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On the inverse scattering of star-shape LC-networks

Abstract : The study of the scattering data for a star-shape network of LC-transmission lines is transformed into the scattering analysis of a Schr¨odinger 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 Schr¨odinger 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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https://hal.inria.fr/inria-00267163
Contributor : Mazyar Mirrahimi <>
Submitted on : Wednesday, March 26, 2008 - 3:48:17 PM
Last modification on : Friday, May 25, 2018 - 12:02:05 PM
Long-term archiving on: : Friday, May 21, 2010 - 12:54:22 AM

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  • HAL Id : inria-00267163, version 1

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Filippo Visco Comandini, Mazyar Mirrahimi, Michel Sorine. On the inverse scattering of star-shape LC-networks. 2008. ⟨inria-00267163⟩

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