To: W4DEX es The Microwave Group. From: Dick, K2RIW 17 Apr 2003. Re: Can 80 to 90% Dish Efficiency be Achieved? -- Yes, and No (it better be big).
Comments on Antenna Efficiency
INTRODUCTION -- In his 4/15/03 submittal, Kent, WA5VJB quoted the Johnson & Jasik "Antenna Engineering Handbook", 2nd edition, 1984, page 36-9 as saying that the reference #16 article authors (Galindo-Israel, Mittra and Cha) are claiming that, "Their analytical techniques are reported to result in efficiencies in the 80 to 90 percent range". Kent is accurately quoting the Handbook, but there is a problem -- I believe the quote is being taken out of context. I'll supply 3 pieces of evidence of this, and I'll provide a further discussion of possible Dish Efficiencies.
(1) Chapter 36 of the Handbook is devoted to "Earth Station Antennas" that are 60 to 300 wavelengths in diameter. As you are about to find out, some great "efficiency magic" is possible when you have a lot of wavelengths to play with.
(2) The type of antennas being discussed on page 36-9 are Double-offset Geometry dish antennas. This means that the feed horn is offset from the hyperbolic-like sub-reflector, and the sub-reflector is offset from the parabolic-like main reflector. These are rather complicated geometries that our Microwaver's may not be able to use, for some time to come (explained below).
(3) The "Analytical Techniques" being discussed are computer-modeled theoretical dish antennas that are using a Cassegrainian-like geometry that employs a "shaped" reflector and sub-reflector. This means that the main reflector is an intentionally distorted parabola, and the sub-reflector is an intentionally distorted hyperbola. The intentional distortions are being used to simultaneously improve the "Illumination Taper" while still providing essentially no unintended "Phase Taper" The computer-modeling techniques had to use "Diffraction Optimization" techniques for which there is no exact Geometric Optics (GO) solution -- whew!
MAXIMUM DISH EFFICIENCY -- I wish we had access to 90% aperture efficient Dish Antennas, and Horn Antennas. We usually do not, and you will soon see why. "Aperture Efficiency" and Sidelobe Levels are often misunderstood, and the detriment they cause is often misquoted. I hope the following material will help.
IT'S ALL IN THE FEED SYSTEM -- The requirements for high efficiency are easy to state, but quite hard to achieve. So, what's required for 100% efficiency -- no Phase Error (no phase taper), and no Amplitude Taper. If my great new "wizz-bang" feed horn system could provide exactly the same number of watts per square cm across my parabolic reflector, no spill-over energy at the edges, and no phase errors, than I'd have what's called a 100% Aperture Efficient dish antenna system.
TRANSMISSION & RECEPTION -- During transmit, almost every possible watt emitted by the antenna would be directed toward the target, and during reception, almost every "possible bit" of the signal hitting the antenna (from the correct direction and polarization) would be absorbed and sent down the feed line -- and it would often peg the S meter. If I had such an antenna, there would be no way that I could improve the transmission or reception, without increasing the size of the antenna.
SIDE LOBES & SCATTERING -- However, newly-instructed antenna engineers are usually quite surprised to find that a theoretical 100% Aperture Efficient (round dish) antenna will still have 1st side lobes that are about 17.5 dB down, and on reception the antenna still has a considerable "Scattering Area" that will show up on a good Instrumentation Radar.
SIDE LOBE ORIGIN -- The side lobes are the result of the Diffraction Effect, caused by the abrupt fall-off of signal at the edge of the antenna. Simplistically, you could say that Mother Nature doesn't like a sharp discontinuity, and she responds by creating those pesky side lobes (they're almost always there).
SCATTERING ORIGIN -- A Free Space vacuum has an "impedance" of 120*Pi (377 ohms). The 100% Aperture Efficient, highly directional, dish antenna, will absorb the maximum signal if it also presents a matched impedance of 377 ohms. However, now there is a 377 ohm antenna across (in parallel with) the free space impedance of 377 ohms. The new local impedance is now 377/2 = 188.5 ohms. A free-space planar wave entering the vicinity of the antenna will "sense" the change in impedance, and a portion of the wave will become scattered at the impedance discontinuity.
MAKE IT DISAPPEAR -- There are ways to make the antenna side lobes as low as you like, and there are ways to lower the Scattering Area as much as you please. But, all of these techniques must be accompanied by an Aperture Efficiency that is considerably lowered -- you can't have it both ways.
IT'S ALL IN THE SIZE OF IT -- I can almost achieve that nearly ideal Illumination Taper (0.0 dB) and Phase Taper (0.0 degrees). However, to have that much control over the radiation characteristics (primary pattern) of the Feed will require the horn to be made from a very large number of radiating elements that have a carefully-controlled amplitude and phase at each element. Such a "Cluster Feed" would really be an elaborate Phase Array Antenna, and I don't think you can come close to achieving the desired primary pattern with less than 1,000 elements -- a feed with about 38 wavelengths of diameter (43 inches [1.1 meters] at 10 GHz).
SMALL CASSEGRAINS -- I'm always amused when I encounter
an enthusiastic new Microwaver who becomes enthralled with a small-dish
Cassegrain antenna system. Quite often they end up with a sub-reflector
design of 1.5 inch diameter at 10 GHz, and they start to worry about the
accuracy requirement for the hyperbolic shape. There is a tried-and-true
rule of thumb among informed antenna engineers, "don't even consider a
Cassegrain system unless the sub-reflector is at least 10 wavelengths in
CONCLUSION -- Concerning those super Aperture Efficiencies we sometimes hear about, they are possible, but difficult to achieve. And, I doubt we will see many of these in our back yards, unless we are talking about elaborate antenna designs that are hundreds of wavelengths in main dish diameter.