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

Above is a short piece of the line to be measured. 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.

## Fixture

The Noelec 1:9 balun (or perhaps Chinese knock off) is available quite cheaply on eBay and provides a good hardware base for a 1:1 version.

Above is a modified device with the original transformer replaced with a Macom ETC1-1T-2TR 1:1 transformer. The replacement is not exactly the same pads, but it is sufficiently compatible to install easily.

See A 1:1 RF transformer for measurements – based on noelec 1:9 balun assembly for more detailed info.

Performance of the fixture is crucial to valid measurement.

## Method 2

This method gives a good estimate of transmission line characteristic impedance and propagation constant.

Above is a plot of |s11| for the DUT for OC termination. It is really important there are no unexpected bumps in this, for whatever reason.

Above is a plot of |s11| for the DUT for SC termination. It is really important there are no unexpected bumps in this, for whatever reason.

Did I mention bumps are a problem? Make sure after OSL calibration that the |s11| response is flat for each of OSL… you can't make good measurements if the cal set are flawed.

So we can calculate \(MLL=\frac{20}{2len} log_{10}| \frac{1+\sqrt{\frac{{Z_{sc}}}{Z_{oc}}}}{1-\sqrt{\frac{{Z_{sc}}}{Z_{oc}}}} |\; dB/m\\\).

Above is a plot of MLL (dB/m) calculated from the measurements saved as s1p files (raw), and fits to two models:

- red x: raw MLL based on the measurements
- blue: a curve fit to the model \(MLL = k_1\sqrt f+k_2f\);
- green: a curve fit to the model \(MLL = k_1\sqrt f\).

The data is a bit noisy, this is a low end analyser, the nanoVNA. Nevertheless, the curve fit SE are less than one tenth the coefficient for both coefficients… good enough.

The green curve is a fit to a model often used and often provided in some analysis tools. It can be seen here that although the slope of the blue line is similar to the green line around 10MHz, the green line slope increases with increasing dielectric loss as frequency increases… the green line is a better model.

We could use the loss model coefficients in ATLC to solve a given line section, for example to find Rin of a quarter wave OC line section at 146MHz.

Above, Zin is 8.048e-1-j3.335e-4Ω, Rin=0.8048Ω.

## Improvements

More advanced techniques include log scan, and avoiding frequencies where clock harmonics etc might degrade accuracy. The nanoVNA's accuracy is limited as witnessed by the noise on the raw plot above, and measures like adjustable bandwith have not improved it in my experience. I did try NanoVNA-App for its averaging, but it still throws memory protection exceptions, so I cannot trust it.

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

# References

- Duffy, O. 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.