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# Mathematical Model of the Multielement Microstrip Reflectarray on the Circular Conductive Cylinder

Keywords:

S. I. Zakovorotny, A. O. Kasyanov, V. A. Obukhovets

Development of a cylindrical microstrip reflective type antenna array mathematical model is the purpose of this paper. The design of an array represents the infinite pure conducting cylinder which covered by homogeneous isotropic magnetodielectical substrate of regular thickness. The periodic microstrip reflectarray is etched on a substrate surface. This lattice is periodic along a longitudinal axis of the cylinder. Microstrip elements can have the arbitrary shape. These printed reradiators are considered pure conducting. The reflectarray elements are excited by locally plane electromagnetic waves. These waves are created by infinitely removed source. As an exciting source in model arbitrary oriented elementary magnetic dipole is used. The integral equation method is an approach, which used for solution of this problem. The system of the integral equations for definition of surface magnetic current distributions of array apertures is obtained. These equations are based on continuity of tangential components of electromagnetic field vectors on a substrate surface, which is free from microstrip elements. Assumptions of infinite remoteness of an exciting source and periodicity of structure allow using the Floquet theorem. That managed to reduce a problem to definition of required current distributions to the unit cell (Floquet channel) of this reflectarray. The system of the integral equations is reduced to the system of linear algebraic equations by a moments method. The coefficients of decomposition on corresponding basic functions of required current distributions are defined. The rooftop functions have been chosen as basic functions. These functions allow to correctly consider required current distributions behavior near to metal edges. The relationships for the generalized impedances and the right part of system of the linear algebraic equations are obtained. The computing algorithm which numerically realized the created full-wave model of a cylindrical reflective antenna array is developed. The numerical results for the developed model are presented.
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May 29, 2020

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