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 ww hh D1D1 D2D2 D 2n D 2t D 1t D 1n ss hh
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