This paper provides the design guidelines for a dual-band rat-race coupler and Gysel power divider with two different amplitude imbalances. The dual-band conditions are established based on the electrical nature of the coupler and dual-band C-section coupled lines/ T-structure/ $Π$-structures instead of using the dual-band equivalent transmission lines. It has been shown here that the same design equations can be utilized in the design of the rat-race coupler and Gysel power divider. The design equations are solved numerically to obtain the electrical parameters of the proposed coupler and power divider. The possible application of dual-band different power division ratios is presented for dual-band polarization controlled by a patch antenna. A design tool has been developed to obtain the coupler and power divider's design parameters and circuit analysis results. A design example of the coupler has been provided to validate the proposed concept.