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  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X
 

Field behavior near the edge of a microstrip antenna by the method of matched asymptotic expansions


Authors: A. Bendali, A. Makhlouf and S. Tordeux
Journal: Quart. Appl. Math. 69 (2011), 691-721
MSC (2000): Primary 34E05, 35Q60, 81T80
Published electronically: June 29, 2011
MathSciNet review: 2893996
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Abstract: The cavity model is a wide-spread powerful empirical approach for the numerical simulation of microstrip antennas. It is based on several hypotheses assumed a priori: a dimension reduction in the cavity, that is, the zone limited by a metallic patch and the ground plane in which is fed the antenna, supplied by the additional condition that the open sides of the cavity act as magnetic walls. An additional important assumption of this model consists in an adequate description of the singular field behavior in the proximity of the edge of the patch. A simplified two-dimensional problem incorporating the main features of the field behavior near the edge of the patch and inside the cavity is addressed. The method of matched asymptotic expansions is used to carry out a two-scale asymptotic analysis of the field relative to the thickness of the cavity. All the empirical hypotheses at the basis of the derivation of the cavity model can thus be recovered. Proved error estimates are given in a simplified framework where the dielectric constants of the substrate are assumed to be 1 in order to avoid some unimportant technical difficulties.


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Additional Information

A. Bendali
Affiliation: University of Toulouse, INSA de Toulouse, Institut Mathématique de Toulouse, UMR CNRS 5219, Département de Génie Mathématique, 135 avenue de Rangueil F31077, Toulouse cedex 1 (France) and CERFACS, 42 Avenue Gaspard Coriolis, 31057 Toulouse Cedex 01 (France)
Email: abendali@insa-toulouse.fr

A. Makhlouf
Affiliation: University of Toulouse, INSA de Toulouse, Institut Mathématique de Toulouse, UMR CNRS 5219, Département de Génie Mathématique, 135 avenue de Rangueil F31077, Toulouse cedex 1 (France)
Email: abdelkader.makhlouf@gmail.com

S. Tordeux
Affiliation: Project-team Magique-3D, INRIA Bordeaux Sud-Ouest. LMA Pau, CNRS UMR 5142, I.P.R.A., Université de Pau et des Pays de l’Adour, avenue de l’Université BP 1155, 64013 PAU Cedex (France) and CERFACS, 42 Avenue Gaspard Coriolis, 31057 Toulouse Cedex 01 (France)
Email: stordeux@insa-toulouse.fr

DOI: http://dx.doi.org/10.1090/S0033-569X-2011-01256-3
PII: S 0033-569X(2011)01256-3
Received by editor(s): March 18, 2010
Published electronically: June 29, 2011
Article copyright: © Copyright 2011 Brown University
The copyright for this article reverts to public domain 28 years after publication.



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