### Tuesday, June 2

## IP4

Mathematical Analysis of Conductive and Superconductive Transmission Lines

1:30 PM-2:15 PM

*Chair: John Berger, Colorado School of Mines*

*Room 246*

The wide use of planar transmission lines in microwave integrated circuits has induced the development of various methods to compute their propagation characteristics.

The speaker will present a theoretical analysis of guided propagation in the so-called microstrip line, which consists of a thin conductive or superconductive strip, placed on a dielectric substrate located on a conductive ground plane. For various models, including asymptotic ones where the microstrip has a negligible thickness, the speaker will discuss existence results for guided modes derived from the spectral theory of Maxwell's operator, and compare the results to those from classical low frequency analysis.

Particular attention will be devoted to the case of superconductive lines: as a consequence of London's equation, superconductive materials have a negative dielectric permittivity epsilon and the change of sign of epsilon has dramatic effects on the mathematical approach.

**Anne-Sophie Bonnet-Ben Dhia**

*ENSTA, France*

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*tjf, 12/17/97*