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arXiv · 2112.01604

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
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Abstract

In the present work, a second-order type 2 PLL with a piecewise-linear phase detector characteristic is analysed. 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 and improves well-known engineering estimates.

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Nikolay V. Kuznetsov, Dmitry G. Arseniev, Mikhail V. Blagov, Mikhail Y. Lobachev, Zhouchao Wei, Marat V. Yuldashev, Renat V. Yuldashev. 2021-12-02. The Gardner problem and cycle slipping bifurcation for type 2 phase-locked loops. https://doi.org/10.1142/s0218127422501383

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