Q Control

Q ControlThe Q Control feature is optional on the NanoScope V-PI.1 refers to the use of a frequency-dependent drive amplitude in TappingMode. “Q” is a measure of the sharpness of the resonant peak and is calculated by dividing the resonant frequency by the width of the resonant peak at half the maximum power (see Figure 1). Power is proportional to amplitude squared, so the frequency interval, γ, between half-peak-power points, equals the interval between A0/√2 points, where A0 is the peak amplitude.

Figure 1: The Q of a Resonance

Q control enables either enhancement or damping of a resonance. That is, Q may be increased or decreased with respect to the natural value that is observed in Cantilever Tune when sweeping over a range of frequencies while holding drive amplitude constant. One application of Q reduction is to damp the lower frequency Active Tip cantilever resonance (i.e., ~50 kHz) while driving probe oscillation at the resonance located at approximately 200 kHz. A typical application of Q enhancement is to increase phase contrast by applying Q control to the cantilever resonant frequency.

As demonstrated in the first example, Q Control need not be applied at the resonant frequency chosen for tapping. However, Q Control may only be applied to a single frequency at a time, so both enhancement and damping cannot be employed simultaneously.

The implementation of Q control is diagrammed in Figure 2. Q Control is a feedback loop. The proprietary signal processing block features programmable control of phase shifting and amplification gain of the cantilever deflection signal. The result of signal processing is mixed with the independently-generated cantilever drive signal to produce a Q controlled cantilever drive. For a mathematical derivation of Q control properties from signal processed feedback, see A Q Control Model.

Figure 2: Q Control Block Diagram

Summarizing, the cantilever piezoelectric actuator (“Piezo” in Figure 2) is driven from two electrical contacts that may be influenced by three sources.

When Q control is active (TappingMode only), an adjustment is mixed into the AC piezo drive signal to achieve the target Q.

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