Equations of Phase-Locked Loops: Dynamics on Circle, Torus and Cylinder

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Yuldashev, R. Yuldashev, Differential equations of Costas loop , Doklady Mathematics , 86 2 , , pp. Kuznetsov, G. Leonov, M. Leonov, P. Seledzhi, M. Leonov, S. Seledzhi, N. Kuznetsov, P. Leonov, and S. Kuznetsov, S. Kudryashova, N. Neittaanmaki, S. Seledzhi, Analysis and synthesis of clock generator, International conference on Physics and Control, Book of selected papers, World Scientific, Seledzhi, Analysis and design of computer architecture circuits with controllable delay line, International Conference on Informatics in Control, Automation and Robotics, Proceedings, Vol.

Pll Performance, Simulation and Design , Ed. Phase-locked loops: principles and practice , Macmillan Press Buchanan, W. Frequency Synthesis by Phase Lock , 2nd ed. Sinchronization systems in communication and control , Prentice-Hall Leonov, G. Frequency-Domain Methods for Nonlinear Analysis.


Petersburg Leonov, G. Phase-locked loops in array processors , Nevsky dialekt , St. Petersburg in Russian Lindsey, W. Proceedings of the IEEE , vol. Frequency synthesizers: theory and design , Wiley Margaris , N. Petersburg in Russian Solonina , A. Petersburg in Russian Stensby , J. Because it was also very successful in south-eastern Asia, a Chinese translation has been provided. His research interests include design, simulation, and applications of phase-locked loops and Costasloops. E-mail: Rolandbest aol. Leonov received his Ph. His research interests, include control theory, dynamical systems and phase synchronization systems.

E-mail: leonov math. Yuldashev received his Ph. He is currently an associate professor in Saint-Petersburg University.

Simulation of Analog Costas Loop Circuits

His research interests include nonlinear models of Costas loops. E-mail: maratyv gmail. His research interests include nonlinear models of phase-locked loops. E-mail: renatyv gmail. Abstract : The analysis of stability and numerical simulation of Costas loop circuits for the high-frequency signals is a challenging task. The problem lies in the fact that it is necessary to observe very fast time scale of input signals and slow time scale of signal's phases simultaneously. To overcome this difficulty, it is possible to follow the classical ideas of Gardner and Viterbi to construct a mathematical model of Costas loop, in which only slow time change of signal's phases and frequencies is considered.

Such an construction, in turn, requires the computation of phase detector characteristic, depending on the waveforms of the considered signals. In this paper, the problems of nonlinear analysis of Costas loops and the approaches to the simulation of the classical Costas loop, the quadrature phase shift keying QPSK Costas loop, and the two-phase Costas loop are discussed.

The analytical method for the computation of phase detector characteristics of Costas loops is described. In this paper, we will discuss simulation methods for various modifications of the Costas loop. Download: JPG. Download: JPG larger image. Lindsey, M. Synchronous communications. Proceedings of the IRE, vol. Stefanovic, S. Ilic, G. An example of a hybrid system: Coherent optical system with Costas loop in receiver-system for transmission in baseband.

Journal of Lightwave Technology, vol. Kaplan, C.

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Wang, W. Applied Optics, vol. Miyazaki, S. Ryu, Y. Namihira, H. WH6, Djordjevic, M. Hasegawa, H. Kanetsuna, M. Optical phase-locked loop performance in homodyne detection using pulsed and CW LO.

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JWB24, Hayami, F. Imai, K. Linewidth investigation for costas loop phase-diversity homodyne detection in digital coherent detection system. An improved optical costas loop PSK receiver: Simulation analysis. Nowsheen, C. Benson, M. Design of a high frequency FPGA acoustic modem for underwater communication. Phase-locked loops: A control centric tutorial. Lyapunov Redesign of analog phaselock loops. Watada, T. Endo, H. Shilnikov orbits in an autonomous third-order chaotic phase-locked loop.

Hinz, I. Konenkamp, E. Behavioral modeling and simulation of phase-locked loops for RF front ends. Almost global stability of phase-locked loops.

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Analog phaselock loop design using Popov criterion. Piqueira, L.

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Considering secondharmonic terms in the operation of the phase detector for second-order phase-locked loop. Suarez, R.

Vendelin, A. Pavio, U. Goyal, X. Lai, J. Nonlinear dynamics of phase-locked loop with the second-order filter. Radiophysics and Quantum Electronics, vol. Kudrewicz, S. Nonlinear dynamics of discrete-time circuits: A survey. International Journal of Circuit Theory and Applications, no. Wang, T. Chiou, S. Nonlinear Phase-locked Loop design using semidefinite programming.

VCO sweep-rate limit for a phase-lock loop. Journal of the Franklin Institute, vol. Wiegand, C. Hedayat, U. Non-linear behaviour of charge-pump phase-locked loops. Advances in Radio Science, vol. Curran, C. Bi, O. Dynamics of charge-pump phase-locked loops. International Journal of Circuits Theory and Applications, vol. Suarez, E. Fernandez, F. Ramirez, S.

Stability and bifurcation analysis of self-oscillating quasi-periodic regimes. Banerjee, B. Conventional and extended time-delayed feedback controlled zero-crossing digital phase locked loop. International Journal of Bifurcation and Chaos, vol. Huque, J. An analytical approximation for the pull-out frequency of a PLL employing a sinusoidal phase detector. ETRI Journal, vol. Chicone, M. Phase-locked loops, demodulation, and averaging approximation time-scale extensions. Jeruchim, P. Balaban, K.

Pederson, K. Tranter, T.

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