Mathematical analysis of conductive and superconductive transmission lines

Anne-Sophie Bonnet-Ben Dhia 1 Karim Ramdani
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : This paper is concerned with a mathematical study of guided propagation in the microstrip transmission lines used in microelectronics. In the first part, the case of a zero-thickness perfectly conducting strip is considered. Using a regularized formulation of Maxwell's equations, it is shown that finding guided modes amounts to the spectral analysis of a noncompact family of self-adjoint operators. The existence of guided modes is then proved thanks to the min-max principle. In the second part, we deal with the case of a zero-thickness superconducting strip. An asymptotic model derived from London's equation is studied and the existence of guided modes is deduced from the case of the perfectly conducting strip. Copyright © 2000 Society for Industrial and Applied Mathematics
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Anne-Sophie Bonnet-Ben Dhia, Karim Ramdani. Mathematical analysis of conductive and superconductive transmission lines. SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2000, 60 (6), pp.2087-2113. ⟨10.1137/S0036139999352420⟩. ⟨hal-01009815⟩

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