Optimum pyramidal horn antenna - H-field


A horn antenna or microwave horn is an antenna that consists of a flaring metal waveguide shaped like a horn to direct radio waves in a beam. Horns are widely used as antennas at UHF and microwave frequencies, above 300 MHz. They are used as feed antennas (called feed horns) for larger antenna structures such as parabolic antennas, as standard calibration antennas to measure the gain of other antennas, and as directive antennas for such devices as radar guns, automatic door openers, and microwave radiometers. Their advantages are moderate directivity, low standing wave ratio (SWR), broad bandwidth, and simple construction and adjustment.

One of the first horn antennas was constructed in 1897 by Bengali-Indian radio researcher Jagadish Chandra Bose in his pioneering experiments with microwaves. The modern horn antenna was invented independently in 1938 by Wilmer Barrow and G. C. Southworth. The development of radar in World War 2 stimulated horn research to design feed horns for radar antennas. The corrugated horn invented by Kay in 1962 has become widely used as a feed horn for microwave antennas such as satellite dishes and radio telescopes.

An advantage of horn antennas is that since they have no resonant elements, they can operate over a wide range of frequencies, a wide bandwidth. The usable bandwidth of horn antennas is typically of the order of 10:1, and can be up to 20:1 (for example allowing it to operate from 1 GHz to 20 GHz). The input impedance is slowly varying over this wide frequency range, allowing low voltage standing wave ratio (VSWR) over the bandwidth. The gain of horn antennas ranges up to 25 dBi, with 10 – 20 dBi being typical.

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 two locations along the wave path where the impedance changes abruptly; the mouth or aperture of the horn, and the throat where the sides begin to flare out. The amount of reflection at these two sites varies with the flare angle of the horn (the angle the sides make with the axis). In narrow horns with small flare angles most of the reflection occurs at the mouth of the horn. The gain of the antenna is low because the small mouth approximates an open-ended waveguide. As the angle is increased, the reflection at the mouth decreases rapidly and the antenna’s gain increases. In contrast, in wide horns with flare angles approaching 90° most of the reflection is at the throat. The horn’s gain is again low because the throat approximates an open-ended waveguide. As the angle is decreased, the amount of reflection at this site drops, and the horn’s gain again increases.

The optimum horn is called some flare angle between 0° and 90° which gives maximum gain and minimum reflection. Most practical horn antennas are designed as optimum horns.

A Pyramidal horn is a horn antenna with the horn in the shape of a four-sided pyramid, with a rectangular cross section. They are a common type, used with rectangular waveguides, and radiate linearly polarized radio waves.

An optimum horn does not give maximum gain for a given aperture size; this is achieved by a very long horn (an aperture limited horn). It gives the maximum gain for a given horn length. Tables showing dimensions for optimum horns for various frequencies are given in microwave handbooks.

For a pyramidal horn, the dimensions that give an optimum horn in the H-field direction are shown here.

Related formulas


aH the width of the aperture in the H-field direction (m)
λwavelength (m)
LHthe slant length of the side in the H-field direction (m)