Short answer: No—the dish doesn’t change the waveguide dimensions of the cantenna.
The can’s internal diameter and the probe/back-short geometry are set by your operating frequency and waveguide mode, not by the reflector. What the dish does affect is the required beam pattern, edge taper, and phase-center placement of the feed.
What stays the same (set by frequency)
Treat the cantenna as a short section of circular waveguide excited in TE₁₁:
- Diameter (d): choose for single-mode TE₁₁ at your frequency (f).
Cutoff for TE₁₁: ( f_{c,11}=\dfrac{1.8412,c}{2\pi a} ) with (a=d/2).
Practical design: pick (f/f_{c,11}\approx 1.25\text{–}1.35) while keeping higher modes above (f) (e.g., (f<0.85,f_{c,21})). - Probe to back-short distance: about (\lambda_g/4), where
( \lambda_g=\dfrac{\lambda_0}{\sqrt{1-(f_{c,11}/f)^2}} ). - Probe length: start near 0.2–0.25 (\lambda_0) (trim for best match).
Example at 1420 MHz (H-line)
- A good starting diameter ≈ 160 mm (single-mode, TE₂₁ still above band).
- (\lambda_0) ≈ 211 mm, (\lambda_g) ≈ 330 mm, so back-short ≈ 83 mm past the probe.
- Probe length ~ 40–55 mm (then tweak for return loss).
These numbers don’t depend on whether your dish is 1.0 m, 1.5 m, or 3 m.
What does depend on the dish (pattern & placement)
Your 150 cm dish mainly sets how the feed should illuminate it, not the internal waveguide sizing:
- Edge taper: choose the feed so that the field at the dish rim is about –10 to –13 dB relative to boresight (helps spillover/noise vs. efficiency).
- F/D matters: the required half-angle to the rim is
( \theta_{\text{edge}}=\arctan!\big((D/2)/F\big) ).
Pick/shape the feed so its pattern hits ~–10 to –13 dB at (\theta_{\text{edge}}). - Phase center: place the cantenna so its phase center sits at the dish focus. For a plain open circular guide, the phase center is a bit inside the aperture; adding a short conical flare or scalar (choked) rings can improve edge taper, reduce spillover, and pull the phase center forward.
Practical tips
- A bare cantenna often has a pattern that’s either too broad (spillover) or not tapered enough for common F/D≈0.35–0.45 dishes. A short conical flare or scalar rings can nail the –10 to –13 dB taper without touching the can’s internal dimensions.
- Optimize S₁₁ at the bench (VNA) by small adjustments of probe length and back-short distance, then adjust feed position at the focus for max aperture efficiency on-sky (Sun/Moon Y-factor helps).