1. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Engineering Electromagnetics 1 0909.301.01 Fall 2004 Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/fall04/eemag1/ Lab Project 2: Pre-lab Lecture September 22, 2004

2. 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

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

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

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

6. 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

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

8. 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

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

10. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University MATLAB PDE Toolbox http://engineering.rowan.edu/~shreek/fall04/eemag1/lectures/pdetoolbox.ppt

11. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Lab Project 2 http://engineering.rowan.edu/~shreek/fall04/eemag1/labs/lab2.html

12. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Intro to MOSFETs http://engineering.rowan.edu/~shreek/fall04/eemag1/lectures/mosfets.ppt

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