• Page 1
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    • Image 1
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    • Table 1
    • Table 2
• Page 3
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  • Titles
    • 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
  • Images
    • Image 1
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• Page 5
  • Titles
    • FUNDAMENTALS OF
    • APPLIED
    • ELECTROMAGNETICS
    • 6/e
    • Fawwaz T. Ulaby
    • Eric Michielssen
    • Urn bertoRavaioli
    • PEARSON
  • Images
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• Page 6
  • Titles
    • Preface to 6/e
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 7
  • Titles
    • Excerpts From the Preface to the Fifth
    • CONTENT
    • Suggested Syllabi
  • Tables
    • Table 1
• Page 8
• Page 9
  • Titles
    • List of Technology Briefs
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    • Image 1
    • Image 2
    • Image 3
  • Tables
    • Table 1
• Page 10
  • Titles
    • Contents
  • Images
    • Image 1
    • Image 2
  • Tables
    • Table 1
• Page 11
  • Tables
    • Table 1
• Page 12
  • Tables
    • Table 1
• Page 13
  • Tables
    • Table 1
• Page 14
  • Images
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• Page 15
  • Titles
    • Introduction: Waves and Phasors
    • Objectives
    • R
    • E
    • T
    • p
    • 1
    • A
    • H
    • c
    • Chapter Contents
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    • Image 1
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• Page 16
  • Titles
    • 16
    • Overview
  • Images
    • Image 1
• Page 17
  • Titles
    • 1-1 Historical Timeline
    • 1-1.1 EM in the Classical Era
    • 1-1.2 EM in the Modem Era
  • Images
    • Image 1
• Page 18
  • Titles
    • 18
    • 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
  • Images
    • Image 1
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• Page 19
  • Titles
    • 19
    • 1-2 Dimensions, Units, and Notation
    • E=xE,
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    • Image 1
    • Image 2
  • Tables
    • Table 1
    • Table 2
• Page 20
  • Titles
    • Chronology 1-1: TIMELINE FOR ELECTROMAGNETICS IN THE CLASSICAL ERA
    • 1752
    • 1733
    • 1745
    • 1671
    • Electromagnetics in the Classical Era
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• Page 21
  • Titles
    • 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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• Page 22
  • Titles
    • 22
    • CHAPTER I INTRODUCTION: WAVES AND PHASORS
    • Telecommunications
    • ON~ ~~~N~"'~:~G~~~. ~A.
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    • Image 4
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• Page 23
  • Titles
    • \-2 DIMENSIONS. UNITS, AND NOTATION
    • Telecommunications
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    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
• Page 24
  • Titles
    • 24
    • CHAPTER 1 INTRODUCTION: WAVES AND PHASORS
    • Chronology 1-3: TIMELINE FOR COMPUTER TECHNOLOGY
    • Computer Technology
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    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
  • Tables
    • Table 1
• Page 25
  • Titles
    • 25
    • ~~:'~~'~~~rE~ ~~!
    • Computer Technology
    • 1-2 DIMENSIONS. UNITS. AND NOTATION
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• Page 26
  • Titles
    • 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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    • Image 1
    • Image 2
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• Page 27
  • Titles
    • (1.7)
    • 1-3.2 Electric Fields
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    • Image 1
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• Page 28
  • Titles
    • +
    • " t /1 ~
    • ", \t/ /x
    • '8/
    • I ~ \
    • , "­
  • Images
    • Image 1
    • Image 2
• Page 29
  • Titles
    • 1-3.3 Magnetic Fields
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    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
• Page 30
  • Titles
    • (Him).
    • 1-3.4 Static and Dynamic Fields
    • JiiOiO
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    • Image 1
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• Page 31
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    • Image 1
• Page 32
  • Titles
    • o
    • 1-4 Traveling Waves
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    • Image 1
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    • Image 6
• Page 33
  • Titles
    • I
    • 4>(x,t)= T-T+4>o
    • \
    • 1-4.1 Sinusoidal Waves in a Lossless Medium
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• Page 34
  • Titles
    • 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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• Page 35
  • Titles
    • co
    • ----=0
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• Page 36
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• Page 37
  • Titles
    • Sinusoidal Waves in a Lossy Medium
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    • Image 1
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• Page 38
  • Titles
    • f
    • (21T: 21T: )
    • ---~
    • --
    • ---
    • y(x)
    • Example 1-1: Sound Wave in Water
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    • Image 1
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• Page 39
  • Titles
    • Example 1-2: Power Loss
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• Page 40
  • Titles
    • a '-- , 'II
    • 1-5 The Electromagnetic Spectrum
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• Page 41
  • Titles
    • 41
    • (1.35)
    • y = Jm(z).
    • x = 9'te(z).
    • 1-6 Review of Complex Numbers
    • o
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    • Image 1
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    • Table 1
    • Table 2
• Page 42
  • Titles
    • 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
    • , '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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• Page 43
  • Titles
    • ( 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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• Page 44
  • Titles
    • Technology Brief 1: LED Lighting
    • Light Sources
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    • Image 1
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• Page 45
  • Titles
    • , 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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• Page 46
  • Titles
    • +
    • v
• Page 47
  • Images
    • Image 1
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  • Tables
    • Table 1
• Page 48
  • Titles
    • 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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• Page 49
  • Titles
    • 1-7 Review of Phasors
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    • Image 1
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• Page 50
  • Titles
    • 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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• Page 51
  • Titles
    • 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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  • Titles
    • 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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• Page 53
  • Titles
    • The PV Cell
    • Technology Brief 2: Solar Cells
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• Page 54
  • Titles
    • Modules, Arrays, and Systems
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• Page 55
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    • 11-
    • "ZX
    • ---
    • l1li
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• Page 56
  • Titles
    • Chapter 1 Relationships
    • B=.~
    • E=R q
    • CHAPTER HIGHLIGHTS
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• Page 57
  • Titles
    • GLOSSARY OF IMPORTANT TERMS
    • PROBLEMS
    • *
  • Images
    • Image 1
• Page 58
  • Titles
    • '---~-x
    • X=o
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    • Image 1
• Page 59
  • Titles
    • (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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• Page 60
  • Titles
    • L
    • i
    • --
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 61
  • Titles
    • Transmission Lines
    • R
    • E
    • T
    • Objectives
    • p
    • 2
    • A
    • H
    • c
    • Chapter Contents
  • Images
    • Image 1
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• Page 62
  • Titles
    • 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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• Page 63
  • Titles
    • - JUUl
    • (m/s).
