CONTROLLING SENSITIVITY OF THE SENSOR WITH DIFFERENTIAL ELECTROSTATIC TRANSDUCERS

The problem of developing a sensor for measuring of moment forces of inertia and gravitation with minimal noise and minimal rigidity of the torsion suspension of proof mass (PM) is formulated. The possibility to solve this problem by a differential capacitive system, which simultaneously provides forming of the useful signal and reducing the torsion rigidity is shown. Sensor’s electromechanical circuit with differential electrostatic system is described. Method of calculating the electrostatic capacitance of the capacitor with an inclined plate is proposed. Calculations of electrical and mechanical forces moment acting on the movable plate of the differential capacitor in quasi-static mode are performed. It is shown that the main factor leading to the pull-in effect in the differential capacitor is the asymmetry of electrostatic system. The coefficient of asymmetry of the differential electrostatic system is introduced. The dependence on voltage of the resonance frequency of the sensor is received. The areas of the quasi-static stability of the system are calculated. It is shown that their boundaries are determined by the value of the coefficient of asymmetry, as well as by the value of the resonant frequency of the PM. It is shown that for reducing the resonant frequency of the sensor in more then ten times an unrealistically low values of the coefficient of asymmetry are required. 

1. Silvestrin P. Control and navigation aspects of the new Earth observation missions of the European Space Agency. Annual Reviews in Control, 2005, vol. 29, no. 2, pp. 247–260.

2. Liu H., Pike W. T., Dou G. Design, Fabrication and Characterization of a Micro-Machined Gravity Gradiometer Suspension. Ratio, 2011, vol. 11, pp. 11206–11234.

3. Vasykov S., Drobishev G. Teoriya i primeneniya elektrostaticheskikh podvesov [Theory and Application of electrostatic suspension]. Moscow, MSTU Publ., 2009, 336 p. (in Russian)

4. Douch K., Christophe B., Foulon B., Panet I., PajotMtivier G., Diament M. Ultra-sensitive electrostatic planar acceleration gradiometer for airborne geophysical surveys. Measurement Science and Technology, 2014, vol. 25, no. 10, pp. 105902.

5. French J.B., Carroll K.A. Gravity gradiometer with torsion flexure pivots. Patent US, no. 8,201,448 B2, 2012.

6. Carr D., Evoy S., Sekaric L., Craighead H., Parpia J. Parametric amplification in a torsional microresonator. Applied Physics Letters, 2000, vol. 77, no. 10, pp. 1545–1547.

7. Milatz J.M. W., van Zolingen J.J. The Brownian Motion of Electrometers. Physica, 1953, vol. 19, pp. 181–194.

8. MacDonald N.C. Bertsch F.M. Shaw K.A., Adams S.G. Capacitance based tunable micromechanical resonators. Patent US no. 5,640,133, 1997.

9. Handtmann M., Aigner R., Meckes A., Wachutka G.K.M. Sensitivity enhancement of MEMS inertial sensors using negative springs and active control. Sensors and Actuators A: Physical, 2002, vol. 97–98, pp. 153–160.

10. pp. 153–160.

11. Park, K.-Y., Lee Ch.-W., Jang H.-S., Oh Y., Ha B. Capacitive sensing type surface micromachined silicon accelerometer with a stiffness tuning capability. The Eleventh Annual International Workshop on Micro Electro Mechanical Systems, Heidelberg, Germany, 1998, pp. 637–642.

12. Flokstra J., Cuperus R., Wiegerink R.J., van Essen M.C. MEMS based gravity gradiometer for Space Application. Cryogenics, 2009, vol. 49, pp. 665–668.

13. Bernstein J., Miller R., Kelley W., Ward P. LowNoise MEMS Vibration Sensor for Geophysical Applications. Journal of Microelectromechanical Systems, 1999, vol. 8, no. 4, pp. 433–438.

14. Allen J. Micro-System Inertial Sensing Technology Overview: report SAND2009-3080. California, Sandia National Laboratories, 2009, 32 p.

