Short- or open-circuited dipole parallel to perfect reflector plane and embedded in substrate and acting at resonance

The properties of an open or short-circuited flat resonant dipole parallel to a reflector plane and embedded in a substrate are given. Simple transmission-line model analysis is used. Correct agreement is obtained between theoretical and experimental results, and literal formulas for radiation resistance and bandwidth are thus justified. To a first approximation, the radiation resistance is independent of the substrate, whose effect is to reduce the length and the bandwidth of the radiating dipole.