Slow wave Chebyshev transformers

The periodic structure to couple slow and fast wave transmission lines in MILOs, linear magnetrons, and BWOs is a stepped transmission line transformer. The slow wave structure is a coaxial line with rectangular corrugations on the outer conductor with smooth metallic walls for the inner conductor. The fast wave structure is a coaxial line with smooth inner and outer metallic conductors, or with outer conductors where the corrugation depth approaches zero. Unit cells, or quarter wave sections, are developed for both binomial and Chebyshev coefficients. The Chebyshev transformer is designed for arbitrary bandwidths from one to larger numbers, and when the bandwidth equals one, the binomial and Chebyshev transformers are identical. Chebyshev coefficients are found with an unpublished report by Ross E. Graves, Stanford University. They are then applied in calculating characteristic impedances for prescribed input and output line impedances. A unique modification is inclusion of slow/fast wave phase velocities with the characteristic impedances for each section of the line.