Study on the Mechanical Behavior of the Varactor of a Micro-Phase Shifter
In this paper static and dynamic response of a
varactor of a micro-phase shifter to DC, step DC and AC
voltages 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
has been studied. It has been shown that applying the DC
voltage shifts down the phase diagram and frequency
response. Also increasing the damping ratio shifts up the
phase diagram.
[1] M Basso., L Giarre., M.Dahleh, I. Mezic, Numerical analysis of
complex dynamics in atomic force microscopes, In: Proceedings of the
IEEE International Conference on Control Applications, Trieste, Italy,
1-4 September: 1026- 1030,1998.
[2] A. Nabian, Gh.Rezazadeh, M.Haddad-Derafshi, A.Tahmasebi,
Mechanical behavior of a circular micro plate subjected to uniform
hydrostatic and non-uniform electrostatic pressure, Microsystem
Technologies 14: 235 240,2008.
[3] S.Senturia, Microsystem Design, Kluwer, Norwell, MA, USA. , 2001
[4] Gh.Rezazadeh, H.Sadeghian, E.Abbaspour, A comprehensive model to
study nonlinear behaviour of multilayered micro beam switches,
Microsystem Technologies, 14(1): 143,2008 .
[5] E.M.Abdel-Rahman, M.I.Younis, A.H.Nayfeh, Characterization of the
mechanical behavior of an electrically actuated microbeam, Journal of
Micromechanical Microengineering 12: 759-766.2002.
[6] Letter to Editor, , "A distributed MEMS phase shifter on a lowresistivity
silicon substrate", Sensors and Actuators A 144, 207-212,
2008.
[7] N.S. Barker, G.M. Rebeiz, Distributed MEMS true-time delay phase
shifters and wide band switches, IEEE Trans. Microw. Theory Tech. 46
(11) , 1881-1890, 1998.
[8] J.S. Hayden, G.M. Rebeiz, , 2-Bit MEMS distributed X-band phase
shifters, IEEE Microwave Guided Wave Lett. 10 (12), 540-542,2000.
[9] J.S. Hayden, A. Malczewski, J. Kleber, C.L. Goldsmith, G.M. Rebeiz, ,
2 and 4-Bit DC 18 GHz microstrip MEMS distributed phase shifters, in:
IEEE MTT-S International Microwave Symposium Digest, Phoenix,
USA, pp. 219-222, 2001.
[10] W. Palei, A.Q. Liu , A.B. Yu, A. Alphones, Y.H. Lee, , "Optimization
of design and fabrication for micromachined true time delay (TTD)
phase shifters"Sensors and Actuators A, 119, 446-454, 2005.
[11] B.K.A.Ngoi , K.Venkatakrishnan, N.R.Sivakumar , T.Bo, ,
"Instantaneous phase shifting arrangement for microsurface profiling of
flat surfaces.optics communications 190, 109-116,2001.
[12] R . Smythe, R. More , , Instantaneous phase measuring interferometry,
Optical Engineering 23(4), 361-365,1984.
[13] T.Mukherjee, G.K. Fedder, White J., Emerging simulation approaches
for micromachined devices, IEEE Transaction Computer Aided Design
Integr Circuits Syst 19: 1572-1589 , 2000 .
[14] S.D.Senturia, N.Aluru, J.White, Simulating the behavior of MEMS
devices, IEEE Comput Sci Eng 4(1): 30-43 , 1997.
[15] R.K.Gupta, Electrostatic pull-in test structure design for in-situ
mechanical property measurement of microelectromechanical systems
(MEMS), Ph.D. dissertation, MIT, Cambridge, MA, 10-27 , 1997.
[16] Gh.Rezazadeh, A.Tahmasebi, M. Zubtsov, Application of piezoelectric
layers in electrostatic mem actuators: Controlling of pull-in voltage,
Microsystem Technologies 12(12): 1163-1170 , 2006.
[17] H.Nayfeh, Mook Nonlinear Oscillations. New York. Wiley,1979.
[18] Gh. Rezazadeh, M. Fathalilou, K. Shirazi, S. Talebian, "A Novel
Relation between Pull-in Voltage of the Lumped and Distributed Models
in Electrostatically-Actuated Microbeams", MEMSTECH-, 22-24
April,2009,Polyana-Svalyava(Zakarpattya), UKRAINE, 31-35,2009.
[19] E. S. Hung and S. D. Senturia ,"Generating efficient dynamical models
forMicroelectromechanical systems from a few finite-element
simulation runs", journal of Microelectromechanical Systems, vol. 8,
pp. 280-289. 1999.
[20] M. I. Younis, E. M. Abdel-Rahman, A. Nayfeh ,"A Reduced-Order
Model for Electrically Actuated Microbeam-Based MEMS", journal
ofMicroelectromechanical systems, vol. 12, no. 5, pp. 672-680, 2003.
[1] M Basso., L Giarre., M.Dahleh, I. Mezic, Numerical analysis of
complex dynamics in atomic force microscopes, In: Proceedings of the
IEEE International Conference on Control Applications, Trieste, Italy,
1-4 September: 1026- 1030,1998.
