An impedance synthesis problem of 2D antenna arrays consisting of slotted spherical radiators, whose geometric centers are located at nodes of a flat rectangular grid with double periodicity, has been solved. The problem is formulated as follows: to determine complex impedances distributed over surfaces of the spherical radiators which allows us to steer the radiation pattern (RP) of the antenna array to given directions. Analytical solution of the impedance synthesis problem (as an alternative to numerical solution) was obtained under the assumption that spherical radiators are excited by axially symmetric magnetic currents with equal amplitudes. The approach was verified by simulation of the five-element linear antenna array. The possibility of RP scanning in a wide range was confirmed by using the synthesized distributions of complex impedances.
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