Uniform plane wave 2014 mk

Engineering ElectromagneticsThe Uniform Plane Wave Nguy ễ n Công Ph ươ ng... Wave Propagation in Free Space 2.. Wave Propagation in Free Space 2... Wave Propagation in Free Space 3... Wa

Engineering Electromagnetics

The Uniform Plane Wave

Nguy ễ n Công Ph ươ ng

I Introduction

II Vector Analysis

III Coulomb’s Law & Electric Field Intensity

IV Electric Flux Density, Gauss’ Law & Divergence

V Energy & Potential

VI Current & Conductors

VII Dielectrics & Capacitance

VIII Poisson’s & Laplace’s Equations

IX The Steady Magnetic Field

X Magnetic Forces & Inductance

XI Time – Varying Fields & Maxwell’s Equations

XII The Uniform Plane Wave

XIII Transmission Lines

XIV Plane Wave Reflection & Dispersion

XV Guided Waves & Radiation

The Uniform Plane Wave

1 Wave Propagation in Free Space

2 Wave Propagation in Dielectrics

3 The Poynting Vector

4 Skin Effect

5 Wave Polarization

Wave Propagation in Free Space (1)

0

∇ .H =

0

∇ = .E

Wave Propagation in Free Space (2)

Wave Propagation in Free Space (3)

Wave Propagation in Free Space (3)

Wave Propagation in Free Space (4)

Wave Propagation in Free Space (5)

xs

xs

d E

k E dz

Wave Propagation in Free Space (6)

Wave Propagation in Free Space (7)

0 0

x y

E H

µ ε

The Uniform Plane Wave

1 Wave Propagation in Free Space

2 Wave Propagation in Dielectrics

3 The Poynting Vector

4 Skin Effect

5 Wave Polarization

Wave Propagation in Dielectrics (1)

Wave Propagation in Dielectrics (2)

1/ 2 2

Wave Propagation in Dielectrics (3)

1/ 2 2

Wave Propagation in Dielectrics (4)

0 0

x y

Wave Propagation in Dielectrics (5)

Find the attenuation of a 2.5 GHz wave propagating in fresh water,

given ε’r = 78, ε’’r = 7, μr = 1.

Ex.

1/ 2 2

9 8

Wave Propagation in Dielectrics (6)

Wave Propagation in Dielectrics (7)

1/ 2 2

Wave Propagation in Dielectrics (8)

1

ε ε

Wave Propagation in Dielectrics (9)

The Uniform Plane Wave

1 Wave Propagation in Free Space

2 Wave Propagation in Dielectrics

3 The Poynting Vector

4 Skin Effect

5 Wave Polarization

The Poynting Vector (1)

The Poynting Vector (2)

The Poynting Vector (3)

1

[1 cos(2 )] 2

T x

The Poynting Vector (4)

[cos(2 2 2 ) cos ] 2

z x

,

1

cos 2

z x

The Uniform Plane Wave

1 Wave Propagation in Free Space

2 Wave Propagation in Dielectrics

3 The Poynting Vector

4 Skin Effect

5 Wave Polarization

Skin Effect (2)

Dielectrics

Conductor 0

H = η

z x

S =   E × H  

2

2 / 0

2 2 / 0

1

cos

1 4

z x

av

z x

E

E e

δ δ

Skin Effect (7)

/ / 0

(1 ) / 0

z jz

xs x

j z x

Conductor

Skin Effect (8)

2

2

2 0

1 ( )

Conductor

The Uniform Plane Wave

1 Wave Propagation in Free Space

2 Wave Propagation in Dielectrics

3 The Poynting Vector

4 Skin Effect

5 Wave Polarization

Wave Polarization (1)

• In the previous sections, E & H are supposed to lie in

fix directions

• However, the directions of E & H within the plane

perpendicular to a z may change as functions of time and position

• λ, v p , S, …

• The instantaneous orientation of field vectors

• Wave polarization: its electric field vector orientation as

a function of time, at a fixed point in space

• H can be found from E

Wave travel Observer

location