  We consider resonant patch antennas, implemented using loaded
transmission-line networks and other exotic structures having engineered
dispersion. An analytical expression is derived for the ratio of radiation
quality factors of such antennas and conventional patch antennas loaded with
(reference) dielectrics. In the ideal case this ratio depends only on the
propagation constant and wave impedance of the structure under test, and it can
be conveniently used to study what kind of dispersion leads to improved
impedance bandwidth. We illustrate the effect of dispersion by implementing a
resonant patch antenna using a periodic network of LC elements. The analytical
results predicting enhanced impedance bandwidth compared to the reference
results are validated using a commercial circuit simulator. Discussion is
conducted on the practical limitations for the use of the proposed expression.
