ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

# Differential Equations and Control Processes (Differencialnie Uravnenia i Protsesy Upravlenia)

## Comments on Van Paemel’s Mathematical Model of Charge-pump Phase-locked Loop

### Author(s):

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

St. Petersburg State University, Russia
Faculty of Mathematics and Mechanics, Professor
PhD in physics and mathematics

St. Petersburg State University, Russia
University of Jyvaskyla, Dept. of Mathematical Information Technology, Finland
Faculty of Mathematics and Mechanics, PhD student

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

### Abstract:

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.

### Keywords

• charge-pump phase-locked loop
• control of oscillators
• nonlinear dynamical model
• synchronization

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