A sequence of anisotropic and isotropic materials of dielectric constant 12 and 10 respectively have been stacked alternatively to form a four-layer stack structure with aperture coupled feed mechanism for excitation. Applying this excitation, orthogonal mode pair TEδ21x and TE2δ1y has been excited at frequencies 7.54 GHz and 7.8 GHz, respectively in YZ and ZX planes to generate circular polarization. A circularly polarized bandwidth in the region (7.54 GHz-7.92 GHz) in conjunction with impedance bandwidth in the region (5.23 GHz-5.52 GHz) with a gain of 5.2 dBi has been accomplished. The designed antenna is appropriate for C-band and weather radar applications. The design assessment has been done using Ansys HFSS. The three stages of antenna design are examined. Further, the design is investigated with a 6-layer structure and an 8-layer structure.