Parabolic antenna equations
Gain: G = η · (π·D / λ)² → G(dBi) = 10·log₁₀(G)
Half-power beamwidth: HPBW ≈ 70 · λ / D degrees (uniform-ish illumination)
First-null beamwidth: FNBW ≈ 2.44 · 70 · λ / D ≈ 1.22·... (≈ 2.34 × HPBW for a circular aperture)
Effective aperture: A_eff = η · π·(D/2)²
Far-field (Fraunhofer) distance: R = 2·D² / λ — measure or point beyond this range
where λ = c/f is the wavelength. The narrower the beam, the higher the gain — but also the tighter your pointing accuracy must be. A good rule of thumb is to keep pointing error below ~1/10 of the HPBW to avoid significant pointing loss.
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