considered model. The solution is based on a study of cycle slipping bifurcation, which improves the well-known engineering estimates.

Funder

the Ministry of Science and Higher Education of the Russian Federation as part of World-class Research Center program

the National Natural Science Foundation of China

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127422501383

Reference42 articles.

1. Qualitative investigation of a system of three differential equations in the theory of phase synchronization

2. Tutorial on dynamic analysis of the Costas loop

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