Pré-Publication, Document De Travail Année : 2025

Monodromy Structure and Harmonic Transfer Function in Lossless Transmission Line Circuits

Résumé

High-frequency (HF) amplifiers are essential components in modern electronic systems, often operating under periodic forcing regimes. Ensuring the local stability of their periodic steady-state responses is critical for reliable performance and safe hardware implementation. While classical methods rely on Floquet theory and harmonic transfer functions (HTFs) to analyze stability in low-frequency settings, these techniques remain underdeveloped for HF amplifiers, where the spatial distribution of components and signal propagation delays must be accounted for. In this work, we study a class of HF amplifiers containing lossless transmission lines, modeled as infinite-dimensional delay systems via the telegrapher's equations. Under realistic highfrequency dissipation assumptions, we prove that instabilities can only arise from eigenvalues of the monodromy operator. Furthermore, we show that the poles of the HTF in the right half-plane coincide with the logarithms of these unstable eigenvalues, thereby extending known results from the time-invariant case to the periodic setting. These findings establish a rigorous foundation for using frequency-domain tools in the stability analysis of HF amplifiers and justify the detection of instabilities via HTF pole locations.

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Dates et versions

hal-05042937 , version 1 (22-04-2025)
hal-05042937 , version 2 (14-10-2025)

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  • HAL Id : hal-05042937 , version 1

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Sébastien Fueyo, Laurent Baratchart, Jean-Baptiste Pomet. Monodromy Structure and Harmonic Transfer Function in Lossless Transmission Line Circuits. 2025. ⟨hal-05042937v1⟩
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