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Mechanical-thermal noise in drive-mode of a silicon micro-gyroscope.

Yang B, Wang S, Li H, Zhou B - Sensors (Basel) (2009)

Bottom Line: By calculating and comparing the noise amplitude due to thermal noise both in the opened-loop driving and in the closed-loop driving, we find that the closed-loop driving does not reduce the RMS noise amplitude.We observe that the RMS noise frequency can be reduced by increasing the quality factor and the drive amplitude in the closed-loop driving system.The experiment and simulation results indicate the electrical noise of closed-loop driving circuitry is bigger than the mechanical-thermal noise and as the driving mass decreases, the mechanical-thermal noise may get bigger than the electrical noise of the closed-loop driving circuitry.

View Article: PubMed Central - PubMed

Affiliation: College of Instrument Science & Engineering, Southeast University, Nanjing 210096, China; E-Mails: srwang@seu.edu.cn ; hsli@seu.edu.cn ; zhoubailing@seu.edu.cn.

ABSTRACT
A new closed-loop drive scheme which decouples the phase and the gain of the closed-loop driving system was designed in a Silicon Micro-Gyroscope (SMG). We deduce the system model of closed-loop driving and use stochastic averaging to obtain an approximate "slow" system that clarifies the effect of thermal noise. The effects of mechanical-thermal noise on the driving performance of the SMG, including the noise spectral density of the driving amplitude and frequency, are derived. By calculating and comparing the noise amplitude due to thermal noise both in the opened-loop driving and in the closed-loop driving, we find that the closed-loop driving does not reduce the RMS noise amplitude. We observe that the RMS noise frequency can be reduced by increasing the quality factor and the drive amplitude in the closed-loop driving system. The experiment and simulation validate the feasibility of closed-loop driving and confirm the validity of the averaged equation and its stablility criterion. The experiment and simulation results indicate the electrical noise of closed-loop driving circuitry is bigger than the mechanical-thermal noise and as the driving mass decreases, the mechanical-thermal noise may get bigger than the electrical noise of the closed-loop driving circuitry.

No MeSH data available.


The experiment results of closed-loop driving.(A) Frequency drift of driving signal for 1 h. (B) Amplitude drift of driving signal for 1h. (C) Frequency spectrum of driving signal.
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f13-sensors-09-03357: The experiment results of closed-loop driving.(A) Frequency drift of driving signal for 1 h. (B) Amplitude drift of driving signal for 1h. (C) Frequency spectrum of driving signal.

Mentions: The experiment results of closed-loop driving are shown in Figure 13. Figure 13(A) and Figure 13(B) are the frequency drift and amplitude drift of driving signal for 1 h respectively. The experiment results show that the standard deviation of drive frequency is 0.0205 Hz, with relative drift 5.0 ppm, the standard deviation of the amplitude 0.0165 mV and relative drift 14.7 ppm, respectively. Figure 13(C) is the frequency spectrum of driving signal. The driving signal is about 100 dB bigger than the ground noise, which is accordance with the result of the Figure 13(B). As a result, both stabilities of driving frequency and amplitude are rather high and the closed loop control is very successful. According to Figure 10, when mx=2.89×10-7(kg), āo = 5um, ωnx= 25,120 (rad/s), we can find that the relative noise of drive frequency is approximately 0.0119 ppm and the relative noise of the amplitude is approximately 0.8 ppm, respectively. The noise comparison is shown in Table 2. So, in this situation, the electrical noise of closed-loop driving circuitry is bigger than the mechanical-thermal noise. With the driving mass decreasing, the mechanical-thermal noise may get bigger than the electrical noise of closed-loop driving circuitry (see Figure 10).


Mechanical-thermal noise in drive-mode of a silicon micro-gyroscope.

Yang B, Wang S, Li H, Zhou B - Sensors (Basel) (2009)

The experiment results of closed-loop driving.(A) Frequency drift of driving signal for 1 h. (B) Amplitude drift of driving signal for 1h. (C) Frequency spectrum of driving signal.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3297147&req=5

f13-sensors-09-03357: The experiment results of closed-loop driving.(A) Frequency drift of driving signal for 1 h. (B) Amplitude drift of driving signal for 1h. (C) Frequency spectrum of driving signal.
Mentions: The experiment results of closed-loop driving are shown in Figure 13. Figure 13(A) and Figure 13(B) are the frequency drift and amplitude drift of driving signal for 1 h respectively. The experiment results show that the standard deviation of drive frequency is 0.0205 Hz, with relative drift 5.0 ppm, the standard deviation of the amplitude 0.0165 mV and relative drift 14.7 ppm, respectively. Figure 13(C) is the frequency spectrum of driving signal. The driving signal is about 100 dB bigger than the ground noise, which is accordance with the result of the Figure 13(B). As a result, both stabilities of driving frequency and amplitude are rather high and the closed loop control is very successful. According to Figure 10, when mx=2.89×10-7(kg), āo = 5um, ωnx= 25,120 (rad/s), we can find that the relative noise of drive frequency is approximately 0.0119 ppm and the relative noise of the amplitude is approximately 0.8 ppm, respectively. The noise comparison is shown in Table 2. So, in this situation, the electrical noise of closed-loop driving circuitry is bigger than the mechanical-thermal noise. With the driving mass decreasing, the mechanical-thermal noise may get bigger than the electrical noise of closed-loop driving circuitry (see Figure 10).

Bottom Line: By calculating and comparing the noise amplitude due to thermal noise both in the opened-loop driving and in the closed-loop driving, we find that the closed-loop driving does not reduce the RMS noise amplitude.We observe that the RMS noise frequency can be reduced by increasing the quality factor and the drive amplitude in the closed-loop driving system.The experiment and simulation results indicate the electrical noise of closed-loop driving circuitry is bigger than the mechanical-thermal noise and as the driving mass decreases, the mechanical-thermal noise may get bigger than the electrical noise of the closed-loop driving circuitry.

View Article: PubMed Central - PubMed

Affiliation: College of Instrument Science & Engineering, Southeast University, Nanjing 210096, China; E-Mails: srwang@seu.edu.cn ; hsli@seu.edu.cn ; zhoubailing@seu.edu.cn.

ABSTRACT
A new closed-loop drive scheme which decouples the phase and the gain of the closed-loop driving system was designed in a Silicon Micro-Gyroscope (SMG). We deduce the system model of closed-loop driving and use stochastic averaging to obtain an approximate "slow" system that clarifies the effect of thermal noise. The effects of mechanical-thermal noise on the driving performance of the SMG, including the noise spectral density of the driving amplitude and frequency, are derived. By calculating and comparing the noise amplitude due to thermal noise both in the opened-loop driving and in the closed-loop driving, we find that the closed-loop driving does not reduce the RMS noise amplitude. We observe that the RMS noise frequency can be reduced by increasing the quality factor and the drive amplitude in the closed-loop driving system. The experiment and simulation validate the feasibility of closed-loop driving and confirm the validity of the averaged equation and its stablility criterion. The experiment and simulation results indicate the electrical noise of closed-loop driving circuitry is bigger than the mechanical-thermal noise and as the driving mass decreases, the mechanical-thermal noise may get bigger than the electrical noise of the closed-loop driving circuitry.

No MeSH data available.