Parabolic antenna

250px|thumb|A 28.5 meter parabolic [[satellite communications antenna at Erdfunkstelle Raisting (Raisting Earth Station), Bavaria, Germany, the biggest facility for satellite communication in the world. It has a Cassegrain-type feed, transmits at 6 Ghz and receives at 4 Ghz with a gain of 64.2 dB]]

A parabolic antenna is an antenna that uses a parabolic reflector, a curved surface with the cross-sectional shape of a parabola, to direct the radio waves. The most common form is shaped like a dish and is popularly called a dish antenna or parabolic dish. The main advantage of a parabolic antenna is that it has high directivity. It functions similarly to a searchlight or flashlight reflector to direct radio waves in a narrow beam, or receive radio waves from one particular direction only. Parabolic antennas have some of the highest gains, meaning that they can produce the narrowest beamwidths, of any antenna type. In order to achieve narrow beamwidths, the parabolic reflector must be much larger than the wavelength of the radio waves used, at UHF and microwave (SHF) frequencies, at which the wavelengths are small enough that conveniently sized reflectors can be used.

Parabolic antennas are used as high-gain antennas for point-to-point communications, in applications such as microwave relay links that carry telephone and television signals between nearby cities, wireless WAN/LAN links for data communications, satellite communications, and spacecraft communication antennas. They are also used in radio telescopes.

The other large use of parabolic antennas is for radar antennas, Thus, a spherical wavefront emitted by a feed antenna at the dish's focus F will be reflected into an outgoing plane wave L travelling parallel to the dish's axis VF.]]

Design

The operating principle of a parabolic antenna is that a point source of radio waves at the focal point in front of a paraboloidal reflector of conductive material will be reflected into a collimated plane wave beam along the axis of the reflector. Conversely, an incoming plane wave parallel to the axis will be focused to a point at the focal point.

A typical parabolic antenna consists of a metal parabolic reflector with a small feed antenna suspended in front of the reflector at its focus, pointed back toward the reflector. The shroud shields the antenna from radiation from angles outside the main beam axis, reducing the sidelobes. It is sometimes used to prevent interference in terrestrial microwave links, where several antennas using the same frequency are located close together. The shroud is coated inside with microwave absorbent material. Shrouds can reduce back lobe radiation by 10 dB. Two techniques are used, often in combination, to control the shape of the beam:

:* Shaped reflectors – The reflector can be given a noncircular shape, or different curvatures in the horizontal and vertical directions, to alter the shape of the beam. This is often used in radar antennas. As a general principle, the wider the antenna is in a given transverse direction, the narrower the radiation pattern will be in that direction.

::* "Orange peel" antenna – Used in search radars, this is a long narrow antenna shaped like the letter "C". It radiates a narrow vertical fan-shaped beam.

thumb|Array of multiple feed horns on a German [[airport surveillance radar antenna to control the elevation angle of the beam]]

:* Arrays of feeds – In order to produce an arbitrary shaped beam, instead of one feed horn, an array of feed horns clustered around the focal point can be used. Array-fed antennas are often used on communication satellites, particularly direct broadcast satellites, to create a downlink radiation pattern to cover a particular continent or coverage area. They are often used with secondary reflector antennas such as the Cassegrain.

Parabolic antennas are also classified by the type of feed, that is, how the radio waves are supplied to the antenna:

Polarization

The pattern of electric and magnetic fields at the mouth of a parabolic antenna is simply a scaled-up image of the fields radiated by the feed antenna, so the polarization is determined by the feed antenna. In order to achieve maximum gain, both feed antennas (transmitting and receiving) must have the same polarization. For example, a vertical dipole feed antenna will radiate a beam of radio waves with their electric field vertical, called vertical polarization. The receiving feed antenna must also have vertical polarization to receive them; if the feed is horizontal (horizontal polarization) the antenna will suffer a severe loss of gain.

To increase the data rate, some parabolic antennas transmit two separate radio channels on the same frequency with orthogonal polarizations, using separate feed antennas; this is called a dual polarization antenna. For example, satellite television signals are transmitted from the satellite on two separate channels at the same frequency using right and left circular polarization. In a home satellite dish, these are received by two small monopole antennas in the feed horn, oriented at right angles. Each antenna is connected to a separate receiver.

