Abstract
An explicit variational principle (Evp) for the propagation constant of em waves is compared with four numerical tools: the Newton-Raphson algorithm solving a transcendental equation, the spectral domain approach (Sda) applied to the Galerkin method, the 3-D simulatorHfss fromHp, and the finite element method (Fem). Each tool analyses a different planar topology: a lossy dielectric slab supporting surface waves, a planar slotline modelled by transmission line parameters (Tlp), a multilayered high-loss co-planar waveguide, and a shielded microstrip line. For these various structures, the evp is more efficient than previous tools yielding the propagation constant; its explicit form and variational nature yield a drastic reduction of the number of iterations.
Résumé
Un principe variationnel explicite (pve) pour I’exposant de propagation d’ondes électromagnétiques est comparé à quatre out numériques: I’algorithme de Newton-Raphson résolvant une équation transcendentale, la méthode de Galerkin appliquée dans le domaine spectral, le simulateur 3-DHfss deHp, et la methode des éléments finis. Chaque outil analyse une structure planaire différente: une plaque dielectrique supportant des ondes de surface, une structure à fente caractérisée par ses parametrés de ligne de transmission, une structure coplanaire multicouches à penes dielectriques élevees et une ligne microruban en boîtier. Pour ces structures, lePve s’avére plus performant que les outils numériques, car sa nature variationnelle explicite permet d’atteindre une même précision tout en réduisant drastiquement le nombre d’itérations.
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Huynen, I., Stockbroeckx, B. Variational principles compete with numerical iterative methods for analyzing distributed electromagnetic structures. Ann. Télécommun. 53, 95–103 (1998). https://doi.org/10.1007/BF02998567
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DOI: https://doi.org/10.1007/BF02998567
Key words
- Electromagnetism
- Distributibuted parameter circuit
- Variational calculus
- Iteration
- Comparative study
- Numerical method
- Planar technology