[time-nuts] Quartz Crystal Motional Movement

Bernd Neubig BNeubig at t-online.de
Sun Jun 26 06:40:55 EDT 2016

Bob Camp:
>Every paper I have ever read on the intrinsic Q of quartz makes the claim that Q * F is a constant ( Q goes up as frequency goes down).  Unless blank diameter gets in the way, this has been true for any >crystals I have ever used. Q does change as overtone changes, but that is not related to the Q of the material. A given blank design may (or may not) be limited by the Q of the quartz at any specific >frequency. That is a function of a lot of things. 
>The material’s properties set a maximum Q you can achieve no matter how good your blank design is and how big the blank. Done properly, the best 5 MHz resonator you can do *will* have 2X the Q of >the best 10 MHz resonator. 

Indeed there is an physical limitation for the Q of piezoelectric resonators, which is given by phonon interactions etc. For quartz this limit is given approximately by Q*f = 15E12. See attached graph (sorry, in German). The real crystal Q is determined by a couple of other factors like 
- damping caused by the suspension (which for circular plano-parallel thickness shear resonators like AT and SC is the larger, the larger the thickness to diameter ratio is. The impact of the suspension can be reduced e.g. by contouring the crystal (beveling, plano-convex or bi-convex shape)
- damping by the surrounding gas (dominating in low-frequency tuning-fork type crystals, important for low- frequency AT-cut crystals, less important for high frequency crystals
- damping effect due to stress and losses between crystal blank and electrodes
- mode of vibration: fundamental is worse than overtones, partly because the electrode losses apply only to two outer interfaces of the vibration sublayers
   rule of thumb for ATs with f in Hz: fundamental  mode: Q*f about 1E12, 3rd overtone Q*f about 2E12 ... 4E12, 5th and higher overtone 4E12 to 8E12.
   for SC-cut 3rd or 5th overtone with optimized design Q*f can go up to 13E12, e.g. Q of a good 10 MHz 3rd is about 1.1 mio to 1.3 mio, a good 100 MHz 5th has a q of 120 000 to 135 000
- in tuning fork crystals (which are all evacuated) Q*F is about 0.6E12 to 1.5E12
Rule of thumb means: these are typical averages , there are exceptions

BTW: This does not apply to the sapphire DIELECTRIC resonators or other kinds of resonators like DRO etc.. Those are different animals.

Have fun


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