Electrically Small Magnetic Dipole Antennas With Quality Factors Approaching the Chu Lower Bound

摘要

We investigate the quality factor $Q$ for electrically small current distributions and practical antenna designs radiating the ${rm TE}_{10}$ magnetic dipole field. The current distributions and the antenna designs employ electric currents on a spherical surface enclosing a magneto-dielectric material that serves to reduce the internal stored energy. Closed-form expressions for the internal and external stored energies as well as for the quality factor $Q$ are derived. The influence of the sphere radius and the material permeability and permittivity on the quality factor $Q$ is determined and verified numerically. It is found that for a given antenna size and permittivity there is an optimum permeability that ensures the lowest possible $Q$, and this optimum permeability is inversely proportional to the square of the antenna electrical radius. When the relative permittivity is equal to 1, the optimum permeability yields the quality factor $Q$ that constitutes the lower bound for a magnetic dipole antenna with a magneto-dielectric core. Furthermore, the smaller the antenna the closer its quality factor $Q$ can approach the Chu lower bound. Simulated results for the ${rm TE}_{10}$-mode multiarm spherical helix antenna with a magnetic core reach a $Q$ that is 1.24 times the Chu lower bound for an electrical radius of 0.192.