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 1-5MHz using a 200mm length coax lead on Port 2 (nanoVNA CH1);
- 35m of CCS RG6/U (close to an electrical quarter wavelength);
- 75-50Ω Minimum Loss Pad (5.72dB); and
- f=1.65MHz (close to a quarter wavelength.

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 0.252864092 -14.895982563 0.447711895 -85.899042128 1.0 0.0 1.0 0.0

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

Above is calculation of Zin=81.37-j11.30Ω from s11 from the .s2p file. Also calculated is MismatchLoss=0.287dB. 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|=-6.98dB.

## So, a bit of accounting is in order

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

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

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, \(TransmissionLoss=-|s21|-InputMismatchLoss \\=6.98-0.286=6.69\: dB\).

The InsertionLoss of the Minimum Loss Pad is 5.7dB, and that must be deducted from the total TransmissionLoss to find the TransmissionLoss of the coax, \(TransmissionLoss_{coax}=TransmissionLoss_{total}-InsertionLoss_{MLP} \\=6.69-5.72=0.97\: dB\)

Note that this is not exactly the Matched Line Loss, the 75Ω line is not perfectly 75Ω, it was terminated by the nominal 75-50Ω Minimum Loss Pad and 50Ω VNA port so there is small standing wave. Nevertheless, MLL will be very close to 0.97dB or 0.028dB/m.

A measurement of Rin of a resonant section very slightly higher in frequency allows calculation of MLL.

Above, calculated MLL assuming Zo is around 78Ω at this frequency (a consequence of increased internal impedance of the centre conductor due to poor skin effect).

You might be tempted to apply (Smith 1995)’s expression for loss due to standing waves \(\frac{Loss_{mismatched}}{Loss_{matched}}=\frac{1+S^2}{2S}\) but this scenario does not satisfy his conditions for it to apply, a much misused expression.

## 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.