Q factors for antennas in dispersive media

Stored energy and Q-factors are used to quantify the performance of small antennas. Accurate and efficient evaluation of the stored energy is also essential for current optimization and the associated physical bounds. Here, it is shown that the frequency derivative of the input impedance and the stored energy can be determined from the frequency derivative of the electric field integral equation. The expressions for the differentiated input impedance and stored energies differ by the use of a transpose and Hermitian transpose in the quadratic forms. The quadratic forms also provide simple single frequency formulas for the corresponding Q-factors. The expressions are further generalized to antennas integrated in temporally dispersive media. Numerical ex-amples that compare the different Q-factors are presented for dipole and loop antennas in conductive, Debye, Lorentz, and Drude media. The computed Q-factors are also verified with the Q-factor obtained from the stored energy in Brune synthesized circuit models.