A rotary annular, around-the-mast, radio frequency coupler having two concentric sets of generally axial loops, one fixed (stator set) and the other rotatable (rotor set) for electromagnetically coupling between a fixed and rotatable structure, such as a rotating antenna sub-system.Two methods and corresponding structure are provided for reducing the power transfer ripple occurring during rotation. These are prime related different loop totals between rotor and stator and angular canting of one loop set with respect to the other.