Short answer: it scales linearly with wavelength.
Longer answer (the bit you actually care about 🙂):
For a hydrogen-line horn (≈1420 MHz, λ ≈ 21 cm), the flare geometry is set in terms of wavelengths, not absolute size. If you scale the antenna up or down for a different frequency, every linear dimension of the flared section scales in direct proportion to λ.
What that means in practice
If you increase the overall size by a factor k (or go to a frequency 1/k as high):
- Horn length → × k
- Aperture width & height → × k
- Flare angle → stays the same
- Phase error across the aperture → stays the same
- Beamwidth → stays the same (in degrees)
- Gain → stays the same (in dBi)
So a horn designed at 1420 MHz will behave identically at, say, 710 MHz if you double all linear dimensions.
Why the flare exists (and why scaling works)
The flared section is doing three things:
- Impedance transformation
Gradually transitions from waveguide impedance to free space (≈377 Ω) - Phase correction
Keeps the aperture field close to planar so the beam stays tight - Edge illumination control
Sets sidelobe level and efficiency
All three depend on electrical length, i.e. distance measured in wavelengths — hence the clean linear scaling.
Typical hydrogen-line horn proportions (rules of thumb)
For ~1420 MHz:
- Aperture size:
~1.5–2.5 λ across for a compact horn
~3–5 λ for higher efficiency / lower sidelobes - Horn length:
~2–4 λ for pyramidal horns
Longer if you want very low phase error - Flare half-angle:
Typically 10–15° (kept constant when scaling)
One important caveat 🚨
Scaling only works cleanly if:
- You keep the same mode (usually TE₁₀)
- The waveguide cutoff ratio is preserved
(i.e. guide wavelength / free-space wavelength unchanged)
If you just “make it bigger” without adjusting waveguide dimensions properly, you can:
- Excite higher-order modes
- Ruin aperture phase
- Lose gain