nanoVNA, MATLAB and (short) cable length

There are various methods of determining the length of a cable acting as a transmission line. The one I’ve used up until getting the nanoVNA is to inject a fast impulse into the cable and measure the reflection time on an oscilloscope. As usual, Alan W2AEW has a good video about this: #88 Cheap and simple TDR using an oscilloscope and 74AC14 Schmitt Trigger Inverter.

Alan also shows a good method of using the nanoVNA to measure cable length: #316: Use NanoVNA to measure coax length – BONUS Transmission Lines and Smith Charts, SWR and more

The author of the code I used in my previous post about nanoVNA and MATLAB, Alex, has as part of his code the use of a TDR Step Response. With this you can look at the step response graph and derive a cable’s length by looking at the dips in the response.

It seemed to me that his code could be extended so that the cable length could be worked out in the code with no need to look at the graph other than to check that it was all ok. Here’s the script that does the calculations: ajfCableLength.m. Make sure you read on to the end of the post to understand its limitations.

You connect the cable you’re measuring to the S11 port of the nanoVNA and run the script. Here’s a sample MATLAB session using one of the cables supplied with my nanoVNA:

>> ajfCableLength
connect: Serial-/dev/tty.usbmodem4001
status:  open
freq: 101
s11:  101
s21:  101
Measuring cable connected to ch0 ...
Velocity factor of cable? 0.66
The calculated cable length is 0.19775 metres.
Show TDR Response plot (Y/n)

The script is perhaps worth explaining. The first part is the difficult bit which Alex provided. The S11 scattering parameters are obtained from the nanoVNA. These s-parameters are converted into a MATLAB rationalfit object which is a mathematical representation of the s-parameter curve. This rationalfit object is then used to derive the TDR step response mathematically. The second part, which I added, looks at the step response to find the last dip in the curve. This gives the return trip time just like in a real TDR. Given the return trip time the cable length is calculated using the velocity factor which the script has already asked the user to provide.

This all works well for short lengths of cable, say up to 2m. But beyond that it all goes haywire and the results are not correct. I fried my brain reading books (see below) on TDR step responses to find out why. I haven’t managed to understand it properly yet. So it’s a matter for further study.

Some of the books I looked at are:

  • Electromagnetics by Kraus. An excellent book, Chapter 12 is the pertinent part.
  • Electromagnetism for Electronic Engineers by Carter.
  • Signals and Systems by Hsu.
  • Techniques for Advanced Cable Testing which is on the Keysight web site.

None of these are easy reading and all assume an understanding of vector arithmetic and calculus.

Easier, is:

  • Practical Digital Signal Processing using Microcontrollers by Ibrahim.

The nanoVNA and MATLAB

The nanoVNA is a cheap but usable vector network analyser. It is good value and very useful for all sorts of RF design and radio ham activities. The model I have has a tiny screen which I can read adequately but it isn’t as comfortable as reading a computer screen. The NanoVNA is a touchscreen device so you need to tap on tiny text to do anything. Again, this is possible but far from comfortable for those of us with ageing eyes. There’s also a bit of screen reflection.

IMG 1105

The nanoVNA can be driven from a PC using a program called nanoVNA-saver which is pretty good. Unfortunately it runs on Microsoft Windows and as I don’t have a PC running Microsoft Windows I have to run it in a VirtualBox VM on my Mac Mini. This works but is a bit clunky and to be honest my Mac mini is a bit long in the tooth and struggles to run virtualised Windows 10 at a reasonable speed.

There is a cross-platform solution based on Python which looks promising. It uses Homebrew on MacOS which clashes with MacPorts which I use. I tried to make it work under MacPorts but fell into the usual maze of incompatible library versions causing the make to fail. So I gave up as I want to play with electronics and not software building. [Update: Rudi, DL5FA kindly helped with this and it looks like the Python Virtual Environment will help when I’ve got the time to try again.]

MATLAB to the rescue! — alex_m has created some MATLAB scripts which allow you to interrogate and control the nanoVNA from MATLAB. Thanks Alex! So if you have MATLAB this may be useful. If you don’t you may be able to convert much of this to Octave but it does use the MATLAB RF Toolbox so you may end up doing a lot of work.  Alex’s scripts produce LogMag, Smith Chart and TDR Step Response graphs. 

Here’s a graph showing my 40m LPF characteristics made using Alex’s scripts.

40m LPF LogMag

I’ve written a couple of scripts based on Alex’s work which I think makes using the nanoVNA easier. Both scripts need an edit to configure the serial link to the nanoVNA. You’ll need Alex’s code too.

The first script ajfCalibrate.m calibrates the nanoVNA for a particular sweep on the S11 port. You have to do this before every measurement that changes the sweep values, so you do it a lot. Here’s how it looks in the MATLAB console. The inputs are in italics.

>> ajfCalibrate
connect: Serial-/dev/tty.usbmodem4001
status: open
Sweep start (MHz)? 7
Sweep stop (MHz) ? 7.2
press RETURN when S11 is open
press RETURN when S11 is shorted
press RETURN when S11 has 50 ohm load
Save [0-4]? 4

The second script ajfVSWR.m produces a chart of VSWR against frequency. Most radio hams are happier with this than the LogMag chart preferred by RF designers. 

I used ajfVSWR to measure my small transmitting loop tuned to the 40m FT8 frequency. As expected it shows the narrow bandwidth in low VSWR that is the drawback of small transmitting loops. 

40m FT8 VSWR

The graph can be zoomed in MATLAB and have data cursors added to show more details.

40m FT8 VSWR 2

The VSWR could be lower. I think I left a metal step-ladder in the attic which is affecting the loop.

ajf? My initials.