There isn’t a single magic thickness that by itself gives 50 Ω — but in practice, for standard rectangular waveguide probe feeds, there is a very reliable working range that lands you close with minimal pain.
The practical answer (what actually works)
For a coax-fed monopole probe exciting TE₁₀:
👉 Probe diameter ≈ 0.02–0.04 λ₀
(at the operating frequency)
At 1420 MHz (λ₀ ≈ 211 mm):
- Diameter ≈ 4–8 mm
- Radius ≈ 2–4 mm
That range almost always allows a clean 50 Ω match with reasonable probe length and backshort position.
Why this range works
In that diameter window:
- Radiation resistance lands in the 40–70 Ω region
- Reactance can be nulled with:
- Probe length trimming or
- Backshort spacing (~λg/4)
If you go thinner than this:
- Resistance rises
- Matching becomes sharp and twitchy
If you go thicker:
- Resistance drops below 30 Ω
- You end up fighting excess capacitance
Very common “known-good” designs
These are widely used in WR-series feeds:
- 3 mm rod → often ~60–70 Ω (slightly long probe)
- 4–5 mm rod → sweet spot for 50 Ω
- 6–8 mm rod → ~30–40 Ω, needs careful shortening
Commercial WR-650 L-band probes are typically ~4.8 mm (3/16″) for exactly this reason.
Important caveat (can’t be ignored)
Probe diameter alone does not set the impedance. You still need:
- Probe length ≈ 0.20–0.25 λg
- Probe location at E-field maximum (center of broad wall)
- Backshort ≈ 0.25 λg behind probe
Thickness just gets you into the right impedance neighborhood.
Bottom line
If you want the least drama:
✅ Use a 4–5 mm copper or brass probe
✅ Trim length for resonance
✅ Slide the backshort for best return loss
That will land you very close to 50 Ω at 1420 MHz.