These SMGs usually measure the proof-mass displacement by capacitive methods, but under normal atmospheric pressure, the minute moving proof-masses are especially susceptible to mechanical noise resulting from molecular agitation. Although accuracy is usually limited by electrical noise and systematic errors, mechanical thermal noise provides a theoretical lower limit for random errors [8-11]. Thus, a proper accounting of thermal noise is essential for the development of higher accuracy tactical and inertial grade gyroscopes.The effects of mechanical-thermal noise on the sense-mode have been presented in the literature [8-11], but discussions of the effects of mechanical-thermal noise on drive-mode can hardly be found in the current literature.

In this paper the effects of mechanical thermal noise on the driving Cilengitide performance of the SMG are mainly derived. Only the influence of the mechanical thermal noise is considered, while the electrical noise, sampling and quantization error, and distortion due to filtering are not considered. Meanwhile, we assume all the other processes run in an ideal manner. In this paper, a stochastic averaging approach is used to take account of the effects of closed-loop drive. The effect of mechanical thermal noise on drive-mode is discussed, then stochastic averaging is used to develop a model for the ��slow�� dynamics which represent the driving amplitude and frequency of the SMG. Both the steady-state and transient response of the model are obtained by stochastic averaging. The spectral density of the random error due to thermal noise on drive-mode is also derived.

2.?Working PrincipleAs shown schematically in Figure 1(A), the micro-gyroscope consists of two silicon frames (outer-frame and inner-frame); the outer-frame is anchored on a glass substrate by six outer support beams and is connected with the inner-frame through four inner support beams. The outer-frame and the fixed interdigitated drive electrode on the glass substrate form the drive capacitors. The alternating drive force of the out-frame along the x-axis is generated through applying alternating current (AC) voltage with direct current (DC) bias voltage to the fixed drive electrode. Since the stiffness of the inner support beam along the x-axis (Kxi Kx) is very large, the outer-frame and the inner-frame are driven together to vibrate along the x-axis by the alternating drive force, which causes the alternating capacitance between the outer-frame and fixed drive-sense electrode. We can capture the drive displacement by detecting the alternating capacitance.