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.
Z0
= √[
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
