The Egan problem on the pull-in range of type 2 PLLs

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The Egan problem on the pull-in range of type 2 PLLs. / Kuznetsov, Nikolay V.; Lobachev, Mikhail Y.; Yuldashev, Marat V.; Yuldashev, Renat V.

In: IEEE Transactions on Circuits and Systems II: Express Briefs, Vol. 68, No. 4, 9258948, 04.2021, p. 1467-1471.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{1cdf3ce852354a1daf589707268c649c,

title = "The Egan problem on the pull-in range of type 2 PLLs",

abstract = "In 1981, famous engineer William F. Egan conjectured that a higher-order type 2 PLL with an infinite hold-in range also has an infinite pull-in range, and supported his conjecture with some third-order PLL implementations. Although it is known that for the second-order type 2 PLLs the hold-in range and the pull-in range are both infinite, the present paper shows that the Egan conjecture may be not valid in general. We provide an implementation of the third-order type 2 PLL, which has an infinite hold-in range and experiences stable oscillations. This implementation and the Egan conjecture naturally pose a problem, which we will call the Egan problem: to determine a class of type 2 PLLs for which an infinite hold-in range implies an infinite pull-in range. Using the direct Lyapunov method for the cylindrical phase space we suggest a sufficient condition of the pull-in range infiniteness, which provides a solution to the Egan problem.",

keywords = "describing function, Detectors, Egan conjecture, Egan problem on the pull-in range, Frequency control, Gardner problem on the lock-in range, global stability, harmonic balance method., hold-in range, Lyapunov functions, Lyapunov methods, nonlinear analysis, Phase locked loops, Phase-locked loop, PLL, Stationary state, Transfer functions, type 2, type II, Voltage-controlled oscillators, harmonic balance method, non-linear analysis",

author = "Kuznetsov, {Nikolay V.} and Lobachev, {Mikhail Y.} and Yuldashev, {Marat V.} and Yuldashev, {Renat V.}",

note = "Publisher Copyright: {\textcopyright} 2004-2012 IEEE.",

year = "2021",

month = apr,

doi = "10.1109/TCSII.2020.3038075",

language = "English",

volume = "68",

pages = "1467--1471",

journal = "IEEE Transactions on Circuits and Systems II: Express Briefs",

issn = "1549-7747",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "4",

}

RIS

TY - JOUR

T1 - The Egan problem on the pull-in range of type 2 PLLs

AU - Kuznetsov, Nikolay V.

AU - Lobachev, Mikhail Y.

AU - Yuldashev, Marat V.

AU - Yuldashev, Renat V.

PY - 2021/4

Y1 - 2021/4

N2 - In 1981, famous engineer William F. Egan conjectured that a higher-order type 2 PLL with an infinite hold-in range also has an infinite pull-in range, and supported his conjecture with some third-order PLL implementations. Although it is known that for the second-order type 2 PLLs the hold-in range and the pull-in range are both infinite, the present paper shows that the Egan conjecture may be not valid in general. We provide an implementation of the third-order type 2 PLL, which has an infinite hold-in range and experiences stable oscillations. This implementation and the Egan conjecture naturally pose a problem, which we will call the Egan problem: to determine a class of type 2 PLLs for which an infinite hold-in range implies an infinite pull-in range. Using the direct Lyapunov method for the cylindrical phase space we suggest a sufficient condition of the pull-in range infiniteness, which provides a solution to the Egan problem.

AB - In 1981, famous engineer William F. Egan conjectured that a higher-order type 2 PLL with an infinite hold-in range also has an infinite pull-in range, and supported his conjecture with some third-order PLL implementations. Although it is known that for the second-order type 2 PLLs the hold-in range and the pull-in range are both infinite, the present paper shows that the Egan conjecture may be not valid in general. We provide an implementation of the third-order type 2 PLL, which has an infinite hold-in range and experiences stable oscillations. This implementation and the Egan conjecture naturally pose a problem, which we will call the Egan problem: to determine a class of type 2 PLLs for which an infinite hold-in range implies an infinite pull-in range. Using the direct Lyapunov method for the cylindrical phase space we suggest a sufficient condition of the pull-in range infiniteness, which provides a solution to the Egan problem.

KW - describing function

KW - Detectors

KW - Egan conjecture

KW - Egan problem on the pull-in range

KW - Frequency control

KW - Gardner problem on the lock-in range

KW - global stability

KW - harmonic balance method.

KW - hold-in range

KW - Lyapunov functions

KW - Lyapunov methods

KW - nonlinear analysis

KW - Phase locked loops

KW - Phase-locked loop

KW - PLL

KW - Stationary state

KW - Transfer functions

KW - type 2

KW - type II

KW - Voltage-controlled oscillators

KW - harmonic balance method

KW - non-linear analysis

UR - http://www.scopus.com/inward/record.url?scp=85098770179&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/a4629a41-50d4-3f66-9ea9-8ac736d72a9c/

U2 - 10.1109/TCSII.2020.3038075

DO - 10.1109/TCSII.2020.3038075

M3 - Article

AN - SCOPUS:85098770179

VL - 68

SP - 1467

EP - 1471

JO - IEEE Transactions on Circuits and Systems II: Express Briefs

JF - IEEE Transactions on Circuits and Systems II: Express Briefs

SN - 1549-7747

IS - 4

M1 - 9258948

ER -

ID: 73410588