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 editorsKuznetsov, N.V.; Lobachev, M.Y.; Yuldashev, M.V.; Yuldashev, R.V.; Kolumbán, G.

Journal or seriesIFAC-PapersOnLine



Publication year2020


Issue number2

Pages range6378-6383


Publication countryUnited Kingdom

Publication languageEnglish


Publication open accessOpenly available

Publication channel open accessOpen Access channel

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


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.

Keywordscontrol theorycontrol engineeringelectronic circuitsoscillationsmathematical models

Free keywordsphase-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 reportingYes

Reporting Year2021

JUFO rating1

Last updated on 2024-03-04 at 20:16