    • - JVlJ'L
    • JUUl-
    • JUUl-
    • JUUl-
    • V,"A' = Vg(t) = Vo cos tot
  • Images
    • Image 1
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• Page 64
  • Titles
    • M
    • TEM Transmission Lines
    • M
    • Higher-Order Transmission Lines
    • 2-1.2 Propagation Modes
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• Page 65
  • Titles
    • 2-2 Lumped-Element Model
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    • Image 1
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• Page 66
  • Titles
    • R' /),z L' /),z
    • C'/),z
    • --------/),z--------
    • --------/),z--------
    • --------/),z--------
    • --------/),z--------
    • • Two-wire line [Fig. 2-4(17)1:
  • Images
    • Image 1
• Page 67
  • Titles
    • , n, (I I)
    • R =- -+-
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    • Image 1
    • Image 2
  • Tables
    • Table 1
• Page 68
  • Titles
    • _J¥fIIC
    • I /1 (b)
    • (Him).
    • G'=O,
    • (F/m).
    • (S/m).
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• Page 69
  • Titles
    • ---------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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• Page 70
  • Titles
    • 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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• Page 71
  • Titles
    • v.+ I v.+ I j¢+
    • 11- IV.-I N-
    • y+ -v;
    • 0_.
    • o 0
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    • Image 1
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• Page 72
  • Titles
    • c,=L
    • _ r;;;;u _ fL'
    • up = fA = ~ .
    • L' = Z5C'
    • Example 2-1: Air Line
  • Images
    • Image 1
• Page 73
  • Titles
    • 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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    • Image 1
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• Page 74
  • Titles
    • 2b
    • Coaxial Cable
    • Module 2.2
    • I· ~ 1
    • G {S/m]
    • I
    • Output
    • Structure Data
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    • Image 1
    • Image 2
    • Image 3
    • Image 4
  • Tables
    • Table 1
• Page 75
  • Titles
    • 2-5 The Lossless Microstrip Line
    • up = --.
    • Fr
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    • Image 1
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• Page 76
  • Titles
    • 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 .
  • Images
    • Image 1
  • Tables
    • Table 1
• Page 77
  • Titles
    • 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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    • Image 1
    • Image 2
    • Image 3
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• Page 78
  • Titles
    • output
    • Rangel ,L..--""' •..•••••. ..........:.~ ......•••........•••........•••.........••.•.......••.• ~;",.,J,
    • Rangel •.•• 14--""'-= .••••.........••••• == ~ ~ 1
    • Input
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    • Image 1
    • Image 2
• Page 79
  • Titles
    • 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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    • Image 1
    • Image 2
    • Image 3
• Page 80
  • Titles
    • z=O
    • d=O
    • I
    • d=!
    • d~r---------------~
    • 2-6.1 Voltage Reflection Coefficient
    • (2.55)
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    • Image 1
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    • Image 5
    • Image 6
    • Image 7
• Page 81
  • Titles
    • 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
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 82
  • Titles
    • =
    • =
    • A'
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    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 83
  • Titles
    • 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
  • Images
    • Image 1
    • Image 2
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• Page 84
  • Titles
    • o
    • "4
    • 2
    • IVcd)1
    • d------------------------~IVol
    • o
    • I A/2 I IV(d)1
    • 4 2 "4
    • 0.2
    • 14 '2 '"4
  • Images
    • Image 1
    • Image 2
    • Image 3
  • Tables
    • Table 1
    • Table 2
• Page 85
  • Titles
    • (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,
  • Images
    • Image 1
    • Image 2
• Page 86
  • Titles
    • 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\ /\~'
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
  • Tables
    • Table 1
    • Table 2
• Page 87
  • Titles
    • 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
  • Images
    • Image 1
    • Image 2
• Page 88
  • Titles
    • [I + r,]
    • I-r,
    • [I + r]
    • ZL=ZO --
    • I-r
    • 2- 7 Wave Impedance of the Lossless Line
  • Images
    • Image 1
• Page 89
  • Titles
    • 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.,
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
    • Image 7
    • Image 8
    • Image 9
  • Tables
    • Table 1
• Page 90
  • Titles
    • 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]
  • Images
    • Image 1
• Page 91
  • Titles
    • Wave and
    • Module 2.5
  • Images
    • Image 1
    • Image 2
• Page 92
  • Titles
    • Technology Brief 3: Microwave Ovens
    • Microwave Absorption
    • II~::
  • Images
    • Image 1
    • Image 2
  • Tables
    • Table 1
• Page 93
  • Titles
    • I
    • Oven Operation
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 94
  • Titles
    • (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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    • Image 1
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    • Image 3
    • Image 4
    • Image 5
• Page 95
  • Titles
    • zli - = 7< ] ~~~~;t
    • *
    • l_
    • 1 -I (WLcq)
    • 1
  • Images
    • Image 1
• Page 96
  • Titles
    • 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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    • Image 7
    • Image 8
    • Image 9
    • Image 10
    • Image 11
• Page 97
  • Titles
    • 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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    • Image 2
    • Image 3
    • Image 4
    • Image 5
• Page 98
  • Titles
    • 98
    • 2-8.6 Matched Transmission Line: ZL = Zo
  • Images
    • Image 1
  • Tables
    • Table 1
• Page 99
  • Titles
    • 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
  • Images
    • Image 1
• Page 100
  • Titles
    • . I!. w !
    • 1\1:+12
    • 2-9.2 Time-Average Power
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    • Image 1
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    • Image 3
    • Image 4
    • Image 5
    • Image 6
    • Image 7
• Page 101
  • Titles
    • 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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    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
• Page 102
  • Titles
    • Open-circuit
    • f·
    • fr = [I"] cos8r•
    • Short-circuit
    • 2-10.1 Parametric Equations
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• Page 103
  • Titles
    • ( 1)2 (1)2
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    • Image 6
    • Image 7
    • Image 8
• Page 104
  • Titles
    • r·
  • Images
    • Image 1
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• Page 105
  • Titles
    • Wave Impedance
    • =.9ZL~2-jl
    • I+r
    • Zed) 1+ r"
    • zed) = -- = -- ,
    • z, 1 - r"
  • Images
    • Image 1
    • Image 2
• Page 106
  • Titles
    • 2-10.3 SWR, Voltage Maxima and Minima
    • s = 1+ Ifl .
    • 4. - I
• Page 107
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    • Image 1
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    • Image 3
• Page 108
  • Titles
    • , 'd'
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    • Image 1
    • Image 2
    • Image 3
• Page 109
  • Titles
    • 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
  • Images
    • Image 1
• Page 110
  • Titles
    • 110
  • Images
    • Image 1
    • Image 2
• Page 111
  • Titles
    • THE SMITH CHART
    • Location
    • .,..
    • O.135A
    • III
    • Location
    • 1-3.3).-1
    • "';1 i :9'L ~ 05 + jl
    • , 'd,
  • Images
    • Image 1
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• Page 112
  • Titles
    • Zin = 0.28 - jOo4O,
    • ZL = 0.6 - jO.8.
