Publisher's Synopsis
Excerpt from Spherical-Wave Source-Scattering Matrix Analysis of Antennas and Antenna-Antenna Interactions
We start our discussion by considering an antenna enclosed within a (fictitious) spherical surface and then go on to give expressions for the exciting and emergent spherical waves in the enclosed region. The totality of exciting waves constitutes the field incident on the spherical region from an external source, while the totality of emergent waves constitutes the field radiated from the spherical region. We complete our preliminary presentation by developing expressions for the conventional antenna parameters of gain and receiving cross-section inter-ms of spherical wave source-scattering-matrix elements. At the same time, following Kerns we derive spherical reciprocity relations, ultimately obtaining the classical relationship between receiving cross section and gain for a reciprocal antenna.
Next, we give an overview of the rotation [44] and translation [16] theorems that are needed for transforming the modal fields between two distinct coordinate systems. This is followed by a presentation of a general solution to the problem of two coupled antennas in terms of spherical-wave source-scattering-matrix coefficients. The resulting liouville-neumann series is very similar to the result obtained by Kerns [26] for the plane-wave scattering-matrix formulation. Following our development of the mutual-coupling relations between two antennas, we go on to consider easily verified special results to build confidence in our formulation. In this regard, we obtain two seemingly different transmission formulas, depending on the transmission direction, which are shown to be equivalent when the antennas are reciprocal. We also show that our expression for the coupling between two antennas reduces to an expression for the radiated electric field when one antenna is an elementary dipole.
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