Nonlinear analysis of classical phase-locked loops in signal's phase space

2015 American Control Conference (ACC)

et al. 2015

Abstract-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.

Section: Discussionsupporting

confidence: 64%

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

Best¹,

2015 American Control Conference (ACC)

et al. 2015

“…Therefore, if the gap between stable and unstable periodic trajectories is smaller than the discretization step, the numerical procedure may slip through the stable trajectory. The case corresponds to the close coexisting attractors and the bifurcation of birth of semistable trajectory [28], [29]. In this case numerical methods are limited by the errors on account of the linear multistep integration methods (see [30], [31]).…”

Section: Simulation In Spicementioning

confidence: 99%

Limitations of PLL simulation: Hidden oscillations in MatLab and SPICE

Bianchi

2015 7th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT)

et al. 2015

Abstract-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.

“…In other words, the simulation will show that the PLL acquires lock, but in reality it is not the case. The considered case corresponds to the coexisting attractors (one of which is so-called hidden oscillation) and the bifurcation of birth of semistable trajectory [13], [14].…”

Section: Simulation Of the Classical Phase-lockedmentioning

confidence: 99%

Limitations of the classical phase-locked loop analysis

2015 IEEE International Symposium on Circuits and Systems (ISCAS)

Neittaanmuaki

et al. 2015

Abstract-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.