The conductance bandwidth of an electrically small antenna in antiresonant ranges

Accurate approximations of the conductance and the conductance bandwidth of an electrically small antenna valid in resonant and antiresonant ranges were found. It was shown that the conductance bandwidth of an antenna tuned on maximal power of radiation is inversely proportional to the magnitude of the frequency derivative of the input impedance Z'(ωcd) of the antenna at frequency of maximal conductance. That is a generalization of the well known relationship, according to which, the conductance bandwidth of an antenna tuned on resonance in a resonant range is inversely proportional to the magnitude of the frequency derivative of the input reactance of the antenna X'0(ω0) at resonant frequency. Obtained approximate formulas display inverse proportionality of the conductance bandwidth to the approximate quality factor of the antenna in resonant and antiresonant ranges. A differential definition of the fractional conductance bandwidth was formulated, which is convenient for the case of closely spaced resonances of an antenna. As an example, numerical calculations for oblate spheroidal and spherical antennas in shells with negative permittivity in resonant and antiresonant ranges was used to confirm accuracy of the obtained approximations of the conductance and the conductance bandwidth of an electrically small antenna.