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应用电磁学基础Fundamentals of Applied Electromagnetics(6th,2010).pdf
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A x (B x C) = B(A . C) - C(A x B)
A . (B x C) = B . (C x A) = C . (A x B)
SOME USEFUL VECTOR IDENTITIES
A . B = A B cos e A B
V(U + V) = VU + VV
VevV) = UVV + VVU
v . (A + B) = V . A + V . B
V . evA) = UV· A + A· VU
V x (U A) = UV x A + VU x A
V x (A + B) = V x A + V x B
V· (A x B) = B· (V x A) - A . (V x B)
V . (V x A) = 0
VxVV=O
V x V x A = V(V . A) - V2A
/ (V . A) dv = fA. ds
/ (V x A) . ds = fA. dl
s c
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FUNDAMENTALS OF
APPLIED
ELECTROMAGNETICS
6/e
Fawwaz T. Ulaby
Eric Michielssen
Urn bertoRavaioli
PEARSON
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Preface to 6/e
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Excerpts From the Preface to the Fifth
CONTENT
Suggested Syllabi
Tables
Table 1
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List of Technology Briefs
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Contents
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Tables
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Introduction: Waves and Phasors
Objectives
R
E
T
p
1
A
H
c
Chapter Contents
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Overview
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1-1 Historical Timeline
1-1.1 EM in the Classical Era
1-1.2 EM in the Modem Era
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CHAPTER I INTRODUCTION: \V/\vES Al\D PHASORS
Radar
Electromagnetic sensors
Global Positioning System (GPS)
Cell
);i_:::--.
~_::"'rl-=.-'
~---~-----~
Telecommun ication
Ultrasound transducer
Ablation catheter
Liver
Ultrasound
Microwave ablation for
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1-2 Dimensions, Units, and Notation
E=xE,
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Table 1
Table 2
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Chronology 1-1: TIMELINE FOR ELECTROMAGNETICS IN THE CLASSICAL ERA
1752
1733
1745
1671
Electromagnetics in the Classical Era
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21
Gauss' Law for Electricity ;
Electromagnetics in the Classical Era
Chronology ir: TIME LINE FOR ELECTROMAGNETICS IN THE CLASSICAL ERA (contrnuedl
1-2 DIMENSIONS, UNITS, AND NOTATION
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CHAPTER I INTRODUCTION: WAVES AND PHASORS
Telecommunications
ON~ ~~~N~"'~:~G~~~. ~A.
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\-2 DIMENSIONS. UNITS, AND NOTATION
Telecommunications
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CHAPTER 1 INTRODUCTION: WAVES AND PHASORS
Chronology 1-3: TIMELINE FOR COMPUTER TECHNOLOGY
Computer Technology
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25
~~:'~~'~~~rE~ ~~!
Computer Technology
1-2 DIMENSIONS. UNITS. AND NOTATION
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1- 3 The Nature of Electromagnetism
The force of gravitation acts at a distance.
1-3.1 The Gravitational Force: A Useful
" t I
\ t I -~
"" \!; "
----~e~ --
, ,
It'
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(1.7)
1-3.2 Electric Fields
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+
" t /1 ~
", \t/ /x
'8/
I ~ \
, "
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1-3.3 Magnetic Fields
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(Him).
1-3.4 Static and Dynamic Fields
JiiOiO
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o
1-4 Traveling Waves
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I
4>(x,t)= T-T+4>o
\
1-4.1 Sinusoidal Waves in a Lossless Medium
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IP
y(x. t) = Yo = A cos T - T '
y(x, T12)
y(x, T14)
-A
T A
y(x, 0)
(1.20)
y(x.t) = A cos T - T
y(x, 0)
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co
----=0
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Sinusoidal Waves in a Lossy Medium
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f
(21T: 21T: )
---~
--
---
y(x)
Example 1-1: Sound Wave in Water
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Example 1-2: Power Loss
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a '-- , 'II
1-5 The Electromagnetic Spectrum
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41
(1.35)
y = Jm(z).
x = 9'te(z).
1-6 Review of Complex Numbers
o
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Table 2
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CHt\PTER I INTRODUCTION: WAVES AND PHASORS
RADIO SERVICES COLOR LEGEND
a I I'!I I H' a I I a~ I: I, ::~ :
I I I In I ~II I I,
FREQUENCY
, II I III 'I I! ! I II ~: I ill II l 1 __
, 'I
HF
MF
VLF
VHF
UNITED
-+2
UHF
••• ' • r I I I!' • 1 liD I • I '
• : ' 01 D "I, ~. II I i I " • n
' • • . 'I f'" I ' '~ : , t:I ,I I "
SHF
i . ~~! R I :fri II lui n ~ ~
, . W.h I n M , ,.0 U ! II III U t1J In
" ' ,,' ~: - D '
1 • ~. ~.I '. , ;
EHF
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( 1.44)
(1.46)
( 1.48a)
( 1.47a)
( 1.48b)
( 1.47b)
ILl I
Izzi - -
Multiplication:
liZ! = tfZ"i*,. (1.43) I
43
Division: For Z2 I- 0,
~ ~
Xi +)'2'
Addition:
( 1.37)
(1.39)
(lAO)
(1.42)
x = [z] cos ()
[z] =tj x2 + y2
y = IzlsmB,
e = tan-I (y/x).
y
Jm(z)
x = Izlcose,
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Technology Brief 1: LED Lighting
Light Sources
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, argon, and xenon) at very low pressure, the electrons collide with the mercury atoms, causing them to excite
v;-
·E 75
'"
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+
v
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Solution:
Jm
0.54 )
v = 3 - j4,
-1 = ejrr = e - jit = 1 L!.!!!r'. ,
v'2
Example 1~3: Working with Complex Numbers
C a) IV I = \i"V"V*
Useful Relations:
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1-7 Review of Phasors
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R
c
- = - IJtc(leiUJT) =IRc -(leilO/)
1-7.1 Solution Procedure
=IReC~ ejW). (1.63)
Jm{[(R+ j~c)T-v,]ej(ot}=o.
= lJte [V,ejw/ J, ( 1.59)
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0.70)
L = 0.2 mH
(V).
....!.... Aej (¢O-IT /2)
i R= 6 Q
--
Example 1-4: RL Circuit
i (t) = I)tc [i ejwt ]
\/1 + w2R2C2
VowC
+ cos(wt + 1>0 - 1>1).
\/1 + w2 R2C2
o 1+ jwRC
= Voej(
\/1 + w2 R2C2 eNI
~1 + w2R2C2
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Answer: (a) I = 150/(R + jwL) = 0.3/-36.9° (A), (b)
(1.73)
(1.72)
(1.71 )
(V).
di
Vs (t) = 5 sin (4 x 104 t ~ 30°)
6 + j4 x 104 x 2 x 10-4
( 1.74)
=---
6 + j8
- -
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The PV Cell
Technology Brief 2: Solar Cells
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Modules, Arrays, and Systems
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11-
"ZX
---
l1li
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Chapter 1 Relationships
B=.~
E=R q
CHAPTER HIGHLIGHTS
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GLOSSARY OF IMPORTANT TERMS
PROBLEMS
*
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'---~-x
X=o
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(V)
(a) 1/1.'
(b) z3
(d) Jm{z}
(e) Jm{z*}
Z) = 51-60° •
(a) zi = 2 + j3 and Z2 = I - j2
(b) Zl = 3 and Z2 = - j3
Z) = -3 + j2,
7.1 = 3 - j2,
(e) Z5 = r'
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L
i
--
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Transmission Lines
R
E
T
Objectives
p
2
A
H
c
Chapter Contents
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B
+
t
l
Load circuit
1------1
B
Receiving-end
Transmission line
A'
+
t
l
2-1.1 The Role of Wavelength
Transmission line
Sending-end
Generator circuit
,----------1
2-1 General Considerations
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- JUUl
(m/s).
- JVlJ'L
JUUl-
JUUl-
JUUl-
V,"A' = Vg(t) = Vo cos tot
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M
TEM Transmission Lines
M
Higher-Order Transmission Lines
2-1.2 Propagation Modes
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2-2 Lumped-Element Model
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R' /),z L' /),z
C'/),z
--------/),z--------
--------/),z--------
--------/),z--------
--------/),z--------
• Two-wire line [Fig. 2-4(17)1:
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, n, (I I)
R =- -+-
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_J¥fIIC
I /1 (b)
(Him).
G'=O,
(F/m).
(S/m).
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---------Ac-------.
dV(z) , , -
--- = (R + jwL) I(z),
ai(z, t) G' ( ) C ,au(z, t)
----az- = U z,t + at'
iV. t) - c' s» u(z + I1z. t)
- -
These are the telegrapher's equations ill phasor form.
di(z) , , -
--;;;- = (G + jWC ) V(z). (2. I 8b)
~-.~--------~--~+
, ili(7.t)
aU(z,t) R"( ) L,ai(z,t)
- = 'zt+ ---
az . , at'
1
0<[' t)
Node
+ -
- = R t{z. t) + L --- .
2-3 Transmission-Line Equations
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I--z
--- = (R + JwL )-- .
dz2 dz
--2- - (R' + jwL')(G' + jwC') V(z) = 0, (2.20)
dz
2-4 Wave Propagation on a Transmission
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v.+ I v.+ I j¢+
11- IV.-I N-
y+ -v;
~ = Zo = __ 0_.
o 0
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c,=L
_ r;;;;u _ fL'
up = fA = ~ .
L' = Z5C'
Example 2-1: Air Line
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CT e = 5.797E7 [Slm]
Two-Wire Line
Module 2.1
output
Structure Data
D = 8.793
R < = 2.952465
Rangel L.:I ~~~~~~~~~i...:...J~ I
Rangel 1 ••.. ~--"- ••...•.•••••..•••••• -""' ••.•...• ~~~ .......•.......• ~ 1
[ Hz}
Input
I
A=0.1978 [m]
[Np/m]
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2b
Coaxial Cable
Module 2.2
I· ~ 1
G {S/m]
I
Output
Structure Data
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2-5 The Lossless Microstrip Line
up = --.
Fr
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t = CO.~,67r·75
lip = --.
~
e r +l (sr-I)( IO)-Xr
Scff = -- + -- I + -
C' = J€ctI
[cr - 0.9 ]0.05
e, + 3
ZO = -- n + 1 + - .
J€ctI S .1'2
f3 = -ftclr .
