Improved Formulas for the Q of Antennas With Highly Lossy Dispersive Materials

Formulas obtained by Yaghjian and Best [ IEEE Trans. Antennas Propagat., vol. 53, pp. 1298-1324, Apr. 2005] for the quality factor (Q) of antennas containing linear passive media that is not too highly lossy and dispersive are generalized to hold in highly lossy dispersive media as well. The generalization is obtained by means of a straightforward, though ad hoc, definition of nonnegative energy densities that determine a Q which is approximately equal to twice the inverse of the matched VSWR half-power fractional impedance bandwidth of the antenna. The Q for a straight-wire antenna embedded in highly lossy dispersive media is computed using the generalized energy densities and is shown to agree closely with twice the inverse of the half-power fractional bandwidth of the antenna. Other antennas modeled by resonant RLC series and parallel circuits with the inductors and capacitors filled with lossy dispersive material further confirm the improvement in the inverse-bandwidth accuracy of the Q computed from the generalized energy densities