• Page 113
  • Images
    • Image 1
    • Image 2
• Page 114
  • Titles
    • 114
    • ry
    • z, = SO.O In]
    • 2-11
    • Impedance Matching
  • Images
    • Image 1
• Page 115
  • Titles
    • Yin = (Cd + jBd) + js,
    • 2-11.1 Lumped-Element Matching
    • M'
    • M
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    • Image 1
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    • Image 3
    • Image 4
    • Image 5
• Page 116
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• Page 117
  • Titles
    • ( I - IfleFi') (I + Ifle-jR')
    • Yd= 1+lflejO' 1+lfle-jW
    • h'l = -----,,--..,-----
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    • Image 1
    • Image 2
    • Image 3
• Page 118
  • Titles
    • Yo
    • YdJ
    • I
    • Yo
    • A
    • 1
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    • Image 1
    • Image 2
    • Image 3
• Page 119
  • Titles
    • o.usz
    • 1 + jO = )'s + 1 + j 1.58,
    • Ys = - jl.58.
    • )'d = 1 - j1.58,
  • Images
    • Image 1
    • Image 2
• Page 120
  • Titles
    • 120
    • 2-11.2 Single-Stub Matching
  • Images
    • Image 1
    • Image 2
• Page 121
  • Titles
    • 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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    • Image 1
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    • Image 3
    • Image 4
    • Image 5
    • Image 6
• Page 122
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    • Image 1
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    • Image 4
  • Tables
    • Table 1
• Page 123
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    • Image 1
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    • Image 3
    • Image 4
  • Tables
    • Table 1
• Page 124
  • Titles
    • 124
    • 2-12 Transients on Transmission Lines
  • Images
    • Image 1
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    • Image 3
• Page 125
  • Titles
    • 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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    • Image 1
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    • Image 3
    • Image 4
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    • Image 6
• Page 126
  • Titles
    • (1/2::: Z S I). (2. 154b)
    • II = -rd~,
    • (0 s z < 1/2),
    • I) = ----"-
    • I 2
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
• Page 127
  • Titles
    • 2-12.2 Bounce Diagrams
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    • Image 1
    • Image 2
    • Image 3
  • Tables
    • Table 1
• Page 128
  • Titles
    • 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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    • Image 1
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    • Image 3
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• Page 129
  • Titles
    • 0.54 V
    • rL = = -----,- = 0.5.
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    • Image 1
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    • Image 3
    • Image 4
    • Image 5
    • Image 6
  • Tables
    • Table 1
• Page 130
  • Titles
    • V]- = frVt = -3 Y,
    • Fr J2.f
    • °
    • V(O, t)
    • -3
    • Ri: - Zo
    • I I I
    • -=-+-
    • Ru Rr Zo'
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 131
  • Titles
    • Microwave Ablation
    • Technology Brief 4: EM Cancer Zappers
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 132
  • Titles
    • High-Power Nanosecond Pulses
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    • Image 1
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    • Image 4
    • Image 5
    • Image 6
    • Image 7
• Page 133
  • Titles
    • 133
    • ~~
    • VI = --"---
    • V 00 = --"---
    • Rg-ZO
    • RL -ZO
    • (Np/m)
    • en)
    • =
    • Chapter 2 Relationships
    • G' a
  • Images
    • Image 1
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    • Image 3
    • Image 4
    • Image 5
• Page 134
  • Titles
    • ru
    • s=--
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 135
  • Titles
    • GLOSSARY OF IMPORTANT TERMS
    • 135
    • '----.....::..-0+
    • t
    • !
    • PROBLEMS
    • *
  • Images
    • Image 1
    • Image 2
• Page 136
  • Titles
    • R'C' = i/c'
    • !L'
  • Images
    • Image 1
    • Image 2
• Page 137
  • Titles
    • Zo = 50 0
    • C=')
    • R=6000
    • L=0.02 mH
    • of ZL.
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    • Image 1
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    • Image 3
    • Image 4
    • Image 5
• Page 138
  • Titles
    • R
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    • Image 1
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    • Image 6
• Page 139
  • Titles
    • 139
    • (a) ZL = (50 - j50) Q
    • * -
    • - -
    • I --*
    • Pin = 291cl ViIi ).
    • Zo= 50 Q
  • Images
    • Image 1
    • Image 2
• Page 140
  • 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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    • Image 1
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    • Image 3
    • Image 4
    • Image 5
    • Image 6
• Page 141
  • Titles
    • III = 3..1/81 12 = 5),/8
    • C B IA
    • (a) Zt = 3Zo•
    • (0 r = j.
  • Images
    • Image 1
    • Image 2
• Page 142
  • Titles
    • ./)
    • 1-0.3A-I/
    • 30n
    • ---0.3/. ---
    • *
    • *
    • 1 = '!
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    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
• Page 143
  • Titles
    • 12 V ----r----.
    • o
    • o
  • Images
    • Image 1
• Page 144
  • Titles
    • Vector Analysis
    • R
    • E
    • T
    • Objectives
    • p
    • 3
    • A
    • H
    • c
    • Chapter Contents
  • Images
    • Image 1
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• Page 145
  • Titles
    • 145
    • Overview
    • z
    • ;- ••.. ---+-~y
    • A = alAI = aA.
    • , A A
    • a=-=-.
    • IAI A
    • 3-1 Basic Laws of Vector Algebra
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 146
  • Titles
    • 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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    • Image 1
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• Page 147
  • Titles
    • 3-1.3 Position and Distance Vectors
    • 3-1.4 Vector Multiplication
    • ~
    • B = kA = akA = x(kAx) + y(kA,) + z(kA,J
    • B
    • ------------'"
    • z
  • Images
    • Image 1
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• Page 148
  • Titles
    • 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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    • Image 1
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    • Image 4
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• Page 149
  • Titles
    • - - - - _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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    • Image 1
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    • Image 3
    • Image 4
    • Image 5
    • Image 6
    • Image 7
  • Tables
    • Table 1
• Page 150
  • Titles
    • ~--------y
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
  • Tables
    • Table 1
• Page 151
  • Titles
    • 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
  • Images
    • Image 1
  • Tables
    • Table 1
• Page 152
  • Titles
    • 152
  • Images
    • Image 1
  • Tables
    • Table 1
• Page 153
  • Titles
    • dlz = d z,
    • dl, = dr.
    • 3-2,2 Cylindrical Coordinates
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    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
• Page 154
  • Titles
    • 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).
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 155
  • Titles
    • o
    • z
    • = rro - zh,
    • , A
    • a=-
    • IAI
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
    • Image 7
• Page 156
  • Images
    • Image 1
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    • Image 3
    • Image 4
  • Tables
    • Table 1
• Page 157
  • Titles
    • (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
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
    • Image 7
• Page 158
  • Titles
    • Technology Brief 5: Global Positioning System
    • Principle of Operation
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 159
  • Titles
    • Differential GPS
  • Images
    • Image 1
    • Image 2
• Page 160
  • Titles
    • 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
  • Images
    • Image 1
    • Image 2
    • Image 3
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• Page 161
  • Titles
    • r· x = x· xa + y. xh = a.
