Efficient computation of antenna coupling and fields within the near-field region

Abstract

The theory, techniques, details of the important equations, and description of two computer programs are presented for calculating efficiently the mutual coupling at a single frequency between any two antennas arbitrarily oriented and separated in free space. Both programs emphasize efficiency and generality, and require, basically, the complex electric far field of each antenna, and the Eulerian angles designating the relative orientation of each antenna. Multiple reflections between the antennas are neglected but no other restrictive assumptions are involved. If an electric field component is desired instead of coupling, the receiving antenna is replaced by a virtual antenna with uniform far field. The first computer program computes coupling (or fields) versus transverse displacement of the antennas in a plane normal to their axis of separation. An efficient fast Fourier transform (FFT) program was made possible by "collapsing" the far-field input data and showing that inmost cases the spectrum integration need cover only the solid angle mutually subtended by the smallest spheres circumscribing the antennas. Limiting the integration to this solid angle artifically band limits the coupling function, thereby allowing much larger integration increments and reducing run times and storage requirements to a feasible amount for electrically large antennas. The second program is based on a spherical wave representation of the coupling function and rapidly computes coupling (or fields) versus separation distance between the antennas. The spherical wave representation emerged naturally from an intriguing characteristic proven for the mutual coupling function; it, like each rectangular component of electric and magnetic field in free space, satisfies the homogeneous wave equation.