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z, (fr-I)( 0.12)
= /9 + 1 x 50 + (9 - I) (0.23 + 0.12)
2 ~ 9+1 9
8eP
Example 2-2: Microstrip Line
60n2
h e2p -2 '
+ -- In(q - I) + 0.29 - -
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output
Rangel ,L..--""' •..•••••. ..........:.~ ......•••........•••........•••.........••.•.......••.• ~;",.,J,
Rangel •.•• 14--""'-= .••••.........••••• == ~ ~ 1
Input
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I lIe
up= =---. -=-
Up ciAo
A = - = - - = - , (2.53)
f f.,fEr .,fEr
(2.49)
(lossless line),
(lossless line). (2.45)
(lossless line), (2.46)
A _ 2rr _ 2rr
- f3 - wJL'C' .
lip = 73 = JL'C"
1
up = -- (m/s),
~
y = ex + jf3 = jwJ L'C I •
a=O
fJ = wJuc I
2-6 The Lossless Transmission Line:
General Considerations
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z=O
d=O
I
d=!
d~r---------------~
2-6.1 Voltage Reflection Coefficient
(2.55)
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81
t: v-
lip = c] Fr Zo = (1201 Fr)
ZL
= ZL + 1 (dimensionless), (2.59)
r = Vo- = ZL - Zo
ZL/Zo-l
=
V- = (ZL - zo) V+.
o ZL + Zo 0
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=
=
A'
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83
r -I r + I
~ [2 ] 1/2
Reflection Coefficient r = WlejOr
nzo
..:::.....:::0 ) = we
. [(Vo+)*CeitJz + Ifie-j&ee-j/lZ)]}'/2
2-6.2 Standing Waves
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o
"4
2
IVcd)1
d------------------------~IVol
o
I A/2 I IV(d)1
4 2 "4
0.2
14 '2 '"4
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(2.72)
(dimensionless),
d . _ { dmax + ')./4, if dmax < ')./4,
s=~= l+lfI
IVlrnin 1 - Ifl
{ n = 1,2, .
n = 0,1, 2, .
d _ Br + 2mr _ OrA nA
max - 2{3 - 4;71" + 2 '
if Or < 0,
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Options: Set Input I Output
Transmission Une Data 1
output
(; Impedance r Admillance
I Update II
Transmission Line Simulator
Length units: a (i. J
Low Loss Approximation
_ul.u
,.
',~::~1r\ /\~'
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87
Zo=50Q,
A = 2 x 0.3 = 0.6 m,
5-1
= 2 x - x 0.12 - tt
= -0.2n (rad)
2n 2n IOn
13-----
(2 + j 1) - I
=
s=~
Example 2-6: Measuring ZJ>
Example 2-5: Standing-Wave Ratio
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[I + r,]
I-r,
[I + r]
ZL=ZO --
I-r
2- 7 Wave Impedance of the Lossless Line
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Load
Z=O
Zo
Transmission line
1--------
z =-1
*
Generator
Example 2-7: Complete Solution for v(z, t)
In 0 RI' 'RI
l+iZLtanPI' (2.79)
z, + z.,
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I
+ (VgZin) ( 1 )
Vo = z, + z., e1fJi + re-jfJi
ZL - Zo
r=~-
z., = Zo ( 1 + ri)
I-ri
v(d, t) = 9ie[V(d) eiwt]
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Wave and
Module 2.5
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Technology Brief 3: Microwave Ovens
Microwave Absorption
II~::
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Table 1
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I
Oven Operation
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(2.86)
, :
CHAPTER 2 TRANSMISSION LINES
jwLeq = j Zo tan (if,
Zf;: - z, ~:,~
d-4------------------------~1
o
V,dd) = Vo+lej/Jd - e-ifi"j = 2jVo+ sinf3d,
- VO+'f'< I 'fJd 2Vo+
/scCd) = ~[eJ'" + e-} ] = -- cosf3d.
Zo Zo
. V,dd) .
Denoting Zr.~ as the input impedance of a short-circuited
2-8.1 Short-Circuited Line
zst _V')C(I) -' Z· ta .f31 (2,.84.)
ill -lsc(l) - Joan· ,.
2-8 Special Cases of the Lossless Line
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zli - = 7< ] ~~~~;t
*
sc ~z __ l_
1 -I (WLcq)
1
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I
z~c_
l--+---~~---+----~----+
d--~--~r----#----~----~
d~+-------------------~
Z~ = -_-- = -JZocotfjI. (2.93)
\loc(d) = Vo+[ej,8d + e-j,8d] = lVo+ cosf3d,
- v+ ljV.+
Zo z,
2-8.3 Application of Short-Circuit! Open-Circuit
2-8.2 Open-Circuited Line
by d--+---~r----+----~----+
96
~
(2.95)
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for I = )../4 + n)../2. (2.97)
Z2
o------OA'
1---).14---
Example 2-10: 1./4 Transformer
forI = n)../2,
Quarter- Wavelength Transformer
Lines of Length' = nA/2
Example 2-9: Measuring Zo and fJ
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98
2-8.6 Matched Transmission Line: ZL = Zo
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Table 1
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2-9.1 Instantaneous Power
\Y.+ I
Answer: I = 5.68 cm. (See -e-)
Review Question 2-11: What is a quarter-wave
2-9 Power Flow on a Lossless
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. I!. w !
1\1:+12
2-9.2 Time-Average Power
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If') (27rt ) 1
T cos- T + tJd + ¢ dt = 2" .
o
Review Question 2-18: Verify that
2-10 The Smith Chart
1
1
IV.+I'
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Open-circuit
f·
fr = [I"] cos8r•
Short-circuit
2-10.1 Parametric Equations
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( 1)2 (1)2
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r·
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Wave Impedance
=.9ZL~2-jl
I+r
Zed) 1+ r"
zed) = -- = -- ,
z, 1 - r"
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2-10.3 SWR, Voltage Maxima and Minima
s = 1+ Ifl .
4. - I
Page 107
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, 'd'
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2-10.4 Impedance to Admittance Transformations
Y Zo
v=-=-=-.
I + r «: j;r I - r
z(d = ";./4) = - -- - YL
1 1- r
YL=-=--
ZL l+r
Y = G + jB
Z = R + jX
R
-X
B = ----,,------,,-
R2 + X2
G
g = - = GZo
B
h= - = BZo
1 R - jX
Z R + jX R2 + X2
Y G B
v= - = -+j- =g+jb
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110
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THE SMITH CHART
Location
.,..
O.135A
III
Location
1-3.3).-1
"';1 i :9'L ~ 05 + jl
, 'd,
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Zin = 0.28 - jOo4O,
ZL = 0.6 - jO.8.
Page 113
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114
ry
z, = SO.O In]
2-11
Impedance Matching
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Yin = (Cd + jBd) + js,
2-11.1 Lumped-Element Matching
M'
M
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( I - IfleFi') (I + Ifle-jR')
Yd= 1+lflejO' 1+lfle-jW
h'l = -----,,--..,-----
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Yo
YdJ
I
Yo
A
1
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o.usz
1 + jO = )'s + 1 + j 1.58,
Ys = - jl.58.
)'d = 1 - j1.58,
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120
2-11.2 Single-Stub Matching
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and Y'l = } b.'I = - j 1.58,
(2) d: = 0.20n.
M
MI---d---
Yo
Example 2-14: Single-Stub Matching
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124
2-12 Transients on Transmission Lines
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z=/
z=O
V(t)
VI (t) = Vo u( t)
Voi---------------
~_ Transmission line
Vgi ~ Zo ]Rt
1--------1--
Vet)
r
U(X)={:)
vor-- ....•
2-12.1 Transient Response
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(1/2::: Z S I). (2. 154b)
II = -rd~,
(0 s z < 1/2),
I) = ----"-
I 2
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2-12.2 Bounce Diagrams
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3T
T
3114
I
r+-r,
1(1/4,4T)
T
3T
3114
V
114
r=[L
V(l14,4T)
128
(1 + r L + r, r L)Vt \
V(l14, t)
vt
T
T
7T 2T 9T
4 4
3T
15T 4T 17T
4 4
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0.54 V
rL = = -----,- = 0.5.
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V]- = frVt = -3 Y,
Fr J2.f
°
V(O, t)
-3
Ri: - Zo
I I I
-=-+-
Ru Rr Zo'
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Microwave Ablation
Technology Brief 4: EM Cancer Zappers
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High-Power Nanosecond Pulses
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133
~~
VI = --"---
V 00 = --"---
Rg-ZO
RL -ZO
(Np/m)
en)
=
Chapter 2 Relationships
G' a
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ru
s=--
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GLOSSARY OF IMPORTANT TERMS
135
'----.....::..-0+
t
!
PROBLEMS
*
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R'C' = i/c'
!L'
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Zo = 50 0
C=')
R=6000
L=0.02 mH
of ZL.
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R
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139
(a) ZL = (50 - j50) Q
* -
- -
I --*
Pin = 291cl ViIi ).
Zo= 50 Q
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Titles
son
---AI2---
A
B
son I-AI2-1
P~v-I-Pav
I
z, = 100 n
ZL = (50 + jlOO) n
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III = 3..1/81 12 = 5),/8
C B IA
(a) Zt = 3Zo•
(0 r = j.
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./)
1-0.3A-I/
30n
---0.3/. ---
*
*
1 = '!
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12 V ----r----.
o
o
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Titles
Vector Analysis
R
E
T
Objectives
p
3
A
H
c
Chapter Contents
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145
Overview
z
;- ••.. ---+-~y
A = alAI = aA.
, A A
a=-=-.
IAI A
3-1 Basic Laws of Vector Algebra
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146
C =A+B = B+A.
C=A+B
=xCr+YCy+zCz. 0.7)
D=A-B
3-1.2 Vector Addition and Subtraction
A = xA, +yAy +zA".
_ A xAx + yA, +zA/
a= - = .
3-1.1 Equality of Two Vectors
A = aA = xA, + yAy + zA/.
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3-1.3 Position and Distance Vectors
3-1.4 Vector Multiplication
~
B = kA = akA = x(kAx) + y(kA,) + z(kA,J
B
------------'"
z
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14X
A
A = IA I = yt A . A .
The dot product obeys both the commutative and distributive
(3.18)
i . Y = y . i = z . i = O.
The cross product is anticommutative and distributive.
A x B = -B x A
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- - - - _I'
.-#---'---t-----,+-I~y
..
A x A = O.
y x z=x e :
A . Y = IAIIYI cos {3 = A cos {3,
Example 3·1: Vectors and Angles
A = x2 + y3 + Z3.
A = IAI = J22 + 32 + 32 = m ,
a= ~ = (x2+Y3+Z3)/m.
--+
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~--------y
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3-2.1 Cartesian Coordinates
Review Question 3-4: If A x B = 0, what is eAB?
Review Question 3-3: If A· B = 0, what is eAB?
