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The wikipedia page for network analyzers mentions "reflection and transmission of electrical networks are easy to measure at high frequencies" but doesn't give any hint on how this is done or what it is that's called "high frequencies" there (I'm guessing it's the GHz spectrum...)

Does this means I can do without a VNA in such cases (using just, say, a spectrum analyzer?)

Could someone elaborate?

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I'm going to assume you're familiar with S-Parameters. S-Parameters change for different frequencies. When using a VNA, you will be testing the circuit at a specific operating frequency. This website shows how you could crudely measure the S-Parameters. A VNA will do the exact same thing in a much more calibrated manner. Thus there is no need to use a spectrum analyzer.

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