The radiation resistance of a microstrip element

The radiation resistance of a rectangular microstrip element printed on a grounded dielectric is evaluated through the use of a bidimensional Fourier transform. The antenna is assumed to be half a guided wavelength long and to have a given width. The Q-factor of the antenna is assumed to be high so that the current in the feed at resonance is negligible. The longitudinal current distribution along the patch is assumed to resemble that of a resonant end-fed half-wavelength segment of a microstrip transmission line. The transversal current is taken to be constant. The resulting integrals are estimated in an asymptotic form using finite series and product expansions. An empirical formula replaces the former one for higher values of dielectric constants. The simple expressions thus derived lend insight into the nature of dependence of the radiation resistance on the various parameters such as width, thickness, and relative dielectric constant. In spite of their simplicity, the formulas provide quite accurate results