I know the method of Hong and Lancaster given in 8.4.1 of their book microstrip filters for RF/microwave applications. I would like to know about other methods.
I don't know the method of Hong and Lancaster. I would measure the resonator using a Vector Analyser, make sure the reference plane was at the resonator port, so that the resonance appears as a circle on the Smith Chart, passing through either the short circuit or open circuit point. The three Q values (QL, QE, Q0) can be calculated using the frequency differences at the intersections of the circle with three pairs of lines.
1. 45 degree lines from the short or open point to the (0,1) and (0,-1) points, for QL
2. curves of unit normalised reactance or susceptance, going from the open or short point to the (0,1) and (0,-1) points, for QE
3. circular arcs joining the short and open points, with their centres at the (0,1) and (0,-1) points, for Q0
I was taught this method over 40 years ago to measure the Qs of magnetron resonators.
The equations for the curves can be derived simply from the expressions for the reflection from a series or parallel LCR circuit at the end of a transmission line.
Can you share the title of a paper to use as a reference? Thank you.
Article RF engineering basic concepts: the Smith chart
This might have something
https://people.engineering.olemiss.edu/darko-kajfez/assets/rfqmeas2b.pdf
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