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The edge diffraction method of analysis utilized in the past to determine amplitude patterns is extended in this paper to predict the radiation phase center of pyramidal horn antennas. A series of extensive phase and amplitude measurements were performed on these antennas to determine the validity of the theoretical results. The measurements were performed over a frequency range of 7.5 to 10.5 GHz in the E plane of the antennas. The phase measurements were accurate to Â±0.2 electrical degrees, so that the phase center locations relative to the horn apertures were repeatably determined to better than 0.010 inch for horn apertures as large as 7 inches. The results of the measurements indicate that excellent agreement is obtained with the theory in predicting the phase center location of the larger horns (kRE > 50). For the smaller horns, however, there is a large discrepancy between the theory and measurements. The measured phase centers of the smaller horns exhibit a large variation with frequency which cannot be explained with the existing theory. Several reasons for the discrepancy are presented, and it is concluded that a more rigorous approach involving higher order modes has to be developed for the smaller horns.