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# VSWR

## VSWR

(OP)
I have three coax cables between a radio and the antenna
with a connector at each end and two connectors in the middle.
I know the VSWR of each cable (from the spec sheet)
Each cable is 50 ohms
assuming a 50 ohm load at the antenna end,
how can I calculate the end to end VSWR?
each cable has a spec requirement of a 1.4 VSWR.
thanks

### RE: VSWR

VSWR is a funny (strange) measure as you can’t really use it directly in many cases. VSWR does not contain the phase information of the reflection coefficient so therefore all you can get is a worst case answer, not necessarily a representative answer.

The ideal thing would be to measure the overall VSWR using a cable analyser, network analyser etc. The fact that you have not done so, suggests you don’t have access to such a beast.

Remember that VSWR specs generally get worse with frequency, although the VSWR of any particular component may not get monotonically larger with frequency.

As an approximation, people do use a rule of multiplying VSWRs to get the resultant VSWR, but for VSWRs up at 1.4 this is not particularly accurate. In any case you would need VSWR specs for your connectors before doing anything.

### RE: VSWR

(OP)
logbook-
I do have a Wiltron scaler network analyzer.
The cable spec says 1.4 VSWR for each of three cables.
The VSWR for the connectors are not specified.
I measured the VSWR for each of the three cables and got
the following (for example) at 10 GHz:
cable 1  1.1
cable 2  1.25
cable 3  1.1      if I multiply the three I get 1.51

Then commected them together and measured and got 1.38

At 14.4 GHz (another example )I got:

cable 1  1.37
cable 2  1.25
cable 3  1.38   Multipling I get 2.36

and after connecting them together I measured  1.47

Does this make sense?
Is there a mathematical relationship I can use?
Is there a test equipment problem Here?

### RE: VSWR

The VSWR you calculated is worse than the value you measured. That is correct. Multiplying the VSWRs gives the worst possible answer.

You may or may not have a test equipment problem. There is nothing in your results which suggests that you do however.

Since you have a scalar analyser we can move up a notch in understanding.

At any particular frequency a cable will have an insertion loss and a reflection coefficient from an ideal load. This reflection coefficient has both magnitude and phase. We don’t know what the phase is because we only have VSWR, which is an "encrypted" form of the reflection coefficient magnitude. If the cables are all the same (you didn’t mention this) then you might expect that the properties would be similar. If they are different types of cable then the phases may be such as to tend to cancel, actually reducing the overall VSWR. Note that insertion loss will tend to reduce the VSWR as it damps the reflected signal. Again the connectors may be improving the response rather than worsening it.

If the cables are relatively fixed and you want to try improving the setup then you can try adding series or shunt resistor-capacitor networks and/or series/shunt resistor-inductor networks. In other words play about with it and see if it gets better or worse. At these frequencies we are talking about increased length of centre conductor or extra width to conductors for more capacitance. With a reasonably fast scanning scalar analyser the re-test is very fast. Don’t think of this as bodging;  you are running an accurate real-time simulation and fine tuning the response

The only way you can do a mathematical job on it is to get hold of a vector analyser and characterise the cables more carefully.

### RE: VSWR

(OP)
However, isn't it true that if I add a series resistance I
will cause a "resistance bump" that is, a change in resistance at that point and a reflection along with increased insertion loss and a greater VSWR?

### RE: VSWR

Well yes and no. A VSWR mismatch means that the impedance doesn’t look like 50 ohms. In general at any spot frequency the input to the cable will look like a resistance in series with a reactance (R + jX). Thus you can compensate for the mismatch at that one frequency by adding resistance if it was too low or adding shunt resistance if it was too high. The trick is to get a broader-band match and that is more difficult. Thus small apparent mismatches can be used to tune the VSWR to get a better response.

If you just have an input to a piece of equipment, and you do nothing to the 50 ohm resistor ,you will get a poor VSWR due to excess series inductance or excess shunt capacitance. It the then usual to tweak the response by adding networks of arbitrary complexity to get a better, more acceptable response. Obviously you can’t make a really rubbish VSWR perfect, but you can make a good VSWR better, but usually not monotonic with frequency. That is the nature of compensation.

Since you don’t have a vector analyser you can’t tell if you need to add resistance or reduce it. Well it will either be one or the other! (But it could be the reactive component that is causing the trouble with VSWR. If you draw a circle on a Smith chart (centred at the middle of the chart) you will see that lots of impedance combinations give the same VSWR.

The problem you have is finding suitable values, and the repeatability of the result. That is going to be a question of experimentation. Whether you should just use better cable to avoid the problem is something only you can decide. I once did a matching circuit for the end of a coax cable consisting of a small wire-ended resistor (about 75R) short-circuited by 4 turns of wire wrapped around the resistor body. This was far from an ideal design, but it was manufactureable and enabled the product to be shipped without the nasty reflection from the mismatched cable.

### RE: VSWR

(OP)
Logbook
Thanks very much for your explanation.
Appreciate it.

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