Dynamic Characteristics and Vibrational Response of a Capacitive Micro-Phase Shifter

Document Type: Research Paper

Authors

1 Mechanical Engineering Department, University of Tabriz

2 Electrical Engineering Department, Urmia University

3 Mechanical Engineering Department, Urmia University

Abstract

The objective of this paper is to control the phase shifting by applying a bias DC voltage and changing the mechanical characteristics in electrostatically-actuated micro-beams. This problem can be more useful in the design of micro-phase shifters, which has not generally been investigated their mechanical behavior. 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 equilibrium positions or fixed pints of the system have been determined and the calculated static and dynamic pull-in parameters have been validated by previous experimental and theoretical results and a good agreement has been achieved. The frequency response of the system has been studied and illustrated that changing applied bias DC voltage affects the resonance frequency and maximum amplitude of the system vibrations. Then, phase diagram of the system for various damping ratio and excitation frequencies has been gained. It has been shown that by changing the bias DC voltage applied on the electrostatically-actuated micro-beam, which can be used as a varactor in phase shifter circuit, the stiffness of the micro-beam changes and consequently the phase shifting can be controlled. Finally, effect of the geometrical and mechanical properties of the micro-beam on the value of the phase shifting has been studied.     

Keywords

[1] Sallese J M., Grabinski W., Meyer V., Bassin C., Fazan P., 2001, Electrical modeling of a pressure sensorMOSFET, Sensors and Actuators A: 94: 53-58.

[2] Nabian A., Rezazadeh G., Haddad derafshi M., Tahmasebi A., 2008, Mechanical behavior of a circular micro plate Subjected to uniform hydrostatic and non-uniform electrostatic pressure, Journal of Microsystem Technologies 14: 235-240.

[3] Rezazadeh G., Fathalilou M., Shabani R., Tarverdilou S., Talebian S., 2009, Dynamic characteristics and forced response of an electrostatically actuated micro-beam subjected to fluid loading, Journal of Microsystem Technologies 15: 1355-1363.

[4] Senturia S., 2001, Microsystem Design, Kluwer, Norwell, MA, USA.

[5] Fathalilou M., Motallebi A., Rezazadeh G., Yagubizade H., Shirazi K., Alizadeh Y., 2009, Mechanical behavior of an electrostatically-actuated micro-beam under mechanical shock, Journal of Solid Mechanics 1: 45-57.

[6] Abdel-Rahman E M., Younis M I., Nayfeh A H., 2002, Characterization of the mechanical behavior of an electrically actuated micro-beam, Journal of Micromechanics and Microengineering 12: 759-766.

[7] Nayfeh A., Younis M. I., 2005, Dynamics of MEMS resonators under superharmonic and subharmonic excitations, Journal of Micromechanics and Microengineering 15: 1840-1847.

[8] Younis M. I., Miles R., Jordy D., 2006, Investigation of the response of microstructures under the combined effect of mechanical shock and electrostatic forces, Journal of Micromechanics and Microengineering 16: 2463-2474.

[9] Rezazadeh G., Fathalilou M., Sadeghi M., 2011, Pull-in voltage of electrostatically-actuated micro-beams in terms of lumped model pull-in voltages using novel design corrective coefficients, Journal of Sensing and Imaging, 10.1007/s11220-011-0065-2.

[10] Shiban K., Bharathi B., 1991, Microwave and Millimeter Wave Phase Shifters 1, Boston, Artech House.

[11] Shiban K., Bharathi B., 1991, Microwave and Millimeter Wave Phase Shifters 2, Boston, Artech House.

[12] Simon JW., Alverson W K., Pippin J E., 1966, A Reciprocal TEM latching ferrite phase shifter, International. Microwave Symposium, 241-246.

[13] Garver R V., 1972, Broadband diode phase shifters, IEEE Transactions on Microwave Theory and Techniques 20:658-674.

[14] Andricos C., Bahi I J., Griffin E L., 1985, C-band 6-bit gas monolithic phase shifter, IEEE Transactions on Microwave Theory and Techniques 33: 1591-1596.

[15] Vorhous J L., Pucel R A., 1982, Monolithic dual-gate GaAs FET digital phase shifter, IEEE Transactions on Microwave Theory and Techniques 30: 982-992.

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

[17] Hayden J S., Rebeiz G M., 2003, Very low-loss distributed X-band and Ka-band MEMS phase shifters using metal–air–metal capacitors, IEEE Transactions on Microwave Theory and Techniques 51(1): 309-314.

[18] Hayden J. S., Rebeiz G. M., 2000, 2-bit MEMS distributed X-band phase shifters, IEEE Microwave Guided Wave Letters 10: 540-542.

[19] Pillans B., Eshelman S., Malczewski A., Ehmke J., Goldsmith C G., 1999, Ka-band RF MEMS phase shifters, IEEE Microwave Guided Wave Letters 9: 520-522.

[20] Malczewski A., Eshelman S., Pillans B., Ehmke J., Goldsmith C L., 1999, X-band RF MEMS phase shifters for phased array applications, IEEE Microwave and Guided Wave Letters 9(12): 517-519.

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

[22] Rezazadeh G., Fathalilou M., Shabani R., 2009, Static and dynamic stabilities of a micro-beam actuated by a piezoelectric voltage, Journal of Microsystem Technologies 15: 1785–1791.

[23] Nayfeh H., Mook, 1979, Nonlinear Oscillations, New York, Wiley and Sons.

[24] Osterberg P M., Senturia S D., 1997, M-TEST: a test chip for MEMS material property measurement using electrostatically actuated test structures, Journal of Microelectromechanical Systems 6:107-118.

[25] Hung E S., Senturia S D., 1999, Generating efficient dynamical models for microelectromechanical systems from a few finite-element simulation runs, Journal of Microelectromechanical Systems 8: 280-289.