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    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
    • Image 7
• Page 162
  • Titles
    • Example 3-7: Cartesian to Cylindrical Transformations
  • Images
    • Image 1
  • Tables
    • Table 1
• Page 163
  • Titles
    • (R, e, ~):
    • R = ia + ib,
    • o
    • _ [\lX2 + V2]
    • (V)
    • 3-3.2 Cartesian to Spherical Transformations
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 164
  • Titles
    • 164
    • 3-3.3 Cylindrical to Spherical Transformations
    • 3-3.4 Distance between Two Points
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    • Image 1
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    • Image 3
    • Image 4
    • Image 5
• Page 165
  • Titles
    • )---------------- ..• 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,
  • Images
    • Image 1
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• Page 166
  • Titles
    • 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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• Page 167
  • Titles
    • (_ 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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  • Titles
    • T
    • Land
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• Page 169
  • Titles
    • 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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  • Titles
    • E
    • J-x
    • Idsl ds
    • +
    • 3-5 Divergence of a Vector Field
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• Page 171
  • Titles
    • .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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  • Titles
    • (a) V·E=-+-' +-.-
    • ax ilv aL
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    • Table 1
• Page 173
  • Titles
    • Technology Brief 6: X-Ray Computed Tomography
    • Principle of Operation
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• Page 174
  • Titles
    • Image Reconstruction
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• Page 175
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• Page 176
  • Titles
    • 176
    • 3-6 Curl of a Vector Field
    • + f xBo' X dx + f xBo' Y dy
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• Page 177
  • Titles
    • 177
    • o
    • \l x B =curlB
    • = .lim _I [it Ii. B .dlJ (3.103)
    • (3.101)
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• Page 178
  • Titles
    • 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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• Page 179
  • Titles
    • = 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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• Page 180
  • Titles
    • ro
    • I~"
    • ,'\.
    • 3-7 Laplacian Operator
    • .av .av .av
    • ax ay az
    • aAx aAv aAz
    • a2v a2v a2v
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• Page 181
  • Titles
    • Chapter 3 Relationships
    • ax ay ilz
    • By az az ax
    • ~ (aBI' aBx)
    • a2v a2v a2v
    • v s
    • s c
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• Page 182
  • Titles
    • 182
    • CHAPTER HIGHLIGHTS
    • GLOSSARY OF IMPORTANT TERMS
    • CHAPTER 3 VECTOR ANALYSIS
• Page 183
  • Titles
    • A(B·A)
    • a a IAI2'
    • A(B ·A)
    • D = B - IAI2
    • PROBLEMS
    • (d) A x C,
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    • Image 1
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    • Table 1
• Page 184
  • Titles
    • y =x -I.
    • (e) P3 = (4, n. 5)
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    • Table 1
• Page 185
  • Titles
    • P3 = (1, -I, 2)
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• Page 186
  • Titles
    • (a) A = xy2 + yxz + z4 at PI = (1, -I, 2)
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• Page 187
  • Titles
    • I/-'\'-~ ~-~\~-/I
    • t t . * + * . t t· * + • • t t
    • t J! :/
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    • Table 1
• Page 188
  • Titles
    • (h) A = x sin C~) + ysin C~'), for -10:s x, y:s 10
    • ~,
    • 1/
    • I \
    • /
    • . " {o
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    • Table 1
    • Table 2
• Page 189
  • Titles
    • 189
    • ~L:Lx
    • t*"----- X
    • ~-_~~_-":!-- x
    • o
    • :kLx
    • (e) E = r (3 - l~r) + zz
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• Page 190
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    • 190
• Page 191
  • Titles
    • Electrostatics
    • c
    • H
    • A
    • p
    • 4
    • T
    • E
    • R
    • Chapter Contents
    • Objectives
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• Page 192
  • Titles
    • 4- 2 Charge and Current Distributions
    • V' ·B=O,
    • Max well's Equations
    • 192
    • 4-1
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• Page 193
  • Titles
    • 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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• Page 194
  • Titles
    • 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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• Page 195
  • Titles
    • /I'\..
    • / . ,
    • 4-3 Coulomb's Law
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• Page 196
  • Titles
    • 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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• Page 197
  • Titles
    • 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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• Page 198
  • Titles
    • 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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  • Titles
    • E
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  • Titles
    • 4-4 Gauss's Law
    • V·D=py
    • f V· D dV = f D . ds.
    • v s
    • s s
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• Page 201
  • Titles
    • 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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• Page 202
  • Titles
    • 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)
  • Tables
    • Table 1
• Page 203
  • Titles
    • f (\7 x E) . ds = f E . dl = 0,
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• Page 204
  • Titles
    • 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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  • Titles
    • 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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• Page 206
  • Titles
    • qd .. ~ ~
    • 4-5.5 Poisson's Equation
    • Pv
    • V-V = V· (VV) = -- + -. - + -. ,
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• Page 207
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• Page 208
  • Titles
    • 4-6.1 Drift Velocity
    • =aE,
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• Page 209
  • Titles
    • 4-6.2 Resistance
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• Page 210
  • Titles
    • (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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• Page 211
  • 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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• Page 212
  • Titles
    • Technology Brief 7: Resistive Sensors
    • Piezoresistivity
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    • Image 1
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    • Table 1
• Page 213
  • Titles
    • -------&-------. Foree (N)
    • ( CiF)
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• Page 214
  • Titles
    • YOU! = Vo (f..R)
    • IE)
    • F=O
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• Page 215
  • Titles
    • 215
    • E
    • E
    • E E E
    • E
    • 1
    • E
    • 1
    • -
    • 4- 7 Dielectrics
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• Page 216
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    • 216
    • 4-7.1 Polarization Field
    • 4-7.2 Dielectric Breakdown
    • D = EoE + P,
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• Page 217
  • Titles
    • fE.dl= !Et.itdl+ !E2.i2dl=0.
    • 4-8 Electric Boundary Conditions
    • (VIm). (4.90) I
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• Page 218
  • Titles
    • Example 4-10: Application of Boundary CondItions
    • J... !J.h
    • ..;.....-~ ... 2"
    • c d
    • ---111-
    • 218
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• Page 219
  • Titles
    • 219
    • z
    • Ell jErx+Efy
    • tan (h = - = ..:.....----
    • E2x = Elx,
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• Page 220
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    • 220
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    • Table 1
• Page 221
  • Titles
    • 4-8.1 Dielectric-Conductor Boundary
    • (4.100a)
    • Elt = Dlt = 0,
    • Din = slEln = Ps·
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• Page 222
  • Titles
    • 4-8.2 Conductor-Conductor Boundary
    • (81 82)
    • (electrostatics) .
