Gain-HPBW relation of uniformly illuminated circular dish antennas

Joachim Köppen DF3GJ Kiel, Jul 2018

### Some brief explanations

The green curve is an approximative relation from Kraus:

*gain = 41000/(HPBW_h * HPBW_v)*
which uses the HPBWs (in degrees) in horizontal and vertical direction to estimate the
solid angle Ω

_{A} of the antenna's main lobe. Kraus (Antennas for all Applications,
3rd ed., 1997) writes: "... formulas like [this] ... are useful in the context that if we know
that an antenna has a 1° pencil beam and small minor lobes, its gain is approximately 41 000
or 46 dB, give or take a decibel or two, but not that the result is accurate to 1/10 of a
decibel or better."

The red curve is a more accurate formula which is also consistent with the HPBW-diameter relation

*HPBW = 58.95701° λ/D*_{eff} for evenly illuminated circular dishes.

The mouse position shows HPBW (half power beam width), BWFN (beam width between first nulls),
and the gain in dBi.