On testing two wire line loss with an analyser / VNA – part 3

This article series shows how to measure matched line loss (MLL) of a section of two wire line using an analyser or VNA. The examples use the nanoVNA, a low end inexpensive VNA, but the technique is equally applicable to a good vector based antenna analyser of sufficient accuracy (and that can save s1p files).

On testing two wire line loss with an analyser / VNA – part 1

This article series shows a method for estimating matched line loss (MLL) of a section of two wire line based on physical measurements (Duffy 2011).

Above is a short piece of the line to be estimated. It is nominal 300Ω windowed TV ribbon. It has copper conductors, 7/0.25, spaced 7.5mm. The dielectric is assumed to be polyethylene… but later measurements suggest is has slightly higher loss than polyethylene. The test section length is 4.07m.

From physical dimensions

Parameters
Conductivity 5.800e+7 S/m
Rel permeability 1.000
Diameter 0.000750 m
Spacing 0.007200 m
Velocity factor 0.850
Loss tangent 1.000e-4
Frequency 146.000 MHz
Twist rate 0 t/m
Length 1.000 m
Results
Zo 301.49-j0.36 Ω
Velocity Factor 0.8500
Twist factor 1.0000
Rel permittivity 1.384
R, L, G, C 2.710030e+0, 1.184609e-6, 1.195499e-6, 1.303216e-11
Length 206.260 °, 3.600 ᶜ, 0.572945 λ, 1.000000 m, 3.924e+3 ps
Line Loss (matched) 4.06e-2 dB
S11, S21 (50) 6.650e-1+j4.265e-1, -3.312e-1+j5.045e-1
Y11, Y21 8.574e-5-j6.647e-3, 7.850e-5-j7.429e-3
NEC NT NT t s t s 8.574e-5 -6.647e-3 7.850e-5 -7.429e-3 8.574e-5 -6.647e-3 ‘ 1.000 m, 146.000 MHz
k1, k2 3.231e-6, 1.072e-11
C1, C2 1.022e-1, 1.072e-2
Mhf1, Mhf2 9.847e-2, 3.268e-4
MLL dB/m: cond, diel 0.039037, 0.001565
MLL dB/m @1MHz: cond, diel 0.003231, 0.000011
γ 4.675e-3+j3.604e+0

 

Above is a set of results from TWLLC.

In the above, the estimated velocity factor is 85% based on experience of measuring a range of windowed ladder lines, loss tangent is an estimate in the range of virgin polyethlyene.

Reconciling with measurement

A test section of line was measured by two techniques at:

It was noted in the previous article that the dielectric component of MLL was higher than expected for good polyethylene. That may be due to impurities like fillers, plasticisers and pigments… especially the latter if carbon black was used.

Above is a plot of the components of MLL from the measurements used in the second article. At the frequency of interest (146MHz), the dielectric component of MLL is smaller than conductor loss, but one would normally expect virgin polyethylene to be perhaps a tenth of that measured.

Conclusions

With experience, estimating MLL from physical measurement can be quite good, good enough for some purposes, and a check on measurements where they are made.

References

  • Duffy, O. Oct 2011. Estimating parameters of two wire transmission lines. https://owenduffy.net/transmissionline/concept/ephmtwtl.htm accessed 24/09/2021.
  • ———. Feb 2016. Calculation of Matched Line Loss from measurement of Zin at resonance or antiresonance of a short circuit or open circuit transmission line section. https://owenduffy.net/files/MllFromZin.pdf.