# Measuring OC and SC transmission line sections

Failure estimating transmission line Zo – λ/8 method – nanoVNA discussed the potential for failure using this ‘no-brainer’ method of estimating differential mode characteristic impedance Zo, providing an NEC-4.2 model to demonstrate effects.

This article reports nanoVNA measurement of a two wire line where no common mode countermeasures were taken.

## A little review of behavior of practical transmission lines

Above is a Smith chart of the complex reflection coefficient Γ (s11) looking into a length of nominally 142Ω transmission line of similar type to that in the reference article, the chart is normalised to Zref=142+j0Ω. Note the locus is a spiral, clockwise with increasing frequency, and centred on the chart prime centre Zref. More correctly it is centred on transmission line Zo, and the keen observer might note that the spirals are offset very slightly downwards, actual Zo is not exactly 142Ω, but 142-jXΩ where X is small and frequency dependent, a property of practical lines with loss.

Above is a Smith chart of the same data, but normalised to Zref=50+j0Ω, ie the prime centre is 50+j0Ω. The spirals are offset, but again they are centred on Zo. It might not look centred on Zo, but note that the spiral inwards is not symmetric on this scale, and if the line was long enough, the spirals converge on Zo.

So what does this spiral with Zref=50+j0Ω translate to in a cartesian plot of |s11| vs f?

Whilst the value of |s11| wrt actual Zo, when mapped under Zref=50+j0Ω (as in the VNA reports), it has a cyclic variation with f.

Now that we know the phenomena to expect of a normal practical (lossy) transmission line, we can review a measurement data set.

## Measurement of a practical line

The DUT is the same test line documented at Measure transmission line Zo – nanoVNA – PVC speaker twin. It is 1m in length and that article documented nominal Zo≈142Ω and VF≈0.667.

The DUT is directly connected to the nanoVNA Port 1 jack (CH0 in nano speak), no measures have been taken to reduce potential for common mode excitation of the system, and the nanoVNA is connected to the desk computer by a USB cable… all a bit non-descript because the only detail that is important is no common mode counter measures used.

Above is a Smith chart of a scan from 1-100MHz. The form is broadly a clockwise spiral from low to high f, but notable deviations at the high and low f end. Beware, it might look like 80% of the locus is a spiral, but it represents more like just 30% of the frequency range.

Let’s look at |s11| for a better perspective.

Above is a plot of |s11| vs f. Recall that we might expect some smooth cyclic variation in |s11| with f, and that accounts for the dip at Marker 1,  but the shenanigans  around 30MHz are an anomaly cause by common mode excitation. Likewise the range 66-100MHz is affected.

This dataset is seriously compromised by common mode excitation of the DUT, the data is worthless and no reliable conclusions can be drawn about the pure differential mode characteristics of the DUT.

Measure transmission line Zo – nanoVNA – PVC speaker twin reported measurements and analysis of the same line section, and it described the common mode countermeasures.

## Conclusions

Common mode current gives rise to unquantified radiation loss and affects the input impedance of the line section.

If countermeasures are apparently needed and are not described, the experimenter may be naive and none were used, and the data is questionable, possibly worthless… certainly suspect until the common mode issue can be clarified.