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

Nikolay V. Kuznetsov,Dmitry G. Arseniev,Mikhail V. Blagov,Mikhail Y. Lobachev,Zhouchao Wei,Marat V. Yuldashev,Renat V. Yuldashev

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS（2022）

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摘要

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.

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关键词

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

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