Analytical Expressions for Spherical Wire Antenna Quality Factor Demonstrating Exact Agreement Between Circuit-Based and Field Integration Techniques

Properties of spherical wire antennas are revisited using a circuit analysis approach. This methodology yields the exact quality factor and axial ratio (AR) of coupled-mode spherical radiators as analytical expressions. The new circuit-based equations are compared to field integration predictions for quality factor, and both are found to agree for a general multipole expansion of the electromagnetic fields. These two predictions of stored energy inside a spherical wire antenna are shown to be equivalent via direct analysis, while predictions of stored energy outside the spherical wire antenna are compared by way of mathematical induction. In addition, the circuit analysis reveals general relations between supplied current and radiated power of spherical wire antennas, resonance conditions of coupled-mode systems, and analytical quantification of the trade-off between the quality factor and AR for TM _{\boldsymbol {1m}} -TE _{\boldsymbol {1m}} radiators. New and simple expressions for the minimum quality factor of circular, near-circular, linear, and general elliptical polarizations are provided.