In the paper, we prove two theorems relating to the theory of thin impedance vibrator radiators excited by a lumped voltage generator under rather general conditions. The first theorem proves that influence of external electrodynamic media on the vibrator current distribution is limited and can be estimated using a small natural parameter. The second theorem ascertains that there exists principal possibility to compensate influence of spatial boundaries upon current distributions on a perfectly conductive vibrator by applying to its surface complex impedance with predetermined variation along the vibrator length. Several corollaries disclose a range of the theorems application and their fundamental importance.
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