On testing two wire line loss with an analyser / VNA – part 3 showed how to estimate two wire line characteristics from dimensions and an estimate of velocity factor. This article does the same for a coax example
To take an example, let’s use one posted online recently:
Stranded Tinned copper center conductor, 0.037″ od Solid, white dielectric (not foamed), 0.113″ od Od of jacket, 0.196″
The dimensions we are interested in are OD of dielectric, 2.97mm (0.113″) and OD of the inner conductor, 0.989mm (0.037″). A solid white dielectric (as opposed to translucent) is likely to be PTFE which has a velocity factor around 0.7 (in most PTFE cables) and we will assume a loss tangent of 1e-4 (typical of non-polar polymers).
Plugging those values into CLLC, we get:
| Parameters | |
| Conductivity | 5.800e+7 S/m |
| Rel permeability | 1.000 |
| Inner diameter | 0.00099 m |
| Outer diameter | 0.00297 m |
| Velocity factor | 0.700 |
| Loss tangent | 1.000e-4 |
| Frequency | 7.000 MHz |
| Length | 100.000 m |
| Results | |
| Zo | 46.16-j0.72 Ω |
| Velocity Factor | 0.7000 |
| Rel permittivity | 2.041 |
| Length | 1200.831 °, 20.958 ᶜ, 3.335641 λ, 100.000000 m, 4.765e+5 ps |
| Line Loss (matched) | 2.844 dB |
| R, L, G, C | 3.012797e-1, 2.199246e-7, 4.541158e-7, 1.032497e-10 |
| S11, S21 (50) | -5.317e-2+j8.620e-3, -3.702e-1-j6.166e-1 |
| Y11, Y21 | 8.817e-3+j1.143e-2, 4.032e-3+j2.320e-2 |
| NEC NT | NT t s t s 8.817e-3 1.143e-2 4.032e-3 2.320e-2 8.817e-3 1.143e-2 ‘100.000 m, 7.000 MHz |
| k1, k2 | 1.071e-5, 1.300e-11 |
| C1, C2 | 3.388e-1, 1.300e-2 |
| Mhf1, Mhf2 | 3.266e-1, 3.964e-4 |
| dB/m @1MHz: cond, diel | 0.010714, 0.000013 |
| γ | 3.274e-3+j2.096e-1 |
Estimated Zo is 46Ω based on the measurements and assumptions. The calculated result is quite sensitive to small error in measurement, the cable’s nominal Zo is probably 50Ω.
Loss will probably be a little higher than estimated, the calculator assumes solid conductors and stranded inner conductor and braided outer conductor increase loss, tinned conductors further increase loss, but silver plated conductors decrease loss.
The cable is likely to be an RG-400 type, the reported measurements are quite close.