A novel technique based on the Fourier transform is applied to analyze a ri
dge waveguide and rectangular coaxial line. On the basis of the image theor
em the ridge waveguide and rectangular coaxial line are transformed into a
guide with an infinite number of grooves. The dispersion relations for the
ridge waveguide and rectangular coaxial line are obtained in rigorous, yet
simple series forms. Numerical computations show that our series solutions
converge fast and agree with others.