Abstract
Main problems of simulation and mathematical modeling of high-frequency signals for analog Costas loop and for analog phase-locked loop (PLL) are considered. Two approachers which allow to solve these problems are considered. In the first approach, nonlinear models of classical PLL and classical Costas loop are considered. In the second approach, engineering solutions for this problems are described. Nonlinear differential equations are derived for both approaches.
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Notes
- 1.
The functions with a finite number of jump discontinuity points differentiable on their continuity intervals
References
Abramovitch D (2002) Phase-locked loops: a control centric tutorial. Proc Am Control Conf 1:1–15
Abramovitch D (2008) Efficient and flexible simulation of phase locked loops, part I: simulator design. In: American control conference, Seattle, pp 4672–4677
Abramovitch D (2008) Efficient and flexible simulation of phase locked loops, part II: post processing and a design example. In: American control conference, Seattle, pp 4678–4683
Banerjee T, Sarkar B (2008) Chaos and bifurcation in a third-order digital phase-locked loop. Int J Electron Commun 62:86–91
Bellescize H (1932) La réception synchrone. L’onde Électrique 11:230–340
Best RE (2007) Phase-lock loops: design, simulation and application. McGraw-Hill, New York
Demir A, Mehrotra A, Roychowdhury J (2000) Phase noise in oscillators: a unifying theory and numerical methods for characterization. IEEE Trans Circuits Syst I 47:655–674
Emura T (1982) A study of a servomechanism for nc machines using 90 degrees phase difference method. Progress Report of JSPE, pp 419–421
Feely O (2007) Nonlinear dynamics of discrete-time circuits: a survey. Int J Circuit Theory Appl 35:515–531
Feely O, Curran PF, Bi C (2012) Dynamics of charge-pump phase-locked loops. Int J Circuit Theory Appl 27. doi:10.1002/cta.1814
Gardner F (1966) Phase–lock techniques. Wiley, New York
Gardner F (1993) Interpolation in digital modems - part i: fundamentals. IEEE Electron Commun Eng J 41(3):501–507
Gardner F, Erup L, Harris R (1993) Interpolation in digital modems - part ii: implementation and performance. IEEE Electron Commun Eng J 41(6):998–1008
Kroupa V (2003) Phase lock loops and frequency synthesis. Wiley, New York
Krylov N, Bogolyubov N (1947) Introduction to non-linear mechanics. Princeton University Press, Princeton
Kudrewicz J, Wasowicz S (2007) Equations of phase-locked loops: dynamics on the circle, torus and cylinder, A, vol 59. World Scientific, Singapore
Kuznetsov NV, Leonov GA, Seledzhi SS (2008) Phase locked loops design and analysis. In: Proceedings of ICINCO 2008 - 5th international conference on informatics in control, automation and robotics, vol SPSMC, pp 114–118. doi:10.5220/0001485401140118
Kuznetsov NV, Leonov GA, Seledzhi SM (2009) Nonlinear analysis of the Costas loop and phase-locked loop with squarer. In: Proceedings of the IASTED international conference on signal and image processing, SIP 2009, pp 1–7
Kuznetsov NV, Leonov GA, Seledzhi SM, Neittaanmäki P (2009) Analysis and design of computer architecture circuits with controllable delay line. In: Proceedings of ICINCO 2009 - 6th international conference on informatics in control, automation and robotics, vol 3 SPSMC, pp 221–224. doi:10.5220/0002205002210224
Kuznetsov NV, Leonov GA, Neittaanmäki P, Seledzhi SM, Yuldashev MV, Yuldashev RV (2010) Nonlinear analysis of phase-locked loop. In: IFAC proceedings volumes (IFAC-PapersOnline), vol 4(1), pp 34–38. doi:10.3182/20100826-3-TR-4016.00010
