Coaxial line with a square shield calculator
Why a square shield
Because square tube or trunking is easier to find and to work than round. Electrically a square shield behaves like a round one about 8 % larger, and that factor is what the formula carries.
| Frequency (MHz) | |
| Fill material | |
| ε of the fill | |
| Inner side of the square shield D₁ (mm) | |
| Centre conductor diameter D₂ (mm) | |
| Characteristic impedance Z₀ (Ω) | |
| Result | |
| Quarter-wave section (λg/4) | |
📐 The formulas
Forward problem — impedance from the geometry:
Z₀ = (59.952 / √ε) × ln(1.0787 × D₁ / D₂)
Inverse problem — the shield side for a wanted impedance:
D₁ = D₂ × e^(Z₀ × √ε / 59.952) / 1.0787
Quarter-wave section:
λg/4 = 299792.458 / (f × √ε) / 4
Symbols:
D₁— inner side of the square shield [mm]D₂— diameter of the centre conductor [mm]ε— permittivity of the filling (1 for air)f— operating frequency [MHz]; λg/4 comes out in millimetres
Where this calculator stops:
- The conductor must be exactly on the axis, or the impedance drifts
- The formula is for the TEM mode: above the shield's cutoff it does not apply
- The centring insulators inside the line lower the impedance slightly
🎯 In practice
- Rigid feeders and lines inside power amplifiers.
- VHF resonators and filters built from square extrusion.
- High-power air lines, where low loss and dielectric strength matter.
Practical advice:
- For 50 Ω in air the shield side comes out about five times the conductor diameter.
- Make the centring insulators from PTFE and space them widely — each one lowers the impedance a little.
- Check the finished line with an analyser: a few percent of assembly error shows up as a noticeable SWR change on VHF.
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UR3PKI. «Coaxial line with a square shield calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/lines/coax_square (licence CC BY-NC-SA 4.0).The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.