Do you remember the Nierdermeyer algorithm that I used ? Those two link might help you Tayeb (if you needs I still have the code that's calculate the Q factor from complex Impedance or Gain):

[1] http://iopscience.iop.org/0957-0233/23/8/085107

[2] http://www.researchgate.net/profile/Thomas_Voglhuber-Brunnmaier/publication/257725791_Evaluating_the_Robustness_of_an_Algorithm_Determining_Key_Parameters_of_Resonant_Sensors/links/00b4953ad35f5a2754000000.pdf.

Article Evaluating the Robustness of an Algorithm Determining Key Pa...

Thank you Etienne.

Actually, the Niedermayer method allows estimating Q factor and fr from circle-fitting. I read his program to understand how he do it .

Thanks again ;)

Yes it is true ! So what you can do is modify the Niedermayer code in order to fit with an ellipsoid instead of circle... But it might be not so easy to implement (and you might have thought about this before..)  

I don't need ellipsoid fitting. For a few days, I was looking for a general circle equation containing Q and fr (or f0) parameter for 2nd  ordre system resonators in ordre to facilitate fitting procedure, but nothing found. Because we can only express circle equation with fr (or f0) and damping coefficient which is not the damping ratio corresponding to 1/2Q. With damping coefficient we need to know another parameter in order to calculate damping ratio....overly complicated ("for me").

But I think that I have found a solution in Niedermayer paper ;)

Thanks Etienne :)

If you can extract first f0 and then fr ( e.g. using a second fit), then you can calculate directly the damping ratio Xi from those two values ( see one of the def. of Xi wrt f0 and fr)

another good idea!