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• Page 223
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    • Input
    • !._Q.!
    • 223
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    • Table 1
• Page 224
  • Titles
    • 224
    • 4-9 Capacitance
    • v
    • +
    • (4,105)
    • Figure 4-23: A de voltage source connected to a capacitor
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    • Table 1
• Page 225
  • Titles
    • leE.ds
    • - fE.dl
    • (F),
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• Page 226
  • Titles
    • 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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• Page 227
  • Titles
    • 4-10 Electrostatic Potential Energy
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• Page 228
  • Titles
    • Technology Brief 8: Supercapacitors as Batteries
    • Capacitor Energy Storage Limitations
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• Page 229
  • Titles
    • Energy Storage Comparison
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• Page 230
  • Titles
    • 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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• Page 232
  • Titles
    • •
    • if
    • l;J \\ C V=o
    • \', l r c
    • -Q
    • v=o
    • if
    • •
    • - - - - - - -' - - - - - ~
    • ~'~
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• Page 233
  • Titles
    • t
    • Chapter 4 Relationships
    • Example 4-13: Image Method for Charge Above
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• Page 234
  • Titles
    • Air ---+--
    • Fluid Gauge
    • Technology Brief 9: Capacitive Sensors
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    • Image 6
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    • Table 1
• Page 235
  • Titles
    • /
    • :=: 1"=,,,1"="11,11
    • Humidity Sensor
    • Pressure Sensor
    • Noncontact Sensors
  • Images
    • Image 1
• Page 236
  • Titles
    • d1 1 .10 C1
    • 1.10
    • 3TC2
  • Images
    • Image 1
• Page 237
  • Titles
    • ,,~:::::::~,
    • I:: r.
    • "I' 1::
    • ,','" =-» c,
    • c
    • Fingerprint Imager
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• Page 238
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    • Image 1
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• Page 239
  • Titles
    • 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
  • Images
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• Page 240
  • Titles
    • 240
    • GLOSSARY OF IMPORTANT TERMS
    • PROBLEMS
    • p; = IOR2 cos2 (J (mC/m3).
    • * . ~
  • Images
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• Page 241
  • Titles
    • 241
    • ,
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    • Image 1
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    • Table 1
• Page 242
  • Titles
    • D = x2(x + y) + y(3x - 2)')
    • ,
    • ,
    • ,
    • ..
    • ..
    • ..
    • ..
    • ..
    • ..
    • ..
    • ,
    • ,
    • ----------------~~------------~x
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• Page 243
  • Titles
    • v
    • v
    • v
    • ....
  • Images
    • Image 1
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• Page 244
  • Titles
    • (a, 0)
    • • 18
  • Images
    • Image 1
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• Page 245
  • Titles
    • 1----1 cm----f
    • (Vim)
    • -
    • ~----------~II:~+~--------~
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    • Image 1
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• Page 246
  • Titles
    • T
    • 1
    • (a)
    • 2cm
    • T
    • 1
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• Page 247
  • Titles
    • r ••••.• --:---i- ... - .... ~
    • , I I.....'
    • : J::D-
    • v
    • +
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• Page 248
  • Titles
    • d - - -. Q = (0, d, d)
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• Page 249
  • Titles
    • Magnetostatics
    • c
    • H
    • A
    • p
    • 5
    • T
    • E
    • R
    • Chapter Contents
    • Objectives
  • Images
    • Image 1
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• Page 250
  • Titles
    • Overview
    • Fm=quxB
    • v ·B;'O,
    • 5-1
    • Magnetic Forces and Torques
  • Images
    • Image 1
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  • Tables
    • Table 1
• Page 251
  • Titles
    • 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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• Page 252
  • Titles
    • 5-1.1 Magnetic Force on a Current-Carrying
  • Images
    • Image 1
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    • Table 1
• Page 253
  • Titles
    • (S.12)
    • (S.11 )
    • 2S3
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
  • Tables
    • Table 1
    • Table 2
• Page 254
  • Titles
    • (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).
  • Images
    • Image 1
    • Image 2
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• Page 255
  • Titles
    • F
    • (S.14)
    • T=dxF
    • 5-1.2 Magnetic Torque on a Current-Carrying
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 256
  • Titles
    • f' gO/H L
    • B FJ
    • f 1 CD
    • Im=iNIA=nffl
    • = (-x~) x (zlhBu) + (x~) x (-Z1bBo)
    • =yfahBo=y/ABo, (5.16)
  • Images
    • Image 1
    • Image 2
  • Tables
    • Table 1
• Page 257
  • Titles
    • Answer: I = 8 rnA. (See e )
    • 5-2 The Biot-Savart Law
    • I dl x R
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 258
  • Titles
    • 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
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
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    • Image 6
• Page 259
  • Titles
    • 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:
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
    • Image 7
• Page 260
  • Titles
    • \
    • " ,
    • - -
    • \
    • t
    • ,
    • ...• , \ \
    • , I I I
    • - .". , I
    • ~ , I I I
    • ..•.. - , , , ,
    • ,~"""" •....
    • """ •.... ~--
    • " ..•.
    • \ ,
    • I \ I
    • , ~
    • ...• ~
    • - ~ , " , \ \ \ t I , ,
    • - , , , , \ \ \ , II , ~
    • - ~'''' \ \ \ \ I 1
    • , - - , " , \ \ \ \ \ \
    • ~ - ~"" \ \ \ \ ,
    • Example 5-3: Magnetic Field of a CIrcular Loop
  • Images
    • Image 1
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    • Image 3
    • Image 4
    • Image 5
    • Image 6
    • Image 7
    • Image 8
    • Image 9
• Page 261
  • Titles
    • (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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    • Image 1
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    • Image 3
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    • Image 5
• Page 262
  • Titles
    • ~ 41 ~
    • 5-2.3 Magnetic Force Between Two Parallel
    • ~ I
    • 4rrr
    • 262
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 263
  • Titles
    • !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
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
• Page 264
  • Titles
    • Technology Brief 10: Electromagnets
    • Basic Principle
  • Images
    • Image 1
    • Image 2
    • Image 3
  • Tables
    • Table 1
• Page 265
  • Titles
    • The Doorbell
    • Magnetic Relays
  • Images
    • Image 1
  • Tables
    • Table 1
• Page 266
  • Titles
    • The Loudspeaker
    • Magnetic Levitation
    • (
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 267
  • Titles
    • 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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    • Image 1
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• Page 268
  • Titles
    • 5-3.2 Ampere's Law
    • , ,
    • VxH=J •.• fH.dl=,.
