sectoral horn flared in the direction of the magnetic or H-field in the waveguide. Conical horn (d) – A horn in the shape of a cone, with a circular cross section. They are used with cylindrical waveguides. Exponential horn (e) – A horn with curved sides, in which the separation of the sides increases as an exponential function of length. Also called a scalar horn, they can have pyramidal or conical cross sections. Exponential horns have minimum internal reflections, and almost constant impedance and other characteristics over a wide frequency range. They are used in applications requiring high performance, such as feed horns for communication satellite antennas and radio telescopes. Corrugated horn – A horn with parallel slots or grooves, small compared with a wavelength, covering the inside surface of the horn, transverse to the axis. Corrugated horns have wider bandwidth and smaller sidelobes and cross-polarization, and are widely used as feed horns for satellite dishes and radio telescopes. Dual-mode conical horn – (The Potter horn ) This horn can be used to replace the corrugated horn for use at sub-mm wavelengths where the corrugated horn is lossy and difficult to fabricate. Diagonal horn – This simple dual-mode horn superficially looks like a pyramidal horn with a square output aperture. On closer inspection, however, the square output aperture is seen to be rotated 45° relative to the waveguide. These horns are typically machined into split blocks and used at sub-mm wavelengths. Ridged horn – A pyramidal horn with ridges or fins attached to the inside of the horn, extending down the center of the sides. The fins lower the cutoff frequency, increasing the antenna's bandwidth. Septum horn – A horn which is divided into several subhorns by metal partitions (septums) inside, attached to opposite walls. Aperture-limited horn – a long narrow horn, long enough so the phase error is a negligible fraction of a wavelength, so it essentially radiates a plane wave. It has an aperture efficiency of 1.0 so it gives the maximum gain and minimum beamwidth for a given aperture size. The gain is not affected by the length but only limited by diffraction at the aperture. Used as feed horns in radio telescopes and other high-resolution antennas. Optimum horn For a given frequency and horn length, there is some flare angle that gives minimum reflection and maximum gain. The internal reflections in straight-sided horns come from the