Nonlinear analysis of PLL by the harmonic balance method

2017/05/05 by Elena V. Kudryashova, Н. В. Кузнецов, Kudryashova, E. V. +7
Engineering · Physics and Astronomy · #Advancements in PLL and VCO Technologies #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Power Quality and Harmonics

paper · pdf · doi:10.48550/arxiv.1705.02354

openalex publication_date 2017/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we discuss the application of the harmonic balance method for the global analysis of the classical phase-locked loop (PLL) circuit. The harmonic balance is non rigorous method, which is widely used %,often without rigorous justification, for the computation of periodic solutions and the checking of global stability. The proof of the absence of periodic solutions is a key step to establish the global stability of PLL and estimate the pull-in range (which is an interval of the frequency deviations such that any solution tends to one of the equilibria). The advantages and limitations of the study of the classical PLL with lead-lag filter using the harmonic balance method is discussed.

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