    • s s
  • Images
    • Image 1
    • Image 2
• Page 269
  • Titles
    • ,
    • - - ~
    • 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
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
• Page 270
  • Titles
    • II = -, 1= - 1.
    • (for rj :::a).
    • 1
    • (for r: :::: 0).
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 271
  • Titles
    • Example 5-6: MagnetiC Field of an Infinite Current Sheet
    • z
    • { -yH
    • H= yH
    • I A t,
    • -y -
    • H= 2
    • '---~ - - - - - - -- -:~
    • r : J:~~!~----LJ ...• ~. +~--Y
    • , , N 1
    • H=-,H = -,-
    • 2nr
    • f H . dl = f (-~H) . ~r d ¢ = - 2n r H = - N I.
    • e 0
  • Images
    • Image 1
• Page 272
  • 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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    • Image 1
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    • Image 4
    • Image 5
• Page 273
  • Titles
    • 1=-- = --.
    • 5-5.1 Electron Orbital and Spin Magnetic
    • 5-5 Magnetic Properties of Materials
    • A- = !!:..- / J.r sv'
    • v'
  • Images
    • Image 1
    • Image 2
• Page 274
  • Titles
    • 274
    • (5.72)
    • 5-5.2 Magnetic Permeability
    • - - - -
    • - -
    • L. ----- - -
    • ( eu) ,
    • eur (e)
    • ----- - L
    • (5.73)
    • en
    • In, = ---,
  • Images
    • Image 1
    • Image 2
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• Page 275
  • Titles
    • 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
  • Images
    • Image 1
  • Tables
    • Table 1
• Page 276
  • Titles
    • B
    • B
    • B
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
  • Tables
    • Table 1
• Page 277
  • Titles
    • (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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    • Image 1
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• Page 278
  • Titles
    • 5-7 Inductance
    • 5-7.1 Magnetic Field in a Solenoid
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    • Image 1
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    • Image 4
• Page 279
  • Titles
    • - 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
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
• Page 280
  • Titles
    • / ~~:-:-:~::::::-::- .. -=-= .. --:--r t
    • N2
    • /,( N), N
    • s
  • Images
    • Image 1
    • Image 2
    • Image 3
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    • Image 5
• Page 281
  • Titles
    • (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 (~) .
  • Images
    • Image 1
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    • Image 6
  • Tables
    • Table 1
• Page 282
  • Titles
    • 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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    • Image 1
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• Page 283
  • Titles
    • 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
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
• Page 284
  • Titles
    • Technology Brief 11: Inductive Sensors
    • Linear Variable Differential Transformer (LVDT)
    • • •
  • Images
    • Image 1
    • Image 2
• Page 285
  • Titles
    • o
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 286
  • Titles
    • Eddy-Current Proximity Sensor
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
• Page 287
  • Images
    • Image 1
• Page 288
  • Titles
    • PROBLEMS
    • o
    • 0B
    • o
    • o
    • 10 0 01
    • o
    • o
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
    • Image 7
  • Tables
    • Table 1
    • Table 2
• Page 289
  • Titles
    • ,
    • ,
    • - - ,
    • -------:-:=.~
    • I
    • ---
    • ~t- .;...i ----I~y
    • n
  • Images
    • Image 1
    • Image 2
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• Page 290
  • Titles
    • ----:....--------1 •... ----- •. x
    • P
  • Images
    • Image 1
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    • Image 3
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    • Image 5
• Page 291
  • Titles
    • T l,-IOA
    • t ~2m-013~IOA
    • _I G)l,-IOA
    • 291
    • H
    • !I
  • Images
    • Image 1
    • Image 2
    • Image 3
  • Tables
    • Table 1
• Page 292
  • Titles
    • r
    • =-z-- X v
  • Images
    • Image 1
    • Image 2
• Page 293
  • Images
    • Image 1
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    • Image 3
    • Image 4
    • Image 5
• Page 294
  • Titles
    • z
    • x
    • A------------y
    • y
    • d
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 295
  • Titles
    • Maxwell's Equations for
    • Objectives
    • R
    • E
    • T
    • p
    • 6
    • A
    • H
    • c
    • Chapter Contents
  • Images
    • Image 1
    • Image 2
• Page 296
  • Titles
    • 296
    • Dynamic Fields
    • 6-1 Faraday's Law
  • Images
    • Image 1
  • Tables
    • Table 1
• Page 297
  • Titles
    • Vcmf = -N d = -N !!... f B· ds
    • s
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 298
  • Titles
    • 6-2 Stationary Loop in a Time-Varying
    • f 1 1
    • R
    • ,
    • R
    • 2
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
• Page 299
  • Titles
    • f liJB
    • c s
    • s s
    • Example 6-1: Inductor In a Changing Magnetic Field
    • V~~f = f E· dl.
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 300
  • Titles
    • 300
    • z
    • (A).
    • = j B· ds
    • = j[BO(Y2+Z3)SinM].ZdS
    • lr d
    • = -3][N(va2Bocoswt.
  • Images
    • Image 1
    • Image 2
• Page 301
  • Titles
    • (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
  • Images
    • Image 1
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    • Image 3
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  • Tables
    • Table 1
• Page 302
  • Titles
    • 1=
    • 6-3 The Ideal Transformer
    • - - - - ~
    • ---
    • ---
    • V~ = -N~ -.
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    • Image 2
    • Image 3
    • Image 4
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• Page 303
  • Titles
    • 6-4 Moving Conductor in a Static
    • :~
    • 11 N2
    • .......... =--
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    • Image 1
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    • Image 6
    • Image 7
  • Tables
    • Table 1
    • Table 2
• Page 304
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    • Image 1
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    • Image 4
    • Image 5
    • Image 6
    • Image 7
  • Tables
    • Table 1
• Page 305
  • Titles
    • z
    • R
    • u
    • (V).
    • Be\']) = iO.2e-O.1Y1 = zO.2e-O.2 (T).
    • Example 6-4: Moving Loop
    • (6.28)
    • o
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
• Page 306
  • Titles
    • f d:
    • VI2 = f (u X B) . dl
    • R 5
    • B0
  • Images
    • Image 1
    • Image 2
  • Tables
    • Table 1
• Page 307
  • Titles
    • y
    • B = 7oRo,
    • B
    • x
    • "
    • o
    • ~'i'­
    • 6-5 The Electromagnetic Generator
  • Images
    • Image 1
    • Image 2
    • Image 3
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• Page 308
  • Titles
    • ~ w
    • + f [( -DW~) x IBo] ·xdx.