3-2 Orthogonal Coordinate Systems
Example 3-2: Vector Triple Product
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152
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dlz = d z,
dl, = dr.
3-2,2 Cylindrical Coordinates
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dz
,
"
"
dsz = z r dr d1>
z
:--
ds~~ = ~ drdz
- -
ds", = ¢I dl; di, = ¢I dr dz (r-z plane),
ds, = Z dl, dl", = zr dr d¢ (r-¢ plane).
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o
z
= rro - zh,
, A
a=-
IAI
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(3,49)
ds", = ell dlR dIg =eIlR dR de
157
dV = dl « dla dt", = R2 sine dR de dd».
R sin a dq,
= R d R + 9 R de + ~ R sin e d ¢,
(3,47)
(3,46)
(3,48)
3-2.3 Spherical Coordinates
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Technology Brief 5: Global Positioning System
Principle of Operation
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Differential GPS
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dcp
o
3-3 Transformations between Coordinate
cpl2:r
S=R2 f sin e' dO f dcp
Example 3-6: Charge In a Sphere
Example 3-5: Surface Area In Spherical Coordinates
3-3.1 Cartesian to Cylindrical Transformations
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r· x = x· xa + y. xh = a.
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Example 3-7: Cartesian to Cylindrical Transformations
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(R, e, ~):
R = ia + ib,
o
_ [\lX2 + V2]
(V)
3-3.2 Cartesian to Spherical Transformations
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164
3-3.3 Cylindrical to Spherical Transformations
3-3.4 Distance between Two Points
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)---------------- ..• y
Answer: P = (4. 2rc/3. rc/3). (See 'B')
A = i(x + y) + Y(y - x) + zz
P2 = (x + dx, y + dy, z + dz)
3-4 Gradient of a Scalar Field
(3.73)
(3.71 )
(3.70)
dT = VT ·dl.
aT aT aT
dT = - dx + - d v + - d z.
ax ay' az
.aT .aT .aT
d.T = x- ·dl +y- ·dl +z- ·dl
ax av ilz
[aT 'IT aT]
= i-+y-(-+z- ·£11.
ax ay az
n ~a .0 ~a
ax oy Jz
d ~ aT .aT • aT
ax ay az
0.69)
dl = x dx + Y dy + z d z,
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166
At (I, -\. 2).
dTI
4-12-2 -10
(3.78)
v
iJT iJT ilr er iJep iJT oz
3-4.1 Gradient Operator in Cylindrical
(3.76)
r-
T2 - TI = I V T . ell.
Example 3-9: Directional Derivative
ilx ay iJz .
= x2x + y2yz + z.'.2.
:-- = ? ? = cos ep ,
aep I.
-- = -- sin e.
ax r
st sr sin ep et
ax iJr r iJep
(3.80)
a,--- -
dT A A A A? (X2 + y3 - Z2)
ffi
et A 1 sr er
VT = r- +.-- +z-.
ilr r aep iJz
(3.81)
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(_ a - I a - I a) (a)
iJ R R ae R sin e a¢ R
= nVo [-y6 + z4].
ax ily az
3-4.2 Properties of the Gradient Operator
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T
Land
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169
r y
r hi
.p x-v
GRADIENT OF A SCALAR FIELD
CD Module 3.2 Gradient
Select a scalar function f i», y, z), evaluate its gradient,
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E
J-x
Idsl ds
+
3-5 Divergence of a Vector Field
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.6. v ....• 0 ~V
iJE\"
ilEz
. az .
. aE, dE\" aEz
div E = - + -' + - .
ax ay ilL
1 ( ee, iJE, iJ£z)
E·ds= -+-+-
[ aEx]
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(a) V·E=-+-' +-.-
ax ilv aL
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Technology Brief 6: X-Ray Computed Tomography
Principle of Operation
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Image Reconstruction
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176
3-6 Curl of a Vector Field
+ f xBo' X dx + f xBo' Y dy
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177
o
\l x B =curlB
= .lim _I [it Ii. B .dlJ (3.103)
(3.101)
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3-6.2 Stokes's Theorem
s c
" (0 B z iJ Br ) " (0 B, 0 B / )
VxB=x -.---.- +y -.---.-
iJy az az ax
Example 3-12: Verification of Stokes's Theorem
+z -----
ax av
3-6.1 Vector Identities Involving the Curl
V x (A + B) = V x A + V x B.
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= I ~ d z
= r5.
=«112.
179
.i. 12 sin e 1
f B . dl = I (z ~) . z d z
I(V x B) ·ds
r a¢ az az ar
= r~~ (COS¢) _ ~~ (COS¢)
= -r-~- + «11-.,- .
I ( a sn )
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ro
I~"
,'\.
3-7 Laplacian Operator
.av .av .av
ax ay az
aAx aAv aAz
a2v a2v a2v
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Chapter 3 Relationships
ax ay ilz
By az az ax
~ (aBI' aBx)
a2v a2v a2v
v s
s c
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182
CHAPTER HIGHLIGHTS
GLOSSARY OF IMPORTANT TERMS
CHAPTER 3 VECTOR ANALYSIS
Page 183
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A(B·A)
a a IAI2'
A(B ·A)
D = B - IAI2
PROBLEMS
(d) A x C,
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y =x -I.
(e) P3 = (4, n. 5)
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P3 = (1, -I, 2)
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(a) A = xy2 + yxz + z4 at PI = (1, -I, 2)
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I/-'\'-~ ~-~\~-/I
t t . * + * . t t· * + • • t t
t J! :/
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(h) A = x sin C~) + ysin C~'), for -10:s x, y:s 10
~,
1/
I \
/
. " {o
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189
~L:Lx
--....L..--__t*"----- X
~-_~~_-":!-- x
o
:kLx
(e) E = r (3 - l~r) + zz
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190
Page 191
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Electrostatics
c
H
A
p
4
T
E
R
Chapter Contents
Objectives
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4- 2 Charge and Current Distributions
V' ·B=O,
Max well's Equations
192
4-1
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4-2.1 Charge Densities
! ! 21°.1-,
Q = Pe dz = 2z (/:L = z () = 10 - C.
° ()
PI = lJ~o M = dt
Example 4-2: Surface Charge Distribution
Example 4-1: Line Charge Distribution
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6r ~
Ps = ., = 2 x IO-r
. 3 x 10--
Q = f Ps ds
= f f (2 x 102r)r dr dif>
3 0
I-M-l
Sq = Pvu . /).s /).t
/'>.q = p,u' /'>.5 Sr,
/'>.q
(4.9)
4-2.2 Current Density
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/I'\..
/ . ,
4-3 Coulomb's Law
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196
E = EI + E2
E
(VIm). (4.19)
4-3. t Electric Field due to Multiple Point Charges
I [ (R - Rd (R - R2) ]
R2 = -x3 + y - z2,
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dE
197
(VIm).
108JrEo
-5 X - 5'4 - z2 -'i
. I08JrEo
x2 - 5'8 - z4 x 10-10
I [2(X2 - 5'2 - z) 4(X6)] -5
4JrEo 27 216
4JrER'- 4JrFR'-
(4.20)
E = JdE = _1_ Ji' Pv dV'
4Jr£ RI2
4-3.2 Electric Field due to a Charge Distribution
41rE RI2
41rE R,2
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z
R'I = =ib + zh.
z
I A'Pedl
pfh (-rb+zh)
Example 4·4: Electric Field of a Ring of Charge
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E
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4-4 Gauss's Law
V·D=py
f V· D dV = f D . ds.
v s
s s
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201
,..
D , q
f f i'Dr·frdifJdz=pth
E= D =r Dr =r~ (4.33)
. . eO eO 271' sor
Example 4-6: Electric Field of an Infinite Line Charge
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Answer: E=YPtYI[rreo(y2+J)]. (See e-)
Answer: E = 0 for R < a;
E = Rpsa2 I(e R2) for R > a. (See e-)
Answer: (a) D = RPvRI3,
(b) D = RPva3/(3R2). (See ~)
4-5 Electric Scalar Potential
(4.36)
(4.35)
(4.34)
(1).
Fcx! = =F; = -'lE.
d W = F ex! . dl = -'1 E . dl
The term "voltage" is short for "voltage potential" lind
4-5.1 Electric Potential as a Function of Electric
dV = - = -E·dl
(4.37)
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f (\7 x E) . ds = f E . dl = 0,
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4-5.2 Electric Potential Due to Point Charges
(4.48b)
(surface distribution),
I J Ps ,
V=- -ds
41r8 R'
v = _1_ J Pv dV' (volume distribution), (4.48a)
41r8 R'
v'
4-5.3 Electric Potential Due to Continuous
(V). (4.43)
p
4-5.4 Electric Field as a Function of Electric
v = _1_ J Pl dl' (line distribution).
41r8 . R'
r
(4.48c)
V=- R-- 'RdR=--
£IV = -E·dl.
£IV = VV· £II.
IE = -VV. (4.51) I
v- _1 '" qi
- 41rs (;;j IR - Ri J
(V). (4.47)
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Example 4-7: Electric Field of an Electric Dipole
E = -V'V
oR + R ae +. R sin e il¢ ,
P'R
V=--.".
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qd .. ~ ~
4-5.5 Poisson's Equation
Pv
V-V = V· (VV) = -- + -. - + -. ,
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4-6.1 Drift Velocity
=aE,
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4-6.2 Resistance
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(4.72)
R I
V = VI - V2 = - f E· dl
+ -
v
= - fiE,. i dl = E,I
J = f J. ds = f erE· ds = a ExA
Example 4-9: Conductance of Coaxial Cable
(4.73)
, J
E=r-
,I , J
(4.70)
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Titles
fa fil I r·rdr
VI =- E·dl=- -- ---
P = ! alEI2 dV
1 (b)
G'= G
I Zn o
= ---
4-6.3 Joule's Law
= (a ExA)(E,l) = IV
P = !E'JdV
(W)(Jou]e's law), (4.79)
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Technology Brief 7: Resistive Sensors
Piezoresistivity
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Table 1
Page 213
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-------&-------. Foree (N)
( CiF)
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YOU! = Vo (f..R)
IE)
F=O
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215
E
E
E E E
E
1
E
1
-
4- 7 Dielectrics
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216
4-7.1 Polarization Field
4-7.2 Dielectric Breakdown
D = EoE + P,
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Page 217
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fE.dl= !Et.itdl+ !E2.i2dl=0.
