## Saturday, February 26, 2022

### A Ham Radio Series 31 - Very Directional, Very High Gain Antennas

There's a niche area of directional antennas that I want to touch on briefly.  The highest gain antennas are going to tend to be the ones that are extremely directional.  Remember the analogy of antenna gain coming from "squeezing the balloon" of the fields coming from the antenna?  The more the fields get squeezed, the narrower the radiated beam gets and the higher the gain goes.

The king of antenna gain is the parabolic dish antenna.  These are the ones that are used for all of the biggest radio telescope observatories, the Deep Space Network, and even for home satellite TV dishes.

The National Radio Astronomy Observatories Very Large Array in New Mexico - also used by the Search for Extraterrestrial Intelligence.  That's the NRAO VLA also used by SETI for the acronym-aware.  NRAO photo from the SETI Institute.

Regardless of size, they're all governed by the same physics.  The gain of a parabolic dish antenna in dB with respect to an isotropic antenna is given by this equation:

where k is a constant for the efficiency, typically 0.5 to 0.6, D is the diameter in meters and the Greek letter Lambda is the wavelength in meters.  It's important to note that the units cancel out algebraically, so while the original said meters, there's really no particular reason to use meters.  Just make sure if you use feet in the diameter, you use feet in the wavelength.  Since the gain is the ratio of dish diameter to the wavelength, the bigger the dish, the higher the gain.  The higher the gain, the narrower the beam.  And just like the gain, there's a simple expression for the beamwidth

(yes, that's 70 - seventy).  So let me create an example based on an aviation weather radar antenna I used to work on.  It's diameter was 0.6 meter, with a frequency of 10.00 GHz.  Wavelength is C/f or 3*10^8/10.00*10^9, or 0.03 m (3cm).  The gain in dBi is
Since the beamwidth depends on the ratio of lambda to D, or 0.03/0.6, BeamW is 70*0.03/0.6 or 3.5 degrees.

That requires quite a bit more precision in pointing and feeding back the direction than your typical HF or VHF antenna, and one reason dishes tend to only be used by microwave experimenters in the ham bands.  All of those dishes in the Very Large Array are computer controlled to all point at their required target - and don't forget they need to track that object across the sky just like an optical telescope.  In the case of the weather radar these numbers approximate, it was precisely driven by stepper motors so that the radar sent out a pulse and waited 8-1/3 milliseconds for the return echoes before stepping over for another pulse.

Have you seen dish antennas that aren't circular?  Many of the small antennas people get on their houses for various services are more elliptical than circular.  Those antennas produce radiation patterns that are also elliptical - they're receive better and the beamwidth is narrower in the direction that the dish is bigger.  For Satellite TV, that's OK.  The loss of gain happens in directions away from the orbit that the signal is coming from.  That part of the antenna wasn't needed.  Also note, they don't need the tracking motors because the satellites aren't moving in the sky.  They always appear to be in the same spot in the sky.

So what's up with all this?  Why do I go down this road?  Because there are ways to do these things without parabolic dishes that I want to talk about.

1. I always thought that the reason for the elliptical reflector was that the feed was off-center and not at prime focus. If the LNB was at prime, the mounting would be a lot more complicated. By using an off-center arrangement, the LNB can be attached to an arm jutting out from the bottom of the dish.

1. Switching to the off axis mount might well have been for ease of manufacture, and it might have been for cutting cost by using a dish just big enough in the important direction and not caring about a symmetrical pattern. My point was the gain is different in both directions and depends on size.

The ones I have experience with were bigger than the small aperture home terminals, but the dish was a segment of a paraboloid and the LNB was positioned at prime focus. One could never do that with optics because of the distortion, but that doesn't matter in radio.

2. How does the dish reflect? It is metallic? How is the diameter and parabolic equation established?

Sorry for the questions if off topic, I am curious. I am a retired EE, but my field was digital and analog. My co-workers and I considered RF to be a black art, and those who were good at it were a class of magicians.

1. They are either metal, like the giant VLA radio telescopes, or they are plastic with a fine metal screen embedded just below the surface. The diameter measurement is just that - tape measure stretched across the dish. In the air, not lying on the surface.

3. Our Uplink antennas were 13 Meter dishes, operating at ~14GHz. We had 64dB of gain, and a .09 degree half-power beamwidth. Paranoid about keeping it on the bird? YOU BETCHA'!

4. 1st rule of antennas: all dimensions are in wavelengths. 2nd rule, beamwidth is approximately the inverse of aperture, in radians. Radians to degrees is about 70. This works for dishes, circular arrays, even linear arrays. IIRC it even works for the diffraction limits of telescope lenses.

1. 1st rule of antennas: all dimensions are in wavelengths. 2nd rule, beamwidth is approximately the inverse of aperture, in radians.

Exactly right and worth putting on a sign on your wall.

5. What is the surface requirement in terms of wavelength? I have designed a few carbon fibre parabolics and looked over their manufacture but never thought about surface roughness.

1. If two areas on the surface were 1/2 wavelength higher/lower than each other, their reflections would cancel, so that's as bad as it gets. The general rule is to keep the surface within 1/4 wavelength and (in optics) it's generally recognized that getting the surface better than 1/10 wave difference doesn't add any improvements to the image. They call that "diffraction limited."

Radio isn't optics because we're not forming an image, so 1/4 wavelength is probably a "good enough" standard. wavelength = c/f where c is the speed of light and f the frequency. So for a 14 GHz antenna (about where DirecTV is - I think) the surface should be within about 0.2" peak to peak of the same curve everywhere.