Harmonic Balance Nonlinear Identification of a Capacitive Dual-Backplate MEMS Microphone

This paper describes the application of a nonlinear identification method to extract model parameters from the steady-state response of a capacitive dual-backplate microelectromechanical systems microphone. The microphone is modeled as a single-degree-of-freedom second-order system with both electrostatic and mechanical nonlinearities. A harmonic balance approach is applied to the nonlinear governing equation to obtain a set of algebraic equations that relate the unknown system parameters to the steady-state response of the microphone. Numerical simulations of the governing equation are also performed, using theoretical system parameters, to validate the accuracy of the harmonic balance solution for a weakly nonlinear microphone system with low damping. Finally, the microphone is experimentally characterized by extracting the system parameters from the response amplitude and phase relationships of the experimental data.

[1]  M. Rossi,et al.  Acoustics and Electroacoustics , 1992 .

[2]  Ali H. Nayfeh,et al.  Characterization of the mechanical behavior of an electrically actuated microbeam , 2002 .

[3]  M. Madou.  Fundamentals of microfabrication , 1997 .

[4]  Litian Liu,et al.  Theoretical and experimental studies of single-chip-processed miniature silicon condenser microphone with corrugated diaphragm , 1997 .

[5]  Jian Liu,et al.  Harmonic Balance Nonlinear Identification of a Capacitive Dual-Backplate MEMS Microphone , 2008 .

[6]  Ali H. Nayfeh,et al.  A reduced-order model for electrically actuated microbeam-based MEMS , 2003 .

[7]  Sami F. Masri,et al.  A Nonparametric Identification Technique for Nonlinear Dynamic Problems , 1979 .

[8]  R. Wolffenbuttel,et al.  Application of electrostatic feedback to critical damping of an integrated silicon capacitive accelerometer , 1994 .

[9]  Wouter Olthuis,et al.  A review of silicon microphones , 1994 .

[10]  Masakazu Iwaki,et al.  Silicon microphone with wide frequency range and high linearity , 2007 .

[11]  Mark Sheplak,et al.  Development of a MEMS Dual Backplate Capacitive Microphone for Aeroacoustic Measurements , 2006 .

[12]  Ole Hansen,et al.  Design of a silicon microphone with differential read-out of a sealed double parallel-plate capacitor , 1996 .

[13]  S. Timoshenko,et al.  THEORY OF PLATES AND SHELLS , 1959 .

[14]  Ali H. Nayfeh,et al.  Parametric identification of nonlinear dynamic systems , 1985 .

[15]  J. E. Warren,et al.  Capacitance Microphone Dynamic Membrane Deflections , 1972 .

[16]  D. Blackstock.  Fundamentals of Physical Acoustics , 2000 .

[17]  P. Rombach,et al.  The first low voltage, low noise differential silicon microphone, technology development and measurement results , 2001, Technical Digest. MEMS 2001. 14th IEEE International Conference on Micro Electro Mechanical Systems (Cat. No.01CH37090).

[18]  William M. Humphreys,et al.  Performance Analysis of a Cost-Effective Electret Condenser Microphone Directional Array , 2003 .

[19]  T. Fournier,et al.  An experimental study of anharmonic micromachined silicon resonators , 1998 .

[20]  P. Zavracky,et al.  Micromechanical switches fabricated using nickel surface micromachining , 1997 .

[21]  Majid Ahmadi,et al.  Nonlinear effects in MEMS capacitive microphone design , 2003, Proceedings International Conference on MEMS, NANO and Smart Systems.

[22]  R. D. Ford,et al.  Electroacoustics;: The analysis of transduction, and its historical background , 1954 .

[23]  T. Bourouina,et al.  A new condenser microphone with a p+ silicon membrane , 1992 .

[24]  Pirmin Hermann Otto Rombach,et al.  Silicon microphones - a Danish perspective , 1998 .

[25]  Jian Liu,et al.  NONLINEAR DYNAMICS OF A DUAL-BACKPLATE CAPACITIVE MEMS MICROPHONE , 2007 .

[26]  Bin Liu,et al.  A new measurement microphone based on MEMS technology , 2003 .

[27]  Ole Hansen,et al.  Micromachined double backplate differential capacitive microphone , 1999 .

[28]  Z. Skvor,et al.  On the acoustical resistance due to viscous losses in the air gap of electrotastic transducers , 1969 .

[29]  P. R. Scheeper,et al.  A silicon condenser microphone: Materials and technology , 1993 .

[30]  V. T. Srikar,et al.  Thermoelastic damping in fine-grained polysilicon flexural beam resonators , 2002 .

[31]  William N. Sharpe,et al.  Effect of specimen size on Young's modulus and fracture strength of polysilicon , 2001 .

[32]  A. Nayfeh,et al.  Institute of Physics Publishing Journal of Micromechanics and Microengineering a Reduced-order Model for Electrically Actuated Microplates , 2022 .

[33]  Reimund Gerhard-Multhaupt,et al.  Silicon‐dioxide electret transducer , 1984 .

[34]  Wouter Olthuis,et al.  Harmonic distortion in silicon condenser microphones , 1997 .

[35]  M. Younis,et al.  A Study of the Nonlinear Response of a Resonant Microbeam to an Electric Actuation , 2003 .

[36]  Hannu Sipola,et al.  Capacitive microphone with low-stress polysilicon membrane and high-stress polysilicon backplate , 2000 .

[37]  Hugh W. Coleman,et al.  Experimentation and Uncertainty Analysis for Engineers , 1989 .

[38]  Jian Liu,et al.  Nonlinear model and system identification of a capacitive dual-backplate MEMS microphone , 2008 .

[39]  Balakumar Balachandran,et al.  Parametric identification of piezoelectric microscale resonators , 2006 .

[40]  Ronald N Miles,et al.  Modeling of viscous damping of perforated planar microstructures. Applications in acoustics. , 2004, The Journal of the Acoustical Society of America.

[41]  M. Sheplak,et al.  Surface and bulk micromachined dual back-plate condenser microphone , 2005, 18th IEEE International Conference on Micro Electro Mechanical Systems, 2005. MEMS 2005..

[42]  Mark Sheplak,et al.  A directional acoustic array using silicon micromachined piezoresistive microphones. , 2003, The Journal of the Acoustical Society of America.