The Parabolic Reflector Antenna (Satellite Dish)  3
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:
The actual gain is in terms of the effective aperture, which is related to the physical area by the efficiency term (). This efficiency term will often be on the order of 0.60.7 for a well designed dish antenna:
Understanding this efficiency will also aid in understanding the tradeoffs involved in the design of a parabolic reflector. The antenna efficiency can be written as the product of a series of terms:
We'll walk through each of these terms.
Radiation EfficiencyThe 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 EfficiencyThe aperture radiation efficiency is a measure of how uniform the Efield is across the antenna's aperture. In general, an antenna will have the maximum gain if the Efield is uniform in amplitude and phase across the aperture (the farfield 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 crosspolarization 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 EfficiencyThe 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 EfficienciesThere are many other efficiencies that I've lumped into the parameter . This is a major of all other "realworld effects" that degrades the antenna's gain and consists of effects such as:
Calculating EfficiencyThe 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:
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 and the F/D ratio.
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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