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How is physically possible to get the value of the characteristic impedance of a certain coaxial cable?

Precisely, in my case I have a coax of 50Ohm impedance, and I need to cut it and connect some alligator clips or some tester leads. Now I thought that this variation maybe will change the characteristic impedance of my coax. Since the device I would connect to it gives an accurate value only if connected to 50Ohm cable, do this variation modify it a lot?

Is there a kind of measurement I can do?

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    \$\begingroup\$ if you have only 1cm (10mm) of center/shield wiring that is not in the coaxial shape, you should get the 50_ohm behavior to well past 100MHz. That means you cannot use "some tester leads" in your wiring. And alligator clips may be a problem, tho you may find some 2cm-long clips. What is the rise-time of your "device" output? Do you have a VSWR goal? \$\endgroup\$ – analogsystemsrf Sep 22 at 9:06
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When you connect to a 50 ohm device, you usually make the connection with a co-axial connector.

Alligator clips, and the tails of wire leading up to them, will introduce a section of higher impedance.

Whether this makes a negligible or a significant difference depends on your operating frequency, and the length of the tails. If you keep them well below 1/10 of a wavelength long, you'll probably get away with it for power transmission, though not for precision impedance measurement. Once they're approaching 1/4 wavelength or more, they'll really mess with your setup, whatever you're trying to do.

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The easiest way is to use TDR (Time Domain Reflectometry).

If you believe that the coax is 50Ω and you want to verify it, you put 50Ω connectors on either end, connect one end to the TDR and terminate the other end with a 50Ω resistor. If you're right, the TDR display will be perfectly flat. If not, the steps on the display will tell you how much the cable deviates from 50Ω. The steps are created when the test signal is reflected by the changes in impedance.

There are analogous ways to do the same kind of test in the frequency domain, but they're less intuitive and take longer to explain.

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Only the part with the clips will be modified the rest will still be 50 ohms.

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    \$\begingroup\$ This doesn't seem to answer the question. \$\endgroup\$ – Ariser Sep 23 at 5:34
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The leads don't change the characteristic impedance on the coaxial cable, they add to the impedance of your test subject.

How would you calibrate away the effect from the coaxial cable with your measurement device? For example, with a VNA you typically connect a short, open, and a \$50~\Omega\$ load to the end of your measurement cable and tell your measurement device to figure out how to compensate the cable. If your device works the same way, you can connect the "calibration kit" (possibly hand made for this occasion) to the alligator clips. If not, you have to estimate the effect from the leads and then subtract their inductance from your device under test.

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