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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
Authors V.G. Koshkid’ko, O.V. Alpatova
Section SECTION II. MATHEMATICAL MODELING OF PHYSICAL PROCESSES AND DEVICES
Month, Year 11, 2015 @en
Index UDC 537.8.029.6
DOI
Abstract Solution of the problem of slot impedance loads infinite array excitation by the plane wave is considered to determine the equivalent surface impedance. Each array element is a slot in the flat perfect conducting screen. Volume V1 takes the halfspace above the perfect conducting screen. Primary field is excitated by the plane wave in this volume. Volume V2 does not contain excitation sources and takes halfspace below the perfect conducting screen. Volume V2 is connected to volume V1 through the slot with the strip conductor placed in the slot aperture. Excitation sources characteristics and problem parameters are independent on z coordinate (two- dimensional problem). The solution of the problem is obtained by the integral equations method. Fields in V1 and V2 volumes were presented in the form of an expansion in spatial Floquet harmonics. Integral equation was obtained by using boundary condition for the electric field in the screen plane, Floquet harmonics orthogonality and continuity condition for fields tangential components in the slot aperture. For calculation of the obtained integral equation the Krylov-Bogolyubov method was used whereby the integral equation was reduced to the system of linear algebraic equations. To overcome mathematical difficulties with the logarithmic singularity in the integral equation kernel Kummer transformation was used for matrix elements calculation. This not only allows 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 the slot width, strip conductor sizes in the slot aperture for several fixed average interval values and on the angle of incidence of the electromagnetic wave. It is shown that the equivalent surface impedance value can be adjusted by changing the slot width and the width of the strip conductor in the slot aperture.

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Keywords Slot impedance load; infinite array; equivalent surface impedance; numerical solution.
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