Broadband, electrically-small spherical-wire and generalized loop antennas exploiting inhomogeneous magnetic cores

It is known that a spherical wire antenna designed to excite solely the TE₀₁ spherical mode exhibits higher radiation Q than does one designed to radiate solely the TM₀₁ spherical mode, when energy internal to the spherical volume is taken into account. It has also been noted that the introduction of a magnetic core into a TE₀₁ mode spherical wire antenna can reduce the radiation Q by reducing the magnetic energy stored in the interior of the sphere. Recently it has been shown that the internal stored magnetic energy cannot be reduced to zero using homogeneous core composed of a lossless magnetic material, and thus a different minimum radiation Q exists which is higher than the external radiation Q but lower than the radiation Q of an empty TE₀₁ mode spherical wire antenna. This minimum Q value is achieved for a particular value of relative permeability that depends on the electrical size of the sphere. Here we analyze the more general case of a TE₀₁ mode spherical wire antenna with a radially inhomogeneous core, specifically, a hollow magnetic core. We show that such an arrangement can reduce the stored energy below that which can be obtained with a homogenous (solid) core and that the interior of the hollow magnetic core may contain a solid or hollow perfect electric conductor which further reduces the internal stored energy. While the reduction in stored energy is not particularly significant, the possible reduction in weight and increase in mechanical robustness is very substantial.