Directional characteristics of a ring aperture radiator

In this paper an explicit analytical expression is presented, it describes a radiation pattern of a scanning ring aperture radiator. Such radiator has a form of a ring with finite width. When the ratio of inner to outer radius changes from 0 to 1 a ring aperture will change from a continuous round aperture to a circular ring radiator. It is shown that this leads to the main lobe narrowing, directivity decreasing and side lobe level increasing.