Short answer: 165 mm is the better choice than 145mm can — it gives a larger aperture (higher gain / narrower beam) while still remaining single-mode for 1420.4 MHz.

Below are the key reasons + practical starting settings you can try.

Why 165 mm is preferable

• Practical guidance used by amateur radio-astronomers places the sweet-spot for hydrogen-line cantennas around ~150–170 mm internal diameter; 165 mm sits inside that range while 145 mm is toward the small end.
• Larger diameter → lower TE11 cutoff, larger effective aperture and better gain / SNR for a weak sky signal, as long as you avoid getting big enough to allow the next higher order mode (TE21) to propagate. Both 145 mm and 165 mm keep TE21 cutoff above 1420 MHz, so both are single-mode, but 165 mm gives the larger aperture with no mode penalty.

Useful computed numbers (for 1420.4058 MHz)

• Free-space wavelength λ₀ ≈ 211 mm.
• TE11 cutoff frequency (circular can) ≈
  • 145 mm dia → fc(TE11) ≈ 1.212 GHz (so 1.42 GHz propagates).
  • 165 mm dia → fc(TE11) ≈ 1.065 GHz.
• TE21 cutoff (higher order) ≈
  • 145 mm → ≈ 2.01 GHz (well above 1.42 GHz).
  • 165 mm → ≈ 1.77 GHz (still above 1.42 GHz).
  (So neither diameter lets TE21 propagate at 1.420 GHz — i.e. both remain single-mode).

Waveguide wavelength (λg) & probe placement — practical starting points

Waveguide wavelength λg = λ₀ / sqrt(1−(fc/f)²). Using the TE11 fc above:

• 145 mm dia → λg ≈ 404 mm → place probe ≈ 0.25–0.40·λg ≈ 100–162 mm from back wall as a tuning range to try.
• 165 mm dia → λg ≈ 319 mm → place probe ≈ 0.25–0.40·λg ≈ 80–128 mm from back wall.
  Many builders report good starting probe positions around 3–3.5 in (≈75–89 mm) for the ~154 mm cans; so use the ranges above and fine-tune while measuring return loss.

Can length, probe tip and other tips

• Can length: many practical designs use ~0.75–1.0·λg (experimentally people report ~0.75·λg works well for 6″ cans). A short choke / flange at the mouth helps control pattern and improve matching.
• Probe (pin) length: start near a quarter-wave in free space (~52–53 mm) and trim for best return loss inside the can. Use an LNA at the probe and an analyzer/SWR meter or NWA to tune.
• Mechanical: 165 mm cans (or buckets) are a bit heavier/larger — make sure mounts and supports are solid. Add a choke/flange or taper if you use the cantenna as a feed for a dish.

Recommendation (practical)

• If you have to pick one: go 165 mm for slightly better gain and more forgiving probe placement — but follow the λg-based probe placement and tune with an analyzer/LNA. If you only have a 145 mm can on hand (coffee can style), it will still work and can detect the hydrogen line; expect a bit less gain and slightly different probe distance/length to tune.

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If you want, I can:

• calculate the exact starting probe distance and probe length for a specific can inner diameter you have, or
• produce a short checklist (dimensions, λg, probe start, length, choke design) for the 165 mm build you plan.

I am thinking of buying a can that is 160mm diameter x 165 mm height.

A 160 mm internal diameter can is actually a very good size for a hydrogen-line cantenna. Here’s what that geometry gives you and what dimensions you should use:

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✔ Mode behaviour for a 160 mm diameter cantenna

Let:

D   = 160 mm
c   = 3e8 m/s
f   = 1420.4058 MHz
λ0  ≈ 211 mm   (free-space wavelength)

TE11 cutoff frequency

Formula (circular waveguide):

fc_TE11 = (1.841 * c) / (pi * D)

Insert numbers (convert D = 0.160 m):

fc_TE11 ≈ (1.841 * 3e8) / (3.1416 * 0.160)
fc_TE11 ≈ 1.10 GHz

TE21 cutoff frequency

fc_TE21 = (3.054 * c) / (pi * D)

Numerically:

fc_TE21 ≈ (3.054 * 3e8) / (3.1416 * 0.160)
fc_TE21 ≈ 1.82 GHz

Since:

fc_TE11 < 1420 MHz < fc_TE21

the can operates single-mode at 1420 MHz (ideal).

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✔ Waveguide wavelength (λg)

Formula:

λg = λ0 / sqrt(1 - (fc_TE11 / f)^2)

Compute ratio:

(fc_TE11 / f) ≈ (1.10 / 1.420) ≈ 0.775
(fc_TE11 / f)^2 ≈ 0.6006

Then:

1 - 0.6006 = 0.3994
sqrt(0.3994) ≈ 0.632

So:

λg = 211 mm / 0.632 ≈ 336 mm

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✔ Probe distance from back of can

Use 0.25–0.40 of λg:

0.25 * λg ≈ 0.25 * 336 ≈ 84 mm
0.35 * λg ≈ 0.35 * 336 ≈ 118 mm

Recommended starting value:

Probe distance = 90–100 mm from the back plate

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✔ Probe (feed pin) length

Start with quarter-wave in free space:

L_probe ≈ λ0 / 4
L_probe ≈ 211 / 4
L_probe ≈ 52–53 mm

Trim by a few mm during tuning.

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✔ Can height: 165 mm

Compare with λg:

165 mm ≈ 0.49 * λg

This height is perfectly acceptable (typical workable range is 0.5 to 1.0 λg).

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✔ Summary (all ASCII)

D = 160 mm
Height = 165 mm (good)
fc_TE11 ≈ 1.10 GHz
fc_TE21 ≈ 1.82 GHz
Operates single-mode at 1420 MHz
λg ≈ 336 mm
Probe distance = 90–100 mm
Probe length = 52–53 mm