A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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-tekijät tai -toimittajat

Julkaisun tiedot

Julkaisun kaikki tekijät tai toimittajat: Kuznetsov, Nikolay V.; Lobachev, Mikhail Y.; Yuldashev, Marat V.; Yuldashev, Renat V.

Lehti tai sarja: IEEE Transactions on Circuits and Systems II: Express Briefs

ISSN: 1549-7747

eISSN: 1558-3791

Julkaisuvuosi: 2021

Volyymi: 68

Lehden numero: 4

Artikkelin sivunumerot: 1467-1471

Kustantaja: Institute of Electrical and Electronics Engineers (IEEE)

Julkaisumaa: Yhdysvallat (USA)

Julkaisun kieli: englanti

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

Julkaisun avoin saatavuus: Avoimesti saatavilla

Julkaisukanavan avoin saatavuus: Osittain avoin julkaisukanava

Julkaisu on rinnakkaistallennettu (JYX): https://jyx.jyu.fi/handle/123456789/72785

Tiivistelmä

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.

YSO-asiasanat: säätöteoria; differentiaaliyhtälöt; elektroniset piirit; värähtelyt

Vapaat asiasanat: 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

Liittyvät organisaatiot

OKM-raportointi: Kyllä

Raportointivuosi: 2021

Alustava JUFO-taso: 2