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Article title EQUIVALENT SURFACE IMPEDANCE OF AN INFINITE ARRAY OF SLOT IMPEDANCE LOADS BASED ON A SLOT IN AN INFINITE PERFECT CONDUCTING SCREEN WITH DIELECTRIC COVERING
Authors V.G. Koshkidko, O.V. Alpatova
Section SECTION II. ELECTRODYNAMICS AND ANTENNA
Month, Year 05, 2016 @en
Index UDC 537.8.029.6
DOI
Abstract The problem of plane wave excitation of slot impedance loads infinite array placed with a period T with dielectric cover is considered to determine the equivalent surface impedance. Each  array element consists of three volumes  V1 , V2 , and V3 .  V1 volume with parameters occupies the halfspace above the boundary. The primary field in this volume is excited by the plane wave. V2 volume with parameters doesn’t contain excitation sources. It is a dielectric cover with thickness t situated between planes y=0 and y=-t . V3 volume with parameters doesn’t contains excitation sources also and has the same geometry as V1 volume. V2 volume is connected with V3 volume by one or several slots in the perfect conducting plane screen on the boundary of V2 and V3 volumes. There is stripline conductor in the aperture of each slot. Excitation sources characteristics  and construction parameters are independent on z coordinate (two-dimensional problem). The problem solution was conducted by the integral equations method. For this purpose fields in V1 , V2 , and V3 volumes were represented as an expansion in the spatial Floquet harmonics. Integral equation was obtained using boundary condition for electric field on the screen plane, Floquet harmonics orthogonality condition, and fields’ tangential components continuity condition on the slot aperture. Obtained integral equation was calculated by the Krylov-Bogolyubov method,  whereby the integral equation was reduced to the system of linear algebraic equations. To overcome the mathematical difficulties with the logarithmic singularity in the integral equation kernel Kummer transformation was used for matrix items calculations. This allows not only to improve series convergence but to identify explicitly the logarithmic singularity and to integrate it analytically. Numerical results are presented as an equivalent surface impedance dependency on structure geometric sizes for several fixed average interval values, the angle of incidence of the electromagnetic wave value, and dielectric layer thickness. It is shown that the equivalent surface impedance value can be varied by changing slot width and stripline conductor width.

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Keywords Slot impedance load; infinite array; dielectric cover; equivalent surface impedance; numerical solution
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