Adaptable frequency counter with phase filtering for resonance frequency monitoring in nanomechanical sensing

Abstract

Nanomechanical sensors based on detecting and tracking resonance frequency shifts are to be used in many applications. Various open- and closed-loop tracking schemes, all offering a trade-off between speed and precision, have been studied both theoretically and experimentally. In this work, we advocate the use of a frequency counter (FC) as a frequency shift monitor in conjunction with a self-sustaining oscillator (SSO) nanoelectromechanical system (NEMS) configuration. We derive a theoretical model for characterizing the speed and precision of frequency measurements with state-of-the-art FCs. Based on the understanding provided by this model, we introduce novel enhancements to FCs that result in a trade-off characteristics which is on a par with the other tracking schemes. We describe a low-cost field-programmable-gate array (FPGA)-based implementation for the proposed FC and use it with the SSO-NEMS device in order to study its frequency tracking performance. We compare the proposed approach with the phase-locked-loop-based scheme both in theory and experimentally. Our results show that similar or better performance can be achieved at a substantially lower cost and improved ease of use. We obtain almost perfect correspondence between the theoretical model predictions and the experimental measurements.