Properties of Sub-Wavelength Spherical Antennas With Arbitrarily Lossy Magnetodielectric Cores Approaching the Chu Lower Bound

For a spherical antenna exciting any arbitrary spherical mode, we derive exact closed-form expressions for the dissipated power and stored energy inside (and outside) the lossy magneto-dielectric spherical core, as well as the radiated power, radiation efficiency, and thus the radiation quality factor. These expressions are valid for the entire range from zero to infinite material loss tangents, with any dispersion of the real parts and an inverse frequency variation of the imaginary parts of permittivity and permeability. For the dipole modes of a sub-wavelength antenna, we demonstrate how an increasing magnetic loss tangent initially leads to a decreasing radiation quality factor, but in the limit of a perfect magnetic conductor (PMC) core the dissipated power tends to zero and the radiation quality factor reaches the fundamental Chu lower bound.