A1 Journal article (refereed)
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 authors or editors

Publication details

All authors or editors: Kuznetsov, N.V.; Lobachev, M.Y.; Yuldashev, M.V.; Yuldashev, R.V.; Kolumbán, G.

Journal or series: IFAC-PapersOnLine

ISSN: 2405-8963

eISSN: 2405-8963

Publication year: 2020

Volume: 53

Issue number: 2

Pages range: 6378-6383

Publisher: Elsevier

Publication country: United Kingdom

Publication language: English

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

Publication open access: Openly available

Publication channel open access: Open Access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/75203

Abstract

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.

Keywords: control theory; control engineering; electronic circuits; oscillations; mathematical models

Free keywords: 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

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2021

JUFO rating: 1