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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 influence of thermal noise to driving performance when ωnx= 25,120 (rad/s), T=300 K, fB=100 Hz, Qx=2,500, āo = 5 μm. (A) The RMS noise displacements with driving mass. (B) The RMS noise frequency with driving mass.
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f10-sensors-09-03357: The influence of thermal noise to driving performance when ωnx= 25,120 (rad/s), T=300 K, fB=100 Hz, Qx=2,500, āo = 5 μm. (A) The RMS noise displacements with driving mass. (B) The RMS noise frequency with driving mass.

Mentions: In Figure 9, the simulation curves of closed-loop driving between Qx=2,500 and Qx=5,000 are compared. From Figure 9(A), we can see that although the quality factor increases, the amplitude of the driving displacement, which is in agreement with the conclusion derived from Equation (37), doesn't change. That is to say, the displacement amplitude has nothing to do with the quality factor. From Figure 9(B), we can see that the augment of quality factor results in the growth of output of the integrator z(t), which is accordant with the Equation (38). According to Equation (47) and Equation (51), when ωnx= 25,120 (rad/s), T=300 K, fB=100 Hz, Qx=2,500, āo = 5 μm, the influence of thermal noise on driving performance in different drive proof masses is shown in Figure 10. From Figure 10, we can see that the RMS noise displacement and the RMS noise frequency decrease with the increase of drive proof mass.


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

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

The influence of thermal noise to driving performance when ωnx= 25,120 (rad/s), T=300 K, fB=100 Hz, Qx=2,500, āo = 5 μm. (A) The RMS noise displacements with driving mass. (B) The RMS noise frequency with driving mass.
© Copyright Policy
Related In: Results  -  Collection

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

f10-sensors-09-03357: The influence of thermal noise to driving performance when ωnx= 25,120 (rad/s), T=300 K, fB=100 Hz, Qx=2,500, āo = 5 μm. (A) The RMS noise displacements with driving mass. (B) The RMS noise frequency with driving mass.
Mentions: In Figure 9, the simulation curves of closed-loop driving between Qx=2,500 and Qx=5,000 are compared. From Figure 9(A), we can see that although the quality factor increases, the amplitude of the driving displacement, which is in agreement with the conclusion derived from Equation (37), doesn't change. That is to say, the displacement amplitude has nothing to do with the quality factor. From Figure 9(B), we can see that the augment of quality factor results in the growth of output of the integrator z(t), which is accordant with the Equation (38). According to Equation (47) and Equation (51), when ωnx= 25,120 (rad/s), T=300 K, fB=100 Hz, Qx=2,500, āo = 5 μm, the influence of thermal noise on driving performance in different drive proof masses is shown in Figure 10. From Figure 10, we can see that the RMS noise displacement and the RMS noise frequency decrease with the increase of drive proof mass.

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.