Wanting to replace our current non standard figure 8, 240v power cable as feeders on the loops with some homemade balanced line I asked ChatGPT for help.
Question.
Dimensions of open wire line with 1mm conductors for 450 ohms impedance.
Answer.
For a two-wire
open-wire transmission line in air, the characteristic impedance is well-approximated by:
Z0≈276log10 (2sd)Z_0 \approx 276 \log_{10}\!\left(\frac{2s}{d}\right)Z0≈276log10(d2s)
Where
- Z0Z_0Z0 = desired impedance
- sss = center-to-center conductor spacing
- ddd = conductor diameter
You specified:
- Desired Z0=450 ΩZ_0 = 450\,\OmegaZ0=450Ω
- Conductor diameter d=1 mmd = 1\,\text{mm}d=1mm
Solve for spacing sss
450=276log10(2s1 mm)450 = 276 \log_{10}\left(\frac{2s}{1\,\text{mm}}\right)450=276log10(1mm2s) log10(2s1 mm)=450276=1.630\log_{10}\left(\frac{2s}{1\,\text{mm}}\right) = \frac{450}{276} = 1.630log10(1mm2s)=276450=1.630 2s1=101.630≈42.6\frac{2s}{1} = 10^{1.630} \approx 42.612s=101.630≈42.6 s=42.62≈21.3 mms = \frac{42.6}{2} \approx 21.3\ \text{mm}s=242.6≈21.3 mm
Result
For a
450-ohm open-wire line using
1 mm diameter conductors:
Center-to-center spacing ≈ 21 mm
(Conductor-to-conductor gap ≈ 20 mm)
If you want, I can generate a table for other impedances or conductor diameters, or provide construction guidelines (spreaders, materials, mechanical spacing tolerances, etc.).
Yes.
Open-Wire Line Dimensions (1 mm Conductor Diameter)
Using the standard formula:
Z0=276log10(2sd)⇒s=d2⋅10Z0/276Z_0 = 276 \log_{10}\left(\frac{2s}{d}\right) \quad\Rightarrow\quad s = \frac{d}{2} \cdot 10^{Z_0/276}Z0=276log10(d2s)⇒s=2d⋅10Z0/276
Where
- d=1 mmd = 1\,\text{mm}d=1mm
- sss = conductor spacing (center-to-center)
Spacing Table (1 mm wire)
| Impedance (Ω) | Required spacing sss (mm) | Gap between conductors (mm) |
|---|
| 300 Ω | 11.2 mm | 10.2 mm |
| 350 Ω | 15.0 mm | 14.0 mm |
| 400 Ω | 18.0 mm | 17.0 mm |
| 450 Ω | 21.3 mm | 20.3 mm |
| 500 Ω | 24.8 mm | 23.8 mm |
| 550 Ω | 28.6 mm | 27.6 mm |
| 600 Ω | 32.8 mm | 31.8 mm |
| 650 Ω | 37.5 mm | 36.5 mm |
| 700 Ω | 42.8 mm | 41.8 mm |
Excellent result.
My RSGB and ARRL reference books collecting dust now.