Stability investigations based on two-port describing functions
ISSN: 0305-6120
Article publication date: 7 May 2019
Issue publication date: 21 June 2019
Abstract
Purpose
Stability of a nonlinear, tuned amplifier has been investigated based on the describing function method. On stability, this paper means global asymptotic stability. The tuned amplifier comprises a saturated amplifying device with feedback and two resonators, at the input and the output. Describing function method here means introduction of the two-port describing functions.
Design/methodology/approach
Describing function method is applied, extended for two ports. Results from complex analysis and matrix algebra are heavily used. The two resonators have identical resonant frequency and bandwidth. Instability is represented by non-vanishing output perturbation for zero-input perturbation. Applying a simple transistor model with saturation and feedback, stability is analyzed in the form of output voltage as a function of input voltage.
Findings
Two-port scattering and admittance describing functions have been introduced. At a certain input voltage amplitude, instability appears in the form of unwanted sidebands, then at a higher input voltage, instability disappears, in good agreement with experiments. The hand calculated stability limits are in good agreement with the computer analysis.
Originality/value
The paper is based on an early publication of the author (Baranyi and Ladvánszky, 1984). Here, the full material is presented, explained step by step, extended and revised. All neglections that were earlier made in the author’s paper have been avoided here. This paper has significant tutorial value as well.
Keywords
Acknowledgements
This work was started with the author’s first master, Dr A. Baranyi, who sadly is no longer with us. At the time, he had sent the paper for review to Prof V. Belevitch, whose book (Belevitch, 1959) has been used as a starting point of the investigations in this study. Prof Belevitch wrote, of this work, “excellent and original.” This appreciation from a world top researcher of the field encouraged the author during the study.
This research was supported by the National Research Development and Innovation Office of Hungary within the Quantum Technology National Excellence Program (Project No. 2017-1.2.1- NKP-2017-00001).
Citation
Ladvanszky, J. (2019), "Stability investigations based on two-port describing functions", Circuit World, Vol. 45 No. 2, pp. 65-79. https://doi.org/10.1108/CW-12-2018-0105
Publisher
:Emerald Publishing Limited
Copyright © 2019, Emerald Publishing Limited