Computation of surface fields excited on arbitrary smooth convex surfaces with an impedance boundary condition

Abstract

Due to an increase in the use of conformal antennas in military and commercial applications, the study of surface fields excited by a current distribution on material coated perfect electric conductor (PEC) surfaces is becoming more important. These surface fields are useful in the efficient evaluation of mutual coupling of conformal slot/aperture antennas as well as in the design/analysis of conformal antennas/arrays which can be mounted on aircrafts, missiles, mobile base stations, etc. On the other hand, impedance boundary condition (IBC) is widely used in surface field problems because it can model a thin material coated (or partially coated) PEC geometry and reduces the complexity of the surface field problem by relating the tangential electric fields to the tangential magnetic fields on the surface. Evaluation of surface fields on the circular cylinder and sphere geometries is a canonical problem and stands as a building block for the general problem of surface fields excited on arbitrary smooth convex surfaces. Therefore, high frequency based asymptotic solutions for the surface fields on a source excited PEC convex surface have been investigated for a long time, and surface fields on such surfaces have been obtained by generalizing the surface field expressions of the PEC cylinder and sphere. In this dissertation, a uniform geometrical theory of diffraction (UTD)-based high frequency asymptotic formulation for the appropriate Green’s function representation pertaining to the surface fields excited by a magnetic current source located on an arbitrary smooth convex surface with an IBC is developed. In the course of obtaining the final UTD-based Green’s function representation, surface field expressions of cylinder and sphere geometries are written in normal, binormal, tangent [(ˆn, ˆb,tˆ)] coordinates and their important parameters such as the divergence factor, the Fock parameter and Fock type integrals are generalized according to the locality of high frequency wave propagation. The surface field expressions for the arbitrary convex impedance surface are then written by blending the sphere and cylinder solutions through blending functions, which are introduced heuristically. Numerical results are selected from singly and doubly curved surfaces. Because of the lack of numerical results for the surface fields for impedance surfaces in the literature, obtained results are compared with those of PEC surfaces in the limiting case where the surface impedance,Zs → 0.