The Wiener-Hopf technique is used to compute the reflection and transmission coefficients related to the junction of perfectly conducting and impedance parallel plate waveguides in the case where the surface impedances of the upper and lower semi infinite plates are different from each other.
The purpose of the present work is to provide a rigorous analysis of the parallel plate wave guide with two opposing rectangular grooves of different depths and filled with different dielectric materials. This configuration may be used as a band-stop filter. The representation of the solution to the three-part mixed boundary-value problem in terms of Fourier integrals leads to a couple of simultaneous modified Wiener-Hopf equations. By using the analytical properties of the functions that occur, the simultaneous modified Wiener-Hopf equations are reduced to the solution of four infinite systems of linear algebraic equations. These systems are solved numerically, and the band-stop filter characteristics of the reflection coefficient are studied in terms of frequency, groove sizes, and the parameters of the filling dielectric material. PACS Nos.: 42.25.Bs, 42.25.Gy, 42.82.Et Résumé : Le but de ce travail est de fournir une analyse rigoureuse du guide d'onde plat parallèle avec deux rainures rectangulaires de profondeurs différentes et remplies de diélectriques différents. Cette configuration peut être utilisée comme filtre coupe-bande. La solution en trois parties avec conditions limites mixtes en fonction d'intégrales de Fourier mène à une paire d'équations modifiées simultanément de Wiener-Hopf. Utilisant les propriétés analytiques des fonctions qui en ressortent, nous réduisons ces équations de Wiener-Hopf à quatre systèmes infinis d'équations linéaires algébriques. Ces systèmes sont solutionnés numériquement et les caractéristiques du filtre coupe-bande des coefficients de réflexion sont étudiés en fonction de la fréquence, la grosseur des rainures et les caractéristiques des diélectriques. [Traduit par la Rédaction] Can.
[1] In the present work a rigorous Wiener-Hopf approach is used to investigate the band-stop filter characteristics of a parallel plate waveguide with finite length impedance loading. The representation of the solution to the boundary-value problem in terms of Fourier integrals leads to two simultaneous modified Wiener-Hopf equations which are uncoupled by using the pole removal technique. The solution involves four infinite sets of unknown coefficients satisfying four infinite systems of linear algebraic equations. These systems are solved numerically and some graphical results showing the influence of the waveguide spacing, surface impedances and the length of the impedance loading on the reflection coefficient are presented.Citation: Tayyar, I: . H., A. Büyükaksoy, and A. Işıkyer (2008), A Wiener-Hopf analysis of the parallel plate waveguide with finite length impedance loading, Radio Sci., 43, RS5005,
SUMMARYThe electromagnetic scattering of the surface wave by a rectangular impedance cylinder located on an inÿnite reactive plane is considered for the case that the impedances of the horizontal and vertical sides of the cylinder can have di erent values. Firstly, the di raction problem is reduced into a modiÿed Wiener-Hopf equation of the third kind and then solved approximately. The solution contains branch-cut integrals and two inÿnite sets of constants satisfying two inÿnite systems of linear algebraic equations. The approximate analytical or numerical evaluations of corresponding integrals and numerical solution of the linear algebraic equation systems are obtained for various values of parameters such as the surface reactance of the plane, the vertical and horizontal wall impedances, the width and the height of the cylinder.
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