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Antenna

Horn Antenna Gain & Beamwidth Calculator

Calculate pyramidal horn antenna gain, E/H-plane beamwidths, and effective aperture area. Design horn antennas for microwave systems. Free, instant results.

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Formula

G=10⋅log10(4π⋅η⋅A/λ2)G = 10·log₁₀(4π·η·A/λ²)
G— Gain (dBi)
η— Aperture efficiency (≈0.5)
A— Aperture area (W×H) (m²)
λ— Wavelength (c/f) (m)
θ_E— E-plane HPBW ≈ 51λ/H (degrees)

How It Works

Horn antenna calculator computes aperture dimensions, gain, and beamwidth for waveguide-fed radiators — microwave engineers, antenna test range operators, and satellite ground station designers use this to design gain standards and feeds for reflector antennas. Gain is determined by aperture area: G = eta * 4*pi*A/lambda^2, where eta is aperture efficiency (typically 0.5-0.7) and A is the horn mouth area, per Balanis's 'Antenna Theory' (4th ed.) and IEEE Standard 149-2021.

Three horn types serve different applications: Pyramidal horns flare in both E and H planes, providing symmetric patterns with 50-70% efficiency and 10-25 dBi gain. Sectoral horns flare in one plane only (E-plane or H-plane), useful for specific pattern shaping. Conical horns fed from circular waveguide provide circularly symmetric patterns ideal for reflector feeds. Standard gain horns (SGH) are calibrated to +/-0.5 dB accuracy for antenna measurements.

Optimum horn design balances aperture size against phase error. For pyramidal horn: L_e = A_e^2/(3*lambda) and L_h = A_h^2/(2*lambda), where L is axial length and A is aperture dimension. A 10 GHz horn with 15 dBi gain requires approximately 60 mm aperture and 100 mm length. Corrugated horns achieve 75-80% efficiency and extremely low sidelobes (< -30 dB) through surface corrugations that equalize E and H plane patterns — preferred for precision measurements and satellite feeds.

Worked Example

Problem: Design a standard gain horn for 10 GHz antenna measurements requiring 17 dBi gain.

Design per IEEE Std 149-2021 methodology:

  1. Wavelength: lambda = c/f = 3e8/10e9 = 30 mm
  2. Required aperture area from gain equation:
G = 17 dBi = 50 (linear) eta = 0.6 (typical pyramidal horn efficiency) A = G * lambda^2 / (4*pi*eta) = 50 * 0.03^2 / (4*3.14159*0.6) = 59.7 cm^2

  1. Aperture dimensions (square aperture for symmetric pattern):
A_e = A_h = sqrt(59.7) = 7.73 cm = 77 mm
  1. Optimum axial lengths for phase uniformity:
L_e = A_e^2 / (3*lambda) = 77^2 / (3*30) = 66 mm (E-plane) L_h = A_h^2 / (2*lambda) = 77^2 / (2*30) = 99 mm (H-plane) Use longer dimension: L = 100 mm for both planes
  1. Waveguide input: WR-90 (22.86 x 10.16 mm) for X-band
- TE10 cutoff: 6.56 GHz (10 GHz well within operating band) - Waveguide to horn transition: gradual flare over 50 mm
  1. Performance verification (calculated):
- Gain: 10*log10(0.6 * 4*pi * 77^2 / 30^2) = 17.1 dBi (meets specification) - 3-dB beamwidth: 70*lambda/A = 70*30/77 = 27 degrees - First sidelobe: -13 dB (typical for uniformly illuminated aperture)
  1. VSWR: < 1.25:1 over 8-12 GHz with proper waveguide flare design
  1. Calibration: Compare against NIST-traceable standard or use three-antenna method per IEEE 149 for absolute gain determination to +/-0.3 dB accuracy