    • = f [(DW~) x iBo] ·xdx
  • Images
    • Image 1
• Page 309
  • 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
  • Images
    • Image 1
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    • Image 3
    • Image 4
    • Image 5
• Page 310
  • Titles
    • Technology Brief 12: EMF Sensors
    • Piezoelectric Transducers
    • 1/ -0
    • --. ./
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
• Page 311
  • Titles
    • -,
    • Faraday Magnetic Flux Sensor
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 312
  • Titles
    • Thermocouple
  • Images
    • Image 1
    • Image 2
• Page 313
  • Titles
    • 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
  • Images
    • Image 1
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• Page 314
  • Titles
    • \
    • faD
    • 12d = - ·ds
    • at
  • Images
    • Image 1
    • Image 2
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    • Image 4
• Page 315
  • Titles
    • 315
    • 6-9 Charge-Current Continuity Relation
    • 6-8 Boundary Conditions for
  • Images
    • Image 1
  • Tables
    • 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.
  • Images
    • Image 1
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• Page 317
  • Titles
    • 6-10 Free-Charge Dissipation in a
    • Electromagnetic Potentials
    • 6-11
    • at E
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• Page 318
  • Titles
    • 318
    • E= -VV
    • v x E+- =0
    • at
    • 6-11.1 Retarded Potentials
    • (dynamic case). (6.70) I
    • v'
    • v'
    • E' = -VV.
    • E=E+-~ .
  • Images
    • Image 1
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• Page 319
  • Titles
    • v'
    • 6-11.2 Time-Harmonic Potentials
  • Images
    • Image 1
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    • Image 6
• Page 320
  • Titles
    • 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'
  • Images
    • Image 1
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    • Image 3
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• Page 321
  • Titles
    • 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
  • Images
    • Image 1
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• Page 322
  • Titles
    • CHAPTER HIGHLIGHTS
    • GLOSSARY OF IMPORTANT TERMS
    • PROBLEMS
    • * . .. .
    • ~------~~~------~
    • ~==:::::::::II
    • Rl
  • Images
    • Image 1
• Page 323
  • Titles
    • T
    • 1
    • ~----------------------~y
    • z
    • (b) cot = n /4
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 324
  • Titles
    • z
    • Yo
    • o
    • o
    • --
    • \
    • 80 ... '
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
    • Image 7
  • Tables
    • Table 1
• Page 325
  • Titles
    • a = 10-4 (S/m)
    • Pv = Par cos w{ (C/m3).
    • T
    • 1
    • I
  • Images
    • Image 1
    • Image 2
    • Image 3
  • Tables
    • Table 1
• Page 326
  • Titles
    • (VIm).
    • (AIm).
    • E = xEosinaycos(wt - kz),
    • E(R, e; t) =
    • , 2 X 10-2
  • Images
    • Image 1
• Page 327
  • Titles
    • Plane-Wave Propagation
    • Chapter Contents
    • R
    • E
    • T
    • Objectives
    • p
    • 7
    • A
    • H
    • c
  • Images
    • Image 1
    • Image 2
• Page 328
  • Titles
    • 32R
    • Unbounded EM Waves
    • , .. ~
    • /,:"-~" .. ",
  • Images
    • Image 1
  • 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
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 330
  • Titles
    • 7-2 Plane-Wave Propagation in Lossless
    • - -
    • E =-.
    • 2- (a2 a2 a2 ) -
    • V E- - - - E
    • - a2+,,2+a2 .
    • - -
    • ~ ~
    • 7-1.2 Wave Equations
  • Images
    • Image 1
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    • Image 3
    • Image 4
    • Image 5
    • Image 6
    • Image 7
    • Image 8
    • Image 9
• Page 331
  • Titles
    • 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)
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
  • Tables
    • Table 1
• Page 332
  • Titles
    • E
    • Example 7-1: EM Plane Wave in Air
    • A = - = = 300 m
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
    • Image 7
• Page 333
  • Titles
    • (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>+)
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
    • Image 7
• Page 334
  • Titles
    • ------------ E
    • H,'
    • y
    • 0.44)
    • -+ -
    • - 1. - A E, (7) A Et(L)
    • H = - z x E = -x _. - + Y _. - .
    • n rJ 1/
    • E- • E- + .. • f.~+. )
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
• Page 335
  • Titles
    • Technology Brief 13: RFID Systems
    • RFID System Overview
    • RFID Frequency Bands
  • Images
    • Image 1
    • Image 2
• Page 336
  • Titles
    • t
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
  • Tables
    • Table 1
• Page 337
  • Titles
    • (7.46)
    • (7.47a)
    • Output
    • - -jkf.
    • Plane Wave
    • Module 7.1
    • 7-3 Wave Polarization
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
  • Tables
    • Table 1
• 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)]
  • Images
    • Image 1
    • Image 2
• Page 339
  • Titles
    • 7-3.2 Circular Polarization
    • 1 [E\,(Z,I)]
    • ••
    • E
    • ,~ -
  • Images
    • Image 1
    • Image 2
• Page 340
  • Titles
    • z
    • ~rnn'
    • Example 7-2: RHC Polarized Wave
  • Images
    • Image 1
    • Image 2
  • Tables
    • Table 1
    • 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
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 342
  • Images
    • Image 1
    • Image 2
  • Tables
    • Table 1
• Page 343
  • Images
    • Image 1
    • Image 2
• Page 344
  • Titles
    • 344
    • Module 7.2 Polarization I
    • UNEAR POLARIZATION
    • OUtput
    • (J f "" QO
    • ModUle 7.3
    • Q t d.11Ik.
    • .BllelJ
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 345
  • Titles
    • Technology Brief 14: Liquid Crystal Display (LCD)
    • Physical Principle
    • LCD Structure
  • Images
    • Image 1
• Page 346
  • Titles
    • /
    • "----~~
    • "----
    • Two-Dimensional Array
  • Images
    • Image 1
    • Image 2
• Page 347
  • Titles
    • 347
    • 1
    • v
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 348
  • Titles
    • 7-4 Plane-Wave Propagation in Lossy
    • (Q). (7.70)
    • (rad/m).
    • (Np/m) ,
    • 1 + (~:r -1
    • { us' [
    • a=w "2
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
    • Image 7
• Page 349
  • 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
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
• Page 350
  • 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
  • Images
    • Image 1
  • Tables
    • Table 1
• Page 351
  • Titles
    • IExol = 4.44
    • E(z, t) = 9lr [xIExoleJ¢oe-aze-Jf!zeJwt]
    • = xIExole-0.126z cos(2rr x \03t - 0.126z + 4>0)
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
• Page 352
  • Titles
    • 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
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
    • Image 7
    • Image 8
    • Image 9
    • Image 10
    • Image 11
• Page 353
  • Titles
    • (7.90)
    • 1
    • Z="",=-- -
    • o
    • - ,
    • --'I
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
    • Image 7
    • Image 8
• Page 354
  • Titles
    • , I , Rs (1 1)
    • R = RI + R2 = - - + -
    • I I
    • n, = a~, = J;r~1l
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 355
  • Titles
    • 7 -6.1 Plane Wave in a Lossless Medium
    • ~ ~
    • k
    • (W/m2). (7.100) I
    • 7 -6 Electromagnetic Power Density
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
• Page 356
  • Titles
    • .•.
