Lecture1 06_07_10 david pozar microwave eng.pptx

8/10/2019 Lecture1 06_07_10 david pozar microwave eng.pptx

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ENE 428

Microwave

Engineering

Lecture 1Introduction, Maxwellsequations, fields in media, andboundary conditions


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SyllabusAsst. Prof. Dr. Rardchawadee Silapunt,

[email protected]

Lecture: 9:30pm-12:20pm Tuesday, CB41004

12:30pm-3:20pm Wednesday, CB41002Office hours : By appointment

Textbook: Microwave Engineering by David M. Pozar (3rd

edition Wiley, 2005)

Recommended additional textbook: AppliedElectromagnetics by Stuart M.Wentworth (2ndedition Wiley,

2007)
mailto:[email protected]:[email protected]


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Homework 10%

Quiz 10%

Midterm exam 40%

Final exam 40%

Grading

VisionProviding opportunities for intellectual growth in the context

of an engineering discipline for the attainment of professionalcompetence, and for the development of a sense of the social

context of technology.


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Course overview

Maxwells equations and boundary conditions for

electromagnetic fields

Uniform plane wave propagation

Waveguides

Antennas

Microwave communication systems


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Microwave frequency range (300 MHz300

GHz)

Microwave components are distributed

components.

Lumped circuit elements approximations are

invalid.

Maxwells equations are used to explaincircuit behaviors( and )

Introduction

EH

http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=52
http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=52http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=52


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From Maxwells equations, if the electric field

is changing with time, then the magnetic field

varies spatially in a direction normal to its orientationdirection

Knowledge of fields in media and boundary conditionsallows useful applications of material properties tomicrowave components

A uniform plane wave, both electric and magnetic fieldslie in the transverse plane, the plane whose normal is thedirection of propagation

E

H

Introduction (2)


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7

Maxwells equations

0

v

BE M

t

DH J

t

D

B

(1)

(2)

(3)

(4)

E.

is the electric field, in volts per meter (V/m).1

.H is the magnetic field, in amperes per meter (A/m).

.D is the electric flux density, in coulombs per meter squared (Coul/m2).

.B is the magnetic flux density, in webers per meter squared (Wb/m2).

.M is the (fictitious) magnetic current density, in volts per meter (V/m2).

J. is the electric current density, in amperes per meter squared (A/m2).

is the electric charge density, in coulombs per meter cubed (Coul/m3).


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Maxwells equations in free space

= 0, r= 1, r= 1

0= 4x10-7Henrys/m

0= 8.854x10-12 farad/m

0

0

EH

tH

Et

Ampres law

Faradays law


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Integral forms of Maxwells equations

(1)

(2)

(3)

0 (4)

C S

C S

S V

S

E dl B d St

H dl D d S It

D d s dv Q

B d s


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Fields are assumed to be sinusoidal or

harmonic, and time dependence with

steady-state conditions

( , , ) cos( ) xE A x y z t a

Time dependence form:

Phasor form:

( , , ) js xE A x y z e a


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Maxwells equations in phasor form

0

S

S

v

E j B M

H J j D

D

B

(1)

(2)

(3)

(4)


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Fields in dielectric media (1)

An applied electric field causes the polarization of the

atoms or molecules of the material to create electric

dipole moments that complements the total displacement

flux,

where is the electric polarization.

In the linear medium, it can be shown that

Then we can write

E

D

2

0 /eD E P C m eP

0 .e eP E

0 0(1 ) .e rD E E E


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Fields in dielectric media (2)

may be complex then can be complex and can beexpressed as

Imaginary part is counted for loss in the medium due todamping of the vibrating dipole moments.

The loss of dielectric material may be considered as an

equivalent conductor loss if the material has aconductivity . Loss tangent is defined as

' ''j

''tan .

'

e


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Anisotropic dielectrics

The most general linear relation of anisotropic

dielectrics can be expressed in the form of atensor which can be written in matrix form as

.x xx xy xz x x

y yx yy yz y y

z zx zy zz z z

D E E

D E E

D E E


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Analogous situations for magneticmedia (1)

An applied magnetic field causes the magnetic

polarization of by aligned magnetic dipole moments

where is the electric polarization.

In the linear medium, it can be shown that

Then we can write

H

2

0 ( ) /mB H P Wb m

mP

.m mP H

0 0(1 ) .m rB H H H


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Analogous situations for magneticmedia (2) may be complex then can be complex and can be

expressed as

Imaginary part is counted for loss in the medium due to

damping of the vibrating dipole moments.

' ''j

m


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Anisotropic magnetic material

The most general linear relation of anisotropic

material can be expressed in the form of a tensorwhich can be written in matrix form as

.x xx xy xz x x

y yx yy yz y y

z zx zy zz z z

B H H

B H H

B H H


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Boundary conditions between twomedia

Ht1

Ht2

Et2

Et1Bn2

Bn1

Dn2

Dn1

n 2 1

2 1

Sn D D

n B n B

2 1

2 1

S

S

E E n M

n H H J


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Fields at a dielectric interface

2 1

2 1

1 2

1 2 .

n D n D

n B n B

n E n E

n H n H

Boundary conditions at an interface between two

lossless dielectric materials with no charge or

current densities can be shown as


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Fields at the interface with a perfectconductor

0

0

0.

S

n D

n B

n E M

n H

Boundary conditions at the interface between a

dielectric with the perfect conductor can be

shown as


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General plane wave equations (1)

Consider medium free of charge

For linear, isotropic, homogeneous, and time-invariant medium, assuming no free magneticcurrent,

(1)

(2)

E

H Et

HE

t


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General plane wave equations (2)

Take curl of (2), we yield

From

then

For charge free medium

( )

H

Et

2

2( )

E

E E EtEt t t

2 A A A

22

2

E EE E

t t

0 E


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Helmholtz wave equation

22

2

E EE

t t

22

2

H HH

t t

For electric field

For magnetic field


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Time-harmonic wave equations

Transformation from time to frequency domain

Therefore

jt

2 ( ) s sE j j E

2

( ) 0 s sE j j E

2 2 0 s sE E


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Time-harmonic wave equations

or

where

This term is calledpropagation constantor we can write

= +j

where = attenuation constant (Np/m)

= phase constant (rad/m)

2 2 0 s sH H

( ) j j


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Solutions of Helmholtz equations

Assuming the electric field is in x-direction and the waveis propagating in z- direction

The instantaneous form of the solutions

Consider only the forward-propagating wave, we have

Use Maxwells equation, we get

0 0cos( ) cos( ) z zx xE E e t z a E e t z a

0 cos( )

z

xE E e t z a

0 cos( ) z yH H e t z a


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Solutions of Helmholtz equations in phasor

form

Showing the forward-propagating fields without time-

harmonic terms.

Conversion between instantaneous and phasor form

Instantaneous field = Re(ejtphasor field)

0

z j zs xE E e e a

0

z j zs yH H e e a


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Intrinsic impedance

For any medium,

For free space

x

y

E j

H j

0 0

0 0

120

x

y

E EH H


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Propagating fields relation

1

s s

s s

H a E

E a H

where represents a direction of propagationa

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Lecture1 06_07_10 david pozar microwave eng.pptx