A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Harmonic balance analysis of pull-in range and oscillatory behavior of third-order type 2 analog PLLs (2020)

Kuznetsov, N.V., Lobachev, M.Y., Yuldashev, M.V., Yuldashev, R.V., & Kolumbán, G. (2020). Harmonic balance analysis of pull-in range and oscillatory behavior of third-order type 2 analog PLLs. IFAC-PapersOnLine, 53(2), 6378-6383. https://doi.org/10.1016/j.ifacol.2020.12.1773

JYU-tekijät tai -toimittajat

Julkaisun tiedot

Julkaisun kaikki tekijät tai toimittajat: Kuznetsov, N.V.; Lobachev, M.Y.; Yuldashev, M.V.; Yuldashev, R.V.; Kolumbán, G.

Lehti tai sarja: IFAC-PapersOnLine

ISSN: 2405-8963

eISSN: 2405-8963

Julkaisuvuosi: 2020

Volyymi: 53

Lehden numero: 2

Artikkelin sivunumerot: 6378-6383

Kustantaja: Elsevier

Julkaisumaa: Britannia

Julkaisun kieli: englanti

DOI: https://doi.org/10.1016/j.ifacol.2020.12.1773

Julkaisun avoin saatavuus: Avoimesti saatavilla

Julkaisukanavan avoin saatavuus: Kokonaan avoin julkaisukanava

Julkaisu on rinnakkaistallennettu (JYX): https://jyx.jyu.fi/handle/123456789/75203

Tiivistelmä

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.

YSO-asiasanat: säätöteoria; säätötekniikka; elektroniset piirit; värähtelyt; matemaattiset mallit

Vapaat asiasanat: phase-locked loop; third-order PLL; type 2 PLL; nonlinear analysis; harmonic balance method; describing function; global stability; birth of oscillations; hold-in range; pull-in range; lock-in range; Egan conjecture

Liittyvät organisaatiot

OKM-raportointi: Kyllä

Raportointivuosi: 2021

JUFO-taso: 1