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Waveguide and horn calculator

Why nothing gets through below the cutoff

A waveguide is not a pipe the signal “flows” along: the wave zigzags inside it, bouncing off the walls. For that zigzag to exist at all, half a wavelength has to fit between the walls. If it does not fit, the field decays exponentially and the guide becomes a dead end.

a 22.86 mmb 10.16 mmfc = c / 2ahorn
The cutoff frequency is set by the broad wall a: below it a wave does not propagate in the guide
Standard size
Broad wall a (mm)
Narrow wall b (mm)
Operating frequency (MHz)
Calculate the horn
Horn aperture A (mm)
Horn aperture B (mm)
Waveguide
TE10 cutoff frequency
TE20 cutoff frequency
Recommended range
Free-space wavelength
Guide wavelength λg
TE10 wave impedance

📐 The formulas​

Cutoff frequencies:

fc(TE10) = c / (2a)        fc(TE20) = c / a        fc(TE01) = c / (2b)
Working range: 1.25·fc … 1.9·fc

Within the working range:

λg = λ₀ / √( 1 − (fc/f)² )
Z(TE10) = 376.73 / √( 1 − (fc/f)² )

Pyramidal horn:

G[dBi] = 10 × log10( 0.51 × 4π × A·B / λ² )
optimum length:  A² = 3·λ·Lh,   B² = 2·λ·Le
HPBW(E) ≈ 54°·λ/B      HPBW(H) ≈ 78°·λ/A

Symbols:​

  • a — the broad wall, b — the narrow one; it is a that sets the cutoff
  • A, B — the horn aperture dimensions
Where this calculator stops:
  • Below cutoff, λg and the impedance are meaningless — the calculator warns you and does not show them
  • Above the TE20 cutoff several modes propagate and the single-mode model no longer applies
  • The 0.51-efficiency horn gain formula is for an optimum horn; in a short one phase error eats the gain
  • Wall losses are not calculated: for copper at 10 GHz they are tenths of a dB per metre

🎯 In practice​

  • Choosing a waveguide for a band. WR-90 is 8.2–12.4 GHz, and the calculator shows where those numbers come from.
  • A dish feed. A horn of a given aperture and the beamwidth it really gives.
  • Checking a home-made transition. You need λg to place the coaxial probe correctly — a quarter wave from the short.
Practical advice:
  1. The coaxial probe goes λg/4 from the closed end — which is why λg matters more here than λ₀.
  2. A horn with an aperture below 2λ adds almost nothing over an open waveguide end.
  3. Aluminium waveguide works perfectly well at 10 GHz: the extra loss over copper is a fraction of a decibel.
  4. Flanges with poor contact lose more than a metre of waveguide does.

© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.

How to cite this calculator
UR3PKI. «Waveguide and horn calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/antennas/waveguide (licence CC BY-NC-SA 4.0).

The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.

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