A1 Journal article (refereed)
The Egan problem on the pull-in range of type 2 PLLs (2021)

Kuznetsov, N. V., Lobachev, M. Y., Yuldashev, M. V., & Yuldashev, R. V. (2021). The Egan problem on the pull-in range of type 2 PLLs. IEEE Transactions on Circuits and Systems II: Express Briefs, 68(4), 1467-1471. https://doi.org/10.1109/tcsii.2020.3038075

JYU authors or editors

Publication details

All authors or editors: Kuznetsov, Nikolay V.; Lobachev, Mikhail Y.; Yuldashev, Marat V.; Yuldashev, Renat V.

Journal or series: IEEE Transactions on Circuits and Systems II: Express Briefs

ISSN: 1549-7747

eISSN: 1558-3791

Publication year: 2021

Volume: 68

Issue number: 4

Pages range: 1467-1471

Publisher: Institute of Electrical and Electronics Engineers (IEEE)

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1109/tcsii.2020.3038075

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/72785


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: control theory; differential equations; electronic circuits; oscillations

Free keywords: phase-locked loop; PLL; type II; type 2; hold-in range; Egan conjecture; Egan problem on the pull-in range; Gardner problem on the lock-in range; Lyapunov functions; nonlinear analysis; global stability; describing function; harmonic balance method

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2021

JUFO rating: 2

Last updated on 2022-20-09 at 14:25