Measurement of coaxial cable impedance

11/21/11

By

Jack Boswell

N0KSF

I had a opportunity recently to acquire some small Teflon coated cable. It had no markings on it to tell what kind of cable it was or the impedance. So, did you ever wonder what the impedance of that piece of unknown coax cable was? Well I did, I started looking on the internet and found some of the information on this site.


http://www.irb.hr/users/stipcevi/ele/coaxweb/index.html


This started me thinking about some technical manuals that I had from IBM using the 453 Tektronics scope. We were able to determine failures in coax cable and twisted pairs on Main Frame computers. Most of this information was used to determine if the cable was shorted or not terminated properly. It also would measure the length of that cable.


So this is how this adventure started out.


Here are the instructions and calculations from the website that I used to test my project.


1) Take a long piece of cable, usually 9-100 feet, the longer the better.

2) Connect one end of the cable to the 10 nanosecond pulse circuit of any frequency. One can use a pulse circuit shown in Fig 2.

Leave the other end of the cable open.



This is where I strayed from the instructions.


A lot of us have good oscilloscopes. You really only need a single channel scope that will get down into the nanoseconds. I have a 453 Tektronics scope but it has issues ( another project not finished ) :-). I also have a 2445 Tektronics scope with a lot of the same features and more. In the IBM manual it used the B Gate to generate our pulse for testing. If you do not have a scope that will generate a pulse, build the circuit in Fig 2.


3) I used the B Gate on the back of the oscilloscope to generate my signal. I connected the cable under test to the B Gate. You measure the signal at the driving end with a single channel scope. Use figure 2 to connect your scope to the unknown coax. There will be two pulses separated by a time lapse required for the pulse to travel down the cable AND BACK. Measure that time laps and divide by two to get the time DeltaT (in nanoseconds) that takes the pulse to travel down the cable (see the Fig 1).

  1. Measure the capacitance of that particular piece of cable, C (in picofarads).


The following is the original author's pictures:



Now, the impedance of the cable is given by:


Z = 1000 * DeltaT / C

where:

Z = impedance in Ohms

DeltaT = one way travel time in nanoseconds through the cable (that is why you divide the time laps between the leading edge of the pulse from Gate B to the next blimp on the scope(Reflected edge))

C = capacitance of the cable in pF


The formula is simple, you don’t need to know the length of the cable, you only need to access one end of the cable.


Equipment needed:

One channel scope.

Capacitance meter

Pulse generator


This is the results of the author's testing from the website.


Measuring a coaxial cable 2 meter long of RG 58 A/U gives 52.6 Ohm, good enough for such a short cable.


Measurement of a coaxial cable 29m long of RG174 50 Ohm cable (see Fig. 3) gives a DeltaT = 153ns, C=3.10nF => Z=49.4 Ohm. Note that the pulses are separated by 306ns, from which I have calculated DeltaT = 306ns/2 = 153ns. Note also that longer cable will yield a smaller reflected pulse.



NOTE 1. The author says that: This formula might work only for coaxial cables! But I would think that it would work with other twisted wires.


NOTE 2. This is the long version of how we get to derive the formula that the author used:

Z = 1000 * DeltaT / C


n = c/v = DeltaT/L= sqrt(epsilon_r * mu_r)

where n = refraction index, v = speed of EM waves in the isolator,

mu_r = 1 because we do not have magnetic medium.

cylindrical_capacitor_capacitance = 2 * Pi * epsilon_0 * epsilon_r * L /

ln(D/d)

epsilon_0 = 8.8542E-12 Farad/meter, vacuum dielectric constant

Z = 138 * log(D/d) / sqrt(epsilon_r) = 59.93* ln(D/d) / n, a formula from

the book published by Howard W. Sams & Co. 1975, page 24-21


Fig. 1. Original and reflected pulses for a

2 meter long coax cable

Fig. 2. Pulser and connection diagram

Fig. 3. Original and reflected pulses for a 29 meter long coax cable


The following is some of the testing that I performed:


I added a short piece of cable with BNC connectors on the back of my 2445 Tektronics scope (so I could get it out front for convenience of connections). I added a BNC Tee connector to the short piece of coax coming from the Gate B output. I connected one side of the Tee to the cable under test using a connector that has a BNC on one side and terminals on the other. I connected my scope to the opposite side of the Tee and measured the time laps between the two pulses.


I measured 45.5 nanoseconds dividing by two to calculate the deltaT. This would give us 22.75 nanoseconds to sub into our formula.


I took my capacitance meter and measured the capacitance at 422.2 picofarad


Z = DeltaT / C


So 45.5 ns divided 2 then the results 22.75 ns divided by 422.2 pf = 53.88 ohms


This is a screen shot of the setup and the measured waveform.







Note: That the first line is the start of the pulse going down the test coax and the second vertical line is the reflected pulse and this is where the measurement is taken and where you get the DeltaT = 45.5 nanoseconds.


I measured a piece of of RG-58 here are the results:


154.3 ns divided 2 = 77.15 ns divided by 1580 pf = 48.829114 ohms


I also measured a piece of 91 ohm cable.


36.5 ns divided by 2 = 18.25 ns divide by 187.3 pf = 97.43 ohms


This was a fun experiment hope this will be helpful to you?