Microwave 01 [相容模式]web.nchu.edu.tw/~ycchiang/MicroWave/Microwave_01.pdf · • Textbook: David M. Pozar, "Microwave Engineering," 3rd edition, Addison Wesley, 2005 ... •

Electromagnetic Theory

1

Introductiont oduct o

• Textbook: David M. Pozar, "Microwave Engineering," 3rd edition, Addison Wesley, 2005R f b k J h F Whi "Hi h F T h i A• Reference book: Joseph F. White, "High Frequency Techniques - An Introduction to RF and Microwave Engineering," Wiley, 2004

• Outline: • Score Distribution:• Outline:1. Introduction2. Transmission Line Theory

• Score Distribution:Homework 20%Mid-term Exam 40%

3. Smith Chart4. S-Parameters5 Resonators

Final Exam 40%

5. Resonators6. Couplers7. Filters8. Mixer9. Amplifiers

2

Introductiont oduct o

Frequency (Hz)

3x105 3x106 3x107 3x108 3x109 3x1010 3x1011 3x1012 3x1013 3x10143x10 3x10 3x10 3x10 3x10 3x10 3x10 3x10 3x10 3x10

ve cast

ave

V t rad

io

red

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Long

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radi

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road

cra

dio

Sho

rt w

ara

dio

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F T V

M b

road

cast

Microwaves

Far I

nfra

r

Infra

red

Visi

ble

lig

103 102 10 1 10-1 10-2 10-3 10-4 10-5 10-6

A

FM

8

Figure 1.1 The electromagnetic spectrum

8The speed of light in free-space: 2.998 10 m/sec

ccf

3

f

Introductiont oduct o

Figure 1.1 The electromagnetic spectrum ( i )

4

(continue).

Introductiont oduct o

• Standard Prefixes

10TteraFactoronAbbreviatiPrefix

9

12 1

2

Prefix Abbreviation Factordeci d 10

10kkil10Mmega10Ggiga

3

6

9 2

3

6

centi c 10milli m 10

i 10

10dd k10hhecto10kkilo

2

3 6

9

12

micro 10nano n 10

i 10

10dadeka 12

15

18

pico p 10femto f 10atto a 10

atto a 10

5

Introduction

• Applications of Microwave Engineering– The difficulties and the opportunities of higher frequencyThe difficulties and the opportunities of higher frequency

• Antenna gain electric size of the antenna• More bandwidth

t 600MH b d idth 1% 6MH

at 600MHz: bandwidth = 1% → 6MHz at 60GHz: bandwidth = 1% → 600MHz

• Microwave signal travel by line of sight and not bent by the ionosphere

• The effective reflection area (radar cross section) electric size of f << fp f < fp f >> fp

the target

• Various molecular, atomic, and nuclear resonances at microwave frequencies (remote sensing, medical diagnostics, heating…)

6

q ( g, g , g )

Introductiont oduct o

• Applications of Microwave Engineering– radar systems (Military Vehicle collision prevention)radar systems (Military, Vehicle collision prevention)– communications systems

• Cellular telephonep• Satellite telephony systems• GPS• DBS• WLANs• UWB• UWB

– environmental remote sensing– medical systemsmedical systems

• A Short History of Microwave Engineering

7

Introductiont oduct o

8

Figure 1.2 (p. 4) Photograph and identification courtesy of J. H. Bryant, University of Michigan.

Mathematics DefinitionsMathematics Definitions

• A field is a spatial distribution of a quantity, which may or may not be a function of time.– Ex: gravitational field.

:form alMathematic

zyxRGMmzyxF

,,,, 2

E: C

d

FB

E

BjE

nE

n

C1E 2E 3E

j

j

n

1 2 3

j

A1

A2

31

qEW cos:fieldby thedoneworkThe E

9

j

jjjAB qEW cos : field by the done work The E

Mathematics DefinitionsMathematics Definitions

: S

dsA

B B B

na na

naS S S

BS cosBS 0

SB

nSaSSB

whereijB

ijn ,a ij

ijS

ijijijS SB

li itthT kij

Sij

ijijS

S dsBSBlim0

:limit theTake

10

ijS 0

Mathematics DefinitionsMathematics Definitions

• Gradient: the vector that represents both the magnitude and the directionof the maximum space rate of increase of a scalar.

dV . dndVVV nagrad

VVV zV

yV

xVV zyx

aaa

11

Mathematics Definitionsat e at cs e t o s

lidid

S sA

A

• Divergence

.limdiv0 v

S

v

A

AAA .

divz

Ay

Ax

A zyx

AA

.11z

BBr

rBrr

zr

B

• Divergence theorem.

