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<p>In this paper, we consider nonlinear dynamics of a control circuit called phase-locked loop and provide a rigorous mathematical analysis to establish conditions under which the lock-in, pull-in, and hold-in ranges, which correspond to different types of system stability, coincide (the Viterbi problem). The analytical results are compared with both computer simulation and estimates of the lock-in and pull-in ranges, known from engineering literature. The comparison shows that those lock-in and pull-in range estimates may lead to cycle slipping and the loss of synchronization, respectively.</p>

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The Viterbi problem on coincidence of phase-locked loop lock-in, pull-in, and hold-in ranges

  • 期刊论文

  • 发表日期：

    2025年3月14日

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  • Nikolay V. Kuznetsov,
  • Mikhail Y. Lobachev,
  • Elena V. Kudryashova,
  • Olga A. Kuznetsova,
  • Dmitry G. Arseniev

摘要

In this paper, we consider nonlinear dynamics of a control circuit called phase-locked loop and provide a rigorous mathematical analysis to establish conditions under which the lock-in, pull-in, and hold-in ranges, which correspond to different types of system stability, coincide (the Viterbi problem). The analytical results are compared with both computer simulation and estimates of the lock-in and pull-in ranges, known from engineering literature. The comparison shows that those lock-in and pull-in range estimates may lead to cycle slipping and the loss of synchronization, respectively.