Parabolic Reflector Antenna Gain

- an overview or tutorial about parabolic reflector gain, the antenna gain formula or equation, and the practical factors affecting the 'dish' antenna gain.

Parabolic reflector antenna gain is one of the key parameters of this type of antenna.

The high level of gain that can be achieved by using a parabolic reflector is one of the main reasons they are used.

Parabolic reflector antenna gain can be as high as 30 to 40 dB - figures that would not be easily achievable using other forms of antenna. Antennas would be mechanically large and unwieldy.

Goldstone antenna - a very large example of a high gain parabolic reflector antenna

The parabolic reflector antenna is ideal for high gain applications. At microwave frequencies where these antennas are normally used, they are able to produce very high levels of gain, and they offer a very convenient and robust structure that is able to withstand the rigours of external use, while still being able to perform well. Many other types of antenna design are not practicable at these frequencies.

High gain parabolic reflector antennas come in a variety of sizes. The most commonly seen are those used for satellite television reception. However parabolic antennas are used in many other applications. Parabolic reflector antennas are also often seen on microwave towers for communications. Larger ones still can often be seen on TV broadcast stations where signals need to be transmitted up to a broadcast satellite and where performance is paramount. Even larger antennas may also be used for other communications or even space research applications. Some these parabolic antennas are many tens of metres across.

The one common feature of all these examples is the parabolic antenna gain, or parabolic dish gain. While the larger antennas have greater levels of parabolic antenna gain, the performance of all these antennas is of prime importance.


Factors affecting parabolic reflector antenna gain

There are a number of factors that affect the parabolic antenna gain. These factors include the following:

  • Diameter of reflecting surface   The larger the diameter of the reflecting surface of the antenna the higher the parabolic reflector gain will be.
  • Antenna efficiency:   The efficiency of the antenna has a significant effect on the overall parabolic reflector gain. Typical figures are between 50 and 70%. Further details are given below.
  • Operational wavelength:   The parabolic reflector antenna gain is dependent upon the reflector size in terms of wavelengths. Therefore if the same reflector is used on two different frequencies, the gain will be different and inversely proportional to the wavelength.

Parabolic reflector antenna gain

The parabolic antenna gain can easily be calculated from a knowledge of the diameter of the reflecting surface, the wavelength of the signal, and a knowledge or estimate of the efficiency of the antenna.

The parabolic reflector antenna gain is calculated as the gain over an isotropic source, i.e. relative to a source that radiates equally in all directions. This is a theoretical source that is used as the benchmark against which most antennas are compared. The gain is quoted in this manner is denoted as dBi.

The standard formula for the parabolic reflector antenna gain is:

The formula to determine the gain of a parabolic reflector antenna in terms of its diameter, operational wavelength and efficiency factor.

Where:
    G is the gain over an isotropic source in dB
    k is the efficiency factor which is generally around 50% to 60%, i.e. 0.5 to 0.6
    D is the diameter of the parabolic reflector in metres
    λ is the wavelength of the signal in metres

From this it can be seen that very large gains can be achieved if sufficiently large reflectors are used. However when the antenna has a very large gain, the beamwidth is also very small and the antenna requires very careful control over its position. In professional systems electrical servo systems are used to provide very precise positioning.

It can be seen that the parabolic reflector gain can be of the order of 50dB for antennas that have a reflector diameter of a hundred wavelengths or more. Whilst antennas of this size would not be practicable for many antennas designs such as the Yagi, and many others, the parabolic reflector can be made very large in comparison to the wavelength and therefore it can achieve these enormous gain levels. More normal sizes for these antennas are a few wavelengths, but these are still able to provide very high levels of gain.

Image of a domestic satellite television parabolic reflector antenna showing the offset feed arrangement to reduce aperture block which reduces the antenna gain.


Parabolic reflector gain efficiency

In the overall gain formula for the antenna, an efficiency factor is included. Typically this may be between 50 and 70% dependent upon the actual antenna.

