[SI-LIST] Re: Crystal datasheet!!

Ashish PANPALIA wrote:

>Hello
>Is there any relationship between the Q factor and frequency tolerance 
>of a crystal? Can I assume both to be the same quantity?
>
>-Ashish
>
> 
>  
>
 
No, not directly at least.

The Q number is a metric that characterizes the 'bandwidth' of the 
crystals resonance. The higher the Q the narrower the resonance. 
Oscillators utilizing high Q resonators have the potential for lower 
phase noise or better jitter performance.

The unloaded Q (Qu) of a quartz crystal is given by:

Qu = 1.2*10^8F/(deltaF*Rs)

where F is the series resonant frequency and deltaF is the 3dB bandwidth 
of the resoantor

So you can see that an increase in the ESR (Rs) will decrease Qu.

Crystals with a high Qu correspondingly have a small bandwidth (deltaF) 
which means that there is a high dZ/dF. Small excursions in frequency 
cause a large change in series impedance (in particular the phase). Iyt 
is this effect that allows crystal resonators to maintain tight 
frequency control with potentially low short and long term drift.



Whe you talk about frequency tolerance you need to define whether it is 
calibration frequency tolerance or frequency tolerance with regards to 
temperature, time or drive level. I suppose some of those effects may be 
loosely tied to the resonators Q, but I think they are probably 3rd or 
4th order effects.

-Ray Anderson
Xilinx Inc.

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