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Understanding Lumped Element Modeling in MEMS Device Analysis

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This article explores the principles of lumped element modeling within MEMS (Micro-Electro-Mechanical Systems), focusing on the reduction of variables, mapping into electrical domains, and approximation techniques. It discusses the importance of tolerances in electric, mechanical, and fluidic systems, highlighting typical tolerances like 3-5% for relative process tolerances and 20-30% for MEMS device tolerances. The text also covers parameter extraction, analysis tools (such as FEM, circuit simulators, and transforms), and approaches to transform partial differential equations into ordinary differential equations while evaluating system dynamics.

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Understanding Lumped Element Modeling in MEMS Device Analysis

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Presentation Transcript

  1. Modelinglevels

  2. Domains • Electric • Mechanical • Electrostatic • Piezoelectric • Piezoresistive • Acoustic • Fluidic

  3. Tolerances Relative processtolerances: 3-5% MEMS devicetolerancecan be 20-30% Product speccan be 0.01 % h

  4. What is lumped element modelling? • Reductionofthenumberof variables • Mappingontoelectricaldomain(optional) Lowrie et. al 2005

  5. It involves • Turning partial differential equations into ordinary differential equations • Approximations and more approximations • (Ab-)use of available tools

  6. Partitioning and choice of variables (x,v) Find values for the parameters (m,k,γ) Couple Analyze Procedure x

  7. Partitioning and choice of variables x Sometimesintuitive displacements Sometimes eigenmodes of a sub-system Partitioning and choiceof variables (x,v) Find values for the parameters (m,k,γ) Couple Analyze

  8. Parameter extraction • Solution of partial differential equations • Formulas • Experiment • Guesswork Partitioning and choice of variables (x,v) Find values for the parameters (m,k,γ) Couple Analyze

  9. Piezoresistance R

  10. Coupling • Often trivial • Sometimes trivial problems • Effort and flow variables • Choice of variable • Sometimesdemanding (FEM) Partitioning and choiceof variables (x,v) Findvalues for the parameters (m,k,γ) Couple Analyze

  11. Tools for analysis • (Generalized) impedance • State variables • Circuit simulators • Transfer function • Transfer matrix • Laplacetransform • Fouriertransform • Convolution • (Measurement) Partitioning and choiceof variables (x,v) Findvalues for the parameters (m,k,γ) Couple Analyze

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