4-8 Electric Boundary Conditions
(VIm). (4.90) I
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Example 4-10: Application of Boundary CondItions
J... !J.h
L- __ ..;.....-~ ... 2"
c d
---111-
218
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219
z
Ell jErx+Efy
tan (h = - = ..:.....----
E2x = Elx,
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Page 220
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220
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4-8.1 Dielectric-Conductor Boundary
(4.100a)
Elt = Dlt = 0,
Din = slEln = Ps·
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4-8.2 Conductor-Conductor Boundary
(81 82)
(electrostatics) .
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Input
!._Q.!
223
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Page 224
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224
4-9 Capacitance
v
+
(4,105)
Figure 4-23: A de voltage source connected to a capacitor
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Page 225
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leE.ds
- fE.dl
(F),
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v
+
z
,
o 0
(4.114)
(4.115)
Q (h)
(4.113) I
Example 4-12: Capacitance Per Unit Length of Coaxial
Line
! C Zn e
(4.117)
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4-10 Electrostatic Potential Energy
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Technology Brief 8: Supercapacitors as Batteries
Capacitor Energy Storage Limitations
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Energy Storage Comparison
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Future Developments
0.01 +----------.------.--------.....,
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Table 1
Page 231
Titles
I mage Method
F = - V We = -z ~ -- = -z -,,- ,
rlz 2EA ~EA
Answer: We = 4.1 J. (See <"1')
4-11
If J
v
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•
if
l;J \\ C V=o
\', l r c
-Q
v=o
if
•
- - - - - - -' - - - - - ~
~'~
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t
Chapter 4 Relationships
Example 4-13: Image Method for Charge Above
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Air ---+--
Fluid Gauge
Technology Brief 9: Capacitive Sensors
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Table 1
Page 235
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/
:=: 1"=,,,1"="11,11
Humidity Sensor
Pressure Sensor
Noncontact Sensors
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d1 1 .10 C1
1.10
3TC2
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,,~:::::::~,
I:: r.
"I' 1::
,','" =-» c,
c
Fingerprint Imager
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Titles
E __ 1_ qi(R - Ri)
1 f AI Ps ds'
E - _1_ f ft' Pe dl'
=z-
E= D =1' Dr =r~
Chapter 4 Relationships (continued)
- - !E'dl
E=-VV
CHAPTER HIGHLIGHTS
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240
GLOSSARY OF IMPORTANT TERMS
PROBLEMS
p; = IOR2 cos2 (J (mC/m3).
* . ~
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241
,
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Page 242
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D = x2(x + y) + y(3x - 2)')
,
,
,
..
..
..
..
..
..
..
,
,
----------------~~------------~x
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v
v
v
....
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(a, 0)
• 18
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1----1 cm----f
(Vim)
-
~----------~II:~+~--------~
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T
1
(a)
2cm
T
1
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r ••••.• --:---i- ... - .... ~
, I I.....'
: J::D-
v
+
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d - - -. Q = (0, d, d)
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Magnetostatics
c
H
A
p
5
T
E
R
Chapter Contents
Objectives
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Overview
Fm=quxB
v ·B;'O,
5-1
Magnetic Forces and Torques
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Page 251
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Fm = quB sin f)
(a)
R
(b)
dW = Fm ·dl = (Fm -u) dt = O. (5.6)
I F = Fe + Fm = qE+ qu X B == q(E + u X B). (5.5) I
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5-1.1 Magnetic Force on a Current-Carrying
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Page 253
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(S.12)
(S.11 )
2S3
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Table 2
Page 254
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(a)
8
Fl = x(2lr) x yBo = z21rBo (N).
Example 5-1: Force on a Semicircular Conductor
R
c
= -Z/ f rBosin¢ d4> = -s u-s; (N).
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F
(S.14)
T=dxF
5-1.2 Magnetic Torque on a Current-Carrying
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f' gO/H L
B FJ
f 1 CD
Im=iNIA=nffl
= (-x~) x (zlhBu) + (x~) x (-Z1bBo)
=yfahBo=y/ABo, (5.16)
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Page 257
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Answer: I = 8 rnA. (See e )
5-2 The Biot-Savart Law
I dl x R
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2SR
,
,
,'R
s
P®dH
(5.23)
5-2.1 Magnetic Field due to Surface and Volume
H= 4~ f Js;/l ds
s
H=4~f J;2RdV
=411' ~
Example 5-2: Magnetic Field of a Linear Conductor
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2S9
(a)
z = -reote.
p
1/2
Jr2 + (1/2)2
-1/2
- Jr2 + (1/2)2
(S.29)
(T).
(S.2S)
R2 -«II 4n 7 d z:
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\
" ,
- -
\
t
,
...• , \ \
, I I I
- .". , I
~ , I I I
..•.. - , , , ,
,~"""" •....
""" •.... ~--
" ..•.
\ ,
I \ I
, ~
...• ~
- ~ , " , \ \ \ t I , ,
- , , , , \ \ \ , II , ~
- ~'''' \ \ \ \ I 1
, - - , " , \ \ \ \ \ \
~ - ~"" \ \ \ \ ,
Example 5-3: Magnetic Field of a CIrcular Loop
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(AIm). (5.34)
I _ I dl
d H = -- Idl x RI = 1 '
4n R2 4n(a- + z2)
_ _ _ I cos (i
(5.36)
5-2.2 Magnetic Field of a Magnetic Dipole
H= 4Jl'R3 (R2cos8 +8sin8)
(for R »a). (5.38)
-
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~ 41 ~
5-2.3 Magnetic Force Between Two Parallel
~ I
4rrr
262
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!B.dS=O.
v . D = p; •••• f D . ds = Q.
5-3.1 Gauss's Law for Magnetism
5-3 Maxwell's Magnetostatic Equations
(5.42)
(5.41 )
I F2 ,fLo/1/2
F~=-=-y--.
~ I 2nd
II' ( ') flO II
= ~ z x -x --
~ 2rrd
, fLo/llll
Zn d
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Technology Brief 10: Electromagnets
Basic Principle
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Page 265
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The Doorbell
Magnetic Relays
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Table 1
Page 266
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The Loudspeaker
Magnetic Levitation
(
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TECHNOLOGY BRIEF 10: ELECTROMAGNETS
267
Figure TF1 0-4: The basic structure of a speaker.
Figure TF10-5: Magnetic trains. (Courtesy Shanghai.com.)
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5-3.2 Ampere's Law
, ,
VxH=J •.• fH.dl=,.
s s
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,
- - ~
269
y
...
.. ...
--_ .•
f HI ·dll = 'I,
,
...
L---~a~------------------~~r
HCa) = .L:
H
H
H
(c)
H
0'
Example 5-4: Magnetic Field of a Long Wire
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II = -, 1= - 1.
(for rj :::a).
1
(for r: :::: 0).
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Example 5-6: MagnetiC Field of an Infinite Current Sheet
z
{ -yH
H= yH
I A t,
-y -
H= 2
'---~ - - - - - - -- -:~
;~.~E ;.~ ... ~._.~~_~.~ __ r : J:~~!~----LJ ...• ~. +~--Y
, , N 1
H=-,H = -,-
2nr
f H . dl = f (-~H) . ~r d ¢ = - 2n r H = - N I.
e 0
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Titles
V x (V x A) = fLJ.
V2A = V(V . A) - V x (V x A),
272
5-4 Vector Magnetic Potential
V·A=O.
"
(5.52)
V = _1-/ Pv dV'.
v'
(5.62)
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1=-- = --.
5-5.1 Electron Orbital and Spin Magnetic
5-5 Magnetic Properties of Materials
A- = !!:..- / J.r sv'
v'
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274
(5.72)
5-5.2 Magnetic Permeability
- - - -
- -
L. ----- - -
( eu) ,
eur (e)
----- - L
(5.73)
en
In, = ---,
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Answer: (a) m.; = 9.3 x 10-24 (A.m2),
(b) M = 7.9 X 105 (AIm). (See )
5-5.3 Magnetic Hysteresis of Ferromagnetic
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Page 276
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B
B
B
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Page 277
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(5.81)
5-6 Magnetic Boundary Conditions
fH.dl= f HI' i, dE+ f H2' i2d£ = I.
e "
(5.82)
0'["2 X (HI - H2)1 = Js : D.
(HI - H2)' t, !11 = J,'" .6./.
f B . ds = 0 •••. I BIn = B2n·1
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5-7 Inductance
5-7.1 Magnetic Field in a Solenoid
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- un I . e . )
A .. zJ.l
B~zJ.l
(5.86)
dB = fl dH = z ) 1 1/1 dz.
-a-!
5-7.2 Self-Inductance
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/ ~~:-:-:~::::::-::- .. -=-= .. --:--r t
__ __ .. _ ~ ~ ~t f 1
N2
/,( N), N
s
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(5.100)
5-7.3 Mutual Inductance
(5.98)
Example 5-7: Inductance of a Coaxial Transmission
4> = If B dr = If I·Ll dr = /Lll In (~) .
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2H2
(5.105)1
Even though this expression was derived Ior a solenoid, it
5-8 Magnetic Energy
Example 5-8: MagnetiC Energy in a Coaxial Cable
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B =. JJ..ol
Ta2
H = z --:;--~...",
L = ~ = ~ = ~ f B· ds
H=-=-,
If') til2 f I
v v
Chapter 5 Relationships
T=mxB
c
V . B = 0 ..•••. f B . ds = 0
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Technology Brief 11: Inductive Sensors
Linear Variable Differential Transformer (LVDT)
• •
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o
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Eddy-Current Proximity Sensor
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PROBLEMS
o
0B
o
o
10 0 01
o
o
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Table 1
Table 2
Page 289
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,
,
- - ,
-------:-:=.~
I
---
~t- .;...i ----I~y
n
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Titles
----:....--------1 •... ----- •. x
P
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T l,-IOA
t ~2m-013~IOA
_I G)l,-IOA
291
H
!I
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Table 1
Page 292
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r
=-z-- X v
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z
x
A------------y
y
d
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Titles
Maxwell's Equations for
Objectives
R
E
T
p
6
A
H
c
Chapter Contents
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296
Dynamic Fields
6-1 Faraday's Law
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Table 1
Page 297
Titles
Vcmf = -N d = -N !!... f B· ds
s
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6-2 Stationary Loop in a Time-Varying
f 1 1
R
,
R
2
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f liJB
c s
s s
Example 6-1: Inductor In a Changing Magnetic Field
V~~f = f E· dl.
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300
z
(A).
= j[BO(Y2+Z3)SinM].ZdS
lr d
= -3][N(va2Bocoswt.
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(Wb),
tr del>
Vemf = -- = 1.2 (V).
dt
Example 6-2: Lenz's Law
eI> = f B· ds = f (-zO.3t)· z ds
s s
= -0.3t x 4 = -1.2t
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1=
6-3 The Ideal Transformer
- - - - ~
V~ = -N~ -.
