What feed is best for your dish This analysis and visual output helps you make the choice

By Paul Wade, N1BWT

Achieving optimum performance from a microwave dish antenna requires that the feed antenna be matched to the parabolic reflector. Traditionally, we have relied on rules of thumb to choose a feed for the dish. Alternatively, a computer program can analyze performance of a feed antenna based on measured or calculated radiation patterns and, more importantly, present the data in a graphical format for easy comprehension. This tool is used to explore a number of published feed designs in an effort to enhance understanding of the performance of dish antennas and feeds.

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Parabolic Antenna Overview

Since I described parabolic dish antenna fundamentals in detail in a previous paper, "Practical Microwave Antennas," a short review of key points should suffice here.1 Figure 1 illustrates the operation of the dish antenna: A feed antenna at the focus of the parabola illuminates (radiates energy toward) the reflector, which reflects that energy into a narrow beam. Part of the feed antenna radiation misses the reflector; this loss is called spillover. Another part of the feed energy is reflected back into the feed antenna and doesn't become part of the main beam; this loss is referred to as feed blockage.

Ideally, all areas of the reflector

1 Notes appear on page 33.

should be illuminated with equal energy from the feed. Figure 2 shows this desired feed pattern as a broken line; since the edges of the parabolic curve are farther away from the focus than the center of the curve, more energy is required at the edges than at the center, but with no energy missing the reflector. An additional requirement is that all the feed energy be in phase, so that it appears to be radiated from a single point at the focus. The desired radiation pattern cannot be realized with real feed antennas, so perfectly uniform illumination cannot be achieved. Figure 2 also shows an idealized typical feed antenna pattern; the difference between the desired feed pattern and the actual feed radiation pattern results in illumination loss because some areas of the reflector are unable to work as effectively as others, as well as the spillover loss of the energy that misses the reflector and continues in an undesired direction.

For each reflector, we try to choose a feed that provides a compromise of illumination loss and spillover loss that yields maximum performance, which we measure by aperture efficiency, a comparison of the actual gain to the maximum theoretical gain achievable for the same aperture area. The traditional rule of thumb for this compromise says that best efficiency occurs when the illumination energy is 10 dB down at the edge of the dish, so the feed should be designed for a radiation pattern which is 10 dB down at the edge of the dish. It isn't necessary to do this for each individual dish; all dishes with the same f/D, the ratio of focal length to diameter, have the same geometry regardless of reflector diameter. Thus, all dishes with the same f/D can use the same feed design, and good feed designs are available for several common values off ID.

Efficiency Calculation

The aperture efficiency of a dish antenna is the amount energy concentrated into the beam divided by the total energy radiated by the feed. The efficiency can calculated by integrating (remember calculus?) the feed pattern radiated over the area of the reflector and dividing the result by the total integrated feed pattern. When this calculation was done by hand, it was usually done by approximating the feed pattern with an idealized cos" feed pattern (n = 3 in this example) as shown in Figure 3, making the integration much easier. With a computer, we can do numerical integration of actual feed patterns, performing the tedious calculations for many data points.

The numerical integration routine I used is borrowed from a BASIC program by W7PUA,2 which is based on a 1947 paper by Cutler3.1 translated the routine to C++, then added some enhancements:

• The data interpolation is more flexible to use whatever feed pattern data is available,

• Feed blockage loss is calculated, and

• The output is graphical for visual comprehension.

I find that a simple curve is easier to understand than tables of numbers or long descriptions. The output format is PostScript, which can be displayed or printed using the free Ghostscript software.4

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