crystal oscillator

See my article below on analyzing crystal oscillators in SPICE. It gives the equations and some typical values.

Regards,

Mike Monett

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SPICE Analysis of Crystal Oscillators: Noise-Rejecting Wideband Sampler:

If you measure the crystal's impedance at resonance (series resonance), you know the ESR (Rseries). Presumably you can also know the resonant frequency, from which you know Lseries*Cseries. Assuming that the anti-resonance (parallel resonance) is removed far enough in frequency from the resonance, you can measure the frequencies at which the phase shift reaches +/-45 degrees (the -3dB points; the points at which the magnitude of the impedance reaches sqrt(2) times that at resonance) and from that you can resolve the Lseries and Cseries: the 3dB points and the resonant frequency will tell you the Q, and Q*Rseries tells you the inductive and capacitive reactances at resonance. You can measure the Cparallel at low frequency and correct your calculations accordingly if you wish. That is to say, you can make additional measurements and refine your model until it matches the measurements to whatever degree you wish. (Some people will refine the model to include additional parasitic resonances near the primary resonance, or the overtone resonances. But you may not care about those.)

There have been articles in the amateur radio magazines as well as various professional engineering journals about measuring crystal parameters. A Google search for "crystal parameter measurement" will turn up a lot of info. In particular, there have been articles in the amateur journals on making a simple fixture that will let you measure the parameters with reasonable accuracy using relatively inexpensive equipment. A frequency counter to accurately resolve the frequencies is the key.

Cheers, Tom

snipped-for-privacy@gmail.com wrote:

Please don't top post.

snipped-for-privacy@gmail.com a écrit :

1pF, 0/-100% ought to do for all practical cases :-)

Seriously, there's nothing you can expect from this kind of datasheet.

If you need something reasonably accurate, either measure it or ask to the manufacturer.

Some assumptions about the crystal Q will give you values that might be 'accurate' enough for your needs.

--
Thanks,
Fred.

Further to what Fred wrote, if you assume Q to be in the range of

10,000 to 50,000 (which I believe is reasonable for small AT-cut crystals not optimized for high Q), and the series resistance to be 50 ohms, and the frequency to be 20MHz, then you can deduce that the reactance will be in the range of 500kohms to 2.5Mohms, and at 20MHz, the capacitance would be between about 3.1fF and 16fF. The equivalent series capacitance of a crystal resonator is generally quite small, like that, and the equivalent inductance is quite large. Those are, of course, electrical equivalents of the piezo-mechanical behavior of the crystal.

WHY do you want to know? If it's for design of something where those parameters are really important, such as a crystal filter, two cases come to mind: first is that you are building something one-off as a hobby thing, in which case you should prepare yourself to make the measurements. It doesn't take much of a "lab" to do it. Second is that you want to put something into production, in which case you should find a crystal vendor that's willing to work with you to specify the crystals sufficiently for the application.

Cheers, Tom

. . .

Have a look here:

for more info on expected Q of AT-cut crystals. You can probably find other papers or ap notes on the web. Try several crystal manufacturers' web sites. Some provide much better applications info than others.

Cheers, Tom

Thanks all, your comments were very informative and helpful.

Regards, Atul