Comments on Van Paemel’s Mathematical Model of Charge-pump Phase-locked Loop
Автор(ы):
Nikolay Vladimirovich Kuznetsov
St. Petersburg State University, Russia
Faculty of Mathematics and Mechanics, Professor
Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, St.Petersburg, Russia
Dr.Sc.
nkuznetsov239@gmail.com
Renat Vladimirovich Yuldashev
St. Petersburg State University, Russia
Faculty of Mathematics and Mechanics, Professor
PhD in physics and mathematics
Michail Vladimirovich Blagov
St. Petersburg State University, Russia
University of Jyvaskyla, Dept. of Mathematical Information Technology, Finland
Faculty of Mathematics and Mechanics, PhD student
Elena Vladimirovna Kudryashova
St. Petersburg State University, Russia
Faculty of Mathematics and Mechanics, Leading Researcher
PhD in physics and mathematics
Olga Aleksandrovna Kuznetsova
St. Petersburg State University, Russia
Faculty of Mathematics and Mechanics, Leading Researcher
PhD in physics and mathematics
Timur Nazirovich Mokaev
St. Petersburg State University, Russia
Faculty of Mathematics and Mechanics, Professor
PhD in physics and mathematics
Аннотация:
The charge-pump phase-locked loop (CP-PLL) is one of widely used
types of the phase-locked loop (PLL). A PLL is essentially nonlinear
control system and its nonlinear analysis is a challenging task.
Recently, we found some flaws in the well-known and frequently cited article "
Analysis of a charge-pump PLL: A new model" published by M. van Paemel
in the IEEE Transactions on Communications journal. In the present brief
note the corresponding numerical and analytical examples are provided
and the ways to correct the flaws are discussed.
Ключевые слова
- charge-pump phase-locked loop
- control of oscillators
- nonlinear dynamical model
- synchronization
Ссылки:
- D. Abramovitch. Phase-locked loops: A control centric tutorial. In American Control Conf. Proc., volume 1, pages 1-15. IEEE, 2002
- P. Acco. Study of the loop ‘a phase lock: Hybrid aspects taken into account. PhD thesis, Toulouse, INSA, 2003
- R. E. Best, N. V. Kuznetsov, G. A. Leonov, M. V. Yuldashev, and R. V. Yuldashev. Tutorial on dynamic analysis of the Costas loop. Annual Reviews in Control, 42:27-49, 2016
- C. Bi, P. F. Curran, and O. Feely. Linearized discrete-time model of higher order Charge-Pump PLLs. In Circuit Theory and Design (ECCTD), 2011 20th European Conference on, pages 457-460. IEEE, 2011
- P. F. Curran, C. Bi, and O. Feely. Dynamics of charge-pump phase-locked loops. International Journal of Circuit Theory and Applications, 41(11):1109-1135, 2013
- F. Gardner. Charge-pump phase-lock loops. IEEE Transactions on Communications, 28(11):1849-1858, 1980
- F. M. Gardner. Phaselock techniques. John Wiley & Sons, New York, 1966
- F. M. Gardner. Phaselock techniques. John Wiley & Sons, 2005
- C. Hangmann, C. Hedayat, and U. Hilleringmann. Stability analysis of a charge pump phase-locked loop using autonomous difference equations. IEEE Transactions on Circuits and Systems I: Regular Papers, 61(9):2569- 2577, 2014
- P. K. Hanumolu, M. Brownlee, K. Mayaram, and Un-Ku Moon. Analysis of charge-pump phase-locked loops. IEEE Transactions on Circuits and Systems I: Regular Papers, 51(9):1665-1674, 2004
- N. V. Kuznetsov, G. A. Leonov, M. V. Yuldashev, and R. V. Yuldashev. Rigorous mathematical definitions of the hold-in and pull-in ranges for phase-locked loops. IFAC-PapersOnLine, 48(11):710-713, 2015
- G. A. Leonov and N. V. Kuznetsov. Nonlinear mathematical models of phase-locked loops. Stability and oscillations. Cambridge Scientific Pub- lishers, 2014
- G. A. Leonov, N. V. Kuznetsov, M. V. Yuldashev, and R. V. Yuldashev. Hold-in, pull-in, and lock-in ranges of PLL circuits: rigorous mathematical definitions and limitations of classical theory. IEEE Transactions on Circuits and Systems-I: Regular Papers, 62(10):2454-2464, 2015
- S. Milicevic and L. MacEachern. Time evolution of the voltage-controlled signal in charge pump PLL applications. In Microelectronics, 2008. ICM 2008. International Conference on, pages 413-416. IEEE, 2008
- S. Sancho, A. Su ́ arez, and J. Chuan. General envelope-transient formula- tion of phase-locked loops using three time scales. IEEE Transactions on Microwave Theory and Techniques, 52(4):1310-1320, 2004
- V. V. Shakhgil’dyan and A. A. Lyakhovkin. Fazovaya avtopodstroika chas- toty (in Russian). Svyaz’, Moscow, 1966
- B. I. Shakhtarin, A. A. Timofeev, and V. V. Sizykh. Mathematical model of the phase-locked loop with a current detector. Journal of Communications Technology and Electronics, 59(10):1061-1068, 2014
- K. Shu and E. Sanchez-Sinencio. CMOS PLL synthesizers: analysis and design. Springer, 2005
- M. van Paemel. Analysis of a charge-pump PLL: a new model. IEEE Transactions on communications, 42(7):2490-2498, 1994
- A. Viterbi. Principles of coherent communications. McGraw-Hill, New York, 1966
