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