Resonance Tuning Cost in Radiation Efficiency of Electrically Small Antennas

Numerical tools are used to predict the upper-bounds on radiation efficiency with and without a constraint on self-resonance. It is demonstrated that the assumption of lossless external tuning produces unrealistic results. The main result of this contribution is that, when realistic (e.g., finite conductivity) materials are used, the cost of resonance tuning in the radiation efficiency of small antenna systems is high and is manifested by a dissipation factor which scales as a fourth power of electrical size.