The parabolic reflector antenna gain efficiency is dependent upon a variety of factors. These are all multiplied together to give the overall efficiency.

The formula showing the summing of the different elements of parabolic reflector antenna gain efficiency.

  • Radiation efficiency:   The radiation efficiency is denoted as kr above. It is governed by the resistive or Ohmic losses within the antenna. It is controlled by the radiation efficiency of the element of the antenna that radiates the RF energy. For most antennas this is high and close to unity. Therefore the radiation efficiency does not have a major effect on the parabolic reflector antenna gain and is normally ignored.
  • Aperture Taper Efficiency:   The aperture taper efficiency is denoted as kt above. It affects the antenna gain because the whole parabolic reflector needs to be properly illuminated for the optimum gain to be achieved. If parts of the surface are not optimally illuminated by the radiated energy from the radiator then the parabolic reflector gain will be reduced. The optimum performance is achieved when the centre is illuminated a little more than the edges.
  • Spillover Efficiency:   The spillover efficiency is denoted as ks above. Any energy that spills over the edge of the reflector surface will reduce the efficiency and hence the parabolic reflector antenna gain. In the ideal case, the reflector surface needs to be equally and fully illuminated and none should spill over the edge. In the real case this is not viable and some reduction in efficiency, and hence the antenna gain is experienced.
  • Surface Error :   In order to provide the highest levels of parabolic reflector antenna gain, the surface must follow the parabolic contour as accurately as possible. Deviations from this will result in poor reflection accuracy. However it is possible to use a gauze for the reflector to reduce weight and wind resistance provided that the holes in the gauze or mesh are small in comparison with a wavelength. The width of the slots or holes in the reflective metal mesh must be less than λ/10.
  • Cross Polarization :   As with any other antenna the polarisation of the transmitted and received signals must match otherwise there is a loss equal to the sine of the angle between the polarisations, assuming linear polarisation.
  • Aperture Blockage:   The physical structure of the feed and other elements of the antenna often mask part of the reflector. This naturally reduces the efficiency and hence the antenna gain. This factor needs to be accommodated within the antenna gain calculation.
  • Non-Single Point Feed:   The focal point of the reflector is a single point. However all antennas have a finite size and therefore this will mean that the antenna extends outside the focal point of the reflector. The larger the radiating element with respect to the reflecting surface, the more of a problem this is and the larger impact it has on the antenna gain.

The term km is used to denote the various miscellaneous efficiency elements that are often more difficult to determine. These include those due to surface effort, cross polarisation, aperture blockage, and the non-single point feed.


Parabolic antenna beamwidth calculation

As the gain of the parabolic antenna, or any antenna, increases, so the beamwidth falls.

Normally the beamwidth is defined as the points where the power falls to half of the maximum, i.e. the -3dB points on a radiation pattern polar diagram.

It is possible to estimate the beamwidth reasonably accurately from the following formula.

The approximate formula to determine the beamwidth of a parabolic reflector antenna between the two -3dB half power points in terms of its diameter and the operational wavelength.

Where:
    G is the gain over an isotropic source in dB
    D is the diameter of the parabolic reflector
    λ is the wavelength of the signal

All dimensions must be in the same units for the calculation to be correct, e.g. both diameter and wavelength in metres, or both in feet, etc..


Optimising parabolic antenna gain

To provide the optimum illumination of the reflecting surface, the level of illumination should be greater in the centre than at the sides. It can be shown that the optimum situation occurs when the centre is around 10 to 11 dB greater than the illumination at the edge. Lower levels of edge illumination result in lower levels of side lobes.

The reflecting surface antenna forms a major part of the whole system. In many respects it is not as critical as may be thought at first. Often a wire mesh may be used. Provided that the pitch of the mesh is small compared to a wavelength it will be seen as a continuous surface by the radio signals. If a mesh is used then the wind resistance will be reduced, and this provides significant advantages.

By Ian Poole


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