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6-4 Moving Conductor in a Static
:~
11 N2
.......... =--
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Page 304
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z
R
u
(V).
Be\']) = iO.2e-O.1Y1 = zO.2e-O.2 (T).
Example 6-4: Moving Loop
(6.28)
o
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f d:
VI2 = f (u X B) . dl
R 5
B0
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Table 1
Page 307
Titles
y
B = 7oRo,
B
x
"
o
~'i'
6-5 The Electromagnetic Generator
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Titles
~ w
+ f [( -DW~) x IBo] ·xdx.
= f [(DW~) x iBo] ·xdx
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Titles
B
Vcmf = V:~f + Ve~f
c
JaB J
= - at . ds + j (u x B) . dl.
s c
6-6 Moving Conductor in a
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Titles
Technology Brief 12: EMF Sensors
Piezoelectric Transducers
1/ -0
--. ./
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-,
Faraday Magnetic Flux Sensor
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Thermocouple
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Id = IJd ·ds = I ~~ -ds, (6.44)
s s
dVc d
dt dt
s s s
a
= --;- (BoA cos2 tot )
a
Example 6-6: Electromagnetic Generator
f H . dl = Ie + f ~~ . ds (Ampere's Jaw). (6.43)
c s
6- 7 Displacement Current
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\
faD
12d = - ·ds
at
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315
6-9 Charge-Current Continuity Relation
6-8 Boundary Conditions for
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Table 1
Page 316
Titles
J
J
I = - d Q = _!!... f p av
1 V· J= -if, (6.54>1
which is known as the charge-current continuity relation, or
f J . ds = - :t f p; dV.
s V
V·J=O,
f J. ds = 0 (Kirchhoff·scurrentlaw).
(6.56)
V, J dV = - -. dV.
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6-10 Free-Charge Dissipation in a
Electromagnetic Potentials
6-11
at E
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318
E= -VV
v x E+- =0
at
6-11.1 Retarded Potentials
(dynamic case). (6.70) I
v'
v'
E' = -VV.
E=E+-~ .
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v'
6-11.2 Time-Harmonic Potentials
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320
Example 6-8: Relating E to H
V(R) = - Pv i e dV' (V). (6.82)
v'
(6.88)
(6.89)
(6.91 )
(6.90)
y Z
a/ay a/az
x
(6.83)
(6.86) I
(6.87)
~ I ~
VxE=-jw~ii
,.",1-
H=--VxE.
A(R) = ; f J{Ri) ;, dV', (6.84)
v'
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Chapter 6 Relationships
B=V'xA
H(z, t) = me [H(Z) ejUJl]
= y 0.11 sine JOIOt - 133z)
'. IOk2 -,kz
V =-N -·ds
s
k=w.j!I£
at
det> d f tr m
V. f = -- = -- B· ds = V mf + V mf
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Titles
CHAPTER HIGHLIGHTS
GLOSSARY OF IMPORTANT TERMS
PROBLEMS
* . .. .
~------~~~------~
~==:::::::::II
Rl
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T
1
~----------------------~y
z
(b) cot = n /4
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Titles
z
Yo
o
o
--
\
80 ... '
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Page 325
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a = 10-4 (S/m)
Pv = Par cos w{ (C/m3).
T
1
I
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(VIm).
(AIm).
E = xEosinaycos(wt - kz),
E(R, e; t) =
, 2 X 10-2
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Titles
Plane-Wave Propagation
Chapter Contents
R
E
T
Objectives
p
7
A
H
c
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Titles
32R
Unbounded EM Waves
, .. ~
/,:"-~" .. ",
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Tables
Table 1
Page 329
Titles
0.3)
- -
V x H = jUJt:cE.
- ( a)-
= (a + jwE)E = jUJ E - ': E.
v ·E= pv/e,
V x E= -jw/LH,
V x ii = J + jUJeE.
~ ~ ~
V x H = J + jwt:E
E(x, y, z; t) = me [R(x, y, z) ejwtJ. (7.1)
7-1.1 Complex Permittivity
RL
Time-Harmonic Fields
7-1
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7-2 Plane-Wave Propagation in Lossless
- -
E =-.
2- (a2 a2 a2 ) -
V E- - - - E
- a2+,,2+a2 .
- -
~ ~
7-1.2 Wave Equations
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7-2.1 Uniform Plane Waves
0.26)
HI' =0,
H~ ( ) - ~E+ -jkz - H+ -jkz
H"o = -ErO'
1 aEt(z)
~ 1 aEt(z)
H,,= -.- =0.
iJE~(z)/iJx = aE~(z)/ay = O.
0.22)
0.21)
~ + ~ + ~ (iE, +yE" +zE;,J
A (aH\' aHx) A. -
z iJx - ay = zjwE:Ez.
Ex(z) = E~(z) + E;(z) = E;oe-jkz + E~oejkz. (7.25)
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Titles
E
Example 7-1: EM Plane Wave in Air
A = - = = 300 m
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(llA/m).
- I, - I - '£+ (z)
- I , ,- , '£-(z) ,E-() 'k
7-2.2 General Relation Between E and H
H
s-.
E '<.
30n 3
[(z, t) = xlE~ol cos(u)t - kz + 4>+)
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------------ E
H,'
y
0.44)
-+ -
- 1. - A E, (7) A Et(L)
H = - z x E = -x _. - + Y _. - .
n rJ 1/
E- • E- + .. • f.~+. )
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Titles
Technology Brief 13: RFID Systems
RFID System Overview
RFID Frequency Bands
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Titles
t
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Tables
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Page 337
Titles
(7.46)
(7.47a)
Output
- -jkf.
Plane Wave
Module 7.1
7-3 Wave Polarization
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Page 338
Titles
I (Ed7o,t»)
IE(L. 1)1 = [a; + a;]lj21 cos(O)t - kL)I.
7-3.1 Linear Polarization
8
Exo = ax.
2 2 Ij2
IE(z. t)1 = [E,(z, t) + Ey(z, t)]
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7-3.2 Circular Polarization
1 [E\,(Z,I)]
••
E
,~ -
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Titles
z
~rnn'
Example 7-2: RHC Polarized Wave
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Table 2
Table 3
Page 341
Titles
tan X = ±- = ±- ,
7-3.3 Elliptical Polarization
H(y, t) = 9te [H(Y) ejM]
(rad/m) ,
4
= -xl z e '
w.,ft;
k=--
.,ft;
-A
E(y) = xEx + zEL
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Tables
Table 1
Page 343
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Titles
344
Module 7.2 Polarization I
UNEAR POLARIZATION
OUtput
(J f "" QO
ModUle 7.3
Q t d.11Ik.
.BllelJ
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Titles
Technology Brief 14: Liquid Crystal Display (LCD)
Physical Principle
LCD Structure
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Titles
/
"----~~
"----
Two-Dimensional Array
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Titles
347
1
v
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7-4 Plane-Wave Propagation in Lossy
(Q). (7.70)
(rad/m).
(Np/m) ,
1 + (~:r -1
{ us' [
a=w "2
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Titles
( £")
a :::= w;/I ff, = i/f- (Np/m), (7.75a)
f3 :::= w.fijii =w...;'"iW (radlm). (7.75b)
V -;; 2£' V e 2w£
7 -4.2 Good Conductor
( E") 1/2
y = jwj;ii 1 - j-;;
7-4.1 Low-Loss Dielectric
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Titles
Example 7-4: Plane Wave in Seawater
4
a
WErSO 2rr x ]03 x 80 x (l0-9/36rr)
=9x105.
=
a.=~
a.
a
= (h ejrr /4) 0.126 = O.044ejrr /4
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Titles
IExol = 4.44
E(z, t) = 9lr [xIExoleJ¢oe-aze-Jf!zeJwt]
= xIExole-0.126z cos(2rr x \03t - 0.126z + 4>0)
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352
Ib~
z
W Envelope W Show S s
Module 7.4 Wan Attenuation
It onr
z
z=oo,,=oo Iml
Phasors
0'
1=5.0"
Average Power Density
-J
-
7-5 Current Flow in a Good Conductor
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Titles
(7.90)
1
Z="",=-- -
o
- ,
--'I
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Titles
, I , Rs (1 1)
R = RI + R2 = - - + -
I I
n, = a~, = J;r~1l
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Titles
7 -6.1 Plane Wave in a Lossless Medium
~ ~
k
(W/m2). (7.100) I
7 -6 Electromagnetic Power Density
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.•.
.•.
.•.
s
.••. ----- ..•.
,
.•. "
" S ,"
/ ..•... -.-~,'
A,ph = 47rRs
Example 7-5: Solar Power
(VIm).
7-6.2 Plane Wave in a Lossy Medium
E(z) = x Ex(z) + y Ey(z)
= (x E,o + y El'o)e-rX7e-i/lL,
- 1 A A -CtZ -jIlT.
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~ ~ ~ ~ Ie ~
Whereas the fields E(J:) and "(7) decay with 7. as e='. the
7-6.3 Decibel Scale for Power Ratios
PI
G = P2' (7.110)
[IE(Z)12] [IE(Z)I]
A = IOlog IE(0)12 = 20 log IE(O)I
(V2/R)
Vi/R
Example 7-6: Power Received by a Submarine Antenna
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Titles
Chapter 7 Relationships
k f
I [ ] } 1/2
a=w 2" 1+(7)-1
I [ ] }1/2
f3=W 2" 1+(7) +1
- 1 ~ -
E= -l'/kxH
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Titles
GLOSSARY OF IMPORTANT TERMS
(mAim).
CHAPTER HIGHLIGHTS
PROBLEMS
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Titles
E = x Eo cos(wt - ky)
(Vim).
(Vim).
z
L----E----/1
a" 1 "
x
(VIm).
*
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Titles
1 ! I! 2
I! I! 2
o 0
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Titles
Wave Reflection and Transmission
c
H
A
p
8
T
E
R
Chapter Contents
Objectives
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8-1.1 Boundary between Lossless Media
z=o
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Titles
(8.1 a)
(8.1 b)
H-,'() • E (z) • Ell -,'klz
z=zx--=y-e' .
Z - x oe ,
Z -zx---y-e .
z=o
z=o
Ei
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Titles
Eo = (T12 - TIl) Eo = rE~,
I (2m) Ei E'i
(X. I I b)
TIl = --,
Fr:
Tl2 = --,
..;s;;
r= E? = 112 -1]1 (normaHncidence), (8.12a)
(8.13) I
8-1.2 Transmission-Line Analogue
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Page 369
Titles
IEilry
8-1.3 Power Flow in Lossless Media
n = 0, 1. 2, , if Or ~ 0,
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Titles
(lossless media), . (Se2l)
A~ = -- = -- = 1 cm.
