Calculation of phase centers of feeds for reflectors when the phase variations are large

The aperture efficiencies of classical symmetrical front-fed or Cassegrain reflector antennas can be factorized in different sub-efficiencies. Of these, the phase efficiency is the only one which depends on the location of the feed relative to the focal point of the reflector, provided the reflector is in the far-field of the feed. We present an improved formula for calculating the location of the phase center which is valid also when the radiation field of the feed has large phase variations. The new formula is applied to two different versions of the hat feed.