Electrical properties of spherical dipole antennas with lossy material cores

A spherical magnetic dipole antenna with a linear, isotropic, homogenous, passive, and lossy material core is modeled analytically, and closed form expressions are given for the internally stored magnetic and electric energies, the radiation efficiency, and radiation quality factor. This model and all the provided expressions are exact and valid for arbitrary core sizes, permeability, permittivity, electric and magnetic loss tangents. Arbitrary dispersion models for both permeability and permittivity can be applied. In addition, we present an investigation for an antenna of fixed electrical size and permittivity, focusing on the effects of magnetic core losses for a simple magnetic dispersion model, to illustrate how stored energies, efficiency and quality factor are affected. This shows that large magnetic losses can be beneficial, as these can produce a relatively high efficiency.