Dave Casler sets out in his Youtube video to answer why two wire transmission line has so little loss . With more than 10,000 views, 705 likes, it is popular, it must be correct… or is it?
He sets a bunch of limits to his analysis, excluding frequency and using lossless impedance transformation so that the system loss is entirely transmission line conductor loss.
He specified 300Ω characteristic impedance using 1.3mm copper and calculates the loop resistance, the only loss element he considers, to be 0.8Ω.
Above is Dave’s calculation. Using his figures, calculated \(Loss=\frac{P_{in}}{P_{out}}=\frac{100}{100-0.27}=1.0027\) or 0.012dB.
Above is my calculation of the DC resistance at 0.395Ω per side, so I quite agree with his 0.8Ω loop resistance… BUT it is the DC resistance, and the RF resistance will be significantly higher (skin effect and proximity effect).
Casler’s is a DC explanation.
Self taught mathematician Oliver Heaviside showed us how to calculate the loss in such a line.
Let’s calculate the loss for that scenario more correctly.
Casler’s 1.3mm 300ohm two wire line |
|
| Parameters | |
| Conductivity | 5.800e+7 S/m |
| Rel permeability | 1.000 |
| Diameter | 0.001300 m |
| Spacing | 0.015000 m |
| Velocity factor | 0.800 |
| Loss tangent | 0.000e+0 |
| Frequency | 14.000 MHz |
| Twist rate | 0 t/m |
| Length | 30.480 m |
| Zload | 300.00+j0.00 Ω |
| Yload | 0.003333+j0.000000 S |
| Results | |
| Zo | 301.80-j0.66 Ω |
| Velocity Factor | 0.8000 |
| Twist factor | 1.0000 |
| Rel permittivity | 1.562 |
| R, L, G, C | 4.864062e-1, 1.261083e-6, 0.000000e+0, 1.384556e-11 |
| Length | 640.523 °, 11.179 ᶜ, 1.779231 λ, 30.480000 m, 1.271e+5 ps |
| Line Loss (matched) | 0.213 dB |
| Line Loss | 0.213 dB |
| Efficiency | 95.21 % |
| Zin | 3.031e+2-j1.940e+0 Ω |
| Yin | 3.299e-3+j2.112e-5 S |
| VSWR(50)in, RL(50)in, MML(50)in | 6.06, 2.892 dB 3.132 dB |
| Γ, ρ∠θ, RL, VSWR, MismatchLoss (source end) | 2.183e-3-j2.105e-3, 0.003∠-43.9°, 50.364 dB, 1.01, 0.000 dB |
| Γ, ρ∠θ, RL, VSWR, MismatchLoss (load end) | -2.990e-3+j1.096e-3, 0.003∠159.9°, 49.938 dB, 1.01, 0.000 dB |
| V2/V1 | 1.973e-1+j9.504e-1, 9.707e-1∠78.3° |
| I2/I1 | 2.055e-1+j9.590e-1, 9.808e-1∠77.9° |
| I2/V1 | 6.576e-4+j3.168e-3, 3.236e-3∠78.3° |
| V2/I1 | 6.164e+1+j2.877e+2, 2.942e+2∠77.9° |
| S11, S21 (50) | 9.347e-1-j6.326e-2, 2.295e-2+j3.253e-1 |
| Y11, Y21 | 8.345e-5+j6.986e-4, -1.011e-5-j3.385e-3 |
| NEC NT | NT t s t s 8.345e-5 6.986e-4 -1.011e-5 -3.385e-3 8.345e-5 6.986e-4 ‘ 30.480 m, 14.000 MHz |
| k1, k2 | 1.871e-6, 0.000e+0 |
| C1, C2 | 5.916e-2, 0.000e+0 |
| MHzft1, MHzft2 | 5.702e-2, 0.000e+0 |
| MLL dB/m: cond, diel | 0.006999, 0.000000 |
| MLL dB/m @1MHz: cond, diel | 0.001871, 0.000000 |
| γ | 8.058e-4+j3.676e-1 |
Above is the complete output from RF Two Wire Transmission Line Loss Calculator.
One of the results shows the values of distributed R, L, G and C per meter, and R is 0.486Ω/m or 14.81 for the 30.48m length, nearly 20 times Dave Casler’s 0.8Ω.
Unsurprisingly, the matched line loss is larger, calculated at 0.213dB, much higher than Dave Casler’s 0.12dB.
Now for a bunch of reasons, the scenario is unrealistic, but mainly:
- the conductor diameter is rather small, smaller than many 300Ω commercial lines and impractical for a DIY line; and
- two wire line is most commonly used with high standing wave ratio and the often ignored loss under the specific mismatch scenario is more relevant.
Conclusion
It is common that the loss in two wire line system underestimates the line loss under mismatch and impedance transformation that may be required as part of an antenna system.
Casler’s DC explanation appeals to lots of viewers, probably hams, and might indicate their competence in matters AC, much less RF.
… Read widely, question everything!