Effects of the Residual Stress and Bias Voltage on the Phase Diagram and Frequency Response of a Capacitive Micro-Structure

Document Type: Research Paper

Authors

1 Department of Mechanical Engineering, Khoy Branch, Islamic Azad University

2 Department of Mechanical Engineering, Khoy Branch, Islamic Azad University,

Abstract

In this paper, static and dynamic behavior of a varactor of a micro-phase shifter under DC, step DC and AC voltages and effects of the residual stress on the phase diagram have been studied. By presenting a mathematical modeling, Galerkin-based step by step linearization method (SSLM) and Galerkin-based reduced order model have been used to solve the governing static and dynamic equations, respectively. The calculated static and dynamic pull-in voltages have been validated by previous experimental and theoretical results and a good agreement has been achieved. Then the frequency response and phase diagram of the system have been studied. It has been shown that increasing the bias voltage shifts down the phase diagram and left the frequency response. Also increasing the damping ratio shifts up the phase diagram. Finally, the effect of residual stress on the phase diagram has been studied.

Keywords


[1] Basso M., Giarre L., Dahleh M., Mezic I., 1998, Numerical analysis of complex dynamics in atomic force microscopes, Proceedings of the IEEE International Conference on Control Applications, Trieste, Italy, 1-4 September: 1026-1030.

[2] Nabian A., Rezazadeh Gh., Haddad-Derafshi M., Tahmasebi A., 2008, Mechanical behavior of a circular micro plate subjected to uniform hydrostatic and non-uniform electrostatic pressure, Micro System Technologies 14: 235-240.

[3] Senturia S., 2001, Micro System Design, Kluwer, Norwell, MA, USA.

[4] Rezazadeh Gh., Sadeghian H., Abbaspour E., 2008, A comprehensive model to study nonlinear behaviour of multilayered micro beam switches, Micro System Technologies, 14(1): 143.

[5] Abdel-Rahman E.M., Younis M.I., Nayfeh A.H., 2002, Characterization of the mechanical behavior of an electrically actuated micro beam, Journal of Micromechanical Micro engineering 12: 759-766.

[6] Letter to Editor, 2008, A distributed MEMS phase shifter on a low-resistivity silicon substrate, Sensors and Actuators A 144: 207-212.

[7] Barker N.S., Rebeiz G.M., 1998, Distributed MEMS true-time delay phase shifters and wide band switches, IEEE Transactions on Microwave Theory and Techniques 46 (11): 1881-1890.

[8] Hayden J.S., Rebeiz G.M., 2000, 2-Bit MEMS distributed X-band phase shifters, IEEE Microwave Guided Wave Lett 10 (12): 540-542.

[9] Hayden J.S., Malczewski A., Kleber J., Goldsmith C.L., Rebeiz G.M., 2001, 2 and 4-Bit DC 18 GHz micro strip MEMS distributed phase shifters, in: IEEE MTT-S International Microwave Symposium Digest, Phoenix, USA , 219-222.

[10] Palei W., Liu A.Q., Yu A.B., Alphones A., Lee Y.H., 2005, Optimization of design and fabrication for micro machined true time delay (TTD) phase shifters., Sensors and Actuators A 119:446-454.

[11] Ngoi B.K.A.,Venkatakrishnan K., Sivakumar N.R., Bo T., 2001 , Instantaneous phase shifting arrangement for micro surface profiling of flat surfaces, Optics Communications 190: 109-116.

[12] Smythe R., More R., 1984, Instantaneous phase measuring interferometry, Optical Engineering 23(4): 361-365.

[13] Mukherjee T., Fedder G.K., White J., 2000, Emerging simulation approaches for micro machined devices, IEEE Transactions on Computer-aided Design of Integrated Circuits and Systems 19: 1572-1589.

[14] Senturia S.D., Aluru N., White J., 1997, Simulating the behavior of MEMS devices, IEEE Comput Sci Eng 4(1): 30-43.

[15] Rezazadeh Gh., Fathalilou M., Sadeghi M., 2011, Pull-in voltage of electro statically-actuated micro beams in terms of lumped model pull-in voltage using novel design corrective coefficients, Sensing and Imaging: An International Journal 12(3):117-131.

[16] Gupta R.K., 1997, Electrostatic pull-in test structure design for in-situ mechanical property measurement of micro electromechanical systems (MEMS), Ph.D. dissertation, MIT, Cambridge, MA, 10-27.

[17] Rezazadeh Gh., Tahmasebi A., Zubtsov M., 2006, Application of piezoelectric layers in electrostatic mem actuators: Controlling of pull-in voltage, Micro System Technologies 12(12): 1163-1170.

[18] Nayfeh H., 1979, Mook Nonlinear Oscillations, Wiley, New York.

[19] Mirovitch L., 2001, Fundamentals of Vibrations, Mc Graw Hill Press, International Edition.

[20] Rezazadeh Gh., Fathalilou M., Shirazi K., Talebian S., 2009, A novel relation between pull-in voltage of the lumped and distributed models in electro statically-actuated micro beams, MEMSTECH, April 22-24, Polyana-Svalyava (Zakarpattya), Ukraine, 31-35.

[21] Hung E.S., Senturia S. D., 1999, Generating efficient dynamical models for micro electromechanical systems from a few finite-element simulation runs, Journal of Micro Electromechanical Systems 8: 280-289.

[22] Younis M.I., Abdel-Rahman E. M., Nayfeh A., 2003, A reduced-order model for electrically actuated micro beam-based MEMS, Journal of Micro Electromechanical Systems 12(5): 672-680.