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 editors: Kuznetsov, Nikolay V.; Arseniev, Dmitry G.; Blagov, Mikhail V.; Lobachev, Mikhail Y.; Wei, Zhouchao; Yuldashev, Marat V.; Yuldashev, Renat V.
Journal or series: International Journal of Bifurcation and Chaos
ISSN: 0218-1274
eISSN: 1793-6551
Publication year: 2022
Volume: 32
Issue number: 9
Article number: 2250138
Publisher: World Scientific Pub Co Pte Ltd
Publication country: Singapore
Publication language: English
DOI: https://doi.org/10.1142/S0218127422501383
Publication open access: Not 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.
Keywords: bifurcation; electronic circuits; signal processing
Free keywords: phase-locked loop (PLL); type-2 PLL; Gardner problem; lock-in range; cycle slipping; Lyapunov function; nonlinear analysis; global stability
Contributing organizations
Ministry reporting: Yes
VIRTA submission year: 2022
JUFO rating: 1