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arXiv · 0805.0936

On the inverse scattering of star-shape LC-networks

Filippo Visco Comandini·Mazyar Mirrahimi·Michel Sorine
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Abstract

The study of the scattering data for a star-shape network of LC-transmission lines is transformed into the scattering analysis of a Schrödinger operator on the same graph. The boundary conditions coming from the Kirchhoff rules ensure the existence of a unique self-adjoint extension of the mentioned Schrödinger operator. While the graph consists of a number of infinite branches and a number finite ones, all joining at a central node, we provide a construction of the scattering solutions. Under non-degenerate circumstances (different wave travelling times for finite branches), we show that the study of the reflection coefficient in the high-frequency regime must provide us with the number of the infinite branches as well as the the wave travelling times for finite ones.

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Filippo Visco Comandini, Mazyar Mirrahimi, Michel Sorine. 2008-05-07. On the inverse scattering of star-shape LC-networks. https://arxiv.org/abs/0805.0936

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