For a hydrogen-line feed made from rectangular box section, the waveguide only needs to be long enough to establish the TE10 mode and accommodate the probe/backshort arrangement.
A useful rule of thumb is:
- Minimum practical length: about 1 free-space wavelength (~210 mm at 1420 MHz)
- Better: 1.5-2 wavelengths (~315-420 mm)
- Longer than about 3 wavelengths (~630 mm) usually gives little benefit
For a 150 x 75 mm or 160 x 80 mm waveguide feed, I would suggest:
- 300-400 mm overall length as a good starting point.
- Place the probe approximately lambda_g/4 from the backshort.
- Leave 200-300 mm of waveguide in front of the probe before the aperture or horn flare.
The guided wavelength at 1420 MHz in a 160 mm wide waveguide is:
lambda_g = lambda / sqrt(1 – (lambda/(2a))^2)
where:
- lambda = 211 mm (free-space wavelength)
- a = 160 mm (waveguide width)
This gives a guided wavelength of about 280-290 mm.
A typical arrangement might therefore be:
- Backshort to probe: ~70 mm
- Probe to aperture: ~250 mm
- Total waveguide length: ~320 mm
If you intend to add a pyramidal flare, the straight waveguide section can be somewhat shorter (around 250-300 mm), since the flare itself helps form the radiation pattern.
For a hydrogen-line dish feed, a 300 mm length of 160 x 80 mm box section with a probe about 70 mm from the back wall is a sensible, practical design and should perform very similarly to a conventional WR-650 feed.