Limitations of the classical phase-locked loop analysis

2015 American Control Conference (ACC)

et al. 2015

Self Cite

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: 84%

Section: Classical Engineering Consideration Of the Costas Loop Omentioning

confidence: 99%

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

Self Cite

“…Also the errors caused by numerical integration (e.g. in MATLAB and SPICE) can lead to unreliable results [28,29,50,51].…”

Section: Remarks On Simulation Of Bpsk Costas Loopmentioning

confidence: 99%

Tutorial on dynamic analysis of the Costas loop

Best¹,

Annual Reviews in Control

et al. 2016

Costas loop is a classical phase-locked loop (PLL) based circuit for carrier recovery and signal demodulation.The PLL is an automatic control system that adjusts the phase of a local signal to match the phase of the input reference signal. This tutorial is devoted to the dynamic analysis of the Costas loop. In particular the acquisition process is analyzed. Acquisition is most conveniently described by a number of frequency and time parameters such as lock-in range, lock-in time, pull-in range, pull-in time, and hold-in range. While for the classical PLL equations all these parameters have been derived (many of them are approximations, some even crude approximations), this has not yet been carried out for the Costas loop. It is the aim of this analysis to close this gap. The paper starts with an overview on mathematical and physical models (exact and simplified) of the different variants of the Costas loop. Then equations for the above mentioned key parameters are derived. Finally, the lock-in range of the Costas loop for the case where a lead-lag filter is used for the loop filter is analyzed.

“…classical books [12, p.12,p15-17], [13, p.7]) while it may lead to unreliable results (see, e.g. [14], [15]). …”

Section: Accepted To Ieee 7th International Congress On Ultra Modern mentioning

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

Self Cite

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.