[R-390] Crystal substitution puzzle

[Gord Hayward]

>
>
>Funny thing though.  Out on the net there's an analysis
>of series- vs parallel-mode crystal operation in an
>oscillator, and his conclusion is that a series-rated
>crystal operated inductively will run above rating,
>not below.  Of course, everything on the web is right :)
>

The phase curve for a crystal starts at -90 deg at low frequencies then 
pops up to +90 deg at the series resonance point
stays up for about 20 kHz then drops back to -90 deg.  With a clean 
crystal, the rise and drops occur over a couple of Hz
but when they are wet the rise is much more gradual and doesn't get to 
+90 deg.  I'm one of the few who run crystals wet,
in my case, immersed in homogenized sheep brains.  -90 deg is 
capacitive, so as the frequency rises the crystal goes
inductive at the series resonance point.  For more information than you 
probably want, look up 'A transverse shear model
of a piezoelectric chemical sensor', G. Hayward and M. Thompson, Journal 
of Applied Physics, Vol 83, pages 2194-2201
(1998).  Yes, the Hayward is me.

Cheers, Gord VE3EOS

-- 

Gordon L. Hayward, Ph.D., P.Eng.,
Associate Professor, Biological Engineering,
School of Engineering, University of Guelph,
Guelph, Ontario, N1G 2W1.