# On testing two wire line loss with an analyser / VNA – part 5

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).

Article On testing two wire line loss with an analyser / VNA – part 2 showed a 1:1 transformer for measuring two wire lines without encouraging significant common mode current.

Online experts suggest that the required transformer is one from 50Ω to Zo of the line being measured. It is often said that:

1. it is necessary to use a transformer from 50Ω to the Zo of the DUT, otherwise the results are invalid; or
2. it is necessary to use a transformer from 50Ω to approximately the Zo of the DUT, otherwise the results are invalid; or
3. it doesn't matter.

Quite a range!

Let's discuss how it works for this case of making measurements of Zsc and Zoc of a specific transmission line section for the purpose of calculating transmission line parameters.

The purpose of the VNA measurement is to capture s11 files looking into the line section over a range of frequencies for the cases of a short circuit and open circuit line termination.

Above is a plot of the magnitude of s11 from scans with a NanoVNA using the transformer referenced earlier, and the fixture OSL calibrated at the transformer DUT terminals.

The challenge here is to make measurements that are low in measurement noise, and in this case we need to focus on |s11| when it is very close to unity. s11 is synonomous with the older transmission line term, the complex reflection coefficient for which I will use Γ.

The jitter or noise on the previous chart is quite small, it is something that one must inspect the measurements for to decide whether they are likely to give valid results.

To calculate transmission line parameters from the SC and OC scans, the s11 or Γ measurements will be transformed to impedance Zl. The function is $$Z_l=Z_0\frac{1+\Gamma}{1-\Gamma}$$. For these measurements |Γ| is very close to 1, and the accuracy of the denominator term $$1-\Gamma$$ becomes very important, and in modern VNAs and the like, the resolution of the ADCs is a source of quantisation noise, possibly crippling noise in low resolution ADCx.

Above is a plot of 1-|Γ| when the measured impedance is divided by different ideal transformer ratios 50Ω, 200Ω, 300, and 450Ω. This is a good approximation the 1-|Γ| that would be observed with a 50Ω instrument followed by a good transformer to the stated reference impedance.

The worse case (minimum 1-|Γ|) is at 10MHz for the 50Ω reference, and it is 0.00283. We need to be able to resolve this small quantity, and allowing for other factors in the geometry of the quadrature detector, we would really like at least 15 bits resolution in the ADC.

Had we used an off the shelf 50:450Ω transformer, the quantity 1-|Γ| is 0.005693, just on twice that of the 50:50Ω transformer, and we could afford and ADC of at least 14 bit resolution. It is an improvement, but only a small one.

If you have an analyser of 8 bit resolution, or even 12 bits, it would not be a good choice for this specific scenario… but it may give useful results from a lossier line section (eg a longer section).

In my own work, I frequently use 50:50Ω, 50:200Ω, 50:450Ω transformers for this sort of measurement.

In the case of the three assertions set out at the beginning, none are correct. It is possible to make valid measurements with or without an impedance transformer, depending on the values of s11 observed and the capability of the instrument on had to resolve very small values of s11. The balun function remains important in lots of measurement setups.

Of course you must SOL calibrate the measurement system on the DUT side of the transformer and the load resistor used must match that stated or assumed in the calibration process.

If your VNA assumes only a 50+j0 L part, then use that value in the calibration process. The calibration is valid, the transformer just serves to remap the impedance seen at the DUT terminals into a better range for the VNA, and the correction process applied means that measured impedances are correctly displayed. s11 and most other derived values are all wrt 50Ω, but the impedances are correct and can be used directly to calculate the transmission line parameters.

Some VNAs provide the facility to renormalise measurements to some other reference impedance. If you use that facility, then all of the s11 and derived figures are wrt that specified Zref.

Above is a screenshot of a NanoVNA-H4 with DiSlord v1.1.0 firmware which can renormalise (in this case Zref=300+j0Ω) on the local display. The instrument is SOL calibrated with a 50+j0Ω load (not 300+j0Ω, the transformation is entirely by calculation). The display shows Z=49.98-j.000637Ω, and all the displayed values are wrt Zref=300+j0Ω.

It is important to look at plots of the measured s11 values, critically assessing the amount of measurement noise or jitter to decide whether the data is good.