A systematic design of dual-band, orthogonallypolarized linear-to-circular polarization (LP-to-CP) converters is proposed. This class of polarization converters can transform linearly-polarized waves into right-and left-hand circularlypolarized (RHCP and LHCP) waves in two separate non-adjacent frequency bands. The reported polarizer is made of three cascaded bianisotropic sheet admittances, spaced by two isotropic dielectric slabs. The electromagnetic problem is studied by means of impedance boundary conditions. A transmission-matrix analysis of periodically-loaded transmission-lines is employed in design. An analytic model is developed and closed-form expressions are derived for the frequency response of each sheet admittance. This method avoids the use of multi-parameter optimization procedures. An example of a dual-band, orthogonally-polarized LP-to-CP converter is proposed for satellite communication applications in the K/Ka-band. The polarizer separately performs LP-to-LHCP and LP-to-RHCP conversions over the transmitting and receiving channels of the K/Ka-band. The design is validated with a prototype. Under normal incidence, the polarizer exhibits axial ratios (ARs) lower than 3 dB over the 18-22.2 GHz (∼21%) and 28.7-30.4 GHz (∼6%) bands. The total transmission is above-1 dB within the same two bands. The performance is stable for scanning angles up to ±45 •. For a 45 • angle of incidence, the AR is lower than 3 dB in the bands 17-22 GHz (∼25.6%) and 28.6-30 GHz (∼4.7%) with a total transmission higher than-1.2 dB.