Modeling and System-level Simulation of Force-balance MEMS ...

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Sensors & Transducers Journal, Vol. 127, Issue 4, April 2011, pp. 88-101 3.2. System-level Simulation of the Force-balance MEMS Comb Accelerometer The above analysis of the sense element proved that the design structure and parameters are appropriate, and from the architect model’s analysis we can get the macro model’s parameters of the sense element: the mass is 5.47 µg; the damping is 2.1 mNm/s; the mechanical spring constant is 357.8 N/m; the initial capacitances (C1 and C2) are 2.25 pF. So we can use these parameters to derive corresponding transfer function of the sense element. We also designed the electronic circuits in Fig. 3, which are the charge amplifier, the high pass filter, the differential operation amplifier, the synchronous demodulator, and the PID controller, and derived the transfer functions of them. Thus we established the system-level model of the MEMS comb accelerometer using the transfer functions according to the real parts in the numerical analysis software MATLAB, which is shown in Fig. 9. a Acceleration Subtract1 Subtract -K- Gain Gain1 1 x' s Integrator 1 x s Integrator1 x -K- Gain2 -K- f(u) x to c1 C1 Signal Generator f(u) x to c Product -1.64E-3s 2 den(s) Transfer Fcn Delta C f(u) x to c2 C2 -10 -1 Gain4 Switch Gain3 Subtract2 Demodulation V Switch1 Signal Generator1 Sign -K- Gain7 1 s Integrator2 butter -10 Analog Filter Design Gain5 -K- du/dt Subtract3 Vf Gain8 Derivative signal before PI Gain6 -K- Fig. 9. System-level model of the force-balance MEMS comb accelerometer system in MATLAB. 98
Sensors & Transducers Journal, Vol. 127, Issue 4, April 2011, pp. 88-101 When the external step acceleration is 1 g, 2 g, 4 g, 6 g, 8 g, the displacement of the proof mass is shown in Fig. 10-a. We can see that the displacement of the proof mass gradually increases firstly because of the external acceleration, but the displacement starts to decrease after a very short time, which is caused by the influences of feedback electrostatic force and the beam’s spring force. After about 0.008 second, the displacements decrease to zero. The according output voltage, which is also the feedback electrostatic voltage, is shown in Fig. 10-b. When the external step acceleration is 1 g, after a very short vibration (about 0.003 second) the output voltage can hold a stable value of 0.1 V; as is shown in Fig. 10-b, the stable value of the output voltage has a good linear relationship with the external acceleration. From Fig. 10, we can get the sensitivity of the MEMS comb accelerometer is 100 mV/g. 14 Displacement [nm] Output Voltage(V) 1.2 12 10 8 6 4 8g 6g 4g 1.0 0.8 0.6 0.4 8g 6g 4g 2 2g 0.2 2g 1g 0 1g 0.000 0.002 0.004 0.006 0.008 0.010 0.0 Time[s] 0.000 0.002 0.004 0.006 0.008 0.010 Time(s) (a) (b) Fig. 10. (a) the displacement response of the proof mass in 1 g step external acceleration Fig.10-b; (b) the output voltage response of the accelerometer system in 1 g step external acceleration. The relationship between the external acceleration and the final output voltage is shown in Fig. 11. Because we defined the bias voltage of the MEMS comb accelerometer as 5 V, so the output voltage is constrained to [-5 V, 5 V]. From Fig. 11, we can see that when the external acceleration is in the range of [-50 g, 50 g], it can hold a very good linear relationship with the output voltage, and we can get the range of the MEMS comb accelerometer is 50g , and the nonlinear distortion is smaller than 0.5 %. If we want to extend the range of the MEMS comb accelerometer, we can reduce the feedback coefficient of the output voltage, which will reduce the sensitivity; and if we want to increase the sensitivity of the MEMS comb accelerometer, we need to enlarge the feedback coefficient of the output voltage, but this will cause the loss the range that the MEMS comb accelerometer can measure. So when we design the real electronic interfaces of the MEMS comb accelerometer, one resistance of the differential operation amplifier can be designed as an adjustable resistance in order to adjust the sensitivity and range of the accelerometer manually. The amplitude-frequency response of the MEMS comb accelerometer is shown in Fig. 12. When we load 20 acceleration signals on the MEMS comb accelerometer with the same amplitude but different frequencies, the final output voltage changes as the frequency change. As is shown in Fig. 12, in the low frequency scale (
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