When we feed a reflector with a narrow beam feed antenna, the narrow beam will under-illuminate the reflector causing reduce the amplitude taper efficiency while decreasing the feed power spilled past the rim of the reflector. However, the feed sidelobe illumination of the reflector will decrease phase error efficiency because the first sidelobe is 180° out of phase with respect to the main feed beam. The following analysis uses aperture theory on a circularly symmetric reflector fed by a feed with circular symmetry.