Dynamical response and noise limit of a parametrically pumped microcantilever sensor in a Phase-Locked Loop

We investigate the response of a digitally controlled and parametrically pumped microcantilever used for sensing in a Phase-Locked Loop (PLL). We develop an analytical model for its dynamical response and obtain an explicit dependence on the rheological parameters of the surrounding viscous medium. Linearization of this model allows to find improved responsivity to density variations in the case of parametric suppression. Experiments with a commercial microcantilever validate the model, but also reveal an increase of frequency noise in the PLL associated with the parametric gain and phase, which, in most cases, restricts the attainable limit of detection. The noise in open-loop is studied by measuring the random fluctuations of the noise-driven deflection of the microcantilever, and a model for the power spectral density of amplitude, phase and frequency noises is discussed and used to explain the frequency fluctuations in the closed-loop PLL. This work concludes that parametric pumping in a PLL does not improve the sensing performance in applications requiring detecting frequency shifts.