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This paper presents the simulation and analysis of a 1-3GHz dual polarization Quad-ridge Horn Antenna (QRHA) to be used for Radio Astronomy applications. The coaxial to waveguide transition is a crucial design aspect of such an antenna. Using the CST Microwave Studio an air cavity coaxial connector to quad-ridge waveguide transition is designed with S11 better than -10 dB for the entire band. The QRHA is characterized for gain, co & cross polarization and edge taper.