The Parabolic Reflector Antenna (Satellite Dish) - 3

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The fields across the aperture of the parabolic reflector is responsible for this antenna's radiation. The maximum possible antenna gain can be expressed in terms of the physical area of the aperture:

peak gain of dish antenna as a function of the aperture area

The actual gain is in terms of the effective aperture, which is related to the physical area by the efficiency term (permittivity, epsilon or dielectric constant). This efficiency term will often be on the order of 0.6-0.7 for a well designed dish antenna:

efficiency applied to gain of dish antennas

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector. The antenna efficiency can be written as the product of a series of terms:

efficiency of antenna

We'll walk through each of these terms.

Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses, as discussed on the efficiency page. Since horn antennas are often used as feeds, and these have very little loss, and because the parabolic reflector is typically metallic with a very high conductivity, this efficiency is typically close to 1 and can be neglected.

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is across the antenna's aperture. In general, an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields). However, the aperture fields will tend to diminish away from the main axis of the reflector, which leads to lower gain, and this loss is captured within this parameter.

This efficiency can be improved by increasing the F/D ratio, which also lowers the cross-polarization of the radiated fields. However, as with all things in engineering, there is a tradeoff: increasing the F/D ratio reduces the spillover efficiency, discussed next.

Spillover Efficiency

The spillover efficiency spillover efficiency is simple to understand. This measures the amount of radiation from the feed antenna that is reflected by the reflector. Due to the finite size of the reflector, some of the radiation from the feed antenna will travel away from the main axis at an angle greater than , thus not being reflected. This efficiency can be improved by moving the feed closer to the reflector, or by increasing the size of the reflector.

Other Efficiencies

There are many other efficiencies that I've lumped into the parameter . This is a major of all other "real-world effects" that degrades the antenna's gain and consists of effects such as:

  • Surface Error - small deviations in the shape of the reflector degrades performance, especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

  • Cross Polarization - The loss of gain due to cross-polarized (non-desirable) radiation

  • Aperture Blockage - The feed antenna (and the physical structure that holds it up) blocks some of the radiation that would be transmitted by the reflector.

  • Non-Ideal Feed Phase Center - The parabolic dish has desirable properties relative to a single focal point. Since the feed antenna will not be a point source, there will be some loss due to a non-perfect phase center for a horn antenna.

    Calculating Efficiency

    The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antenna's radiation pattern. Instead of introducing complex formulas for some of these terms, we'll make use of some results by S. Silver back in 1949. He calculated the aperture efficiency for a class of radiation patterns given as:

    typical patterns used to construct other radiation patterns

    TYpically, the feed antenna (horn) will not have a pattern exactly like the above, but can be approximated well using the function above for some value of n. Using the above pattern, the aperture efficiency of a parabolic reflector can be calculated. This is displayed in Figure 1 for varying values of polar angle and the F/D ratio.

    aperture efficiency

    Figure 1. Aperture Efficiency of a Parabolic Reflector as a function of F/D or the angle , for varying feed antenna radiation patterns.

    Figure 1 gives a good idea on design of optimal parabolic reflectors. First, D is made as large as possible so that the physical aperture is maximized. Then the F/D ratio that maximizes the aperture efficiency can be found from the above graph. Note that the equation that relates the ratio of F/D to the angle can be found here.

    In the next section, we'll look at the radiation pattern of a parabolic antenna.

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