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.

N1 - Publisher Copyright: © 2022 World Scientific Publishing Company.

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 -