Modeling levels

# Modeling levels

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## Modeling levels

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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. 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

10. 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