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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.


Closed-loop response (gray) and averaged equation simulation (black) when Vref = 0.7 > Vrefo. (A) The curve of the drive displacement with time. (B) The curve of the output of integrator z(t) with time.
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f8-sensors-09-03357: Closed-loop response (gray) and averaged equation simulation (black) when Vref = 0.7 > Vrefo. (A) The curve of the drive displacement with time. (B) The curve of the output of integrator z(t) with time.

Mentions: Figures 7 and 8 are the simulated closed-loop response and averaged equation simulation curves when Vref = 0.3 < Vrefo and Vref = 0.7 > Vrefo. The simulation result indicates the envelope curve of the closed-loop response is basically the same as the curve of the averaged equation. The tiny differences come from the simplification of the integrator and truncation error in simulation. From Figure 8, when Vref = 0.7 > Vrefo, we can see that the envelope curve of the closed-loop response is also basically the same as the curve of averaged equation. Meanwhile, z ≈0, revealing that the above gain branch circuit does not work normally, which is in agreement with the practical situation. Thus, the averaged equation can be applied to the situations when Vref > Vrefo through the limit of the working scale of z(t).


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

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

Closed-loop response (gray) and averaged equation simulation (black) when Vref = 0.7 > Vrefo. (A) The curve of the drive displacement with time. (B) The curve of the output of integrator z(t) with time.
© Copyright Policy
Related In: Results  -  Collection

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

f8-sensors-09-03357: Closed-loop response (gray) and averaged equation simulation (black) when Vref = 0.7 > Vrefo. (A) The curve of the drive displacement with time. (B) The curve of the output of integrator z(t) with time.
Mentions: Figures 7 and 8 are the simulated closed-loop response and averaged equation simulation curves when Vref = 0.3 < Vrefo and Vref = 0.7 > Vrefo. The simulation result indicates the envelope curve of the closed-loop response is basically the same as the curve of the averaged equation. The tiny differences come from the simplification of the integrator and truncation error in simulation. From Figure 8, when Vref = 0.7 > Vrefo, we can see that the envelope curve of the closed-loop response is also basically the same as the curve of averaged equation. Meanwhile, z ≈0, revealing that the above gain branch circuit does not work normally, which is in agreement with the practical situation. Thus, the averaged equation can be applied to the situations when Vref > Vrefo through the limit of the working scale of z(t).

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.