SVddv sAA

12

Mathematics DefinitionsMathematics Definitions

• Curl

AAAAAA xyzxyz aaaA .

yxxzzy zyx aaaA

.

zyx

zyx

aaa

A zyx AAAzyx

1zr r

aaa

A .

zr ArAAzrr

A

13

Maxwell’s Equationsa we s quat o s

Differential form

E

B M

Integral form

dl ds ds

E B M

t

E M

HD

J

C S Sdl ds ds

t

dl ds ds ds

E B M

H D J D I

t

H J

D

C S S S

S V

t tds dv Q

H J

D

I

0 B 0

Sds

B

continuity equation:

Figure 1.3 (p. 7)The closed contour C and surface S

i d i h F d ’ l

0t

J

14

associated with Faraday’s law.

Maxwell’s Equationsa we s quat o s

phasor form:(with time dependence)j te

0

The constitutive relations:

( for free space)D E

( , , , ) Re ( , , ) j tx y z t E x y z e

E j B M

E

E j H M

0

0 ( for free space)B H

E j B M

H j D J

D

E j H M

H j E J

D

0

D

B

0

D

B

complex permittivity:

0

complex permittivity:1

1 tan 1 tanej

j j

loss tangent: tan

0 1 tan 1 tanpermeability:

1

rj j

j

loss tangent: tan

15

0 1 m j

Maxwell’s Equationsa we s quat o s

Figure 1.4a/b (p. 9)Arbitrary volume, surface, and line currents. (a) Arbitrary electric and magnetic volume current densities. (b) Arbitrary electric and

16

magnetic surface current densities in the z = z0 plane.

Maxwell’s Equationsa we s quat o s

Figure 1.4c/d (p. 9)Arbitrary volume, surface, and line currents. (c) Arbitrary electric and magnetic line currents. (d) Infinitesimal electric and magnetic dipoles

17

parallel to the x-axis.

Boundary Conditionsou da y Co d t o s

Figure 1.5 (p. 12)Figure 1.5 (p. 12)Fields, currents, and surface charge at a general interface between two media.

S V

D ds dv

2 1ˆ

similarly,sn D D

Figure 1.6 (p. 12)Closed surface S for equation (1.29).

2 1ˆ ˆ n B n B

18

Closed surface S for equation (1.29).

Boundary Conditionsou da y Co d t o s

ˆC S S

E dl j B ds M ds

E E M

2 1 ˆ

similarly,

sE E n M

Figure 1.7 (p. 13) 2 1ˆ sn H H J g (p )

Closed contour C for Equation (1.33).

Dielectric interface

ˆ ˆD D

PEC interface

ˆ D

PMC interface

ˆ 0n D

1 2

1 2

ˆ ˆ

n D n D

n B n B

ˆ 0sn D

n B

0

ˆ 0

ˆ

n D

n B

E M

1 2

1 2

ˆ ˆ

ˆ ˆ

n E n E

n H n H

ˆ 0

ˆ s

n E

n H J

ˆ

ˆ 0

sn E M

n H

19

Wave Equation and Plane WavesWave quat o a d a e Waves

HjE equationscurl twoCombine

EjH

thenidentity, vector use and

EkE 0equations Helmholtz have we

22

HkH :solutions General

022

EH

eEE rkj

ˆ10

ˆandtheofnOrientatio1.8 Figure

nkkHE EnH wave.plane general afor vectors

and,,theofn Orientatio 0nkkHE

20

Wave Equation and Plane WavesWave quat o a d a e WavesMedium ofType

j

or Conductor Good

Lossy General0

LosslessQantity

yp

j

jjω

jωγjωγ

21

1constantnpropagatioComplex

k

2/ReRe0constantn Attenuatio2/ImImconstant Phase

jj

k21

21Impedance

sss

222W l th

21depthSkin

ppp vvv velocityPhase

Wavelength

21

ppp

Wave Equation and Plane WavesWave Equation and Plane WavesExample 2.1(舊版)

• A plane wave with a frequency of 3GHz is propagating inA plane wave with a frequency of 3GHz is propagating in an unbounded material with r = 7 and r = 3. Compute the wavelength, phase velocity, and wave impedance for thiswavelength, phase velocity, and wave impedance for this wave.