Kuznetsov NV, Leonov GA, Seledzhi SM, Yuldashev MV, Yuldashev RV (2011) Method for determining the operating parameters of phase-locked oscillator frequency and device for its implementation. Patent RU2449463 C1
Kuznetsov NV, Neittaanmäki P, Leonov GA, Seledzhi SM, Yuldashev MV, Yuldashev RV (2011) High-frequency analysis of phase-locked loop and phase detector characteristic computation. In: ICINCO 2011 - proceedings of the 8th international conference on informatics in control, automation and robotics vol 1, pp 272–278. doi:10.5220/0003522502720278
Kuznetsov NV, Leonov GA, Neittaanmäki P, Seledzhi S, Yuldashev MV, Yuldashev RV (2012) Simulation of phase-locked loops in phase-frequency domain. In: International congress on ultra modern telecommunications and control systems, IEEE Press, pp 364–368
Kuznetsov NV, Leonov GA, Yuldashev MV, Yuldashev RV (2012) Nonlinear analysis of Costas loop circuit. In: ICINCO 2012 - proceedings of the 9th international conference on informatics in control, automation and robotics 1:557–560. doi10.5220/0003976705570560
Leonov GA (2006) Phase-locked loops. Theory and application. Autom Remote Control 10:47–55
Leonov GA (2008) Computation of phase detector characteristics in phase-locked loops for clock synchronization. Dokl Math 78(1):643–645
Leonov GA, Kuznetsov NV, Seledzhi SM (2006) Analysis of phase-locked systems with discontinuous characteristics. In: IFAC proceedings volumes (IFAC-PapersOnline), vol 1, pp 107–112. doi10.3182/20060628-3-FR-3903.00021
Leonov GA, Kuznetsov NV, Seledzhi SM (2009) Nonlinear analysis and design of phase-locked loops. In: Automation control - theory and practice. In-Tech, New York, pp 89–114. doi:10.5772/7900
Leonov GA, Kuznetsov NV, Yuldahsev MV, Yuldashev RV (2011) Computation of phase detector characteristics in synchronization systems. Dokl Math 84(1):586–590. doi:10.1134/S1064562411040223
Leonov GA, Kuznetsov NV, Yuldahsev MV, Yuldashev RV (2012) Analytical method for computation of phase-detector characteristic. IEEE Trans Circuits Syst II Express Briefs 59(10):633–647. doi:10.1109/TCSII.2012.2213362
Leonov GA, Kuznetsov NV, Yuldashev MV, Yuldashev RV (2012) Differential equations of Costas loop. Dokl Math 86(2):723–728. doi:10.1134/S1064562412050080
Lindsey W (1972) Synchronization systems in communication and control. Prentice-Hall, New Jersey
Lindsey W, Simon M (1973) Telecommunication systems engineering. Prentice Hall, New Jersey
Margaris W (2004) Theory of the non-linear analog phase locked loop. Springer, New Jersey
Stiffler JP (1964) Bit and subcarrier synchronization in a binary psk communication system Natl Telemetering Conf
Suarez A, Quere R (2003) Stability analysis of nonlinear microwave circuits. Artech House, New Jersey
Suarez A, Fernandez E, Ramirez F, Sancho S (2012) Stability and bifurcation analysis of self-oscillating quasi-periodic regimes. IEEE Trans Microw Theory Tech 60(3):528–541
Thede L (2005) Practical analog and digital filter design. Artech House, New Jersey
Tretter SA (2007) Communication system design using DSP algorithms with laboratory experiments for the TMS320C6713TM DSK. Springer, New York
Viterbi A (1966) Principles of coherent communications. McGraw-Hill, New York
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Best, R.E., Kuznetsov, N.V., Leonov, G.A., Yuldashev, M.V., Yuldashev, R.V. (2014). Nonlinear Analysis of Phase-locked Loop-Based Circuits. In: Machado, J., Baleanu, D., Luo, A. (eds) Discontinuity and Complexity in Nonlinear Physical Systems. Nonlinear Systems and Complexity, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-01411-1_10
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