Effective radius of R-KR array lens feed

An R-KR lens is a cylindrical cavity, loaded with matched RF input/output elements equally spaced around its circumference, wherein a TEM wave propagates between parallel conducting plates. It is used as a feed network for modern cylindrical antenna arrays. A proper phase excitation of the array elements is essential for obtaining scanned beams that are well shaped with low sidelobes. It is first shown, by the basic geometrical approach, how this phase excitation is dependent on the ratio K between the lens radius and the array radius. Then an effective lens radius is determined from a set of lens inter-element coupling phases, where the phases are obtained either from modal analysis of a lens model, or from measurements of an actual lens.