[time-nuts] Old Crystal.

[Bernd Neubig]

Hi,
 in general you are right. But for a 1 MHz crystal it is fair to assume the XC0 is much higher than the crystal impedance around the series resonance. Therefore, in good approximation you can consider the crystal like a series resonance R-L-C circuit in the vicinity of series resonance. C0 can be measured separately with a conventional R-L-C- meter far-off resonance.
This is the basis of the evaluation I have described, which needs only three frequencies. And it is sufficient to use this method up to about 30 ~ 50 MHz without significant loss of accuracy.
For higher accuracy the real and imaginary part of the admittance can be used. Theoretically this allows to determine the four parameters at 2 suitable frequencies. Unsing three frequencies gives you already some additional degree of freedom (accuracy).
The latter method is described in some of my publications and found is standardized in IEC standard 60444-5.

Bernd

----- Bob kb8tq  wrote-----

You need to extract Cm, Lm and Rm ( motional resistance, capacitance, inductance) for the mode you are looking at. You also need C0. Once you have those you can come up with Q. Because of the interaction between C0 and the other parameters, you need to extract them all. ( yes, you could extract Fs and leave out Lm, it’s still three parameters plus C0). 

Bob