Theory of the directional pattern of a pyramidal horn

A method is presented for calculating the directional pattern of a pyramidal horn antenna from first principles by diffraction theory. It is based on first finding the field in the plane of the aperture, both inside and outside the physical aperture. This is then transformed to find the far-field pattern. The field in the aperture plane is made up of contributions from the primary wave reaching the aperture, whose phase surfaces are assumed to be spherical, edge waves propagating in the plane of the apertures and edge waves that have been reflected from inside the horn. The edge waves traveling in the plane of the aperture are the main object of interest. They propagate not only perpendicular to the edges, but also diffract parallel to the edges because of the finite length of the edges. By taking this fully into account, a directional pattern over the whole forward hemisphere can be predicted for any given frequency from the geometry of the horn. For a particular horn the principal cuts agree with direct measurements made at the National Physical Laboratory, Teddington, UK, to within about 4 dB (except near deep minima).