~ Fr 3
Example 8-1: Radar Radome Design
, ,
(a)
~
d
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Titles
EI (z) = xEi(e-Y1L + reYI7),
_ Ei
HI (z) = y --2.(e-Ylz - reYP'),
Ei
Er
r..JH'
z= 0
8-1.4 Boundary between Lossy Media
Medium 1
(n = 0, \,2 .... )
= - +n -
4 2
1}1 = fFH = t! :::: 120rr (Q),
1}2 = Y -;; = y -;;; . Fr :::: v'2.2s = SOrr (Q),
Example 8-2: Yellow Light Incident upon a Glass
Surface
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Titles
- Eb 'kk
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~-Fz
r= ,
~+Fz
with cel = (Bl - jUllw) and eC2 = (£2 - jU2/w). (See 4,.)
8-2 Snell's Laws
~ ..
., ~
~ ,
.. '
...
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Titles
sinOt = "Ill = JILISI
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Titles
Example 8-4: Light Beam Passing through a Slab
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376
8- 3 Fi ber Optics
(8.39)
(8.37)
. ne
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Titles
I-T-J
..•.. f\f\f\
Example 8·5: Transmission Data Rate on Optical Fibers
I I
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Titles
Technology Brief 15: Lasers
•
'11
Basic Principles
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Titles
•
•
Wavelength (Color) of Emitted Light
Principle of Operation
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8-4 Wave Reflection and Transmission at
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-. r. 0 'k
8-4.1 Perpendicular Polarization
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x
z=o
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1 •. L=1 +f'l.. (859)1
(8.60)
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(VIm).
(VIm).
8-4.2 Parallel Polarization
lEt 12 (62)2
. kl 'In
E1 =E~ +E~
8t = 14S.
Al = - = 1m
kl '
COSel + ../(c2/c1) - sin28j
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Titles
cosBi
I'll = (I + ['II) -n . (8.67)
cos 171
11 rJ2 1J2
x
Transmitted Wave
Reflected Wave
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rs.x»
8-4.3 Brewster Angle
Os" = sin-I
(for III = 1l2). (8.12)
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Titles
Answer: r .L = -0.48, <~ = 0.52, rll = -0.16,
8-5 Reflectivity and Transmissivity
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i j IE~ol
Pr s. A IE~LOI2 A 0
Pt st IE~LOI2 A 0
lEt 12
+ ----='=L. A cos Ot.
RII + Til = 1,
~1~~~~X::'>.1~~:~~',~~:,:· '~{~~~~~
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-(E2/E])cosaj + J(8218» - sin2aj
(82Iel) cos aj + J (e2/EI) - sin2 OJ
----r======:;;===- = -0.435.
I EX81T1ple 8-7: Beam of Light
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Table 1
Page 390
Titles
Technology Brief 16: Bar-Code Readers
Basic Operation
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Page 391
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Titles
8-6 Waveguides
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Page 393
Titles
y = b .--..,.----..,.---:-:---r-----
" \ : : : /\./'-+--
y = 0 L----\~':r.--/-' ------- ------.. z
/
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8- 7 General Relations for E and H
E = x Ex + y ii, + i E 7..
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8-8 TM Modes in Rectangular
k=w,fili.
ay .
. ~ Bez .-
aev ae, .-
B!J, ahx . _
ax ay
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Titles
- --, + - --, + k~ = O.
k; -b'
t, = o,
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Titles
o
~\t-lj2··\
rrltl\\~
o~:l:plllr.f=~
bdt':l:g~li~
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Titles
f3 = u: 11- (17) 2., (TE and TM) (8.107)
Ex E\' f3TJ 1- (ff'Il1I1)2
ZTM = -=- = - ~ = - = 1/
Er - - f3 + - + - .
Example 8·8: Mode Properties
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Titles
- (mn X) (I1n \') "f3
~ jWJ1 (lin) (mnx) . (/lny)
x kl; b a b
~ jfi (/In) (mnx) . (nny)
~ -jWJ1 (mn) . (lnnx) (nny)
~" jfi (mn) .' (mnx) . (flny) e-j(3z,
kc a a b
8-9 TE Modes in Rectangular Waveguide
x sin(1.5n x IDIOt - 109nL)
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Page 401
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401
\
\
\
~mfO""
up = 7i .
I
8-10 Propagation Velocities
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Titles
(8. I 19b)
1 JTX
z =z+-.
II JTX
~ WJ.1 (JT) (JTX) 'I<
, 4 a a
~ (Wf.J..JT Ho ) 'I isrx ] 'jJ
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Titles
-
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Titles
CHAPTER 8 WAVE REFLECTlO'J i\\:f) TRi\\:Sl\lISSION
, .... Cl) Module ~tJ Rectangular \Ya,·eguidl·
o
Input
8-11
Cavity Resonators
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Titles
8-] ] .1 Resonant Frequency
- "/3 '/3 (m7tx) (n7tY)
-
o
---- .4//2
------- A
,
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Titles
8-11.2 Quality Factor
2a
Example 8-11 : Q of a Resonant Cavity
- [n x 12.6 x 109 x 4n x 10-7 x 5.8 x 107]1/2
a
Q=-
= 3 x 5.89 X 10-7 ::::::: 9,500.
Q = 8s [a3(d + 2b) + d3(a + 2b)]
/',.f ::::::: flO I
::::::: 1.3 MHz.
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Titles
Chapter 8 Relationships
407
_ Eb _ 2112
r - --,... - ---'----
T=I+f
..;e;; - .j£;;
..;e;; + .j£;;
f.l = -.- = ""-------'----
T.l = -.- =
fll=-' =------
rll=-j =
lJsll = sin-I 1 = tan-I rei
upoJ(m)2 (n)2 (P)2
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Titles
z=o
I-d-I
(Vim).
PROBLEMS
*
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Page 410
Titles
4
\
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Page 411
Titles
,.
-~
...... I
A .. .::: •••
T
1
fJr = I
,-d-I
T
t
1
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Titles
~
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Titles
Radiation and Antennas
R
E
T
Objectives
p
9
A
H
c
Chapter Contents
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Titles
416
-
'" -' '-'
Incident
~))
Wave launched
Overview
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Titles
~
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Titles
4lH
Q = (R, 0, 9)
.•
9-1 The Hertzian Dipole
A=- -- zlodz
.110 (e-jkR)
4;r R
A(R) = 110 f Je J sv'
4;r R' .
v'
(9.1 )
(A),
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Titles
- I -
jwco
4rr kR (kR)2 •
~ lolk2 -kR [ j I j] .
Eo = -- lJoe J - + -- - -- Sill e
4lf k R (kR)2 (kR)3 '
9-1.1 Far-Field Approximation
~ A A fLolol (e-jkR)
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Titles
Dipole
9-1.2 Power Density
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Titles
F(8, ¢) = F(e) = sin2 a.
•..
F(e, ¢) = S(R. e. ¢)
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Titles
y
~CJ.)~t == ====,°=10 II I· • 1
Module 9.1
9-2 Antenna Radiation Characteristics
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Titles
= R2Smax f f F(8, ¢) sin e' de d¢
9-2.1 Antenna Pattern
dA = R2 sin B dB d¢
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Titles
o
~
'2- -5
~
~
~
~
s
9-2.2 Beam Dimensions
For an isotropic antenna with F (0. ¢) = 1 in all directions,
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Titles
4~ ff F(8, ¢) dQ
9-2.3 Antenna Directivity
o
co
.£
.~
;.a -20
§
o
~
-5 70
'5 80
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Tables
Table 1
Page 426
Titles
F(D,1')
Example 9-1: Antenna Radiation Properties
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Titles
Example 9-2: Directivity of a Hertzian Dipole
4rr
JJ F(e,
f f sin3 e de d
9-2.4 Antenna Gain
= f ~ d = 2rr
F(e) = cos? e
Qp = JJ rio.
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Titles
(dimensionless). (9.29) I
9-2.5 Radiation Resistance
c 3 x 1O~
47rR2 I57r/(~ (/)2 2 2 (1)2
I"" - 2
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Titles
9-3 Half- Wave Dipole Antenna
,
~ ,/
1
/ = ..i12
L~-'/2
1
/= ).12
1
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Titles
- ,
= Su . 1
Sma, = So
15/(?
9-3. I Directivity of ).,/2 Dipole
15/0//{COS[(7r/2)cose]}- .
( -JkR)
E!! = / dE!!.
£9 = j6010 (COS[(:i~~ COSO]} (e-~kR), (9.44a)
- £9
H9=-·
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Titles
I
T
).14
l
II
9-3.3 Quarter- Wave Monopole Antenna
9-3.2 Radiation Resistance of 'A/2 Dipole
Images
Image 1
Image 2
Page 432
Titles
,
,
,
9-4 Dipole of Arbitrary Length
Images
Image 1
Image 2
Tables
Table 1
Page 433
Titles
B = -- -- sm e z
X i: sin[k(l12 - z)] dz
+ J eJkZCOSOSin[k(l12+Z)ldzj.
see) = IEel2 = 15/J [cos (¥ cose) - cos (¥)]2
(c) /=3AI2
Images
Image 1
Image 2
Image 3
Image 4
Page 434
Titles
Technology Brief 17: Health Risks of EM Fields
Physiological Effects of EMFs
Images
Image 1
Image 2
Page 435
Titles
-
Bottom Line
Images
Image 1
Image 2
Image 3
Image 4
Image 5
Page 436
Titles
E~
:;;: -€. 100
~ i 10
Images
Image 1
Image 2
Image 3
Image 4
Tables
Table 1
Table 2
Page 437
Titles
Data
I
:q
I
Set Antenna Parameters
Images
Image 1
Image 2
Image 3
Image 4
Page 438
Titles
- ~
IEd- IEd-
9-5 Effective Area of a Receiving
Images
Image 1
Image 2
Image 3
Image 4
Image 5
Image 6
Image 7
Image 8
Image 9
Page 439
Titles
R
9-6 Friis Transmission Formula
Images
Image 1
Image 2
Image 3
Image 4
Image 5
Image 6
Image 7
Image 8
Page 440
Titles
Pree = --- = ---------
Example 9·4: Satellite Communication System
10 =---~-
9-7 Radiation by Large-Aperture
Images
Image 1
Image 2
Page 441
Images
Image 1
Image 2
Image 3
Image 4
Page 442
Titles
442
----
----
----
Ya
I R ::! uP Il, (9.73) I
Images
Image 1
Page 443
Titles
E(R, e, ¢) =;: -R- u», ¢),
h(e)= I
sinor i, sin () / A)
= Eo . -L;
2Eo/\
~ 2Eolv
A
smc r = - .
