[SI-LIST] Re: Crystal datasheet!!
- From: Ray Anderson <reanderson@xxxxxxxxxxxxx>
- To: ashish.panpalia@xxxxxx
- Date: Thu, 25 Nov 2004 09:13:39 -0800
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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