Dimensioning Flat Equivalent Radiators

We deal with the problem of modeling a radiator/scatterer using an equivalent radiator. The problem amounts at determining shape and size of a radiating surface
${\mathscr D}^{\prime} $
producing, on a region
${\mathscr D}$
, an electromagnetic field close to that generated by the primary radiator/scatterer. For a fixed equivalent radiator’s shape, we deal here with the dimensioning issue only. The approach exploits the singular value decomposition (SVD) of the operators relating the radiator/scatterer to the field on
${\mathscr D}$
and the equivalent panel to the field on
${\mathscr D}$
. The size of the equivalent radiator is determined by minimizing the error between the primary radiated/scattered field and that radiated using
${\mathscr D}^{\prime} $
. The error is expressed as a Hermitian, positive semidefinite quadratic form: the dimensioning problem thus consists of determining the size of the equivalent radiator maximizing its minimum eigenvalue. The maximization is performed by choosing the size value leading to an error dropping below a prescribed maximum tolerated threshold. We present numerical test cases for a planar radiator with rectangular shape.