S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Engineering Electromagnetics 1 0909.301.01 Fall 2004 Shreekanth Mandayam ECE Department Rowan University.

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Presentation transcript:

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Engineering Electromagnetics Fall 2004 Shreekanth Mandayam ECE Department Rowan University Lab Project 2: Pre-lab Lecture September 22, 2004

S. Mandayam/ EEMAG-1/ECE Dept./Rowan UniversityPlan Poisson’s/Laplace’s Equations Analytical solutions for a parallel plate capacitor Electrostatic boundary conditions Numerical solution of Laplace’s Equation Finite difference approximation Finite element approximation MATLAB PDE Toolbox Lab Project 2

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University EEMAG-1: Topics Today

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Poisson’s & Laplace’s Equations

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Analytical Solution: 1-D Case x = 0 x = d V s = 10V charge-free region

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Boundary Conditions Why do we need boundary conditions? Equations describing e-mag fields are differential equations Solution + Constant

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Electrostatic BCs Two types of BCs Basic Equations

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University The Dielectric-Dielectric Boundary E1E1 E2E2 E 2n E 2t E 1t E 1n   ww hh D1D1 D2D2 D 2n D 2t D 1t D 1n   ss hh

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Numerical Solution: 2-D Laplacian Field x y h h

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University MATLAB PDE Toolbox

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Lab Project 2

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Intro to MOSFETs

S. Mandayam/ EEMAG-1/ECE Dept./Rowan UniversitySummary