Quality Factor and Radiation Efficiency of Dual-Mode Self-Resonant Spherical Antennas With Lossy Magnetodielectric Cores

For spherical antennas consisting of a solid magnetodielectric lossy core with an impressed surface current density exciting a superposition of the ${\rm TE}_{mn}$ and ${\rm TM}_{mn}$ spherical modes, we analytically determine the radiation quality factor $Q$ and radiation efficiency $e$ . Also, we determine the relative mode excitation, as a function of the core material parameters, which ensures self-resonance. For the specific case of a dual-${\rm TE}_{m1}$ , ${\rm TM}_{m1}$ dipole antenna of half a wavelength circumference, we show quantitatively, how $Q/e$ and $e$ behave, and can be optimized as functions of permeability and magnetic loss tangent. We obtain $Q/e$ values well below the Chu lower bound with fair efficiencies up to 71% – 84%.