Resonant behavior of a small aperture backed by a conducting body

The problem of an electrically small aperture in a conducting screen backed by a conducting body is analyzed. It is found that aperture-body resonances can occur for which the power transmitted through the aperture backed by a conducting body is much larger than that when the body is not present. An example is an electrically small aperture resonated by a capacitor across its midpoint. In the loss-free case, the transmission cross section of a small resonated aperture is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3λ²/4π</tex> independent of the size or shape of the aperture. For actual conductors, the transmission cross section will be increasingly reduced by conduction loss as the aperture is made smaller.