Coax Cable Matching

These measurements are done using a technique known as Time Domain Reflectometry.

TDR is based on the fact that when there are discontinuities in a transmission line, some of the incident power is reflected towards the source.

The farther the discontinuity from the source, the longer it will take for the reflected energy to come back. This is used to determine, for instance, where an underground cable is damaged, so you don't have to dig the entire length to find the fault and make a repair.

The basic setup consists of a fast rise/fall time pulse generator and an oscilloscope.

Since my main purpose was to observe the reflections on a transmission line driving a ham radio antenna, I wanted to limit the energy of the radiated signal in order to reduce the potential for interference.

I used the 1 Pulse Per Second output of my timing receiver which has about 10nS rise/fall times. At this low repetition rate, I had to use a digital storage oscilloscope. A conventional oscilloscope would not have provided sufficient brightness.

If you are testing a transmission line terminated by a conventional load or other, non-radiating circuit, you can use a higher repetition rate and a conventional oscilloscope. The repetition rate is limited by the length of the transmission line and its velocity factor. You can use any frequency between 10 kHz and 1 MHz that gives you good brightness on your oscilloscope. You need an oscilloscope with at least 60 MHz bandwidth to see pictures equivalent to those below.

Here is the schematic of the test setup:

For the CH 1 connection, I used a BNC T so that the length of the connection between the junction of R1 and the cable under test (point A) and the input of the oscilloscope was very short.

The scope is used with high input impedance (typically 1 Mohm in parallel with 20pF), and the cables are plugged directly into the scope.

Initially, R1 was set to a very low value (the timing receiver has very low output impedance.) So I did some experiments later with a series resistance at the input of the cable (R1 > 0) to match the generator to the cable.

All pictures in this series were taken without any matching resistance between the output of the pulse generator and the cable. The PPS signal has about 5V peak amplitude into an open circuit and about the same into a 50 ohm load.

These pictures were taken on CH 2, with R1 = 0 and a good quality 50 ohm coaxial cable about 4 feet in length, the type of cable you might use on the bench for general purpose RF work.

(I will take pictures on CH 1 and post them later).

Here is the response of the cable with R2 = ∞ (open):

Notice the high level of ringing. If this signal was to drive a logic gate, there might be problems.

Here is the same cable with R2 = 50 ohm, still no resistance at the generator output (R1 = 0).

Now the Cable Under Test is a 50 feet long cable of 75 ohm characteristic impedance with no termination at the far end (R2 = ∞, or open) and R1 = 0:

Here is the same cable with a 50 ohm termination (R2 = 50 ohms):

Finally, there is the same 50 feet long 75 ohm cable with a 75 ohm termination (R2 = 75 ohms):

Conclusions

• Impedance matching is important, even more so when the cable is long and the signals have fast rise time (or wide bandwidth).
• In most cases where signal integrity is important but power transfer is not (low power signals), it is sufficient to match the load impedance to the cable to eliminate ringing.

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