Modal analysis based equivalent circuit model and its verification for a single cMUT cell

This paper presents the lumped equivalent circuit model and its verification of both transmission and reception properties of a single cell capacitive micromachined ultrasonic transducer (cMUT), which is operating in a non-collapse small signal region. The derivation of this equivalent circuit model is based on the modal analysis techniques, harmonic modes are included by using the mode superposition method; and thus a wide frequency range response of the cMUT cell can be simulated by our equivalent circuit model. The importance of the cross modal coupling between different eigenmodes of a cMUT cell is discussed by us for the first time. In this paper the development of this model is only illustrated by a single circular cMUT cell under a uniform excitation. Extension of this model and corresponding results under a more generalized excitation will be presented in our upcoming publication (Mao et al 2016 Proc. IEEE Int. Ultrasonics Symp.). This model is verified by both finite element method (FEM) simulation and experimental characterizations. Results predicted by our model are in a good agreement with the FEM simulation results, and this works for a single cMUT cell operated in either transmission or reception. Results obtained from the model also rather match the experimental results of the cMUT cell. This equivalent circuit model provides an easy and precise way to rapidly predict the behaviors of cMUT cells.

[1]  R. Pritchard.  Mutual Acoustic Impedance between Radiators in an Infinite Rigid Plane , 1960 .

[2]  A. Savoia,et al.  Acoustic coupling in capacitive microfabricated ultrasonic transducers: modeling and experiments , 2005, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[3]  Kwan Kyu Park,et al.  CMUT as a chemical sensor for DMMP detection , 2008, 2008 IEEE International Frequency Control Symposium.

[4]  Transmit and receive of a cMUT cell: Modeling and experiments , 2014 .

[5]  F. Teston,et al.  A finite difference model For cMUT devices , 2005, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[6]  B.T. Khuri-Yakub,et al.  Finite-element analysis of capacitive micromachined ultrasonic transducers , 2005, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[7]  Giosue Caliano,et al.  An accurate model for capacitive micromachined ultrasonic transducers , 2002, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[8]  Omer Oralkan,et al.  Capacitive micromachined ultrasonic transducers for medical imaging and therapy , 2011, Journal of micromechanics and microengineering : structures, devices, and systems.

[9]  Chun-Hway Hsueh,et al.  Modelling of bonded multilayered disks subjected to biaxial flexure tests , 2006 .

[10]  Mario Kupnik,et al.  Capacitive Micromachined Ultrasonic Transducers for Therapeutic Ultrasound Applications , 2010, IEEE Transactions on Biomedical Engineering.

[11]  B.T. Khuri-Yakub,et al.  Finite element analysis of underwater capacitor micromachined ultrasonic transducers , 2002, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[12]  H. Tilmans.  Equivalent circuit representation of electromechanical transducers: I. Lumped-parameter systems , 1996 .

[13]  Abdullah Atalar,et al.  An improved lumped element nonlinear circuit model for a circular CMUT cell , 2012, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[14]  H. Tilmans.  Micro-mechanical sensors using encapsulated built-in resonant strain gauges , 1991 .

[15]  H. Tilmans.  Equivalent circuit representation of electromechanical transducers: II. Distributed-parameter systems , 1997 .

[16]  P.-C. Eccardt,et al.  Linear and nonlinear equivalent circuit modeling of CMUTs , 2005, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[17]  H. Koymen,et al.  An equivalent circuit model for transmitting capacitive micromachined ultrasonic transducers in collapse mode , 2011, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[18]  B.T. Khuri-Yakub,et al.  Analytically calculating membrane displacement and the equivalent circuit model of a circular CMUT cell , 2008, 2008 IEEE Ultrasonics Symposium.

[19]  Scott D. Snyder,et al.  Active Control of Noise and Vibration Second Edition Volume 1 , 2012 .

