An Iterative Solution for the Reflection Coefficient of a Flanged Waveguide Antenna

Schwarz´s iterative procedure of overlapping regions is employed to solve for the reflection coefficient at the open end of a flanged parallel-plate waveguide antenna, with the flange being of arbitrary flare angle. It is shown that by dividing the junction into circular and semi-infinite rectangular and sectoral sub-regions, and using Green´s functions of each, the problem is reduced to the solution of a system of integral equations of the Fredholm type. The solution for the reflection coefficient of an H-plane sectoral horn is also obtained as a special case when the flare angle is less than 180° and therefore the rectangular and sectoral sub-regions directly overlap. It is shown that, in addition to being relatively simple and efficient, the solution also leads to geometrical insight into the problem whereby the magnitude of the reflection coefficient is related to the area of the overlapping region.