Reaching the Chu Lower Bound on Q With Magnetic Dipole Antennas Using a Magnetic-Coated PEC Core

We analytically solve the radiation problem for a spherical magnetic dipole antenna with a material-coated perfectly electrically conducting core. Using the closed-form expressions derived for the internal and external stored energies as well as for the radiation quality factor $Q$, we determine the optimal geometrical and material parameters of the antenna. We show that the optimal permeability of the coating increases as the coating becomes thinner; as a result, the energy stored in it and the radiation quality factor $Q$ reduce. In the limit of an infinitely thin coating, the optimal permeability tends to infinity, the internal stored energy vanishes, and the $Q$ reaches the Chu lower bound, irrespective of the antenna electrical size $ka$ and permittivity of the coating.