A new coaxial-to-quad-ridged circular waveguide transition is presented which works simultaneously in the downlink (20 GHz) and uplink (30 GHz) Ka-bands with linear polarization. The transition comprises a double-ridge section with a back cavity fed by a coaxial probe and a transitional section where the second pair of ridges is added. The device open-end has equal symmetry planes in order to allow feeding previously designed dual-linear polarization quad-ridged devices selecting either linear polarization simply by rotating this launcher by 90°. The same procedure can be used for circular polarization with post-processing. Reflection level at the coaxial port is below -10 dB for all band. The overall length of the designed coaxial-to-waveguide transition is 48.1 mm. The proposed transition was simulated with CST Microwave Studio and HFSS.