Nonlinear Analysis of Phase-Locked Loop with Squarer

Abstract The phase-locked loop with squarer is a classical phase-locked loop (PLL) based carrier recovery circuit. Simulation of the loop is nontrivial task, because of high-frequency properties of considered signals. Simulation in space of signals’ phases allows one to overcome these difficulties, but it is required to compute phase detector characteristic. In this paper for various waveforms of high-frequency signals new classes of phase detector characteristics are computed for the first time. The problems of rigorous mathematical analysis of the control signal of voltage-controlled oscillator are discussed. Nonlinear model of PLL with squarer is constructed.

[1]  D.Y. Abramovitch,et al.  Efficient and flexible simulation of phase locked loops, part I: Simulator design , 2008, 2008 American Control Conference.

[2]  Evon M. O. Abu-Taieh,et al.  Comparative Study , 2020, Definitions.

[3]  G. Leonov,et al.  On stability by the first approximation for discrete systems , 2005, Proceedings. 2005 International Conference Physics and Control, 2005..

[4]  J. E. Rooda,et al.  Convergent Systems Design: Anti-Windup for Marginally Stable Plants , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[5]  Nikolay V. Kuznetsov,et al.  Analytical-numerical methods for investigation of hidden oscillations in nonlinear control systems , 2011 .

[6]  G. Leonov,et al.  Hidden attractor in smooth Chua systems , 2012 .

[7]  Nikolay V. Kuznetsov,et al.  High-frequency Analysis of Phase-locked Loop and Phase Detector Characteristic Computation , 2011, ICINCO.

[8]  V. YuldashevR.,et al.  Computation of Phase Detector Characteristics in Synchronization Systems , 2012 .

[9]  R. V. Yuldashev,et al.  Analytical methods for computation of phase-detector characteristics and PLL design , 2011, ISSCS 2011 - International Symposium on Signals, Circuits and Systems.

[10]  F. Ramirez,et al.  Stability and Bifurcation Analysis of Self-Oscillating Quasi-Periodic Regimes , 2012, IEEE Transactions on Microwave Theory and Techniques.

[11]  P Hajdú,et al.  [Analytical methods I]. , 1975, Arzneimittel-Forschung.

[12]  Gennady A. Leonov,et al.  Computation of phase detector characteristics in phase locked loops for clock synchronization , 2008 .

[13]  Anirban Sarkar,et al.  Second-degree digital differentiator-based power system frequency estimation under non-sinusoidal conditions , 2010 .

[14]  Nikolay V. Kuznetsov,et al.  Time-Varying Linearization and the Perron Effects , 2007, Int. J. Bifurc. Chaos.

[15]  D. Abramovitch.  Efficient and flexible simulation of phase locked loops, part II: Post processing and a design example , 2008, 2008 American Control Conference.

[16]  G. Leonov,et al.  Localization of hidden Chuaʼs attractors , 2011 .

[17]  G. Leonov,et al.  Hidden oscillations in dynamical systems , 2011 .

[18]  Mykola Hayvanovych,et al.  Algorithms for finding hidden groups and their structure from the streaming communication data , 2009 .

[19]  G.W. Chang,et al.  A comparative study of voltage flicker envelope estimation methods , 2008, 2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century.

[20]  Orla Feely,et al.  Dynamics of charge-pump phase-locked loops , 2013, Int. J. Circuit Theory Appl..

[21]  Almudena Suarez,et al.  Stability Analysis of Nonlinear Microwave Circuits , 2003 .

[22]  Nikolay V. Kuznetsov,et al.  Algorithms for searching for hidden oscillations in the Aizerman and Kalman problems , 2011 .

[23]  Orla Feely.  Nonlinear dynamics of discrete-time circuits: A survey , 2007, Int. J. Circuit Theory Appl..

[24]  I. VagaitsevV.,et al.  Localization of hidden Chua ’ s attractors , 2022 .

[25]  Nikolay V. Kuznetsov,et al.  Nonlinear Analysis and Design of Phase-Locked Loops , 2009 .

[26]  Bishnu Charan Sarkar,et al.  Chaos and bifurcation in a third-order digital phase-locked loop , 2008 .

[27]  T. S. West.  Analytical Method , 1969, Nature.

[28]  Nikolay V. Kuznetsov,et al.  Analytical Method for Computation of Phase-Detector Characteristic , 2012, IEEE Transactions on Circuits and Systems II: Express Briefs.

[29]  Daniel Y. Abramovitch,et al.  Phase-locked loops: a control centric tutorial , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[30]  G.A. Leonov,et al.  Nonlinear analysis of phase-locked loop , 2010, PSYCO.

[31]  G. Leonov,et al.  Frequency-Domain Methods for Nonlinear Analysis: Theory and Applications , 1996 .

[32]  Nikolay V. Kuznetsov,et al.  Hidden oscillations in nonlinear control systems , 2011 .

[33]  Nikolay V. Kuznetsov,et al.  Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua’s circuits , 2011 .

[34]  Nikolaos I. Margaris.  Theory of the Non-linear Analog Phase Locked Loop , 2004 .