A1 Journal article (refereed)
The Gardner Problem and Cycle Slipping Bifurcation for Type-2 Phase-Locked Loops (2022)


Kuznetsov, N. V., Arseniev, D. G., Blagov, M. V., Lobachev, M. Y., Wei, Z., Yuldashev, M. V., & Yuldashev, R. V. (2022). The Gardner Problem and Cycle Slipping Bifurcation for Type-2 Phase-Locked Loops. International Journal of Bifurcation and Chaos, 32(9), Article 2250138. https://doi.org/10.1142/S0218127422501383


JYU authors or editors


Publication details

All authors or editorsKuznetsov, Nikolay V.; Arseniev, Dmitry G.; Blagov, Mikhail V.; Lobachev, Mikhail Y.; Wei, Zhouchao; Yuldashev, Marat V.; Yuldashev, Renat V.

Journal or seriesInternational Journal of Bifurcation and Chaos

ISSN0218-1274

eISSN1793-6551

Publication year2022

Volume32

Issue number9

Article number2250138

PublisherWorld Scientific Pub Co Pte Ltd

Publication countrySingapore

Publication languageEnglish

DOIhttps://doi.org/10.1142/S0218127422501383

Publication open accessNot open

Publication channel open access

Web address of parallel published publication (pre-print)https://arxiv.org/abs/2112.01604


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.


Keywordsbifurcationelectronic circuitssignal processing

Free keywordsphase-locked loop (PLL); type-2 PLL; Gardner problem; lock-in range; cycle slipping; Lyapunov function; nonlinear analysis; global stability


Contributing organizations


Ministry reportingYes

VIRTA submission year2022

JUFO rating1


Last updated on 2024-12-10 at 14:00