Horn Antenna Simulator: Aperture Gain & Beamwidth Calculator

simulator intermediate ~10 min
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G = 19.8 dBi — standard gain horn

A pyramidal horn with 5λ × 4λ aperture at 10 GHz produces 19.8 dBi gain with E-plane beamwidth of 14° and H-plane beamwidth of 13.4° — a typical standard gain horn for microwave measurements.

Formula

G = 10 log₁₀(4π × ε_ap × A_w × A_h / λ²) dBi
θ_E ≈ 56° × λ / A_h (E-plane HPBW)
θ_H ≈ 67° × λ / A_w (H-plane HPBW)

The Natural Radiator

A horn antenna is the simplest and most intuitive way to launch electromagnetic energy from a waveguide into free space. Just as cupping your hands around your mouth projects sound directionally, flaring a waveguide into a horn shapes the electromagnetic wave into a directed beam. First used by Jagadish Chandra Bose in his 1897 microwave experiments, horn antennas remain indispensable in microwave engineering, satellite communications, and antenna measurement laboratories.

Aperture & Gain

The gain of a horn antenna is fundamentally determined by its aperture area relative to the wavelength squared. A larger aperture captures (or radiates) more wavefront area, producing a narrower beam and higher gain. However, the aperture illumination is not uniform — it tapers toward the edges — reducing the effective area. The aperture efficiency factor (typically 50-60%) accounts for this taper, phase errors, and spillover losses.

E-Plane and H-Plane Patterns

A pyramidal horn has different beamwidths in the two principal planes because the aperture field distributions differ. In the E-plane (parallel to the electric field), the illumination has a cosine taper; in the H-plane, it is more uniform. This asymmetry makes the E-plane beamwidth narrower per unit aperture than the H-plane. Corrugated horns use circumferential grooves to equalize the two planes, producing a symmetric, low-sidelobe beam ideal for reflector feeds.

Standard Gain Horns

Because horn gain can be calculated from geometry with remarkable accuracy (±0.3 dB), standard gain horns serve as the primary calibration reference in antenna measurement. A pair of identical horns, separated by a known distance, allows absolute gain determination using the Friis transmission equation with no other reference needed. Every antenna range in the world relies on this simple, elegant calibration technique.

FAQ

What is a horn antenna?

A horn antenna is a waveguide whose cross-section gradually increases (flares) to form an aperture that radiates into free space. The flare provides a smooth impedance transition from the waveguide to free space, resulting in low reflection loss and predictable radiation patterns. Horns are widely used as feeds for dish antennas and as gain standards.

How is horn antenna gain calculated?

Gain depends on aperture area and efficiency: G = 4πε_ap × A / λ², where A is the physical aperture area and ε_ap is the aperture efficiency (typically 0.5-0.6). Larger apertures produce higher gain but require longer horns to maintain acceptable phase error across the aperture.

What is an optimum horn?

An optimum horn maximizes gain for a given horn length by choosing aperture dimensions that produce exactly 3 dB of phase taper across the aperture. For a pyramidal horn, the optimum E-plane aperture is A_h = √(2λL) and the H-plane aperture is A_w = √(3λL).

Why are horn antennas used as gain standards?

Horn antennas have highly predictable gain that can be accurately calculated from dimensions alone, with uncertainty typically less than 0.5 dB. They are broadband, mechanically simple, and have no critical tuning adjustments. This makes them ideal references for calibrating other antennas through gain comparison measurements.

Sources

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