The Radiansphere around a Small Antenna

TLDR

The radiansphere, with radius λ/2π where near‑field and far‑field components are equal, defines the boundary of a small antenna’s influence. The authors model a small antenna as a coil on a perfect spherical magnetic core and employ a conducting shell the size of the radiansphere to separately measure radiation and loss resistances. The radiation power factor equals the ratio of the antenna’s volume to that of the radiansphere, and comparable small antennas (C or L) can achieve a fraction of this ratio.

Abstract

The "radiansphere" is the boundary between the near field and the far field of a small antenna. Its radius is one radianlength (λ/2π), at which distance the three terms of the field are equal in magnitude. A "small" antenna is one somewhat smaller than the radiansphere, but it has a "sphere of influence" occupying the radiansphere. The power that theoretically can be intercepted by a hypothetical isotropic antenna is that which flows through the radiansphere or its cross section, the "radiancircle." From a small electric dipole, the far field of radiation is identified as a retarded magnetic field. Between two such dipoles, the far mutual impedance is that of mutual inductance, expressed in terms of space properties and the radiansphere. A small coil wound on a perfect spherical magnetic core is conceived as an ideal small antenna. Its radiation power factor is equal to the ratio of its volume over that of the radiansphere. A fraction of this ratio is obtainable in various forms of small antennas (C or L) occupying a comparable amount of space. A radiation shield, in the form of a conducting shell the size of the radiansphere, enables separate measurement of radiation resistance and loss resistance.