If the signal from one polarization channel is received by the oppositely polarized antenna, it will cause crosstalk that degrades the signal-to-noise ratio. The ability of an antenna to keep these orthogonal channels separate is measured by a parameter called cross polarization discrimination (XPD). In a transmitting antenna, XPD is the fraction of power from an antenna of one polarization radiated in the other polarization. For example, due to minor imperfections a dish with a vertically polarized feed antenna will radiate a small amount of its power in horizontal polarization; this fraction is the XPD. In a receiving antenna, the XPD is the ratio of signal power received of the opposite polarization to power received in the same antenna of the correct polarization, when the antenna is illuminated by two orthogonally polarized radio waves of equal power. If the antenna system has inadequate XPD, cross polarization interference cancelling (XPIC) digital signal processing algorithms can often be used to decrease crosstalk.

Dual reflector shaping

In the Cassegrain and Gregorian antennas, the presence of two reflecting surfaces in the signal path offers additional possibilities for improving performance. When the highest performance is required, a technique called dual reflector shaping may be used. This involves changing the shape of the sub-reflector to direct more signal power to outer areas of the dish, to map the known pattern of the feed into a uniform illumination of the primary, to maximize the gain. However, this results in a secondary that is no longer precisely hyperbolic (though it is still very close), so the constant phase property is lost. This phase error, however, can be compensated for by slightly tweaking the shape of the primary mirror. The result is a higher gain, or gain/spillover ratio, at the cost of surfaces that are trickier to fabricate and test. Other dish illumination patterns can also be synthesized, such as patterns with high taper at the dish edge for ultra-low spillover sidelobes, and patterns with a central "hole" to reduce feed shadowing.

Gain

thumb|The [[Five-hundred-meter Aperture Spherical Telescope (FAST) radio telescope in Guizhou, China, completed in 2016. With an effective aperture of 300 meters, it is the largest filled aperture parabolic antenna in the world. The cabin containing the feed antenna, suspended by cables in the air over the dish, has not been installed yet.]]

The directive qualities of an antenna are measured by a dimensionless parameter called its gain, which is the ratio of the power received by the antenna from a source along its beam axis to the power received by a hypothetical isotropic antenna. The gain of a parabolic antenna is:

:<math>G = \frac{4 \pi A}{\lambda^2}e_A = \left(\frac{\pi d}{\lambda}\right)^2 e_A</math>

where:

<math>A </math> is the area of the antenna aperture, that is, the mouth of the parabolic reflector. For a circular dish antenna, <math>A = \pi d^2/4</math>, giving the second formula above.
<math>d</math> is the diameter of the parabolic reflector, if it is circular.
<math>\lambda</math> is the wavelength of the radio waves.
<math>e_A</math> is a dimensionless parameter between 0 and 1 called the aperture efficiency. The aperture efficiency of typical parabolic antennas is 0.55 to 0.70.

It can be seen that, as with any aperture antenna, the larger the aperture is, compared to the wavelength, the higher the gain. The gain increases with the square of the ratio of aperture width to wavelength, so large parabolic antennas, such as those used for spacecraft communication and radio telescopes, can have extremely high gain. Applying the above formula to the 25-meter-diameter antennas often used in radio telescope arrays and satellite ground antennas at a wavelength of 21 cm (1.42 GHz, a common radio astronomy frequency), yields an approximate maximum gain of 140,000 times or about 52 dBi (decibels above the isotropic level). The largest parabolic dish antenna in the world is the Five-hundred-meter Aperture Spherical radio Telescope in southwest China, which has an effective aperture of about 300 meters. The gain of this dish at 1.42 GHz is roughly 90 million, or 80 dBi.

Aperture efficiency e<sub>A</sub> is a catchall variable which accounts for various losses that reduce the gain of the antenna from the maximum that could be achieved with the given aperture. The major factors reducing the aperture efficiency in parabolic antennas are:

Feed spillover – Some of the radiation from the feed antenna falls outside the edge of the dish and so does not contribute to the main beam.
Feed illumination taper – The maximum gain for any aperture antenna is only achieved when the intensity of the radiated beam is constant across the entire aperture area. However, the radiation pattern from the feed antenna usually tapers off toward the outer part of the dish, so the outer parts of the dish are "illuminated" with a lower intensity of radiation. Even if the feed provided constant illumination across the angle subtended by the dish, the outer parts of the dish are farther away from the feed antenna than the inner parts, so the intensity would drop off with distance from the center. Hence, the intensity of the beam radiated by a parabolic antenna is maximum at the center of the dish and falls off with distance from the axis, reducing the efficiency.
Aperture blockage – In front-fed parabolic dishes where the feed antenna is located in front of the dish in the beam path (and in Cassegrain and Gregorian designs as well), the feed structure and its supports block some of the beam. In small dishes such as home satellite dishes, where the size of the feed structure is comparable with the size of the dish, this can seriously reduce the antenna gain. To prevent this problem these types of antennas often use an offset feed, where the feed antenna is located to one side, outside the beam area. The aperture efficiency for these types of antennas can reach 0.7 to 0.8.
Shape errors – Random surface errors in the shape of the reflector reduce efficiency. This loss is approximated by Ruze's Equation.

