What is widest diameter that works effectively for making hydrogen line cantennas?

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Widest usable diameter for a hydrogen-line cantenna

For a round “cantenna” (a short section of circular waveguide) working at the hydrogen line (1420.4 MHz), the widest internal diameter that still gives single-mode operation (only TE11 mode) is about:

D_max ≈ 0.205 m (≈20.5 cm ≈ 8.1 in)

Most practical cantennas use:

120–180 mm (4.7–7.1 in)
with ~154 mm (6 in) being a common sweet spot.

Why: a circular can behaves like an air-filled waveguide. The cutoff frequency of a mode is:

fc = (X_mn * c) / (pi * D)

where

• X_mn = Bessel root for that mode
  • TE11: X_11 = 1.841
  • TE21: X_21 = 3.054
• c = speed of light ≈ 3.0e8 m/s
• D = waveguide diameter (meters)
• fc = mode cutoff frequency (Hz)

For hydrogen line work (f = 1.420e9 Hz), solve for diameter:

1. TE11 cutoff diameter:

D_TE11 = (1.841 * c) / (pi * f)
       ≈ 0.124 m  (12.4 cm)

Below this, the TE11 mode cannot propagate — the cantenna does not work.

2. TE21 cutoff diameter:

D_TE21 = (3.054 * c) / (pi * f)
       ≈ 0.205 m  (20.5 cm)

Above this, TE21 also propagates — pattern and impedance get messy.

So the useful single-mode diameter window is:

12.4 cm  <  D  <  20.5 cm

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Practical guidance

• Best performance is usually around 150–170 mm internal diameter.
• Larger diameters approach the TE21 cutoff and create multiple modes, complicating matching and beam shape.
• Probe placement typically ends up around 0.25–0.40 lambda_g from the back wall, where lambda_g is the waveguide wavelength (longer than free-space 21-cm).

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