• SolSol.m/sec. 1055.6

3710311 7

8

00

rrrrp

cv 00 rrrr

m. 0218.0103

1055.69

7

f

vp103f

. 8.246733770 r

22

7r

Wave Equation and Plane WavesWave Equation and Plane WavesExample 1.1

• A plane wave propagating in a lossless dielectric material has an electric field given as Ex = E0cos(1.51x1010t – 61.6z). Determine the wavelength, phase velocity, and wave impedance for this wave, and the dielectric constant of the medium.

S l• Sol.

22 rad/sec, 1051.1 10 .m 6.61 1k

)2251/(/104521051.1 810

m. 102.06.61

22

k

)225.1/( m/sec. 1045.26.61

8 ck

vp

501100.328

2

c

.8.3073770

.50.11045.2 8

p

r v

23

. 8.3075.10 r

Wave Equation and Plane WavesWave Equation and Plane WavesExample 1.2

• Compute the skin depth of alumina copper gold andCompute the skin depth of alumina, copper, gold, and silver at a frequency of 10 GHz.

• Sol 11122• Sol. .11003.51

104101

222 3

710

fs

1 .m 1014.810816.3

11003.5 77

3Al,

s

10606110035 73 .m 1060.610813.5

1003.5 77

3Cu,

s

m10867110035 73 .m 1086.710098.4

1003.5 7Au,

s

.m 1040.611003.5 77

3Ag

s

24

10173.6 7Ag, s

Wave Equation and Plane WavesWave quat o a d a e Waves

21 ˆˆ

:direction in traveling wavePlane0eyExEE

zzjk

21

21

polarized linearly 0 and 0 If

xEE

y

21

polarized linearly 0 and 0 If

yEE

LHCP RHCP

21

:angle at the polarizedlinearly realboth ,0 and 0 If EE

zjk

jEeyjxEEEjEE 0

1 ˆ ˆ is that , If 0021

1

21-tan EE

zjk

zjk

eyjxEEEjEE

eyjxjEEzH

0

0

ˆˆisthatIf

ˆ ˆˆ1 RHCP 0

zjkeyjxjEEzH

eyjxEEEjEE

0 ˆ ˆˆ1 LHCP

isthat ,If

0

0021

25

Energy and Powere gy a d owe

vector identity

HEEHHE

vector identity

ss MHJEHEjE 222

Maxwell’s equationsMaxwell s equations

sdHEvdHESV

vdMHJEvdHEjvdEV ssVV

222

:theoremsPoynting'sP S oP

VSV ss vdEsdHEvdMHJE 2

21

21

:theoremsPoynting2

P

VV

vdEHjvdHE 2

2

2222

26

lP

Plane Wave Reflectiona e Wave e ect o

zjki eExE 0

0ˆ

zjki

i

eEyH 00

0

0

1ˆ

zt

TeTExE

0 ˆ

zt eETyH

0ˆ

zjkr eExE 0

0 ˆ

zjkr eEyH 0

00

ˆ

00

0 21

T

Figure 1.12 (p. 27)Plane wave reflection from a lossy medium; normal incidence.

00

27

Plane wave reflection from a lossy medium; normal incidence.

Oblique IncidenceOb que c de ce

kkk sinsinsin:lawssSnell' tri kkk sinsinsin :lawssSnell 211

12 coscosonPolarizati Parallel

it

2

12

cos2

coscos

i

it

T12

1:

coscos it

angleBrewster

2111sin

b

l i ildi

ti

coscos

onPolarizatilar Perpendicu

12

Figure 1.13 (p. 35)Geometry for a plane wave obliquely incident at h i f b di l i i

i

ti

T

coscoscos2

coscos

2

12

28

the interface between two dielectric regions. ti coscos 12

The Reciprocity Theoreme ec p oc ty eo e

sdHEHEvdHEHESV

12211221

vdMHMHJEJEV

12212112

dHEdHE SS

sdHEsdHE 1221

vdMHJE 2121

Figure 1.15 (p. 40)Geometry for the Lorentz reciprocity theorem.

vdMHJE

V

V

1212

2121

29

Image Theoremage eo e

Original ImageGeometry Equivalent

Original ImageGeometry Equivalent

Figure 1 17 (p 44)Figure 1.17 (p. 44)Electric and magnetic current images. (a) An electric current parallel to a ground plane. (b) An electric current normal to a ground plane. (c) A magnetic current parallel to a ground plane. (d) A magnetic current normal to a ground plane

30

(d) A magnetic current normal to a ground plane.