Circuit models for the lowest-order modes radiating from within an arbitrarily-shaped envelope have been developed based on the exact circuits for spherical modes and the radar scattering from a conductor of the arbitrary shape. These circuits predict lower bounds on the Q of small antennas with any combination of coupling between modes. Circuit parameters are tabulated for a range of shapes, and the procedure for computing parameters for other shapes is explained. The bounds on a small circularly-polarized cylindrical antenna illustrate an application. Predictions for scattering by the arbitrary envelope filled with a high μ or ε material serve to validate the procedure.
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H.L. Thal (2012) studied this question.