Spectral domain analysis of wall admittances for circular and annular microstrip patches and the effect of surface waves

Wall admittances for circular and annular ring microstrip antennas have been determined, including the effect of the substrate. The magnetic current model is used and the analysis is carried out in Hankel transform domain. The final expressions for wall admittances are obtained in integral form. The contributions of the surface wave to the wall conductances have been determined by evaluating the integrals near the singularity using the singularity extraction technique. The radiation conductance has been determined by simple integration. The value of wall susceptance, obtained in this paper, agrees well with Kirchhoff's equivalent extension formula. A closed form expression for wall susceptance for the
TM_{1n}
mode has been obtained by curve fitting the numerical values. The effect of the substrate on wall admittance has been found to be significant for higher order modes and is shown to explain the measured input impedance of an annular ring microstrip antenna.