An antenna system of coaxial elements and terminating impedances produces controlled bandwidth, broadband, and wideband performance under a variety of near field influences, with capability for simultaneous and alternating reception and radiation of electromagnetic radio energy. The antenna system enables broader bandwidths within miniaturized areas of confinement relative to wavelength. Singular elements of the system enable, and a plurality of elements of the system are combined to form specific bandpass, band reject, duplexing, and diplexing for radio frequencies as a function of the antenna system. The antenna system features complex terminating impedances which combine with characteristic impedances of coaxial structures to yield efficient radiating and matching functions for radio energy over a controlled bandwidth. The antenna system simultaneously utilizes the skin effect of electron flow with different vectors flowing on the internal and the external surfaces of the outside conductor of coaxial antenna elements with different vectors.