  Nanomechanical resonators can serve as high performance detectors and have
potential to be widely used in the industry for a variety of applications. Most
nanomechanical sensing applications rely on detecting changes of resonance
frequency. In commonly used frequency tracking schemes, the resonator is driven
at or close to its resonance frequency. Closed-loop systems can continually
check whether the resonator is at resonance and accordingly adjust the
frequency of the driving signal. In this work, we study three resonance
frequency tracking schemes, a feedback-free (FF), a self-sustaining oscillator
(SSO), and a phase-locked loop oscillator (PLLO) scheme. We improve and extend
the theoretical models for the FF and the SSO tracking schemes, and test the
models experimentally with a nanoelectromechanical system (NEMS) resonator. We
employ a SSO architecture with a pulsed positive feedback topology and compare
it to the commonly used PLLO and FF schemes. We show that all tracking schemes
are theoretically equivalent and that they all are subject to the same speed
versus accuracy trade-off characteristics. In order to verify the theoretical
models, we present experimental steady-state measurements for all tracking
schemes. Frequency stability is characterized by computing the Allan deviation.
We obtain almost perfect correspondence between the theoretical models and the
experimental measurements. These results show that the choice of the tracking
scheme is dictated by cost, robustness and usability in practice as opposed to
fundamental theoretical differences in performance.