15. Jiang X., Wang F., Kraft M., Boser B.E. An integrated surface micromachined capacitive lateral accelerometer with 2µG/√Hz resolution. Solid-State Sensor, Actuator and Microsystems Workshop. South Carolina, USA, 2002, pp. 202–205.

16. Chuang Wan-Chun, Lee Hsin-Li, Chang Pei-Zen, Hu Yuh-Chung Physical Sensors. Review on the Modeling of Electrostatic MEMS. Sensors, 2010, vol. 10, № 6, pp. 6149–6171.

17. Braginskij V. B. Izmereniye malykh sil v fizicheskikh experementakh [Measurement of small forces in physics experiments]. Moscow, Nauka Publ., 1974, 152 p. (in Russian)

18. Myhyrov N.I., Efremov G.I. Elekrtomekhanicheskiye mikroustrojstva [Electromechanical microdevices]. Minsk, Belaruskaya navuka Publ., 2012, 257 p. (in Russian)

19. Mobki H., Rezazadeh Gh., Sadeghi M., VakiliTahami F., Seyyed-Fakhrabadi M.-M. A comprehensive study of stability in an electro-statically actuated microbeam. International Journal of Non-Linear Mechanics, 2013, vol. 48, pp. 78–85.

20. Balan N.N., Vasin V.A., Ivashov E.N., Lvov B.G., Nevskij A.B. Ingeneriya tynnelnykh preobrazovatelej [Engineering tunnel converters]. Ivanteyevka, NII predel’nykh tekhnoligij Publ., 2012, 204 p. (in Russian)

21. Gupta R.К., Hung E.S., Yang Y.-J., Ananthasuresh G.K., Senturia S.D. Pull-in dynamics of electrostaticallyactuated beams. Solid-State Sensor and Actuator Workshop Late News Paper. South Carolina, USA, 1996, pp. 2–6.

22. Dias R.A., Cretu E., Wolffenbuttel R., Rocha L.A. Pull-in-based μg-resolution accelerometer: Characterization and noise analysis. Sensors and Actuators A: Physical, 2011, vol. 172, no. 1, pp. 47–53.

23. Zhang Y., Zhao Y. Numerical and analytical study on the pull-in instability of micro-structure under electrostatic loading. Sensors and Actuators A: Physical, 2006, vol. 127, pp. 366–380.

24. Zhang W.M., Yan H., Peng Zhi-Ke, Meng G. Electrostatic pull-in instability in MEMS/NEMS: A review. Sensors and Actuators A: Physical, 2014, vol. 214, pp. 187–218.

25. Dittmer J., Dittmer A., Judaschke R., Büttgenbach S. Modeling and Design of Electrostatic Voltage Sensors Based on Micro Machined Torsional Actuators. Technical Proceedings of the 2008 NSTI Nanotechnology Conference and Trade Show. Danville, 2008, vol. 3, pp. 521–524.

26. Puers R., Lapadatu D. Electrostatic forces and their effects on capacitive mechanical sensors. Sensors and Actuators A: Physical, 1996,, vol. 56,, pp. 203–210.

27. Mekid S., Gilavdary I. Differential capacitance torque sensor. Patent US no. 8,893,563, 2014.

28. McNeil A., Lin Y., Miller T. Differential capacitive sensor and method of making same. Patent US no. 7,610,809, 2009.

29. Elata D. On the static and dynamic response of electrostatic actuators. Technical Sciences, 2005, vol. 53, no. 4, pp. 373–384.

30. Matveev A.N. Elektrichestvo i magnetizm [Electricity and Magnetism]. Moscow, Vysshaya shkola Publ., 1983, 463 p. (in Russian)

31. Gao L., Zhao D. The Fringing Capacitance of an Inclined Plate Capacitor. Fundamental J. Mathematical Physics, 2012, vol. 2, pp. 11–17.

32. Bernstein J. An Overview of MEMS Inertial Sensing Technology. Sensors online [Electronic resource]. Available at: http://www.sensorsmag.com/sensors/acceleration-vibration/an-overview-mems-inertial-sensing-technology-970. Date of access: 19.02.2015.