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Ultra low amplitude quartz oscillator

Discussion in 'Electronic Design' started by Daniel Haude, Sep 6, 2004.

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  1. Daniel Haude

    Daniel Haude Guest

    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

    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.

  2. Phil Hobbs

    Phil Hobbs Guest

    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.


    Phil Hobbs
  3. I read in that Daniel Haude>) about 'Ultra low amplitude quartz oscillator',
    Provided that's above the system noise level, you stand a chance.
    And thus the Q is huge, which may be good for the noise level.
    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.
  4. Daniel Haude wrote...
    Isn't that routine for the AFM crowd?
  5. Tim Wescott

    Tim Wescott Guest

    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.
  6. Ken Smith

    Ken Smith Guest

    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

    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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