Is there a difference between calculation of Q-factor in S-Parameter results using magnitude or dB scale?

[Morteza.teymoori]

I want to calculate the Q-factor using the S-parameter results. However, it came to my attention results significantly is different when I use the s-parameter magnitude (range [0 1]) compared with when I use dB scale.
Calculation method:
1. Magnitude
Q=f0/(FWHM)

2. dB scale
Q=f0/(df)
df=f2-f1 where f1 and f2 have 3dB difference that the resonance strength in f0.

The difference between these two are so huge. For example while the Q-factor appears to be 1700 when I use dB scale, the result for Q-factor calculation using magnitude is around 60-80.

What is my mistake?

 

[FvM]

FWHM corresponds to -6 dB bandwidth, so the results are surely different.

 

[Morteza.teymoori]

FWHM corresponds to -6 dB bandwidth, so the results are surely different.

Really? So which one is correct? what is the standard calculation of Q-Factor? and also what would be the correct ratio corresponding to 3 db?

 

[FvM]

If you refer to the pole-pair Q of a first order band pass filter, -3 dB is correct. It corresponds to half-power bandwidth, magnitude = 0.707.