Many wireless communication applications such as satellite communications use circularly-polarized (CP) signals, with the requirement for easy switching of the polarization sense between up-link and down-link. Specifically, in satellite communications, the trend is also to move to higher frequencies and integrate the receiving and transmitting antennas in one dual-band terminal. However, these simultaneous demands make the design and fabrication of the composing parts very challenging. We propose here a dual-band dual-linear to circular polarization converter that works in transmission mode. The working principle of this polarizer is explained through an example for Ka-band satellite communications at 19.7-20.2 GHz and 29.5-30 GHz. The LP-to-CP converter is a single panel composed of identical unit-cells with thickness of only 1.05 mm and size of 5.3 mm × 5.3 mm. Due to its operation in transmission mode, the polarizer can be combined with a simple dual-band dual-LP antenna to obtain the desired dual-band dual-CP single antenna. However, the unique property of this polarizer is yet the fact that it converts a given LP wave, e.g. x-polarization, to orthogonal CP waves at the two non-adjacent frequency bands, e.g. LHCP at lower band and RHCP at higher band. The polarizer is tested both with 20 GHz and with 30 GHz LP rectangular horns to illuminate a dual-band transmit-array (TA) to obtain wide-angle steering of CP beams. The performance of the polarizer and its association with the TA is evaluated through simulation and measurements. We also present design guidelines for this type of polarizer.