Feedback-induced phase noise in microcantilever-based oscillators

When electronic feedback is used around resonant microcantilevers, their native resonance frequency f0 and that under feedback fFB = f0 ± Δf differ. This not only gives a wrong measurement of f0 due to the feedback-induced error ± Δf, but also degrades the performances of oscillating loops. The static frequency shift Δf appearing in constant-gain loops due to feedback forces in phase with z(t) becomes a frequency noise when the loop gain changes randomly as in oscillating loops by the action of noise on the gain limiter of the loop. This is the source of phase noise this paper reveals for the first time that can be summarized by this sentence: the imperfect actuation of feedback loops in cantilever-based oscillators is a source of their phase noise. We show how to reduce this noise by a tight phase control in the loop gain to drive cantilevers by forces exactly in quadrature respect to their instantaneous displacement z(t).