Stored Energy and Quality Factor of Spherical Wave Functions–in Relation to Spherical Antennas With Material Cores

We present closed-form expressions for central properties of spherical wave functions of arbitrary order in relation to arbitrarily sized spherical antennas with lossless solid material cores. These properties are the electric or magnetic spherical surface current distribution radiating a spherical wave, the excitation coefficients for the internal and external spherical waves, the radiated power, the internal and external stored electric and magnetic energies, the difference of total electric and total magnetic energy, the cavity and radiating resonance conditions, and the quality factor. We investigate the variation of the internal/external and electric/magnetic stored energies with the electrical size of the antenna to study their relative significance for the quality factor.