The authors present comprehensive theoretical analysis and experimental realization of active control for the self-oscillating quartz tuning fork (TF). It is shown that the quality factor can be increased (decreased) by adding the signal of any phase lag, with respect to the drive signal, in the range of to ( to ), where is the characteristic constant of TF. Experimentally, the nominal value of is decreased to or increased to in ambient condition, where the minimum detectable force is estimated to be at . The novel control scheme demonstrated in the widely used quartz TF is expected to contribute much to scanning probe microscopy of, in particular, soft and biological materials.
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The follower (inverter) is the active electrical component which produces a fixed phase lag of 0° (180°).
Equation (4) can be appoximated to the Lorentzian form by ignoring the first term and the term in the brackets. Comparing to the Lorentzian, is approximated to the angular frequency, which makes the real part of the denominator of Eq. (4) vanish, whereas is given by the proportional coefficient of in the imaginary part.
