An antenna is provided for operating within the electrically small antenna regime (i.e., ka≅0.5), and having bandwidth performance quite close to fundamental limits. The antenna of the invention, in various embodiments, is based upon spherical resonator structures that are characterized by a performance factor (Q/Qchu,) close to 1.5. The antenna combines a resonator structure determined according to the method of the invention with an appropriate transmission line feeding arrangement, such that the resonator effectively couples the transmission line mode to the radiating spherical harmonic mode in an impedance-matched manner.