This paper presents the analysis of the mode characteristics of an annular ring microstrip patch antenna for circular polarization with attachment mode using method of moments in the spectral domain. For a probe excitation, the input impedance are obtained by using the single mode approximation for both the $TM_{11}$ and $TM_{12}$ modes and compared with those by Vector Hankel Transform. While the $TM_{11}$ mode has a high Q, it is a poor radiating mode; the $TM_{12}$ mode is more suitable for antenna applications. It is also shown that the bandwidth of the $TM_{12}$ mode is wider than that of the $TM_{11}$ mode in terms of axial ratio for circular polarizatio