[time-nuts] Re: Is SC the most stable cut for lowest phase noise?

[Richard (Rick) Karlquist]

Yet another interesting time nuts conversation.
A few comments:

1  A number of comments stated as a "fact" that
higher unloaded Q for the resonator
corresponds to lower phase noise.  This
idea evidentially comes from looking at analysis
of a so-called free running oscillator with a simple
LC tank or microwave resonator, as published by
Edson, Kurakawa, and Cutler/Leeson.  However,
even in this case, what matters is the LOADED Q,
and the drive level to the sustaining amplifier.
A given drive level will have a particular phase
noise and flicker noise floor associated with it.
Incidentally, the resonator should be critically
coupled, in which case Ql = 1/2 Qu, for optimum
phase noise.,

2.  With a piezo electric resonator, the intrinsic
flicker noise of the resonator dominates, and it
isn't related to Q (unloaded to loaded).  The
sustaining amplifier ordinarily is not a factor.

3.  I personally measured the intrinsic phase noise
of a free-standing 10811 crystal and compared it to
the phase noise of a 10811 oscillator with that
same crystal installed.  The conclusion was that the
oscillator phase noise was basically the same as
the intrinsic crystal noise, except at large
frequency offsets.

4.  The only possible scenario I can see for why
an SC cut might have better phase noise is if you
don't have a very good oven.  Then ADEV at long
averaging times starts to go up.  In that case,
an SC cut might help because of improving tempco.

5. Phase noise at large offsets (>1kHz) depends
on the buffer amplifier design.  The grounded base
design in the 10811 is the optimum first stage.
Unfortunately, the 2nd and 3rd stages in the 10811
degrade its phase noise.  This has little or nothing
to do with the cut of the crystal or anything else
about it.  (The idea for this was published by U. Rhode
and later patented by Burgoon of HP).

6.  The primary motivation for the SC cut at the
HP Santa Clara division (where I worked) was to be
able to put it into a frequency counter used for
field maintenance.  The idea was that the technician
could carry it from his truck into the worksite
and plug it, starting from a cold oven.  Then, in
only 15 minutes, the counter met some accuracy spec.
With a 10544, it would take many times longer to get to
the same accuracy.  Jack Kusters used to say that
"SC" actually stood for "Santa Clara" :-)

Rick N6RK