A rectangular-waveguide structure consisting of a series of constrictions and cavities is analyzed and shown to have the properties of a wide-band filter. The lower cutoff of the lowest-frequency pass band is due to the natural cutoff behavior of the waveguide itself. The upper cutoff of this band is due to the succession of discontinuities. Under the assumption of no dissipation in the filter sections, exact equations for the image parameters of the filter are derived. These equations take full account of the discontinuities and their interaction. As a by-product of this analysis, formulas are obtained for the exact equivalent circuits of three rectangular-waveguide structures: (a) a cavity formed by two changes inheight (Fig. 2(a));(b) an increase of height followed by a short-circuiting wall (Fig. 2 (b));(c) the hypothetical case of an increase of height followed by an open-circuiting wall (Fig. 2 (c)). It is shown how the analysis of structure (b) may be used to obtain an improved solution for ridge waveguide. The writer will cover the more practical problems of filter design and experimental verification in another paper.