[20]  W. Benecke,et al.  Derivation of a 1D CMUT model from FEM results for linear and nonlinear equivalent circuit simulation , 2003, IEEE Symposium on Ultrasonics, 2003.

[21]  E. M. Strohm,et al.  Sound velocity and attenuation measurements of perfluorocarbon liquids using photoacoustic methods , 2011, 2011 IEEE International Ultrasonics Symposium.

[22]  A. Atalar,et al.  Radiation impedance of an array of circular capacitive micromachined ultrasonic transducers , 2010, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[23]  J. Lardies,et al.  Dynamic and acoustic modeling of capacitive micromachined ultrasonic transducers , 2011, 2011 IEEE International Ultrasonics Symposium.

[24]  David T. Porter,et al.  Self‐ and Mutual‐Radiation Impedance and Beam Patterns for Flexural Disks in a Rigid Plane , 1964 .

[25]  B. Khuri-Yakub,et al.  Surface micromachined capacitive ultrasonic transducers , 1998, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[26]  Ivo Senjanović,et al.  Natural vibrations of thick circular plate based on the modified Mindlin theory , 2014 .

[27]  Patrick Leehey,et al.  Acoustic impedance of rectangular panels , 1979 .

[28]  V. Rochus,et al.  A general multi-mode lumped equivalent circuit model for circular cMUT cells , 2016, 2016 IEEE International Ultrasonics Symposium (IUS).

[29]  C. H. Sherman,et al.  Analysis of Acoustic Interactions in Transducer Arrays , 1966, IEEE Transactions on Sonics and Ultrasonics.

[30]  D. Certon,et al.  A multiscale model for array of capacitive micromachined ultrasonic transducers. , 2010, The Journal of the Acoustical Society of America.

[31]  P.-C. Eccardt,et al.  5F-1 Analytical Models for Micromachined Transducers - An Overview (Invited) , 2006, 2006 IEEE Ultrasonics Symposium.

[32]  Sylvain Ballandras,et al.  Periodic finite element/boundary element modeling of capacitive micromachined ultrasonic transducers , 2005 .

[33]  H. Koymen,et al.  Equivalent circuit-based analysis of CMUT cell dynamics in arrays , 2013, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[34]  Dominique Certon,et al.  Design of broadband linear micromachined ultrasonic transducer arrays by means of boundary element method coupled with normal mode theory , 2015, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control.

[35]  S. Severi,et al.  Poly-SiGe-based CMUT array with high acoustical pressure , 2012, 2012 IEEE 25th International Conference on Micro Electro Mechanical Systems (MEMS).

[36]  X. Rottenberg,et al.  Consistent analytical model for single and dual thickness capacitive Micromachined Ultrasound Transducers (cMUT) , 2012, 2012 13th International Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems.

[37]  Arthur W. Leissa,et al.  THREE-DIMENSIONAL VIBRATIONS OF THICK CIRCULAR AND ANNULAR PLATES , 1998 .

[38]  Rudra Pratap,et al.  Elasto-Electrostatic Analysis of Circular Microplates Used in Capacitive Micromachined Ultrasonic Transducers , 2010, IEEE Sensors Journal.

[39]  H. Koymen,et al.  Parametric linear modeling of circular cMUT membranes in vacuum , 2007, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[40]  B. Nauwelaers,et al.  FEM simulation and measurement validation of a cMUT cell , 2014, 2014 15th International Conference on Thermal, Mechanical and Mulit-Physics Simulation and Experiments in Microelectronics and Microsystems (EuroSimE).

[41]  Wei You,et al.  Exploring multiple-mode vibrations of capacitive micromachined ultrasonic transducers (CMUTs) , 2013 .

[42]  A. Ronnekleiv,et al.  CMUT array modeling through free acoustic CMUT modes and analysis of the fluid CMUT interface through Fourier transform methods , 2005, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[43]  Jaime Zahorian,et al.  A large-signal model for CMUT arrays with arbitrary membrane geometry operating in non-collapsed mode , 2013, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control.