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Following situation (apologies for my potential stupidity, I am very new to RF): I am doing a reflection/S11 measurement using a cut-off piece of coaxial cable (no stub, just a straight cut).

The idea is to get the reflection response of a circuit to be touched/approached with said cable ("the probe"). Now, my first approach was to do a measurement of the S11 coming from the probe without any sample, so just using air as termination and then to subtract it from whatever I get when attaching the probe to the sample. But this obviously does not take into account that there are standing waves (and plenty thereof) in the piece of cable I am using as a probe which behave differently with the different termination that is the sample and thus will show up in my measurement and look bad. They occur at more frequencies than the fairly broadband behaviour of the circuit, but they still don't look good.

Is there a way, ideally by calculation, to eliminate the influence of these standing waves / the probe?

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Yes what you are planning on doing is very common in RF measurements. You need to follow the well established process of 1 port calibration. You will need 3 calibration standards Open, Short and Load to determine the three error terms involved and eliminate them.

See this, page 12 specifically

http://emlab.uiuc.edu/ece451/appnotes/Rytting_NAModels.pdf

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