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Time-consuming soldering process is required for waveguide-fed planar antennas with probe excitation of radiating elements. It is desirable to implement a sophisticated process for mass production. One of the candidates is a capacitor antenna in the waveguide etched under the radiating element as shown. In this study, input admittance of the circular capacitor antenna in a parallel plate waveguide is analyzed. The mode matching method is applied as a waveguide bifurcation problem in cylindrical coordinates. To construct analytical solution of edge admittance through the direct inversion or residue calculus method, the effect of disk curvature on the reflection coefficient is asymptotically neglected. The resultant expression of infinite products finally reduces to a simple closed form through appropriate approximations and sum formulas. Matching posts manufacturable by via-hole process are added inside the capacitor and the effect is calculated by the radial line equivalent circuit. Experimental verification is given.