A rigorous expression for the frequency derivative of the input reactance or susceptance of an arbitrary antenna is derived by integration of Maxwell's equations. This expression is shown to depend on the polarization properties of the far field of the antenna and on a quantity which may be interpreted as the electromagnetic energy stored in its near field. The theorem gives a precise theoretical foundation to an intuitive analysis, based on network theorems, which has been used with some success to predict the bandwidth properties of antennas.
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Curt A. Levis (1957) studied this question.
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