Analytical Method for Computation of Phase-Detector Characteristic

Discovery of undesirable hidden oscillations, which cannot be found by simulation, in models of phase-locked loop (PLL) showed the importance of development and application of analytical methods for the analysis of such models. Approaches to a rigorous nonlinear analysis of analog PLL with multiplier phase detector (classical PLL) and linear filter are discussed. An effective analytical method for computation of multiplier/mixer phase-detector characteristics is proposed. For various waveforms of high-frequency signals, new classes of phase-detector characteristics are obtained, and dynamical model of PLL is constructed

Limitations of the classical phase-locked loop analysis

Nonlinear analysis of the classical phase-locked loop (PLL) is a challenging task. In classical engineering literature simplified mathematical models and simulation are widely used for its study. In this work the limitations of classical engineering phase-locked loop analysis are demonstrated, e.g., hidden oscillations, which can not be found by simulation, are discussed. It is shown that the use of simplified dynamical models and the application of simulation may lead to wrong conclusions concerning the operability of PLL-based circuits

Limitations of PLL simulation: hidden oscillations in MatLab and SPICE

Nonlinear analysis of the phase-locked loop (PLL) based circuits is a challenging task, thus in modern engineering literature simplified mathematical models and simulation are widely used for their study. In this work the limitations of numerical approach is discussed and it is shown that, e.g. hidden oscillations may not be found by simulation. Corresponding examples in SPICE and MatLab, which may lead to wrong conclusions concerning the operability of PLL-based circuits, are presented

A short survey on nonlinear models of the classic Costas loop: rigorous derivation and limitations of the classic analysis

Rigorous nonlinear analysis of the physical model of Costas loop --- a classic phase-locked loop (PLL) based circuit for carrier recovery, is a challenging task. Thus for its analysis, simplified mathematical models and numerical simulation are widely used. In this work a short survey on nonlinear models of the BPSK Costas loop, used for pre-design and post-design analysis, is presented. Their rigorous derivation and limitations of classic analysis are discussed. It is shown that the use of simplified mathematical models, and the application of non rigorous methods of analysis (e.g., simulation and linearization) may lead to wrong conclusions concerning the performance of the Costas loop physical model.Comment: Accepted to American Control Conference (ACC) 2015 (Chicago, USA