Ray analysis of mutual coupling between antennas on a convex surface

Abstract

An approximate asymptotic solution is presented for the electromagnetic fields which are induced on an electrically large perfectly conducting smooth convex surface by an infinitesimal magnetic or electric current moment on the same surface. This solution can be employed to calculate the mutual coupling between antennas on a convex surface in an efficient and accurate manner. In this solution, the surface fields propagate along Keller's surface ray paths, and their description remains uniformly valid within the shadow boundary transition region including the immediate vicinity of the source. Furthermore, the effect of surface ray torsion on the surface fields is indicated in the present solution, through a factor <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T/k</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</tex> denotes the surface ray torsion and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> is the surface curvature in the ray direction. This solution is deduced from the asymptotic solutions to simpler canonical problems. Numerical results for the mutual coupling between slots in cylinders and cones are presented, and are shown to compare very well with experiments.