Fano matching bandwidth bounds for small loop antennas based on spherical wave scattering

Fundamental impedance matching bounds for electrically small loop antennas are derived based on spherical wave scattering in the low-frequency limit. A small lossless loop antenna is represented as a two-port network between the excitation port and the fundamental TE spherical wave port. The low-frequency asymptotic expression for the wave reflection coefficient is found and the classical Fano approach is applied to derive integral equalities for the magnitude of the reflection coefficient. A basic loop, one with a series-C element, and one with a parallel-C element are analyzed. The bandwidth upper bounds as functions of the antenna dimension, the port impedance, and the circuit parameters are presented.