TY - JOUR

T1 - Nonlinear Analysis of Charge-Pump Phase-Locked Loop

T2 - The Hold-In and Pull-In Ranges

AU - Kuznetsov, Nikolay

AU - Matveev, Alexey

AU - Yuldashev, Marat

AU - Yuldashev, Renat

N1 - Funding Information: Manuscript received February 27, 2021; revised June 12, 2021; accepted July 14, 2021. Date of publication August 10, 2021; date of current version September 30, 2021. This work was supported in part by the Russian Science Foundation under Project 19-41-02002 and in part by the Leading Scientific Schools of Russia Project under Grant NSh-2624.2020.1 (publication fee). This article was recommended by Associate Editor J. Juillard. (Corresponding author: Nikolay Kuznetsov.) Nikolay Kuznetsov is with the Faculty of Mathematics and Mechanics, Saint-Petersburg State University, 199034 Saint Petersburg, Russia, also with the Faculty of Information Technology, University of Jyväskylä, 40014 Jyväskylä, Finland, and also with the Institute for Problems in Mechanical Engineering, Russian Academy of Science, 199178 Saint Petersburg, Russia (e-mail: nkuznetsov239@gmail.com). Publisher Copyright: © 2004-2012 IEEE.

PY - 2021/10

Y1 - 2021/10

N2 - In this paper a fairly complete mathematical model of CP-PLL, which reliable enough to serve as a tool for credible analysis of dynamical properties of these circuits, is studied. We refine relevant mathematical definitions of the hold-in and pull-in ranges related to the local and global stability. Stability analysis of the steady state for the charge-pump phase locked loop is non-trivial: straight-forward linearization of available CP-PLL models may lead to incorrect conclusions, because the system is not smooth near the steady state and may experience overload. In this work necessary details for local stability analysis are presented and the hold-in range is computed. An upper estimate of the pull-in range is obtained via the analysis of limit cycles. The study provided an answer to Gardner's conjecture on the similarity of transient responses of CP-PLL and equivalent classical PLL and to conjectures on the infinite pull-in range of CP-PLL with proportionally-integrating filter.

AB - In this paper a fairly complete mathematical model of CP-PLL, which reliable enough to serve as a tool for credible analysis of dynamical properties of these circuits, is studied. We refine relevant mathematical definitions of the hold-in and pull-in ranges related to the local and global stability. Stability analysis of the steady state for the charge-pump phase locked loop is non-trivial: straight-forward linearization of available CP-PLL models may lead to incorrect conclusions, because the system is not smooth near the steady state and may experience overload. In this work necessary details for local stability analysis are presented and the hold-in range is computed. An upper estimate of the pull-in range is obtained via the analysis of limit cycles. The study provided an answer to Gardner's conjecture on the similarity of transient responses of CP-PLL and equivalent classical PLL and to conjectures on the infinite pull-in range of CP-PLL with proportionally-integrating filter.

KW - Charge-pump PLL

KW - CP-PLL

KW - Gardner conjecture

KW - hidden oscillations

KW - phase-locked loops

KW - VCO overload

KW - Charge pumps

KW - LIMITATIONS

KW - Phase frequency detectors

KW - MODEL

KW - SIMULATION

KW - Phase locked loops

KW - CIRCUITS

KW - HIDDEN OSCILLATIONS

KW - PLL

KW - Voltage-controlled oscillators

KW - STABILITY ANALYSIS

KW - Stability criteria

KW - Circuit stability

KW - Mathematical model

UR - http://www.scopus.com/inward/record.url?scp=85116235622&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/71ae389c-8fc0-3645-8325-ac3805f2194b/

U2 - 10.1109/TCSI.2021.3101529

DO - 10.1109/TCSI.2021.3101529

M3 - Article

AN - SCOPUS:85116235622

VL - 68

SP - 4049

EP - 4061

JO - IEEE Transactions on Circuits and Systems

JF - IEEE Transactions on Circuits and Systems

SN - 1549-8328

IS - 10

ER -