A new method of impedance synthesis of antenna array radiation fields based on a single methodological conception is presented. At first, an approximate solution for the current in the thin vibrator with variable impedance was obtained using the partial averaging operation of the integraldifferential equation. The variable impedance of the vibrator was taken into account in the form of an integral coefficient averaged along the vibrator length. The approach turns out to be common for radiators with impedance coatings of different configurations and (or) different distributions of lumped impedances. It is established that the shape of the vibrator radiation pattern (RP) does not depend on the form of the impedance distribution function, and it is determined only by the averaged value of the impedance distribution along the vibrator axis. The solution shows that the impedance coating of a symmetrical thin vibrator excited at the center by the voltage δ-generator affects the shape of the radiation pattern in the wave zone, and the effect is directly proportional to the small natural parameter of the problem. The synthesis problem of the radiator impedances for the spatial scanning of the RP was solved for the linear vibrator array. The analytical solution of the problem was obtained for the equidistant array of symmetric vibrators with equal excitation currents. The possibility of changing the RP shape over a wide range by varying the intrinsic complex impedances of the vibrators is demonstrated for an equidistant linear array consisting of 5 half-wave vibrators located at a distance of one eighth wavelength from each other in the free space.
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