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# RE: DISH BEAM WIDTH

```> Hello All,
> I recently acquired a TVRO 12 foot dish, with the mesh
> reflector. I have been trying to calculate the 3db beam width
> in degrees, the books I have are not clear on the formula.
> Does anyone have the correct math formula ?

The beamwidth of the dish is not affected by the f/D -- it is dependent on
the size and wavelength.

In general, the beamwidth of an aperture that is X wavelengths in size is
a numerical constant of between 1 and 2, which is a function of such things
as
- is the aperture square or round?
- how is power transmitted by the feed distributed across the aperture?
(i.e. are the edges illuminated as brightly as the center)

As an example, in University Optics classes, a standard example is a
uniformly illuminated circular aperture, which yields a beamwidth of 1.22/X
radians = 70/X degrees. The 1.22 number is often called the "Airy Criterion"
(which arises from the size of diameter of the J1 Bessel function).

So, depending on the illumination, your 12' dish is 3.66 meters in diameter.
At a wavelength of 13 cm, the quantity I called X is about 28.15
wavelengths. Therefore the beam will be about

(Airy criterion = 1.22)/(28.15 wavelengths) = .043 radians = 2.5
degrees.

In a practical sense, to use a big dish you need to point it to an accuracy
of better than a ~1/5 of a beamwidth, that is about 0.5 degrees, which is
the size of the moon. This requirement is often the killer for many amateurs
using BUDs (Big Ugly Dishes). BTW --  In case you think of getting a signal
randomly, there are about 4000 beam "spots" on the sky!

Your calculation of f/D is necessary to determine what kind of feed to use
in the dish. You want the pattern of the feed concentrate power on the dish
and start to fall off by the edge. Taking AL7EB's comments , you dish has
f/D of about 0.4. This is not surprising and is very common for "simple"
dishes. The pattern of a dipole or an open-throated piece of waveguide
pretty well matches f/D=0.4 and so this depth has been used for years. When
you look at the dish from the feed, the rim of the dish is about a 60 degree
angle from the center (120 deg full width). An f/D=0.4 dish has the feed
sticking up about twice the depth of the dish.

Some modern dishes have f/D in the 0.25 to 0.3 range. When viewed from the
side, the feed is buried in the dish. This requires a feed that has power
out to 180 degrees, which is not easy to do!

73, Tom

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