An approach for dimensioning equivalent radiators

We deal with the problem of determining the shape and dimensions of a radiating panel S capable to radiate fields approximating any one in a pre-assigned set with a controllable error on a region D. The set of fields to be approximated is the one that can be radiated/scattered by a set of sources/scatterers on which weak a priori information is available. In this sense, the panel S is 'equivalent' to the primary sources/scatterers. The weak information assumed here is geometrical information on the sources/scatterers and, in particular, that they are confined to a sphere of known radius. We propose, for a flat panel of fixed shape, an approach for the solution of the dimensioning problem. The method is based on the use of the Singular Value Decomposition (SVDs) approach and determines the dimensions of the 'equivalent' radiating panel by keeping the maximum approximation error in the mentioned set below a certain acceptable value. The error expression involves a Hermitian, positive definite quadratic form so that the maximum error can be evaluated through its minimum eigenvalue. Numerical results are presented for an equivalent, planar radiator of rectangular shape.