One port resonator critical coupling Q factor measurement using S11

Question

I saw this youtube video which says there are two methods measuring unloaded Q factor. He says there are two options as shown bellow. I have a one port resonator. I could not find anywhere the theory of 2.5 dB he says in the video. Is there some book that shows that? Thanks. https://www.youtube.com/watch?v=5DgmH9XsfLA&t=1s

Beats me. What's being calculated? Why the arbitrary cutoff (2.5dB)? What is the circuit, how is it wired, what are we measuring? — Tim Williams, Aug 12 '23 at 14:28

score 1 · Accepted Answer · answered Aug 12 '23 at 20:46

He is simply doing what he says, applying the approach in Matthaei, Young and Jones, "Microwave Filters, Impedance-Matching Networks, and Coupling Structures", section 11.02 on how to measure the Q of a resonator. He has digitized Fig 11.02-3, with an approximation that is valid for these two ranges:

One port resonator critical coupling Q factor measurement using S11

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