  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
examples 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.
