The wide-band matching area for a small antenna

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/omega^{3}, normalized to unit frequency (omega_{1} = 1)-It has unit width for the high-pass band above this frequency. In terms of the familiar matching exponentmu = ln 1/|rho|, the matching area over this scale is limited to3 pi p_{1}, whereP_{1}is the (small) radiation power factor atomega_{1}. The corresponding limit on matching efficiency is6 pi p_{1}. A double-tuned matching network can approach2/pithis area over any bandwidth on this scale.