Minimization of Antenna Quality Factor

Optimal currents on arbitrarily shaped radiators with respect to the minimum quality factor are found using a simple and efficient procedure. The solution starts with a reformulation of the problem of minimizing quality factor <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> as an alternative, so-called dual, problem. Taking advantage of modal decomposition and group theory, it is shown that the dual problem can easily be solved and always results in minimal quality factor <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula>. Moreover, the optimization procedure is generalized to minimize quality factor <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> for embedded antennas, with respect to the arbitrarily weighted radiation patterns, or with prescribed magnitude of the electric and magnetic near fields. The obtained numerical results are compatible with previous results based on the composition of modal currents, convex optimization, and quasi-static approximations; however, using the methodology in this paper, the class of solvable problems is significantly extended.

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