Measure transmission line Zo – nanoVNA – PVC speaker twin demonstrated measurement of transmission line parameters of a sample of line based on measurement of the input impedances of a section of line with both a short circuit and open circuit termination. From Zsc and Zoc we can calculate the Zo, and the complex propagation constant \(\gamma=\alpha + \jmath \beta\), and from that, MLL.
Above is a plot of:
- 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 \(MLL = k_1\sqrt f\) based on measurements from 5-10MHz; and
- a curve fit to the AC6LA (Johnson) model (coefficients created with ZPLOTS).
Looking at the higher frequencies first, the green curve does not track measurements, and the higher slope of ‘measured' MLL suggests there is significant contribution from dielectric loss that is not captured by the \(MLL = k_1\sqrt f\) model. The other two models are quite good at the mid to higher frequencies.
At the lower frequencies, there are few data points and measurements on the nanoVNA were noisy, so the scatter of few points makes estimation challenging. To the eye, I fancy that the brown curve is probably an overestimate of the MLL. It is a more complicated model, it is harder to compute, yet it seems likely that it is an overestimate. It is difficult to choose between the green and blue curves at low frequencies given the data and noise.
Overall, only the blue curve seems a good estimator at low, mid and high frequencies. That is not to say that would be the case for other line types.
I might comment that the study has some underlying weaknesses:
- it used a low grade VNA, and measurement noise is an issue;
- the frequency sweep was limited by the basic nanoVNA mode to 101 points, and worse, linearly spaced (which causes undue emphasis on the higher frequency points at the expense of capturing the low frequency effects well).
At least one nanoVNA client application can do log sweeps of larger set of points, but on my inspection at the time, it had other defects that cause me to set it aside.
I downloaded DiSlord's nanoVNA firmware v1.0.69 and installed it for the measurements in this article. I used the nanoVNA-App v1.1.207 as the PC Client. I was already aware of issues in nanoVNA-App, so I tried a quite old nanoVNA_mod v3 and experienced the same issues with DiSlord firmware. I gathered information to report the problems, but DiSlord's github repo does not have that version, I was told only reliable versions go on github… enough said?
So, I have reverted to ttrftech firmware v0.8.0, no frills, but it seems correct and reliable.