Method to Determine the Closed-Loop Precision of Resonant Sensors from Open-Loop Measurements

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Resonant sensors determine a sensed parameter by measuring the resonance frequency of a resonator. For fast continuous sensing, it is desirable to operate resonant sensors in a closed-loop configuration, where a feedback loop ensures that the resonator is always actuated near its resonance frequency, so that the precision is maximized even in the presence of drifts or fluctuations of the resonance frequency. However, in a closed-loop configuration, the precision is not only determined by the resonator itself, but also by the feedback loop, even if the feedback circuit is noiseless. Therefore, to characterize the intrinsic precision of resonant sensors, the open-loop configuration is often employed. To link these measurements to the actual closed-loop performance of the resonator, it is desirable to have a relation that determines the closed-loop precision of the resonator from open-loop characterisation data. In this work, we present a methodology to estimate the closed-loop resonant sensor precision by relying only on an open-loop characterization of the resonator. The procedure is beneficial for fast performance estimation and benchmarking of resonant sensors, because it does not require actual closed-loop sensor operation, thus being independent on the particular implementation of the feedback loop. We validate the methodology experimentally by determining the closed-loop precision of a mechanical resonator from an open-loop measurement and comparing this to an actual closed-loop measurement.

Original languageEnglish
Pages (from-to)14262-14272
JournalIEEE Sensors Journal
Issue number23
Publication statusPublished - 2020

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Allan deviation
  • frequency precision
  • limit of detection
  • mass resolution
  • noise
  • phase-locked loop
  • resonant sensor
  • resonator


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  • LEaDing Fellows

    Gutierrez, A., Dols Perez, A., Bae, D., Sahoo, H., Wang, W., Lam, K. L., Raimondo, A., Steffelbauer, D. B., Lesne, E. L., Ragno, E., Amador, G. J., Šiaudinyte, L., Sand, M., Robinson Garcia, N., Abil, Z., Purkarthofer, E., Noardo, F., Tasić, J. K., Marin, L., Angeloni, L., loddo, M., Stockill, R. H. J., Franklin, S. W., Hensen, B. J., Dennis, M. J., Afroza Islam, S. T., Kim, T., Manzaneque Garcia, T., Tiringer, U., Marques Penha, F., Esteban Jurado, C., Timmermans, E., McCrum, I. T., Pool, F., Forn-Cuní, G., Will, G., Barrett, H. E., Everett, J. A. C., Kostenzer, J., Luksenburg, J., Hirvasniemi, J., Desai, J., Ruibal, P., Albury, N. J., March, R., Eichengreen, A., Muok, A. R., Cochrane, A., Ravesteijn, B., Riumalló Herl, C. J., Meeusen, C., Biaggi, C., Granger, C., Cecil, C., Fosch Villaronga, E., Sánchez López, E. S., Loehrer, E., da Costa Gonçalves, F., Giardina, F., Wu, H., Gleitz, H. & Khatri, I.


    Project: Research

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