A radial power combiner/divider capable of a higher order (for example, N=24) of power combining/dividing and a 15% bandwidth (31 to 36 GHz). The radial power combiner/divider generally comprises an axially-oriented mode transducer coupled to a radial base. The mode transducer transduces circular TE01 waveguide into rectangular TE10 waveguide, and the unique radial base combines/divides a plurality of peripheral rectangular waveguide ports into a single circular TE01 waveguide end of the transducer. The radial base incorporates full-height waveguides that are stepped down to reduced-height waveguides to form a stepped-impedance configuration, thereby reducing the height of the waveguides inside the base and increasing the order N of combining/dividing. The reduced-height waveguides in the base converge radially to a matching post at the bottom center of the radial base which matches the reduced height rectangular waveguides into the circular waveguide that feeds the mode transducer
