Method and apparatus to implement frequency stabilization of a resonator

Patent metadata

Field	Value
Publication number	US-10352974-B2
Application number	US-201615189967-A
Country	US
Kind code	B2
Filing date	Jun 22, 2016
Priority date	Jun 22, 2016
Publication date	Jul 16, 2019
Grant date	Jul 16, 2019

Abstract

A method of characterizing frequency fluctuations of a resonator comprising the steps of: a) driving the resonator, in a linear regime, by simultaneously applying two periodical driving signals having respective frequencies, the frequencies being different from each other and from a resonant frequency of the resonator, but contained within a resonance linewidth thereof; b) performing simultaneous measurements of response signal of the resonator at the frequencies of the periodical driving signal; and c) computing a value representative of a correlation between the measurements, the value being indicative of frequency fluctuations of the resonator. An apparatus for implementing such a method is provided.

First claim

The invention claimed is:

1. A method of characterizing frequency fluctuations of a resonator having a resonant frequency f 0 utilizing a frequency fluctuation characterization apparatus, comprising the steps of:
a) generating simultaneously, with at least one signal generator, two periodical driving signals having respective frequencies f 1 , f 2 , said frequencies being different from each other, but contained within a resonance linewidth of the resonator, generating a resonator drive signal responsive to the two periodical driving signals, and driving the resonator with the resonator drive signal;
b) performing simultaneous measurements of a response signal of said resonator at the frequencies f 1 , f 2 , of said periodical driving signals, comprising measurements of time-varying phases of the response signal, with a signal sensing device; and
c) computing a correlation between said measurements with a signal processor responsive to the signal sensing device, said correlation being indicative of frequency fluctuations of the resonator, said correlation being utilized in a feedback system to control a resonant frequency of the resonator to compensate for the frequency fluctuations.

2. The method of claim 1 wherein step a) comprises driving the resonator in a linear regime.

3. The method of claim 1 wherein the frequencies f 1 and f 2 are both different from the resonant frequency f 0 .

4. The method of claim 1 , further comprising a step b′), carried out before step c), of performing filtering of said time-varying phases.

5. The method of claim 4 wherein said filtering is a band-pass filtering.

6. The method of claim 1 , wherein:
step b) comprises performing a plurality of measurements of the time-varying phases of the response signal at said frequencies f 1 , f 2 using different integration times τ 1 and performing band-pass filtering of each measured time-varying phase using a filter whose bandwidth is centered on a frequency inversely proportional to the respective integration time; and
step c) comprises computing a correlation between band-pass filtered time-varying phases of said spectral components of the resonance signal for each integration time.

7. The method of claim 6 further comprising:
a step d) of using the value computed during step c) for determining a range of integration times wherein the response signal of the resonator is dominated by frequency fluctuations thereof; and
a step e) of performing a feedback-loop control on the resonant frequency of the resonator within a frequency range corresponding to said range of integration times.

8. The method of claim 1 , wherein step c) comprises converting the measured time-varying phases to time-varying frequency values using a frequency-phase relationship of said resonator, and computing a correlation thereof.

9. The method of claim 1 , further comprising performing closed-loop control of the frequencies of the periodical driving signals using the respective measured time-varying phases as feedback signals, and wherein step c) comprises computing a correlation of said frequencies.

10. The method of claim 1 wherein said simultaneous measurements are performed by heterodyne detection.

11. The method of claim 1 wherein said simultaneous measurements are performed by homodyne detection.

12. The method of claim 1 wherein said resonator is a MEMS and/or NEMS.

13. An apparatus for characterizing frequency fluctuations of a resonator comprising:
a driving signal generator configured for simultaneously generating at least the two periodical driving signals at different frequencies f 1 , f 2 , said frequencies being different from each other, but contained within a resonance linewidth of the resonator;
a circuit configured to receive the two periodical driving signals and based on the two periodical driving signals generate a resonator drive signal and provide the resonator with the resonator drive signal;
at least one sensing device, configured for performing simultaneous measurements of a response signal of said resonator at the frequencies f 1 , f 2 of said periodical driving signals, and configured for measuring time-varying phases of the response signal; and
a signal processor, configured for computing a correlation between said measurements of a response signal of said resonator, said correlation being indicative of frequency fluctuations of the resonator, said correlation being utilized in a feedback system to control a resonant frequency of the resonator to compensate for the frequency fluctuations.

14. The apparatus of claim 13 , wherein the signal processor is configured for performing filtering of said time-varying phases.

15. The apparatus of claim 14 wherein said filtering is a band-pass filtering.

16. The apparatus of claim 13 , wherein:
the sensing device is configured for performing a plurality of measurements of the time-varying phases of said response signal at the frequencies of said periodical driving signals using different integration times τ I ;
the signal processor is configured for performing band-pass filtering of each measured time-varying phase using a filter whose bandwidth is centered on a frequency inversely proportional to the respective integration time; and for computing a value representative of a correlation between band-pass filtered time-varying phases of said spectral components of the resonance signal for each integration time.

17. The apparatus of claim 16 wherein the signal processor is further configured for determining a range of integration times wherein the response signal of the resonator is dominated by frequency fluctuations thereof, the apparatus further comprising a feedback loop controller configured for controlling the resonant frequency of the resonator within a frequency range corresponding to said range of integration times.

18. The apparatus of claim 13 , wherein the signal processor is configured for converting the measured time-varying phases to time-varying frequency values using a frequency-phase relationship of said resonator, and computing a correlation thereof.

19. The apparatus of claim 13 further comprising two feedback loops configured for performing closed-loop control of the frequencies of the periodical driving signals using the respective measured time-varying phases as feedback signals, and wherein the signal processor is configured for computing a correlation of said frequencies.

Assignees

• Commissariat Energie Atomique

Inventors

• Sansa Perna Marc
• Hentz Sébastien
• Jourdan Guillaume

Classifications

• H03J3/12

  Electrically-operated arrangements for indicating correct tuning · CPC title

• G01R29/26

  Measuring noise figure; Measuring signal-to-noise ratio · CPC title

• B81B3/0032

  Structures for transforming energy not provided for in groups B81B3/0021 - B81B3/0029 · CPC title

• B81B2201/0271

  Resonators; ultrasonic resonators · CPC title

• G01R23/15 Primary

  Indicating that frequency of pulses is either above or below a predetermined value or within or outside a predetermined range of values, by making use of non-linear or digital elements {(indicating that pulse width is above or below a certain limit)} · CPC title