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Ultra low amplitude quartz oscillator

D

Daniel Haude

Jan 1, 1970
0
Hi folks,
some colleagues approached me about this, thinking I might be able to
build something for them. I don't think it'll work though.

What they want to do is to oscillate a quartz cantilever at about 100kHz
with an amplitude in the order of a few angstroms. This translates to an
electrical ampltitude across the electrodes of less than a mV and a total
oscillation energy of about 20 eV!

The oscillator would be mounted in a vacuum so air damping wouldn't be an
issue.

Of course it's no problem to just drive the quartz with a small AC voltage
to get it to oscillate with the desired amplitude, but is it possible to
operate the quartz as a resonating oscillator at such low levels? At the
end of about two meters of cable?

I don't think it can be done, but I'm always very pessimistic. 20eV,
sheesh! A single UV light quant! I'd welcome any ideas on this. The
objective, by the way, is to measure changes in the resonant frequency of
the cantilever caused by a force gradient.

Thanks,
--Daniel
 
P

Phil Hobbs

Jan 1, 1970
0
Daniel said:
Hi folks,
some colleagues approached me about this, thinking I might be able to
build something for them. I don't think it'll work though.

What they want to do is to oscillate a quartz cantilever at about 100kHz
with an amplitude in the order of a few angstroms. This translates to an
electrical ampltitude across the electrodes of less than a mV and a total
oscillation energy of about 20 eV!

The oscillator would be mounted in a vacuum so air damping wouldn't be an
issue.

Of course it's no problem to just drive the quartz with a small AC voltage
to get it to oscillate with the desired amplitude, but is it possible to
operate the quartz as a resonating oscillator at such low levels? At the
end of about two meters of cable?

I don't think it can be done, but I'm always very pessimistic. 20eV,
sheesh! A single UV light quant! I'd welcome any ideas on this. The
objective, by the way, is to measure changes in the resonant frequency of
the cantilever caused by a force gradient.

Thanks,
--Daniel
Many moons ago (1988), I built one of the earliest magnetic force microscopes
(and the very first to go into commercial production). It used a magnetic
cantilever vibrating at 200 kHz, with amplitudes of a nanometer or two, read
out with a focused-beam interferometer. It achieved good SNR with spatial
resolutions of 250 angstroms, which was the world record at the time (I'm not
sure what the record is now).

The limiting factor is the thermal noise vibration of the resonator.
Classical equipartition says that the equilibrium energy in each vibration
mode is kT/2 (13 meV at room temperature). The integral of the total
position noise power over frequency will be kT/2, and the shape of the noise
spectrum will be the same as the crystal's frequency response. (This is
exactly how you derive the Johnson noise formula for a resistor.) Kinetic
and potential energy will each have this kT/2 mean value in each mode.

Since the energy of the oscillation you're aiming at is much more than kT/2,
your SNR should be quite good.

To drive it, you might want to put a 1 ohm : 49 ohm voltage divider at the
crystal end of the cable. This will let you use a much higher drive power,
and have that much more immunity to pickup and so on. It will also reduce
the resistive loading of the resonance, and so improve the Q somewhat.

Cheers,

Phil Hobbs
 
J

John Woodgate

Jan 1, 1970
0
I read in sci.electronics.design that Daniel Haude
hysnet.uni-hamburg.de>) about 'Ultra low amplitude quartz oscillator',
What they want to do is to oscillate a quartz cantilever at about 100kHz
with an amplitude in the order of a few angstroms. This translates to an
electrical ampltitude across the electrodes of less than a mV and a
total oscillation energy of about 20 eV!

Provided that's above the system noise level, you stand a chance.
The oscillator would be mounted in a vacuum so air damping wouldn't be
an issue.

And thus the Q is huge, which may be good for the noise level.
Of course it's no problem to just drive the quartz with a small AC
voltage to get it to oscillate with the desired amplitude, but is it
possible to operate the quartz as a resonating oscillator at such low
levels? At the end of about two meters of cable?
Probably not as the resonant element, because of the very low energy,
but as a frequency-control element, probably you can. Its Q is likely to
be much greater that that of any discrete resonant circuit, so it could
take charge of the frequency.

But I wouldn't go so far as to suggest exactly how to do it.
 
W

Winfield Hill

Jan 1, 1970
0
Daniel Haude wrote...
What they want to do is to oscillate a quartz cantilever at about 100kHz
with an amplitude in the order of a few angstroms. This translates to an
electrical ampltitude across the electrodes of less than a mV and a total
oscillation energy of about 20 eV!

Isn't that routine for the AFM crowd?
 
T

Tim Wescott

Jan 1, 1970
0
Phil said:
Many moons ago (1988), I built one of the earliest magnetic force
microscopes (and the very first to go into commercial production). It
used a magnetic cantilever vibrating at 200 kHz, with amplitudes of a
nanometer or two, read out with a focused-beam interferometer. It
achieved good SNR with spatial resolutions of 250 angstroms, which was
the world record at the time (I'm not sure what the record is now).

The limiting factor is the thermal noise vibration of the resonator.
Classical equipartition says that the equilibrium energy in each
vibration mode is kT/2 (13 meV at room temperature). The integral of
the total position noise power over frequency will be kT/2, and the
shape of the noise spectrum will be the same as the crystal's frequency
response. (This is exactly how you derive the Johnson noise formula for
a resistor.) Kinetic and potential energy will each have this kT/2 mean
value in each mode.

Since the energy of the oscillation you're aiming at is much more than
kT/2, your SNR should be quite good.

To drive it, you might want to put a 1 ohm : 49 ohm voltage divider at
the crystal end of the cable. This will let you use a much higher drive
power, and have that much more immunity to pickup and so on. It will
also reduce the resistive loading of the resonance, and so improve the Q
somewhat.

Cheers,

Phil Hobbs

So if you did this you'd have to use a Kelvin connection with a 4-wire
cable? If you didn't use the crystal to set the frequency of your
oscillator you should still be able to drive it with a high-impedance
source (perhaps with a pad at the end of the cable, but with a high
impedance toward the crystal). Then you can measure it's phase on the
return line with a quadrature multiplier or whatever.
 
K

Ken Smith

Jan 1, 1970
0
Hi folks,
some colleagues approached me about this, thinking I might be able to
build something for them. I don't think it'll work though.

What they want to do is to oscillate a quartz cantilever at about 100kHz
with an amplitude in the order of a few angstroms. This translates to an
electrical ampltitude across the electrodes of less than a mV and a total
oscillation energy of about 20 eV!

Just a thought:

I assume they want the drive to be at resonance. If you can make this
cantilever look like a 4 terminal device I suggest you think about the
following.

If you have a low noise VCO tuned near the resonance of the device, the
phase shift from the input terminals to the output terminals will depend
on the difference between the drive frequency and resonance. You can use
a multiplying type of phase detector and an integrator to slowly shift the
VCO onto frequency. The nice thing about this is that it should work even
if the SNR is less than one.
 
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