[2] A. Nabian, Gh.Rezazadeh, M.Haddad-Derafshi, A.Tahmasebi,
Mechanical behavior of a circular micro plate subjected to uniform
hydrostatic and non-uniform electrostatic pressure, Microsystem
Technologies 14: 235 240,2008.
[3] S.Senturia, Microsystem Design, Kluwer, Norwell, MA, USA. , 2001
[4] Gh.Rezazadeh, H.Sadeghian, E.Abbaspour, A comprehensive model to
study nonlinear behaviour of multilayered micro beam switches,
Microsystem Technologies, 14(1): 143,2008 .
[5] E.M.Abdel-Rahman, M.I.Younis, A.H.Nayfeh, Characterization of the
mechanical behavior of an electrically actuated microbeam, Journal of
Micromechanical Microengineering 12: 759-766.2002.
[6] Letter to Editor, , "A distributed MEMS phase shifter on a lowresistivity
silicon substrate", Sensors and Actuators A 144, 207-212,
2008.
[7] N.S. Barker, G.M. Rebeiz, Distributed MEMS true-time delay phase
shifters and wide band switches, IEEE Trans. Microw. Theory Tech. 46
(11) , 1881-1890, 1998.
[8] J.S. Hayden, G.M. Rebeiz, , 2-Bit MEMS distributed X-band phase
shifters, IEEE Microwave Guided Wave Lett. 10 (12), 540-542,2000.
[9] J.S. Hayden, A. Malczewski, J. Kleber, C.L. Goldsmith, G.M. Rebeiz, ,
2 and 4-Bit DC 18 GHz microstrip MEMS distributed phase shifters, in:
IEEE MTT-S International Microwave Symposium Digest, Phoenix,
USA, pp. 219-222, 2001.
[10] W. Palei, A.Q. Liu , A.B. Yu, A. Alphones, Y.H. Lee, , "Optimization
of design and fabrication for micromachined true time delay (TTD)
phase shifters"Sensors and Actuators A, 119, 446-454, 2005.
[11] B.K.A.Ngoi , K.Venkatakrishnan, N.R.Sivakumar , T.Bo, ,
"Instantaneous phase shifting arrangement for microsurface profiling of
flat surfaces.optics communications 190, 109-116,2001.
[12] R . Smythe, R. More , , Instantaneous phase measuring interferometry,
Optical Engineering 23(4), 361-365,1984.
[13] T.Mukherjee, G.K. Fedder, White J., Emerging simulation approaches
for micromachined devices, IEEE Transaction Computer Aided Design
Integr Circuits Syst 19: 1572-1589 , 2000 .
[14] S.D.Senturia, N.Aluru, J.White, Simulating the behavior of MEMS
devices, IEEE Comput Sci Eng 4(1): 30-43 , 1997.
[15] R.K.Gupta, Electrostatic pull-in test structure design for in-situ
mechanical property measurement of microelectromechanical systems
(MEMS), Ph.D. dissertation, MIT, Cambridge, MA, 10-27 , 1997.
[16] Gh.Rezazadeh, A.Tahmasebi, M. Zubtsov, Application of piezoelectric
layers in electrostatic mem actuators: Controlling of pull-in voltage,
Microsystem Technologies 12(12): 1163-1170 , 2006.
[17] H.Nayfeh, Mook Nonlinear Oscillations. New York. Wiley,1979.
[18] Gh. Rezazadeh, M. Fathalilou, K. Shirazi, S. Talebian, "A Novel
Relation between Pull-in Voltage of the Lumped and Distributed Models
in Electrostatically-Actuated Microbeams", MEMSTECH-, 22-24
April,2009,Polyana-Svalyava(Zakarpattya), UKRAINE, 31-35,2009.
[19] E. S. Hung and S. D. Senturia ,"Generating efficient dynamical models
forMicroelectromechanical systems from a few finite-element
simulation runs", journal of Microelectromechanical Systems, vol. 8,
pp. 280-289. 1999.
[20] M. I. Younis, E. M. Abdel-Rahman, A. Nayfeh ,"A Reduced-Order
Model for Electrically Actuated Microbeam-Based MEMS", journal
ofMicroelectromechanical systems, vol. 12, no. 5, pp. 672-680, 2003.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:63244", author = "Mehrdad Nouri Khajavi and Sajjad Ahoui Ghazvin and Ghader Rezazadeh and Mohammad Fathalilou", title = "Study on the Mechanical Behavior of the Varactor of a Micro-Phase Shifter", abstract = "In this paper static and dynamic response of a
varactor of a micro-phase shifter to DC, step DC and AC
voltages 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
has been studied. It has been shown that applying the DC
voltage shifts down the phase diagram and frequency
response. Also increasing the damping ratio shifts up the
phase diagram.", keywords = "MEMS, Phase Shifter, Pull-in Voltage, PhaseDiagram", volume = "4", number = "9", pages = "893-7", }
