The Horn Antenna

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Horn Antenna Radiation Patterns

Introduction to Horn Antennas

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (I've heard of horn antennas operating as high as 140 GHz). Horn antennas often have a directional radiation pattern with a high antenna gain, which can range up to 25 dB in some cases, with 10-20 dB being typical. Horn antennas have a wide impedance bandwidth, implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR). The bandwidth for practical horn antennas can be on the order of 20:1 (for instance, operating from 1 GHz-20 GHz), with a 10:1 bandwidth not being uncommon.

The gain of horn antennas often increases (and the beamwidth decreases) as the frequency of operation is increased. This is because the size of the horn aperture is always measured in wavelengths; at higher frequencies the horn antenna is "electrically larger"; this is because a higher frequency has a smaller wavelength. Since the horn antenna has a fixed physical size (say a square aperture of 20 cm across, for instance), the aperture is more wavelengths across at higher frequencies. And, a recurring theme in antenna theory is that larger antennas (in terms of wavelengths in size) have higher directivities.

Horn antennas have very little loss, so the directivity of a horn is roughly equal to its gain.

Horn antennas are somewhat intuitive and relatively simple to manufacture. In addition, acoustic horn antennas are also used in transmitting sound waves (for example, with a megaphone). Horn antennas are also often used to feed a dish antenna, or as a "standard gain" antenna in measurements.

Popular versions of the horn antenna include the E-plane horn, shown in Figure 1. This horn antenna is flared in the E-plane, giving the name. The horizontal dimension is constant at w.

e-plane (E plane) horn antenna

Figure 1. E-plane horn antenna.

Another example of a horn antenna is the H-plane horn, shown in Figure 2. This horn is flared in the H-plane, with a constant height for the waveguide and horn of h.

h-plane or H plane horn antenna

Figure 2. H-Plane horn antenna.

The most popular horn antenna is flared in both planes as shown in Figure 3. This is a pyramidal horn, and has a width B and height A at the end of the horn.

horn flared in both the E and H-plane: pyramidal horn antenna

Figure 3. Pyramidal horn antenna.

Horn antennas are typically fed by a section of a waveguide, as shown in Figure 4. The waveguide itself is often fed with a short dipole, which is shown in red in Figure 4. A waveguide is simply a hollow, metal cavity (see the waveguide tutorial). Waveguides are used to guide electromagnetic energy from one place to another. The waveguide in Figure 4 is a rectangular waveguide of width b and height a, with b>a. The E-field distribution for the dominant mode is shown in the lower part of Figure 1.

waveguide used to feed horn antennas

Figure 4. Waveguide used as a feed to horn antennas.

Fields and Geometrical Parameters for Horn Antennas

Antenna texts typically derive very complicated functions for the radiation patterns of horn antennas. To do this, first the E-field across the aperture of the horn antenna is assumed to be known, and the far-field radiation pattern is calculated using the radiation equations. While this is conceptually straight forward, the resulting field functions end up being extremely complex, and personally I don't feel add a whole lot of value. If you would like to see these derivations, pick up any antenna textbook that has a section on horn antennas. (Also, as a practicing antenna engineer, I can assure you that we never use radiation integrals to estimate patterns. We always go on previous experience, computer simulations and measurements.)

Instead of the traditional academic derivation approach, I'll state some results for the horn antenna and show some typical radiation patterns, and attempt to provide a feel for the design parameters of horn antennas. Since the pyramidal horn antenna is the most popular, we'll analyze that. The E-field distribution across the aperture of the horn antenna is what is responsible for the radiation.

The radiation pattern of a horn antenna will depend on B and A (the dimensions of the horn at the opening) and R (the length of the horn, which also affects the flare angles of the horn), along with b and a (the dimensions of the waveguide). These parameters are optimized in order to taylor the performance of the horn antenna, and are illustrated in the following Figures.

geometry of horn antenna, cut in the H-plane

Figure 5. Cross section of waveguide, cut in the H-plane.

cut of the waveguide in the E-plane

Figure 6. Cross section of waveguide, cut in the E-plane.

Observe that the flare angles (flare angle in the E-plane and flare angle for horn antenna) depend on the height, width and length of the horn antenna.

Given the coordinate system of Figure 6 (which is centered at the opening of the horn), the radiation will be maximum in the +z-direction (out of the screen).

coordinate system used in evaluating horn antennas

Figure 7. Coordinate system used, centered on the horn antenna opening.

The E-field distribution across the opening of the horn antenna can be approximated by:

electric field distribution across the aperture of a horn antenna

The E-field in the far-field will be linearly polarized, and the magnitude will be given by:

far fields radiated from a horn antenna

The above equation states that the far-fields of the horn antenna is the Fourier Transform of the fields at the opening of the horn. Many textbooks evaluate this integral, and end up with supremely complicated functions, that I don't feel sheds a whole lot of light on the patterns.

In the next section, we'll look at the radiation patterns for horn antennas.


Next: Radiation Patterns for Horn Antennas

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