Optimum core parameters for an electrically-small TE1 (loop) mode antenna with an inhomogeneous magneto-dielectric core

Recent work concerning TE₁ mode spherical wire antennas, essentially generalized loop antennas, has shown that: (1) the introduction of a lossless, homogeneous magnetic core into the interior of a TE₁ mode spherical wire antenna cannot force the internal stored magnetic energy to zero, but rather only to a minimum value which depends on the external electrical size of the spherical antenna as well as the dielectric polarizability of the core; (2) the minimum value for internal energy is obtained with a particular finite, optimum value of permeability; and (3) employing a homogeneous core of this optimum permeability can actually make the antenna more conducive to supporting undesired modes, such as the TM₁ (electric dipole) mode. In particular, the parasitic TM₁ mode exhibits a series resonance at nearly the same point (electrical radius) at which minimum internal energy is effected for the TE₁ mode. More recently, it was shown that a radially inhomogeneous core consisting of a conducting kernel and a magnetic mantle can reduce the internal magnetic energy of a TE₁ mode spherical wire antenna even lower than can a homogeneous magnetic core. While the reduction in stored energy is not particularly significant, the possible reduction in weight and increase in mechanical robustness afforded by this geometry are very substantial. Here it is shown that for the kernel/mantle construction the series resonance of the parasitic TM₁ mode is well away from the point of minimum TE₁ mode energy, and thus an optimum design will not suffer from parasitic TM₁ modes. Also, an approach for determining the optimum permeability and thickness of the mantle for the inhomogeneous core is presented.