Little dry theory here but very handy if you want to see how much gain a dish has in a blink of an eye.
i made these graphs in 2001 with mathlab and converted the graps to gif's.
it would also be possible to make an excel sheet
with these formulas and create your own graphs.
let me explain some things in advance:
w is the wavelength and
0.24 is approx 1240-1300mhz
0.13 is approx 2320-2400mhz
0.09 is approx 3405mhz
and so on.
n is the efficiency of the antenne in the focal point and the dish itself.
100% is not possible but 60% is quiet the average.
dish apperture is the diameter of
h(x) is the gain of the system in dBd.
on 23cm or
23dBd on 13cm or
36dBd on 3cm
in the graphs you can also see that doubling the diameter of the dish will result in a gain of approx. 6db on every frequency.
Formulas for parabolic antenna's
Relationship between the focal point f, diameter D and depth d of a parabolic
f = D^2/16d
(formula corrected now, cant beleive i had this wrong)
The gain in dBd of a parabolic antenna:
G:=10 log [n(Pi*(x/w))^2] -2
x = Diameter of the dish (m)
n = the normalized antenna efficiency (typically .60-.80)
w = wavelength of radiation (m)
-2 because I want the result to be in dBd, not dBi.
Here are some graphs of important frequenties(w in meters).