  We use time-domain electromagnetic simulations to determine the spectral
characteristics of the Hydrogen Epoch of Reionization Arrays (HERA) antenna.
These simulations are part of a multi-faceted campaign to determine the
effectiveness of the dish's design for obtaining a detection of redshifted 21
cm emission from the epoch of reionization. Our simulations show the existence
of reflections between HERA's suspended feed and its parabolic dish reflector
that fall below -40 dB at 150 ns and, for reasonable impedance matches, have a
negligible impact on HERA's ability to constrain EoR parameters. It follows
that despite the reflections they introduce, dishes are effective for
increasing the sensitivity of EoR experiments at relatively low cost. We find
that electromagnetic resonances in the HERA feed's cylindrical skirt, which is
intended to reduce cross coupling and beam ellipticity, introduces significant
power at large delays ($-40$ dB at 200 ns) which can lead to some loss of
measurable Fourier modes and a modest reduction in sensitivity. Even in the
presence of this structure, we find that the spectral response of the antenna
is sufficiently smooth for delay filtering to contain foreground emission at
line-of-sight wave numbers below $k_\parallel \lesssim 0.2$ $h$Mpc$^{-1}$, in
the region where the current PAPER experiment operates. Incorporating these
results into a Fisher Matrix analysis, we find that the spectral structure
observed in our simulations has only a small effect on the tight constraints
HERA can achieve on parameters associated with the astrophysics of
reionization.
