A dominant‐mode wave guide radiating through a slot into a half‐space may be regarded from a network viewpoint, with the half‐space represented by a number of spherical transmission lines, the wave‐guide feed by a single uniform transmission line and the slot by a coupling network. This paper contains (a) an investigation of how many spherical transmission lines are necessary to represent adequately the far field (gain pattern) of the slot antenna, and (b) an approximate theoretical evaluation (by a variational calculation) and experimental check of the equivalent circuit parameters of a slot‐coupled junction of a rectangular and spherical wave guide, when the far field can be well represented by the dominant spherical mode. The results are useful in connection with a method of measuring the electromagnetic scattering properties of obstacles located in a half‐space illuminated by a wave‐guide‐fed slot antenna.