out one and three wavelengths. Dual reflectors (Cassegrain or quarter of a wavelength deep SO that the electric short circuit at the Gregorian) and offset reflectors have subtended angles between 30 base of the slot is transformed to a magnetic short circuit at the top degrees and 7 degrees, leading to feed diameters of between three of the slot. The result is that the azimuthal magnetic field is forced and ten wavelengths. to zero at the corrugations and the azimuthal electric field is zero Of particular interest in horn feed design is the polarisation per- due to the ridges. Consequently the boundary conditions of the TE formance and the quality of a feed is usually expressed by the level and TM modes are identical and the mutual propagating modes are of the peak cross-polarisation. The radiation characteristics of horns linear combinations of the two parts. The design procedure for are predicted by a two part process. Firstly the fields in the aperture corrugated horns is well understood (Clarricoats, 1984a) and it is are computed from a knowledge of the guided wave behaviour possible to accurately predict the radiation characteristics. inside the horn. Secondly the aperture fields are used to compute the radiated fields. The Fourier transform method has been found to work very well for the case of horns. The main types will now be 17.4.4.5 Array feeds briefly described. For more details see (Love, 1976; Love, 1986). They are used to form multiple beam and shaped beam reflector antennas used on satellites, Figure 17.11(e). The individual ele- 17.4.4.1 Rectangular or square horns ments of the array can be any type of horn, although for compact- ness small diameter open ended waveguides are preferred. The These are the simplest type of horn, Figure 7.11(a) but they are rarely used as feeds for reflectors because they have very high cross-polarisation unless the aperture size is large. 17.4.4.2 Small conical horns These can have reasonably good cross polarisation performance, Figure 17.11(b). They are widely used