Practical Tips

  • ✓For antenna range measurements, use standard gain horns calibrated to +/-0.5 dB — commercial SGHs from vendors (Narda, Pasternack, A-INFO) include calibration certificates traceable to national standards
  • ✓Specify corrugated horns for reflector feeds — their symmetric patterns with < -25 dB sidelobes minimize spillover loss and improve overall aperture efficiency by 5-10% versus smooth-wall horns
  • ✓For field measurements, verify horn calibration annually and protect aperture from physical damage — dents or corrosion on horn edges degrade pattern symmetry and gain accuracy

Common Mistakes

  • ✗Neglecting aperture efficiency in gain calculations — theoretical maximum (eta = 1) is never achieved; use eta = 0.5-0.6 for pyramidal, 0.7-0.8 for corrugated horns
  • ✗Ignoring phase error from inadequate horn length — short horns have curved phase front causing gain reduction and increased sidelobes; maintain L > A^2/(2*lambda) for < 45-degree edge phase error
  • ✗Using wrong waveguide size — horn must connect to waveguide supporting dominant mode at operating frequency; WR-90 for 8-12 GHz, WR-62 for 12-18 GHz, WR-42 for 18-26 GHz
  • ✗Assuming constant efficiency versus frequency — efficiency varies across waveguide band due to mode matching and aperture distribution changes; characterize at multiple frequencies for precision work

Frequently Asked Questions

Gain is set by aperture area and efficiency: G = eta * 4*pi*A/lambda^2. Doubling aperture dimensions (quadrupling area) adds 6 dBi gain. Doubling frequency (halving lambda) adds 6 dBi gain for same physical size. Efficiency depends on horn type: smooth pyramidal 50-60%, sectoral 40-50%, corrugated 70-80%. For a 20 dBi gain horn at 10 GHz (lambda = 30 mm) with 60% efficiency: A = 100*0.03^2/(4*pi*0.6) = 0.012 m^2 = 110 mm x 110 mm aperture.
Horns provide predictable, calculable gain based on geometry — no resonance tuning required. Comparison at 10 GHz: Dipole: 2.15 dBi, requires balun. Patch: 6-8 dBi, narrow bandwidth. Horn (100 mm aperture): 17 dBi, inherently wideband. Dish (1 m): 40 dBi, requires feed horn. Horns excel as: (1) Gain standards with +/-0.5 dB accuracy. (2) Reflector feeds with controlled illumination. (3) Wideband antennas (2:1 bandwidth typical). (4) Moderate-gain applications where simplicity is valued.
Options: (1) Larger aperture — practical limit around 20-25 dBi before size becomes unwieldy. (2) Corrugated design — adds 1-2 dB through higher efficiency. (3) Lens correction — dielectric lens equalizes phase across aperture for +1-2 dB. (4) Array of horns — 2x2 array adds 6 dB but requires corporate feed network. (5) Reflector feed — horn illuminating parabolic dish achieves 30-50 dBi combined gain. For maximum gain, use horn as feed for reflector antenna; the horn shapes the illumination pattern while the reflector provides aperture gain.
E-plane sectoral horn flares only in the electric field plane (perpendicular to broad waveguide wall), producing narrow beamwidth in E-plane and wide in H-plane. H-plane sectoral horn flares in the magnetic field plane (parallel to broad wall), producing narrow H-plane beamwidth and wide E-plane. Pyramidal horn flares in both planes, allowing independent control of E and H beamwidths. Conical horn (circular waveguide) has equal beamwidths in all planes. Choose based on required pattern: sectoral for fan beams, pyramidal for pencil beams, conical for circularly symmetric illumination.
Corrugated horns achieve 70-80% efficiency (versus 50-60% for smooth walls) through three mechanisms: (1) Equal E and H plane patterns — corrugations force field distribution to have same beamwidth in both planes, improving reflector illumination uniformity. (2) Low sidelobes (< -25 dB) — reduces spillover past reflector edge, minimizing noise pickup from warm Earth. (3) Low cross-polarization (< -30 dB) — corrugations suppress higher-order modes that cause cross-pol. These properties are critical for satellite earth stations where G/T (gain-to-noise-temperature ratio) determines link performance. Corrugated horns add 20-30% to horn cost but improve system G/T by 0.5-1 dB.

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