Nonlinear circuit analysis for time-variant microelectromechanical system capacitor systems

Electrostatic transducers, consisting of time-variant capacitors, are utilised in many types of microelectromechanical system (MEMS) devices. Linear circuit theory is based on the premise of time-invariant passive devices. Time-variant capacitors generally result in one or more nonlinear differential equations that must be solved to obtain expressions for the voltage across or the current through the capacitor. An iterative approach can be used to provide an approximate solution to the nonlinear differential equation model of the Thevenin equivalent RC circuit. This solution technique is verified through comparison with a MATLAB Simulink ® simulation of a MEMS capacitor that sinusoidally varies with time because of external stimuli.

[1]  Norihisa Miki,et al.  Flexible capacitive sensor encapsulating liquids as dielectric with a largely deformable polymer membrane , 2012 .

[2]  T. Kenny,et al.  Quality factors in micron- and submicron-thick cantilevers , 2000, Journal of Microelectromechanical Systems.

[3]  R.N. Dean,et al.  Characterization and Experimental Verification of the Nonlinear Distortion in a Technique for Measuring the Relative Velocity Between Micromachined Structures in Normal Translational Motion , 2007, IEEE Sensors Journal.

[4]  Paul M. Weaver,et al.  Vertical comb drive actuator for the measurement of piezoelectric coefficients in small-scale systems , 2013 .

[5]  A. Sundaram,et al.  MEMS-Based Electronically Steerable Antenna Array Fabricated Using PCB Technology , 2008, Journal of Microelectromechanical Systems.

[6]  T. G. Brown,et al.  Harsh military environments and microelectromechanical (MEMS) devices , 2003, Proceedings of IEEE Sensors 2003 (IEEE Cat. No.03CH37498).

[7]  Frank L. Lewis,et al.  The lateral instability problem in electrostatic comb drive actuators: modeling and feedback control , 2006 .

[8]  Y.C. Lee,et al.  Digitally positioned micromirror for open-loop controlled applications , 2002, Technical Digest. MEMS 2002 IEEE International Conference. Fifteenth IEEE International Conference on Micro Electro Mechanical Systems (Cat. No.02CH37266).

[9]  Ying Liu,et al.  Capacitive humidity sensor with a coplanar electrode structure based on anodised porous alumina film , 2012 .

[10]  Yiming Li,et al.  Monotone iterative method for numerical solution of nonlinear ODEs in MOSFET RF circuit simulation , 2010, Math. Comput. Model..

[11]  A. Kourepenis,et al.  Error sources in in-plane silicon tuning-fork MEMS gyroscopes , 2006, Journal of Microelectromechanical Systems.

[13]  Christopher Wilson,et al.  A synthetic voltage division controller to extend the stable operating range of parallel plate actuators , 2011, 2011 IEEE International Conference on Control Applications (CCA).

[14]  Lili Dong,et al.  Closed-loop voltage control of a parallel-plate MEMS electrostatic actuator , 2010, Proceedings of the 2010 American Control Conference.

[15]  Gary K. Fedder,et al.  A DRIE CMOS-MEMS gyroscope , 2002, Proceedings of IEEE Sensors.

[16]  David J. Elton,et al.  A Capacitive Fringing Field Sensor Design for Moisture Measurement Based on Printed Circuit Board Technology , 2012, IEEE Transactions on Instrumentation and Measurement.