12 - Measuring the impedance of Coax using a nanoVNA

Measuring the Impedance of Coaxial Cable 

Published in Contact - the magazine of the Bangor and District Amateur Radio Society (BDARs)

I have many random lengths of coaxial cable, some marked and some not. Whilst most of it is 50 Ohm cable, some of it is 75 Ohms and I needed to find out which is which.

I bought a NanoVNA for about £30. The screen is small but I only use it attached to a PC (NanoSaver software). I have used the NanoVNA as an antenna analyser but you can use it for so much more it can measure resistance and reactance at various frequencies.

There is a reasonably obscure way of working out the impedance of unknown cable by using the Lamda/8 method. Unknown to me until Google found a post in the NanoVNA group.io pages. It is very simple to do – attach a length of the coax to the main port of the VNA with the other end of the cable open circuited.

You sweep the cable for its R +/- jX impedance over a range of frequencies from low to high and find the frequency of its first ¼ wave resonance. This is easily seen as a ¼ wave of transmission line will transform the open circuit at the open end of the coax to a short circuit – zero or low resistance and zero or low reactance. It doesn’t matter what length of cable you use. The same data can be used to calculate VF, the Velocity Factor but that didn’t matter to me on this occasion – I just wanted to make some Chokes and Transformers.

Having found the frequency where R and X were lowest – note on the graph below that the scale for X has zero about half way up the right hand. I got 13.44MHz and an impedance of 2.284 – J1.18 Ohm (I happened to be using about 5m of cable so I knew 13-14MHz was in the right ballpark for a quarter wave)

The lamda/8 method requires measuring the impedance at half this frequency so I dutifully set the frequency to sweep from 6.5MHz to 6.8MHz and read off the impedance at 6.67MHz which is seen in the next diagram. – we need the reactance figure – the one after the – j in this case you see that this is Z = 48.4 – j 52.6 so this is “50 Ohm” cable (actually 52.6 Ohms).

You don’t need to know how this method works but if you want to know; it is because the impedance Z of an open circuit transmission line is given by the formula

Z = -j Z₀ COTANGENT ( 2πf * Line_Length )

Line_Length expressed in fractions of wavelength or fractions of cycles of Frequency.

If the line_length is lamda/8 then we have the COTANGENT (π/4) which is 1 so at that particular magic length the measured impedance is –j Z₀

There is more detail at http://www.antenna-theory.com/tutorial/txline/transmission6.php although it is fairly heavy going and it uses a slightly more longwinded approach of measuring impedance of the open circuit coax and the impedance of the short circuited coax and then using the formula.

Z_{0 =} √[ Zshort * Zopen ]

I tried this alternative method on my VNA and got poor results, (10 Ohms out) Although my AA-30 Rig expert antenna analyser gave readings of 48 Ohms which is reasonable. I think the Lamda/8 method is simpler to use, avoids square roots and complex numbers! A third method sometimes quoted is to use the square root of the shorted cable inductance divided by the open circuit capacitance. My VNA gave inaccurate results using this. As did my AA-30.

 

While writing this I found a very good reference at http://www.rfcec.com/ in chapter 3 part 27 – measuring Zo. He says the lamda/8 is more accurate using a shorted cable (and a modified equation) but it is ok to use the open circuit cable – my results were fine.

Now I know I have 50 Ohm cable I can wind some chokes on my FT240 Ferrite cores!

Next article is on how to design chokes