S(R,e,¢)= ' .'1' 'I'
9-8 Rectangular Aperture with Uniform
Images
Image 1
Image 2
Image 3
Image 4
Page 444
Titles
444 CHAPTER 9 RADIATION AND ANTENNAS
9-8.1 Beamwidth
(9.87)
(9.80)
(9.85)
. A
smfh = 0.44 - .
Ix
nl, .
T SIn H2 = 1.39,
-I 30 I
Y = (lx/A) sin () -
I Pu = 2Ill " 2 sin 0, = 0.88/:
F(fJ) = S(R. e)
Smax
Images
Image 1
Image 2
Tables
Table 1
Page 445
Titles
9-8.2 Directivity and Effective Area
txt
Images
Image 1
Image 2
Image 3
Image 4
Image 5
Page 446
Titles
9-9 Antenna Arrays
Images
Image 1
Image 2
Image 3
Image 4
Image 5
Tables
Table 1
Page 447
Titles
'r
447
l~. 1 I ~ 1
Se(R, 0, ¢) = -IEe(H. e, ¢lI" = --21.t~((1. ¢)I".
2r}o 2rJoR
(9.94)
(9.93)
Images
Image 1
Image 2
Page 448
Titles
= L Ai T !cW, cp),
Ej(Rj, e, cp) = Aj -- Ie(e, cp).
Images
Image 1
Image 2
Image 3
Image 4
Image 5
Page 449
Titles
Q
•
id
Images
Image 1
Image 2
Image 3
Image 4
Image 5
Image 6
Image 7
Page 450
Titles
450
~--)j2--~
y
x
ao= I
f
1
Figure 9-28: Two half-wave dipole array of Example 9-5.
2(T( T()
S(R,e)=SOFa(e)=4S0COS "2cose-4" .
II + ejxl2 = lejx/2(e-jx/2 + ejx/2)12
'. 71 [e-jx/2 + ejx/2112
= leJ~/21- 2 ---:----
= cos e' - - = 0
S(R,e) ?(n n)
Images
Image 1
Image 2
Image 3
Image 4
Image 5
Page 451
Titles
J
D
Images
Image 1
Image 2
Tables
Table 1
Page 452
Titles
-----<__.-+-- ...•.. -_ z (East)
d
~I
~--------~~---------'~z
Images
Image 1
Image 2
Image 3
Image 4
Page 453
Titles
9-10 N-ElementArray with Uniform
)..
. 2 (n )
Images
Image 1
Image 2
Image 3
Image 4
Image 5
Image 6
Page 454
Titles
=
= 11 + ejYl2,
Images
Image 1
Image 2
Image 3
Image 4
Image 5
Page 455
Titles
9-10 N-ELEMENT ARRAY WITH UNIFORM PHASE DISTRIBUTION
z
455
Images
Image 1
Image 2
Image 3
Page 456
Titles
9-11 Electronic Scanning of Arrays
Images
Image 1
Image 2
Image 3
Image 4
Page 457
Titles
9-11.1 Uniform-Amplitude Excitation
z
Images
Image 1
Image 2
Image 3
Image 4
Image 5
Page 458
Titles
(9.122)
9-1 1.2 Array Feeding
458
Images
Image 1
Image 2
Image 3
Image 4
Page 459
Titles
noup
Page 460
Titles
o 2noJr (/).f. ) (f - 10 GHZ)
Images
Image 1
Image 2
Page 461
Titles
/O.s
I(is
Images
Image 1
Image 2
Image 3
Page 462
Titles
Chapter 9 Relationships
).3D
Ae = -.-
Rrad ~ 73 Q
H¢=-
S(R, e) = 71' R2 sin2 e
H¢=-
S(R, e) = 20 2 sin2 e
x ).
i. y
D---"'--
.. 2nd
Images
Image 1
Image 2
Image 3
Page 463
Titles
CHAPTER HIGHLIGHTS
GLOSSARY OF IMPORTANT TERMS
Page 464
Titles
rt«. ¢) = { ~:
rte, ¢) = I
PROBLEMS
Images
Image 1
Image 2
Page 465
Titles
for 0 < z ::: 1/2,
fez) = { 100 - Zz] I),
Images
Image 1
Image 2
Image 3
Image 4
Page 466
Titles
I
1
I
I
----------- 5 km -----------1
I-d-I
(a) d = ),,/4,
Images
Image 1
Image 2
Image 3
Page 467
Titles
i!(N - j - I)!
Images
Image 1
Image 2
Tables
Table 1
Page 468
Titles
Satellite Communication Systems
10
R
E
T
p
A
H
c
Chapter Contents
Objectives
Images
Image 1
Image 2
Page 469
Titles
---.I!L.'--~ .""
Satellite Communication Systems
10-1
Application Examples
Images
Image 1
Image 2
Image 3
Image 4
Image 5
Image 6
Page 470
Titles
Ro
G --,- = Msw· Ro.
W
_ [GMeJ1!3
Images
Image 1
Image 2
Image 3
Page 471
Titles
10-2 Satellite Transponders
Images
Image 1
Tables
Table 1
Page 472
Titles
•
•
---------------------,
•...
g I~ --
~ I~----i
~ .
:;
Images
Image 1
Image 2
Image 3
Image 4
Image 5
Image 6
Tables
Table 1
Page 473
Titles
~..n
~ ~~ '0 r:;
~ 'fJ,9'
10-3 Communication-Link Power
Images
Image 1
Image 2
Image 3
Image 4
Image 5
Page 474
Titles
10-4 Antenna Beams
(10.9)
(10.8)
Pri = 1(8) r; = 1(8) PICICr (~)2
(10.11)
(10. I 2)
Images
Image 1
Image 2
Image 3
Image 4
Page 475
Titles
10-5 RADAR SENSORS
10-5 Radar Sensors
Images
Image 1
Image 2
Image 3
Page 476
Titles
10-5.1 Basic Operation of a Radar System
10-5.2 Unambiguous Range
Images
Image 1
Image 2
Image 3
Page 477
Titles
(to. 15)
2R) 2R/
--- ~ -- + r.
e c
----- R
J- - - - - - ~..,..
--
_-\----R~~-
.....•... -
10-5.3 Range and Angular Resolutions
/
2R
T=-,
I----r-I
cTp c
Ru= - = -. (10.14)
2 2/p
Images
Image 1
Image 2
Image 3
Image 4
Image 5
Page 478
Titles
\ ---------1
==_-.-_-_l_-_- - - - RAx=fJR
J ---
----------
(
10-6 Target Detection
Images
Image 1
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Image 3
Image 4
Image 5
Image 6
Image 7
Image 8
Image 9
Page 479
Titles
479
(10.24)
(10.22)
[ p.G2J...2a. JI/4
(10.21)
(10.18)
- - -
---
- -
---
- - -
---
---
r;
r.o»,
Prer = Stat = --2 (W). (10.20)
Images
Image 1
Image 2
Image 3
Image 4
Image 5
Image 6
Page 480
Titles
1.\
Ic=Tc+T«.
r:
10-7 Doppler Radar
Images
Image 1
Image 2
Image 3
Image 4
Image 5
Page 481
Titles
10-8 Monopulse Radar
1 E3-
Images
Image 1
Image 2
Image 3
Page 482
Titles
(a)
1--------1
3--------'
4------ .
~ u
"",
-,
'\';
/
- - - -~-
Images
Image 1
Image 2
Image 3
Image 4
Image 5
Image 6
Image 7
Image 8
Page 483
Titles
~--
. efC: ;:~
Images
Image 1
Image 2
Image 3
Image 4
Image 5
Image 6
Page 484
Titles
41T2
Chapter 10 Relationships
2 2fp
_ Prj _ i(e) PtGtGr (_)..._)2
Sn- ------
Pni KTsysB 41T R
!:ix = {3R
P _ t t
r - (41T)3 R4
Ur 2u
fd = -2- = -- cos s
Page 485
Titles
CHAPTER HIGHLIGHTS
GLOSSARY OF IMPORTANT TERMS
PROBLEMS
Page 486
Page 487
Titles
and Abbreviations
x
I
D
N
A
E
p
p
A
Symbols, Quantities,Units,
Images
Image 1
Image 2
Image 3
Tables
Table 1
Page 488
Images
Image 1
Tables
Table 1
Page 489
Tables
Table 1
Page 490
Images
Image 1
Tables
Table 1
Page 491
Titles
A
p
p
E
N
D
I
x
B
Material Constants of Some
Common Materials
Images
Image 1
Image 2
Tables
Table 1
Page 492
Titles
MATERIAL CONSTANTS OF SOME COMMON MATERIALS
APPENDIX B
492
Images
Image 1
Tables
Table 1
Table 2
Page 493
Titles
Mathematical Formulas
x
I
D
E N
C
p
p
A
. (x + V) (x - v)
(X + v) (x - y)
Trigonometric Relations
Images
Image 1
Image 2
Image 3
Page 494
Titles
cos x = 1 - - + - + ... :::: 1 - -
Images
Image 1
Page 495
Titles
x
I
D
N
D
E
p
A P
Answers to Selected Problems
1.3 A = 10 cm
Chapter 1
Images
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Image 2
Image 3
Image 4
Image 5
Page 496
Titles
Chapter 2
2.37 I = )..14 + 11)..12
Chapter 3
• IA(l. -1. 2)1 Y
Page 497
Titles
c
Chapter 4
Images
Image 1
Page 498
Titles
Chapter 5
Chapter 6
Chapter 7
Images
Image 1
Image 2
Page 499
Titles
Chapter 8
Chapter 9
Images
Image 1
Page 500
Titles
Chapter 10
Images
Image 1
Page 501
Images
Image 1
Page 502
Images
Image 1
Page 503
Titles
A
503
Images
Image 1
Page 504
Titles
504
B
c
INDEX
Images
Image 1
Page 505
Titles
INDEX
o
E
505
Images
Image 1
Page 506
Titles
506
F
INDEX
Page 507
Titles
G
H
J
507
Images
Image 1
Page 508
Titles
508
K
L
M
INDEX
Images
Image 1
Page 509
Titles
INDEX
N
o
p
509
Images
Image 1
Page 510
Titles
510
Q
A
s
INDEX
Images
Image 1
Image 2
Page 511
Titles
INDEX
T
511
Images
Image 1
Page 512
Titles
512
u
v
w
x
z
Page 513
Titles
.•.
