Boundary conditions, statics, wave propagation
E8-202 Class 2 Dipanjan Gope
• Maxwell’s equations
• Applications of Computational Electromagnetics
• Electrostatics and Magnetostatics
• Wave equation and propagation
• Scalar and vector potentials
• Surface equivalence principle
• Greens Function
• Boundary conditions
• Linear algebra for computational EM
Module 1: Review of EM Principles
3
• C. A. Balanis, Advanced Engineering Electromagnetics, Wiley and Sons:
Chapter 1,3,4
References
Boundary Conditions
Js
H H
n
( 2 1)
D s
D
n ( 2 1)
What about PEC?
0 )
( 2 1
E E n
0 )
( 2 1
B B n
5
Electrostatics
0
E
D
Magnetostatics
J H
0
B
0
J
7
Wave Equation
2 0
2
E E
2 0
2
H Ji H
F F
F 2
Use Identity
Equation Forms
2 0
2 f 2 k2 0
Laplace Poisson Helmholtz
2 Laplace Operator Div. of grad of
9
Laplace Operator
http://en.wikipedia.org/wiki/Laplace_operator
Wave Eqn Soln: 1D Plane Wave
2 0
2
E E
Source Free Region
jkz jkz
z Ae Be
E
k
Propagation constant
Wave number
Phase constant
Attenuation constant
11
Some Terms for Wave Propagation
Travelling Wave
Standing Wave
Decaying Wave
Phase Velocity
Group Velocity
Wave Eqn Soln: Rectangular Waveguide
j z y j z
yx x
x
z
z Be
Ae
y D
y C
x D
x C
E
] sin
cos [
] sin
cos [
2 2
1 1
13
Wave Eqn Soln: Cylindrical Waveguide
j z j z
m m
x
z
z Be
Ae
m D
m C
Y D J
C E
] sin
cos [
] [
2 2
1 1
Wave Eqn Soln: Spherical Waveguide
cos( ) cos( )
] sin
cos [
] [
2 2
1 1
m n m
n
m m
x
BQ AP
m D
m C
r y
D r
j C E