Optimal Currents on Arbitrarily Shaped Surfaces
An optimization problem has been formulated to find a resonant current extremizing various antenna parameters. The method is presented on, but not limited to, particular cases of gain $G$ , quality factor $Q$ , gain to quality factor ratio $G/Q$ , and radiation efficiency $\eta $ of canonical shapes with conduction losses explicitly included. The Rao–Wilton–Glisson basis representation is used to simplify the underlying algebra while still allowing surface current regions of arbitrary shape to be treated. By switching to another basis generated by a specific eigenvalue problem, it is finally shown that the optimal current can, in principle, be found as a combination of a few eigenmodes. The presented method constitutes a general framework in which the antenna parameters, expressed as bilinear forms, can automatically be extremized.