Determining the three-dimensional phase center of an antenna

A method for determining the best-fit phase center of an antenna is presented. Electrically small antennas with simple patterns and linear polarizations can have well-defined phase centers, but this is not the case for antennas with more sophisticated patterns, including those with circular polarization. In general, the phase center is sensitive to the angular range of interest, the weighting over that angular range, and of course the frequency. The formulation is developed here for finding the physical location on an antenna which corresponds to a minimum variance for an antenna's angularly weighed phase pattern. Examples using measurements of specialist precision GPS antennas are used to give a feel for the results. A brute-force search is used, but the relatively small nature of the problem means that the solution is quick when using a standard personal computer.