By P.J.B. Clarricoats
Corrugated horns are typical and hugely effective, particularly of their use as feeds for microwave reflector antennas. This e-book is dedicated to the speculation and layout of corrugated horns and scalar feeds and explains why hybrid mode feeds are excellent feeds for reflectors
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Extra info for Corrugated horns for microwave antennas
29) then Hz is finite and Ez = 0. The cut-off is therefore an //-type and in the limit as tends to be zero, the mode exhibits pure TE properties with A tending to infinity. 26 Cylindrical corrugated waveguides Eqn. 30) then Ez is finite and E2 = 0. The cut-off is therefore an E-type in the limit as 0 tends to zero, the mode exhibits pure TM properties with A tending to zero. Notice that for H-mode cut-off the boundary condition corresponds to that of a TE mode in a uniform waveguide of radius rx while for #-mode cut-off the boundary condition corresponds to that of a TM mode in a uniform waveguide of radius r0.
For EH l m modes, we begin at |3 = 0 with A = — °° and pure TE conditions. For the lowest order EH l m mode, the pass-band is narrow and the wave terminates with 0 = oo at the same point that the HEn mode reaches the balanced-hybrid condition. We have termed this first EH l m mode the EH n mode, but some authors, for example, Dragone , simply refer to this mode as 4the surface wave mode'. Such nomenclature is ambiguous for obvious reasons. The next EH l m mode, our EH 12 , remains a fast wave through the first balanced-hybrid condition where the corrugation depth is approximately A/4, it has A = 0 and behaves as a pure TM mode when the corrugation depth is A/2, it becomes a slow wave when A = + 1 and mode terminates when the corrugation depth is 3A/4.
Fig. 20 shows theoretical values of TE n mode reflection coefficient obtained Or -50 16 19 22 25 28 31 frequency, GHz 34 37 Fig. 22 Return loss of a corrugated horn with semi-flare angle of 4 degrees and aperture radius 3-14 cm  by Clarricoats and Saha  in a study in which the parameters r1/r0 and r1/rh were varied rh being the radius of the uniform circular waveguide. A comparison between experiment and theory is shown in Fig. 21 where the agreement lies within experimental accuracy. e.