Resonance and supergain effects in small ferromagnetically or dielectrically loaded biconical antennas

The input impedance and the radiation pattern of thin biconical antennas which contain materials of high dielectric permittivity
\epsilon
and high magnetic permeability
\mu
can be evaluated by methods due to Schelkunoff and Tai. Examination of numerical results shows that resonances of the input impedance are obtainable for antenna lengths much shorter than that of the ordinary half-wave dipole. It becomes also apparent, however, that the impedance bandwidth at these resonances is narrow and decreases with increasing
\epsilon
and
\mu
. Analysis of the pertinent equations leads to the following conclusions concerning radiation patterns: 1) The pattern of an antenna which is small in terms of free-space wavelengths
\lambda
and is also small in terms of material wavelengths,
\lambda/\sqrt{\mu\epsilon}
, is essentially that of a small current element in air; 2) If the biconical antenna is small in terms of free-space wavelengths, but is large in terms of material wavelengths the radiation pattern is also that of a small current element, except in certain well defined and very narrow frequency bands where multilobe or narrow lobe patterns appear. A similar "supergain" effect has been noted by Knudsen [33] in his discussion of small loops which carry currents of varying phase.