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

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The Gardner Problem and Cycle Slipping Bifurcation for Type-2 Phase-Locked Loops. / Kuznetsov, Nikolay V.; Arseniev, Dmitry G.; Blagov, Mikhail V.; Lobachev, Mikhail Y.; Wei, Zhouchao; Yuldashev, Marat V.; Yuldashev, Renat V.

In: International Journal of Bifurcation and Chaos, Vol. 32, No. 9, 2250138, 01.07.2022.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{9a8ccaa350084708a73dfac8900341ea,

title = "The Gardner Problem and Cycle Slipping Bifurcation for Type-2 Phase-Locked Loops",

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. ",

keywords = "cycle slipping, Gardner problem, global stability, lock-in range, Lyapunov function, nonlinear analysis, Phase-locked loop (PLL), type-2 PLL",

author = "Kuznetsov, {Nikolay V.} and Arseniev, {Dmitry G.} and Blagov, {Mikhail V.} and Lobachev, {Mikhail Y.} and Zhouchao Wei and Yuldashev, {Marat V.} and Yuldashev, {Renat V.}",

note = "Publisher Copyright: {\textcopyright} 2022 World Scientific Publishing Company.",

year = "2022",

month = jul,

day = "1",

doi = "10.1142/S0218127422501383",

language = "English",

volume = "32",

journal = "International Journal of Bifurcation and Chaos in Applied Sciences and Engineering",

issn = "0218-1274",

publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

number = "9",

}

RIS

TY - JOUR

T1 - The Gardner Problem and Cycle Slipping Bifurcation for Type-2 Phase-Locked Loops

AU - Kuznetsov, Nikolay V.

AU - Arseniev, Dmitry G.

AU - Blagov, Mikhail V.

AU - Lobachev, Mikhail Y.

AU - Wei, Zhouchao

AU - Yuldashev, Marat V.

AU - Yuldashev, Renat V.

PY - 2022/7/1

Y1 - 2022/7/1

N2 - 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.

AB - 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.

KW - cycle slipping

KW - Gardner problem

KW - global stability

KW - lock-in range

KW - Lyapunov function

KW - nonlinear analysis

KW - Phase-locked loop (PLL)

KW - type-2 PLL

UR - http://www.scopus.com/inward/record.url?scp=85134335445&partnerID=8YFLogxK

U2 - 10.1142/S0218127422501383

DO - 10.1142/S0218127422501383

M3 - Article

AN - SCOPUS:85134335445

VL - 32

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

SN - 0218-1274

IS - 9

M1 - 2250138

ER -

ID: 98811985