Gain = 10·log10(η(πD/λ)²) dBi.
HPBW ≈ k·λ/D with k = 70° (common engineering convention for
a typically-tapered circular aperture; uniform illumination gives k ≈ 58.4°).
First-null BW ≈ 2.44λ/D rad. Focal length f = D·(f/D);
depth d = D²/(16f); far field at 2D²/λ.
Pyramidal horn
Optimum-gain pyramidal horn per Balanis ch. 13: solves design equation (13-56) for
χ by Newton iteration (bisection fallback), starting at χ₁ = G₀/(2π√(2π)).
Then ρe = χλ, ρh = (G₀²/8π³)λ/χ,
a₁ = √(3λρh), b₁ = √(2λρe).
Equal axial lengths pe = ph make the horn physically realizable.
Verification recomputes G = (4π/λ²)·0.51·a₁b₁
(≈51% aperture efficiency of the optimum horn).
Design file
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