For a hydrogen-line (1420.405 MHz) cantenna, the “ideal length” depends on which style of design you’re aiming for. A cantenna is really a short section of cylindrical waveguide, so its diameter matters more than its length — but length still affects efficiency and pattern.

Below is the practical answer used by radio astronomers:

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⭐ 1. Waveguide Diameter (Most Important)

Cutoff frequency for circular waveguide:

fc = (1.8412 * c) / (2 * π * a)

Where:

c  = 3e8 m/s

a  = radius of can

fc = cutoff frequency

For the hydrogen line:

f0 = 1420.405 MHz

Best practice:

fc ≈ 0.75 to 0.80 * f0  

=> fc ≈ 1.05 to 1.15 GHz

Solving gives:

diameter ≈ 150–160 mm

(About 6.0–6.25 inches).

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⭐ 2. Ideal Cantenna Length

Free-space wavelength:

lambda0 = c / f0

lambda0 = 3e8 / 1.420e9

lambda0 ≈ 0.211 m  (≈ 21.1 cm)

Guided wavelength λg inside the can is slightly longer:

lambda_g ≈ 24–26 cm

Rule of thumb:

ideal_length ≈ 0.5 to 1.0 * lambda_g

Therefore:

ideal_length ≈ 12–26 cm  (5–10 inches)

Most hydrogen-line cans use:

18–22 cm  (7–9 inches)

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⭐ 3. Probe Dimensions & Position

Quarter-wave probe in free space:

lambda0 / 4 ≈ 21 cm / 4 ≈ 5.3 cm

Shortened inside waveguide:

probe_length ≈ 45–50 mm

probe_offset_from_back ≈ 45–55 mm

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📌 Summary (ASCII-ready)

CAN DIAMETER: 150–160 mm (6–6.25 inches)

CAN LENGTH:   18–22 cm (7–9 inches)

LENGTH RANGE: 12–26 cm (5–10 inches)

PROBE LENGTH: 45–50 mm

PROBE OFFSET: 45–55 mm

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