Images
Image 1
FUNDAMENTAL
CONSTANT
PHYSICAL
SYMBOL
CONSTANTS
VALUE
speed of light in vacuum
gravitational constant
Boltzmann's constant
elementary charge
permittivity of free space
permeability of free space
electron mass
proton mass
Planck's constant
intrinsic impedance of free space
c
G
K
e
EO
/-to
me
mp
h
r]()
2.998 x 108 ~ 3 x 108 m/s
6.67 x 10-11 N·m2/kg2
1.38 x 10-23 J/K
1.60 x 10-19 C
8.85 x 10-12:::::
3JJr x 10-9 F/m
4n x 10-7 Him
9.11 x 10-31 kg
1.67 x 10-27 kg
6.63 x 10-34 J·s
376.7 ~ 120n n
MAXWELL'S
EQUATIONS
Gauss's law
Faraday's law
Gauss's law for magnetism
Ampere's law
V·D = a;
aB
VxE=-- at
an
VxH=J+- at
SYMBOL MAGNITUDE
& SUBMULTIPLE
PREFIX
PREFIXES
SYMBOL MAGNITUDE
MULTIPLE
PREFIX
exa
peta
tera
giga
mega
kilo
E
P
T
G
M
k
1018
1015
1012
109
106
103
milli
micro
nano
pico
femto
atto
m
J1
n
P
f
a
10-3
10-6
10-9
10-12
10-15
10-18
W hen this book in draft form, each student was asked to write a brief statement describing his or her
understanding of what role electromagnetics
plays in science,
technology, and society. The following
statement, submitted by Mr. Schaldenbrand, was selected for inclusion here:
Electromagnetics
has done more than just help science.
Since we have such advanced
communications, our understanding of other nations and nationalities has increased exponentially.
This understanding has led and will lead the governments of the world to work towards global peace.
The more knowledge we have about different cultures,
the less foreign these cultures will seem. A
global kinship will result, and the by-product will be harmony. Understanding is the first step, and
communication is the means. Electromagnetics holds the key to this communication, and therefore
is an important subject for not only science, but also the sake of humanity.
Mike Schaldenbrand, 1994
The University of Michigan
SOME USEFUL
VECTOR
IDENTITIES
A . B = A B cos eA B
A x B = nAB sin8AB
Scalar
(or dot) product
Vector
(or cross) product.
it normal
to plane containing A and B
A . (B x C) = B . (C x A) = C . (A x B)
A x (B x C) = B(A . C) - C(A x B)
V(U + V) = VU + VV
VevV) = UVV + VVU
v . (A + B) = V . A + V . B
V . evA) = UV· A + A· VU
V x (U A) = UV x A + VU x A
V x (A + B) = V x A + V x B
V·
(A x B) = B· (V x A) - A . (V x B)
V . (V x A) = 0
VxVV=O
V x V x A = V(V . A) - V2A
(V . A) dv = fA.
5
ds
(V x A) . ds = fA.
c
dl
/
V
/
s
Divergence
theorem (s encloses V)
Stukes's theorem (S bounded
by C)
FUNDAMENTALS OF
APPLIED
ELECTROMAGNETICS
6/e
Fawwaz T. Ulaby
University of Michigan, Ann Arbor
Eric Michielssen
University of Michigan, Ann Arbor
Urn bertoRavaioli
University of Illinois, Urbana-Champaign
PEARSON
Upper Saddle River
Cape Town . Dubai
. Toronto
Delhi· Mexico City· Sao Paulo· Sydney. Hong Kong. Seoul· Singapore· Taipei· Tokyo
. Milan . Munich . Paris
. Columbus
. Madrid
. Boston
. London
. San Francisco
. New York . Amsterdam
. Montreal
Preface to 6/e
line circuits;
generate
analyze
allow the user
to interactively
Building on the core content and style of its predecessor,
this sixth edition (6/e) of Applied Electromagnetics
introduces
to help students develop a deeper
new features designed
understandi ng of electromagnetic
concepts and appl ications.
Prominent among them is a set of 42 CD simulation modules
that
and design
transrnission
spatial patterns of the
electric and magnetic fields induced by charges and currents;
visualize in 2-D and 3-D space how the gradient, divergence,
and curl operate on spatial functions; observe the temporal and
spatial waveforms of plane waves propagating in loss less and
lossy media; calculate
inside
and generate radiation patterns for
a rectangular waveguide;
linear antennas
These are valuable
learning tools; we encourage students to use them and urge
instructors to incorporate them into their lecture materials and
homework assignments.
and display field distributions
and parabolic dishes.
Additionally, by printing this new edition in full color, graphs
and illustrations now more efficiently convey core concepts,
and by expanding the scope of topics of the Technology Briefs,
fundamentals and
additional bridges between electromagnetic
their counLless engineering
and scientific
applications
are
established.
In summary:
New to this edition
• A set of 42 CD-interactive simulation modules
• New/updated Technology Briefs
• Full-color
figures and images
• New/updated end-of-chapter problems
• Updated bibliography
Acknowledgments
As authors, we were blessed to have worked on this book
with the best team of professionals: Richard Carnes, Leland
Pierce, Janice Richards, Rose Kernan, and Paul Mailhot. We are
exceedingly grateful for their superb support and unwavering
dedication to the project.
We enjoyed working on this book. We hope you enjoy
learning from it.
FAWWAZ T. ULABY
ERIC MICHIELSSEN
UMBERTO RAVAIOLJ
6
PREFACE
Excerpts From the Preface to the Fifth
Edition
CONTENT
The book begins by building a bridge between what should be
to a third-year electrical engineering student and the
familiar
(EM) material covered in the book. Prior
electromagnetics
student will have
to enrolling in an EM course.
taken one or more courses
He or she should
be familiar with circuit analysis, Ohm's
law, Kirchhoff's
current and voltage laws, and related topics. Transmission
lines constitute
circuits
and e1ectromagnetics. Without having to deal with vectors
to
or
a natural bridge between electric
already familiar
the student
in circuits.
a typical
concepts
fields,
uses
impedance matching,
the reflection and transmission
learn about wave motion,
of power, phasors.
and many of the
properties of wave propagation in a guided structure. All of
these newly learned concepts will prove invaluable later (in
Chapters 7 through 9) and will facilitate the learning of how
plane waves propagate in free space and in material media.
Transmission lines are covered in Chapter 2, which is preceded
I with reviews of complex numbers and phasor
in Chapter
analysis.
The next part of the book, contained in Chapters 3 through 5,
covers vector analysis, electrostatics, and magnetostatics. The
electrostatics chapter begins with Maxwell's equations for the
time-varying case, which are then specialized to electrostatics
thereby providing the student with an
and magnetostatics,
Suggested Syllabi
Two-Semester Syllabus
6 credits (42 contact hours per semester)
Hours
4
Sections
All
One-Semester
4 credits (56 contact hours)
Syllabus
Sections
All
Hours
4
2-1 to 2-8 and 2-11
All
4-1 to 4-10
5-1 to 5-5 and 5-7 to 5-8
6-1 to 6-3, and 6-6
7-1 to 7-4, and 7-6
8-1 to 8-3, and 8-6
9-1 to 9-6
None
Total
12
8
8
7
3
42
6
7
9
10
5
3
40
2
8
8
6
5
2
3
6
7
6
-
I
56
0
1
Chapter
Introduction:
Waves and Phasors
Transmission Lines
2
3 Vector Analysis
4
5 Magnetostatics
Electrostatics
All
All
All
All
Exams
Total for first semester
6 Maxwell's Equations
for Time-Varying Fields
Plane-wave Propagation
7
8 Wave Reflection
and Transmission
Radiation and Antennas
Satellite Communication
Systems and Radar Sensors
Exams
9
10
All
All
All
All
All
Extra Hours
Total for second semester
PREFACE
7
fields and sets
6 deals with time-varying
the
in Chapters 7 through 9. Chapter 7
stage for the material
covers plane-wave propagation in dielectric and conducting
media, and Chapter 8 covers reflection and transmission at
discontinuous
to fiber
optics, waveguides and resonators.
and introduces
the student
boundaries
overall framework for what
her why electrostatics and magnetostatics
the more general
time-varying case.
is to come and showing him or
are special cases of
Chapter
In Chapter 9, the student
is introduced to the principles of
radiation by currents flowing in wires, such as dipoles, as well as
~oradiation by apertures, such as a horn antenna or an opening
in an opaque screen illuminated by a light source.
in today's technological
To give the student a taste ofthe wide-ranging applications of
electromagnetics
society, Chapter 10
concludes the book with overview presentations of two system
satellite communication systems and radar sensors.
examples:
in this book was written for a two-semester
it is possible to trim it down to
four-credit course. The
for each of these two
sequence of six credits, but
generate a syllabus for a one-semester
accompanying
syllabi
options.
table provides
The material
MESSAGE TO THE STUDENT
interactive CD-ROM accompanying
this book was
The
developed with you, the student, in mind. Take the time to use it
in conjunction with the material
in the textbook. The multiple-
window feature of electronic displays makes it possible to
design interactive modules with "help" buttons to guide the
student through the solution of a problem when needed. Video
animations can show you how fields and waves propagate in
time and space, how the beam of an antenna array can be made
to scan electronically, and examples of how current
is induced
in a circuit under the influence of a changing magnetic field.
The CD-ROM is a useful resource for self-study. Use it!
ACKNOWLEDGMENTS
looking and esthetically
My sincere gratitude goes to Roger DeRoo, Richard Carnes and
I am indebted to Roger DeRoo for his painstaking
Jim Ryan.
review of several drafts of the manuscript.
Richard Carnes
is unquestionably the best technical
typist I have ever worked
with; his mastery of IbTEX,coupled with his attention to detail,
made it possible to arrange the material
in a clear and smooth
format. The artwork was done by Jim Ryan, who skillfully
transformed my rough sketches into drawings
that are both
professional
I am also
pleasing.
grateful to the following graduate students for reading through
parts or all of the manuscript
and for helping me with the
solutions manual: Bryan Hauck, Yanni Kouskoulas, and Paul
Siqueira.
Special
thanks are due to the reviewers for their valuable
comments and suggestions. They include Constantine Balanis
of Arizona State University, Harold Mott of the University of
Alabama. David Pozar ofthe University of Massachusetts, S. N.
Prasad of Bradley University, Robert Bond of New Mexico
Institute of Technology, Mark Robinson of the University of
Colorado at Colorado Springs, and Raj Mittra of the University
I appreciate the dedicated efforts of the staff at
of Illinois.
Prentice Hall and I am grateful
for their help in shepherding
through the publication process in a very timely
this project
manner.
l also would like to thank Mr. Ralph Pescatore for
copy-editing the manuscript.
FAWWAZ T ULAllY
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