Decomposition of the electromagnetic energy into its stored and radiated
parts is instrumental in the evaluation of antenna Q and the corresponding
fundamental limitations on antennas. This decomposition is not unique and there
are several proposals in the literature. Here, it is shown that stored energy
defined from the difference between the energy density and the far field energy
equals the new energy expressions proposed by Vandenbosch for many cases. This
also explains the observed cases with negative stored energy and suggests a
possible remedy to them. The results are compared with the classical explicit
expressions for spherical regions where the results only differ by ka that is
interpreted as the far-field energy in the interior of the sphere. Numerical
results of the Q-factors for dipole, loop, and inverted L-antennas are also
compared with estimates from circuit models and differentiation of the
impedance. The results indicate that the stored energy in the field agrees with
the stored energy in the Brune synthesized circuit models whereas the
differentiated impedance gives a lower value for some cases. The corresponding
results for the bandwidth suggest that the inverse proportionality between
bandwidth and Q depends on the relative bandwidth or equivalent the threshold
of the reflection coefficient. The Q from the differentiated impedance and
stored energy are most useful for relative narrow and wide bandwidths,
respectively
