Harmonic balance analysis of pull-in range and oscillatory behavior of third-order type 2 analog PLLs

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Harmonic balance analysis of pull-in range and oscillatory behavior of third-order type 2 analog PLLs. / Kuznetsov, N. V.; Lobachev, M. Y.; Yuldashev, M. V.; Yuldashev, R. V.; Kolumbán, G.

в: IFAC-PapersOnLine, Том 53, № 2, 2020, стр. 6378-6383.

Результаты исследований: Научные публикации в периодических изданиях › статья в журнале по материалам конференции › Рецензирование

BibTeX

@article{19b3249533b346beb732a62426303862,

title = "Harmonic balance analysis of pull-in range and oscillatory behavior of third-order type 2 analog PLLs",

abstract = "The most important design parameters of each phase-locked loop (PLL) are the local and global stability properties, and the pull-in range. To extend the pull-in range, engineers often use type 2 PLLs. However, the engineering design relies on approximations which prevent a full exploitation of the benefits of type 2 PLLs. Using an exact mathematical model and relying on a rigorous mathematical thinking this problem is revisited here and the stability and pull-in properties of the third-order type 2 analog PLLs are determined. Both the local and global stability conditions are derived. As a new idea, the harmonic balance method is used to derive the global stability conditions. That approach offers an extra advantage, the birth of unwanted oscillations can be also predicted. As a verification it is shown that the sufficient conditions of global stability derived by the harmonic balance method proposed here and the well-known direct Lyapunov approach coincide with each other, moreover, the harmonic balance predicts the birth of oscillations in the gap between the local and global stability conditions. Finally, an example when the conditions for local and global stability coincide, is considered.",

keywords = "Birth of oscillations, Describing function, Egan conjecture, Global stability, Harmonic balance method, Hold-in range, Lock-in range, Nonlinear analysis, Phase-locked loop, Pull-in range, Third-order PLL, Type 2 PLL",

author = "Kuznetsov, {N. V.} and Lobachev, {M. Y.} and Yuldashev, {M. V.} and Yuldashev, {R. V.} and G. Kolumb{\'a}n",

note = "Publisher Copyright: Copyright {\textcopyright} 2020 The Authors. This is an open access article under the CC BY-NC-ND license Copyright: Copyright 2021 Elsevier B.V., All rights reserved.; 21st IFAC World Congress 2020 ; Conference date: 12-07-2020 Through 17-07-2020",

year = "2020",

doi = "10.1016/j.ifacol.2020.12.1773",

language = "English",

volume = "53",

pages = "6378--6383",

journal = "IFAC-PapersOnLine",

issn = "2405-8971",

publisher = "Elsevier",

number = "2",

}

RIS

TY - JOUR

T1 - Harmonic balance analysis of pull-in range and oscillatory behavior of third-order type 2 analog PLLs

AU - Kuznetsov, N. V.

AU - Lobachev, M. Y.

AU - Yuldashev, M. V.

AU - Yuldashev, R. V.

AU - Kolumbán, G.

PY - 2020

Y1 - 2020

N2 - The most important design parameters of each phase-locked loop (PLL) are the local and global stability properties, and the pull-in range. To extend the pull-in range, engineers often use type 2 PLLs. However, the engineering design relies on approximations which prevent a full exploitation of the benefits of type 2 PLLs. Using an exact mathematical model and relying on a rigorous mathematical thinking this problem is revisited here and the stability and pull-in properties of the third-order type 2 analog PLLs are determined. Both the local and global stability conditions are derived. As a new idea, the harmonic balance method is used to derive the global stability conditions. That approach offers an extra advantage, the birth of unwanted oscillations can be also predicted. As a verification it is shown that the sufficient conditions of global stability derived by the harmonic balance method proposed here and the well-known direct Lyapunov approach coincide with each other, moreover, the harmonic balance predicts the birth of oscillations in the gap between the local and global stability conditions. Finally, an example when the conditions for local and global stability coincide, is considered.

AB - The most important design parameters of each phase-locked loop (PLL) are the local and global stability properties, and the pull-in range. To extend the pull-in range, engineers often use type 2 PLLs. However, the engineering design relies on approximations which prevent a full exploitation of the benefits of type 2 PLLs. Using an exact mathematical model and relying on a rigorous mathematical thinking this problem is revisited here and the stability and pull-in properties of the third-order type 2 analog PLLs are determined. Both the local and global stability conditions are derived. As a new idea, the harmonic balance method is used to derive the global stability conditions. That approach offers an extra advantage, the birth of unwanted oscillations can be also predicted. As a verification it is shown that the sufficient conditions of global stability derived by the harmonic balance method proposed here and the well-known direct Lyapunov approach coincide with each other, moreover, the harmonic balance predicts the birth of oscillations in the gap between the local and global stability conditions. Finally, an example when the conditions for local and global stability coincide, is considered.

KW - Birth of oscillations

KW - Describing function

KW - Egan conjecture

KW - Global stability

KW - Harmonic balance method

KW - Hold-in range

KW - Lock-in range

KW - Nonlinear analysis

KW - Phase-locked loop

KW - Pull-in range

KW - Third-order PLL

KW - Type 2 PLL

UR - http://www.scopus.com/inward/record.url?scp=85103366683&partnerID=8YFLogxK

U2 - 10.1016/j.ifacol.2020.12.1773

DO - 10.1016/j.ifacol.2020.12.1773

M3 - Conference article

AN - SCOPUS:85103366683

VL - 53

SP - 6378

EP - 6383

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

SN - 2405-8971

IS - 2

T2 - 21st IFAC World Congress 2020

Y2 - 12 July 2020 through 17 July 2020

ER -

ID: 78768773