Abstract
We present a theoretical study of guided modes in the most commonly used transmission line: the microstrip line. It consists of a thin conductive strip placed on a dielectric substrate, which is located on a perfectly conductive ground plane. Two cases are considered: the case of a perfectly conductive strip; and the case of a superconductive one. In the model used, the dissipative losses are neglected. However, since one is looking for modes which are confined near the strip, the metallic cavity surrounding the line is not taken into account. Consequently, in both cases, the study of guided modes amounts to the spectral analysis of a family of non-compact self-adjoint operators, which is realized thanks to the min-max principle.
Highlights
The wide use of planar transmission lines in microwave integrated circuits has induced the development of various methods to compute their propagation characteristics
The most common structure is the so-called microstrip line which consists of a thin conducting strip placed on a dielectric substrate located on a conducting ground plane
Guided modes are confined between the ground plane and the strip
Summary
To cite this version: 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. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. 2087–2113 c 2000 Society for Industrial and Applied Mathematics Vol 60, No 6, pp. 2087–2113 c 2000 Society for Industrial and Applied Mathematics
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