  Existing optimization methods are used to calculate the upper-bounds on
radiation efficiency with and without the constraint on self-resonance. These
bounds are used for the design and assessment of small electric-dipole-type
antennas. We demonstrate that the assumption of lossless, lumped, external
tuning skews the true nature of radiation efficiency bounds when practical
material characteristics are used in the tuning network. A major result is
that, when realistic (e.g., finite conductivity) materials are used, small
antenna systems exhibit dissipation factors which scale as $(ka)^{-4}$, rather
than $(ka)^{-2}$ as previously predicted under the assumption of lossless
external tuning.
