Ok, lets get real here.
Temperature variations, could cause a phase shift but a very very slow one, the
degree would depend on the
Q of the filter, temperature coefficient of the crystal, and capacitor and how
well it is isolated from turbulent air.
I am not new to the game of making sensitive measurements using high Q filters.
I would be more concerned with the phase changes due to the fractional Hz 1/f
noise of the input threshold voltages of the FET's
also any trigger circuit that may follow used to feed counters etc in
instruments preceding and following the doubler. I am surprised
that you aren't complaining about the sideband noise produced by the Brownian
motion of nitrogen molecules inside the crystal case.
In this case it is a 2 pole filter and once the phasing capacitor is adjusted
the only the mechanical vibrational resonance of the
crystal really counts.
If you are interested in High Q resonators, phase shift, etc. you might want
to take a look at Review of Scientific Instruments 60, 3035 (1989),
"Use of a helical resonator as a capacitive transducer in vibrating reed
measurements" where a helical resonator
is used to measure the vibrations of small crystals with an sensitivity of
10e-7 Angstroms per square root Hertz bandwith.
Also, take a look at citations in other papers and patents referencing this
design.
I just tried to describe a simple very pure sine wave doubler for your
readers.
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