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A wave-guide-to-coaxial-line junction having a better than 2-to-1 bandwidth with less than 2-to-1 voltage-standing-wave ratio was required in the design of microwave filters and receiver transmission systems. Several types of junctions satisfying these requirements were designed using simple transmission-line theory. One type designed for a standard wave-guide cross section has a bandwidth ratio of 2.7 to 1. The design method is presented in this report with a detailed description of a number of particular junctions. Some of these models are for use with very thin wave guide, which is ideally suited for wave-guide filters; some for use with the more usual rectangular cross sections; and one for use with ridge ("loaded") wave guide. The latter junction is capable of at least a 6-to-1 bandwidth.