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A special frequency scale is proposed for use in describing the fundamental limitation on wide-band matching of a small antenna by means of a fixed reactive network. This scale isu = - 1/ω³, normalized to unit frequency (ω₁ = 1)-It has unit width for the high-pass band above this frequency. In terms of the familiar matching exponentμ = ln 1/\|ρ\|, the matching area over this scale is limited to3 π p₁, whereP₁is the (small) radiation power factor atω₁. The corresponding limit on matching efficiency is6 π p₁. A double-tuned matching network can approach2/ area over any bandwidth on this scale.
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H.A. Wheeler (1983) studied this question.
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