A synthesis problem of a 2D array of thin linear vibrators, whose geometric centers are located at the nodes of a flat rectangular grid with double periodicity solved. The problem can be formulated as follows. A 2D antenna array radiates monochromatic electromagnetic waves into free space. Suppose that the array radiation pattern (RP) can be scanned in space by varying complex surface impedances of separate vibrators. Then, it is necessary to determine vibrator surface impedances to control the direction of the RP maximum. The analytical solution of the impedance synthesis problem, as an alternative to a numerical solution of a two-dimensional equation system, was obtained under two assumptions: the vibrators are excited by electric currents of equal amplitudes, and the RP of each radiator does not differ from that of an isolated radiator. Verification of theoretical formulas will be done by comparing them with relations known for one-dimensional equidistant arrays.
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