This article is demonstration of measurement of Transmission Loss in a section of coaxial transmission line. The scenario is chosen to expose the experiment to some of the things that complicate such measurements.

The very popular nanoVNA-H will be used to make the measurements.

The scenario:

- nanoVNA fully calibrated from 1.5-1.8MHz using a 200mm length coax lead on Port 2 (nanoVNA CH1);
- 10m of RG58C/U; and
- f=1.65MHz.

Above is a block diagram of the test configuration. nanoVNA measurements are wrt 50Ω, so \(P=\frac{V^2}{50}\) and \(V=\sqrt{50P}\).

1650000 0.019864771 -5.590068373 0.986123401 -18.626393762 1.0 0.0 1.0 0.0

Above is a record from the .s2p file in MA format.

Above is calculation of Zin=52.07-j0.1722Ω from s11 from the .s2p file. Also calculated is MismatchLoss=0.002dB. This method of calculating MismatchLoss is only correct if either source or load impedance is purely real, which is true in this case.

Converting the magnitude of s21 from the .s2p file, we get |s21|=-0.12dB.

## So, a bit of accounting is in order

Let’s review some meanings of terms (in the 50Ω matched VNA context):

- \(TransmissionLoss=\frac{PowerIn}{PowerOut}=\frac{P_1}{P_2}\);
- \(s11=\frac{V_{1r}}{V_{1i}}\);
- \(InputMismatchLoss=\frac{P_{1i}}{P_{1}}=\frac1{(1-|s11|^2)}\);
- \(s21=\frac{V_{2i}}{V_{1i}}\); and
- \(InsertionLoss=\frac{P_{1}}{P_{2}} \approx \frac{P_{1i}}{P_{2i}} =\frac1{|s21|^2}\).

It is assumed that Zin of VNA Port 2 is 50+j0Ω, and that therefore P2r=0. Error in Zin of VNA Port 2 flows into the results. A 10dB attenuator is fitted to Port 2 prior to calibration to improve accuracy of Zin.

With the quantities expressed in dB, we can derive that \(TransmissionLoss=-|s21|-InputMismatchLoss\).

In the example given above, \(TransmissionLoss=-|s21|-InputMismatchLoss \\=0.120-0.002=0.12\: dB\).

In the example given above, \(InsertionLoss=-|s21|=0.12\: dB\).

Because this is a nominally matched scenario, reflected power at the input and output ports is very small and InsertionLoss≈TransmissionLoss.

The calculated figure is lower than might be expected from the datasheet, but there are issues with interpolation of loss figures in the transition region.

Zo of the nominally 50Ω cable is not exactly Zo at the test frequency. Indications are that it is around 50.95-j1.16Ω (see above). At this frequency, skin effect is not fully developed and internal impedance of the centre conductor becomes more significant, raising Zo.

## References

- Smith, P. 1995. Electronic applications of the Smith chart 2nd ed. Noble Publishing Tucker.

## Conclusions

The Transmission Loss of a line section may not be directly given by any measures displayed by a VNA, it may take some interpretation and some accounting for elements that can be measured.