On the Radiation Resistance of Planar Monopole Antennas

We present an analytical formula for the radiation resistance of planar short monopole antennas. The linear element of the antenna is placed parallel to a ground plane, extending beyond its edge. The approach, based on the solution for scattering of a plane wave impinging on a perfectly conducting half-plane, uses a combination of the reciprocity theorem, Fresnel integral approximation, and Poynting theorem to derive an analytical expression for the radiation resistance of such monopoles shorter than about lambda/10. The analytical results are in very good agreement with measurements and numerical simulation results carried out for a large and finite-size ground plane. It is found that the short planar monopole shows a radiation resistance that has a dominant term depending linearly-instead of quadratically-on the monopole height, thus providing relatively high values for quite short lengths. The same methodology is also applied to the case of a planar short dipole parallel to the half-plane´s edge. However, a much lower radiation resistance is obtained in that case. The impact of these results on bent planar monopole designs is briefly discussed.