Efficiency and Q for small antennas using Pareto optimality

Small antennas suffer from high Q values and low efficiency. In this paper, we extend previous physical bounds on antennas to include efficiency. The analysis is based on convex optimization, Pareto optimality, and explicit expressions of the stored electric and magnetic energies and Ohmic losses as quadratic forms in the current density. The resulting current distributions offer insight and present performance bounds for antennas designed within the considered geometry. The results are illustrated for planar geometries modeled as resistive sheets.