For theoretical considerations of mutual interference (at frequencies between 2 and approximately 30 GHz; typically in the Fixed Satellite Service) where specific antenna performance has not been defined, a reference antenna based on Recommendation ITU-R S.465 is used to calculate the interference, which will include the likely sidelobes for off-axis effects.

Radiation pattern

thumb|[[Radiation pattern of a German parabolic antenna. The main lobe (top) is only a few degrees wide. The sidelobes are all at least 20 dB below (1/100 the power density of) the main lobe, and most are 30 dB below (if this pattern was drawn with linear power levels instead of logarithmic dB levels, all lobes other than the main lobe would be much too small to see).]]

In parabolic antennas, virtually all the power radiated is concentrated in a narrow main lobe along the antenna's axis. The residual power is radiated in sidelobes, usually much smaller, in other directions. Since the reflector aperture of parabolic antennas is much larger than the wavelength, diffraction usually causes many narrow sidelobes, so the sidelobe pattern is complex. There is also usually a backlobe, in the opposite direction to the main lobe, due to the spillover radiation from the feed antenna that misses the reflector.

Beamwidth

The angular width of the beam radiated by high-gain antennas is measured by the half-power beam width (HPBW), which is the angular separation between the points on the antenna radiation pattern at which the power drops to one-half (-3 dB) its maximum value. For parabolic antennas, the HPBW θ is given by:

:<math>\theta = k\lambda / d \,</math>

where k is a factor which varies slightly depending on the shape of the reflector and the feed illumination pattern. For an ideal uniformly illuminated parabolic reflector and θ in degrees, k would be 57.3 (the number of degrees in a radian). For a typical parabolic antenna, k is approximately 70.

The radiation-field pattern can be calculated by applying Huygens' principle in a similar way to a rectangular aperture. The electric field pattern can be found by evaluating the Fraunhofer diffraction integral over the circular aperture. It can also be determined through Fresnel zone equations.

<math>E=\int \int \frac {A}{r_1} e^{j (\omega t - \beta r_1)} dS=\int \int e^{2\pi i(lx+my)/\lambda} dS</math>

where <math>\beta=\omega/c=2\pi /\lambda</math>. Using polar coordinates, <math>x=\rho \cdot \cos \theta</math> and <math>y=\rho \cdot \sin \theta</math>. Taking account of symmetry,

<math>E=\int\limits_{0}^{2\pi}d\theta \int\limits_{0}^{\rho_0}e^{2\pi i\rho \cos \theta l/\lambda} \rho d\rho </math>

and using first-order Bessel function gives the electric field pattern <math>E(\theta) </math>,

where <math>D</math> is the diameter of the antenna's aperture in meters, <math>\lambda</math> is the wavelength in meters, <math>\theta</math> is the angle in radians from the antenna's symmetry axis as shown in the figure, and <math>J_1 </math> is the first-order Bessel function. Determining the first nulls of the radiation pattern gives the beamwidth <math>\theta_0</math>. The term <math>J_1(x)=0</math> whenever <math>x=3.83</math>. Thus,

<math>\theta_0=\arcsin \frac {3.83 \lambda}{\pi D} = \arcsin \frac {1.22 \lambda}{D} </math>.

When the aperture is large, the angle <math>\theta_0</math> is very small, so <math>\arcsin (x)</math> is approximately equal to <math>x</math>. This gives the common beamwidth formulas, However, the early development of radio was limited to lower frequencies at which parabolic antennas were unsuitable, and they were not widely used until World War II, when microwave frequencies began to be employed.

After World War I when short waves began to be used, interest grew in directional antennas, both to increase range and make radio transmissions more secure from interception. Italian radio pioneer Guglielmo Marconi used parabolic reflectors during the 1930s in investigations of UHF transmission from his boat in the Mediterranean. The Voyager 1 spacecraft launched in 1977 is currently 24.2 billion kilometers from Earth, the furthest manmade object in space, and it's 3.7 meter S and X-band Cassegrain antenna (see picture above) is still able to communicate with ground stations. The advent of computer design tools in the 1970s—such as NEC, capable of calculating the radiation pattern of parabolic antennas—has led to the development of sophisticated asymmetric, multi-reflector and multi-feed designs in recent years.

References

External links

Animation of Propagation from a Parabolic Dish Antenna from YouTube