    • .•.
    • .•.
    • 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.
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
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    • Image 6
• Page 357
  • Titles
    • ~ ~ ~ ~ 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
  • Images
    • Image 1
    • Image 2
    • Image 3
  • Tables
    • Table 1
• Page 358
  • 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
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 359
  • Titles
    • GLOSSARY OF IMPORTANT TERMS
    • (mAim).
    • CHAPTER HIGHLIGHTS
    • PROBLEMS
  • Images
    • Image 1
• Page 360
  • Images
    • Image 1
• Page 361
  • Images
    • Image 1
    • Image 2
• Page 362
  • Titles
    • E = x Eo cos(wt - ky)
    • (Vim).
    • (Vim).
    • z
    • L----E----/1
    • a" 1 "
    • x
    • (VIm).
    • *
  • Images
    • Image 1
    • Image 2
• Page 363
  • Titles
    • 1 ! I! 2
    • I! I! 2
    • o 0
  • Images
    • Image 1
• Page 364
  • Titles
    • Wave Reflection and Transmission
    • c
    • H
    • A
    • p
    • 8
    • T
    • E
    • R
    • Chapter Contents
    • Objectives
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 365
  • Images
    • Image 1
    • Image 2
• Page 366
  • Titles
    • 8-1.1 Boundary between Lossless Media
    • z=o
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
• Page 367
  • 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
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
  • Tables
    • Table 1
• Page 368
  • 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
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
  • Tables
    • Table 1
• Page 369
  • Titles
    • IEilry
    • 8-1.3 Power Flow in Lossless Media
    • n = 0, 1. 2, , if Or ~ 0,
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 370
  • Titles
    • (lossless media), . (Se2l)
    • A~ = -- = -- = 1 cm.
    • ~ Fr 3
    • Example 8-1: Radar Radome Design
    • , ,
    • (a)
    • ~
    • d
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
• Page 371
  • 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
  • Images
    • Image 1
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    • Image 3
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    • Image 5
• Page 372
  • Titles
    • - Eb 'kk
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 373
  • Titles
    • ~-Fz
    • r= ,
    • ~+Fz
    • with cel = (Bl - jUllw) and eC2 = (£2 - jU2/w). (See 4,.)
    • 8-2 Snell's Laws
    • ~ ..
    • ., ~
    • ~ ,
    • .. '
    • ...
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 374
  • Titles
    • sinOt = "Ill = JILISI
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 375
  • Titles
    • Example 8-4: Light Beam Passing through a Slab
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
• Page 376
  • Titles
    • 376
    • 8- 3 Fi ber Optics
    • (8.39)
    • (8.37)
    • . ne
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 377
  • Titles
    • I-T-J
    • ..•.. f\f\f\
    • Example 8·5: Transmission Data Rate on Optical Fibers
    • I I
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 378
  • Titles
    • Technology Brief 15: Lasers
    • •
    • '11
    • Basic Principles
  • Images
    • Image 1
    • Image 2
• Page 379
  • Titles
    • •
    • •
    • Wavelength (Color) of Emitted Light
    • Principle of Operation
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 380
  • Titles
    • 8-4 Wave Reflection and Transmission at
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 381
  • Titles
    • -. r. 0 'k
    • 8-4.1 Perpendicular Polarization
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
• Page 382
  • Titles
    • x
    • z=o
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
• Page 383
  • Titles
    • 1 •. L=1 +f'l.. (859)1
    • (8.60)
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
• Page 384
  • Titles
    • (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
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 385
  • Titles
    • cosBi
    • I'll = (I + ['II) -n . (8.67)
    • cos 171
    • 11 rJ2 1J2
    • x
    • Transmitted Wave
    • Reflected Wave
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 386
  • Titles
    • rs.x»
    • 8-4.3 Brewster Angle
    • Os" = sin-I
    • (for III = 1l2). (8.12)
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
• Page 387
  • Titles
    • Answer: r .L = -0.48, <~ = 0.52, rll = -0.16,
    • 8-5 Reflectivity and Transmissivity
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 388
  • Titles
    • 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~~:~~',~~:,:· '~{~~~~~
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
    • Image 7
• Page 389
  • Titles
    • -(E2/E])cosaj + J(8218» - sin2aj
    • (82Iel) cos aj + J (e2/EI) - sin2 OJ
    • ----r======:;;===- = -0.435.
    • I EX81T1ple 8-7: Beam of Light
  • Images
    • Image 1
    • Image 2
  • Tables
    • Table 1
• Page 390
  • Titles
    • Technology Brief 16: Bar-Code Readers
    • Basic Operation
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 391
  • Images
    • Image 1
    • Image 2
• Page 392
  • Titles
    • 8-6 Waveguides
  • Images
    • Image 1
  • Tables
    • Table 1
• Page 393
  • Titles
    • y = b .--..,.----..,.---:-:---r-----
    • " \ : : : /\./'-+--
    • y = 0 L----\~':r.--/-' ------- ------.. z
    • /
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
• Page 394
  • Titles
    • 8- 7 General Relations for E and H
    • E = x Ex + y ii, + i E 7..
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 395
  • Titles
    • 8-8 TM Modes in Rectangular
    • k=w,fili.
    • ay .
    • . ~ Bez .-
    • aev ae, .-
    • B!J, ahx . _
    • ax ay
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
    • Image 7
• Page 396
  • Titles
    • - --, + - --, + k~ = O.
    • k; -b'
    • t, = o,
  • Images
    • Image 1
• Page 397
  • Titles
    • o
    • ~\t-lj2··\
    • rrltl\\~
    • o~:l:plllr.f=~
    • bdt':l:g~li~
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
• Page 398
  • 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
  • Images
    • Image 1
    • Image 2
• Page 399
  • 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)
  • Images
    • Image 1
    • Image 2
• Page 400
  • Images
    • Image 1
    • Image 2
  • Tables
    • Table 1
• Page 401
  • Titles
    • 401
    • \
    • \
    • \
    • ~mfO""
    • up = 7i .
    • I
    • 8-10 Propagation Velocities
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 402
  • 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
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 403
  • Titles
    • -
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 404
  • Titles
    • CHAPTER 8 WAVE REFLECTlO'J i\\:f) TRi\\:Sl\lISSION
    • , .... Cl) Module ~tJ Rectangular \Ya,·eguidl·
    • o
    • Input
    • 8-11
    • Cavity Resonators
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
    • Image 7
    • Image 8
    • Image 9
    • Image 10
• Page 405
  • Titles
    • 8-] ] .1 Resonant Frequency
    • - "/3 '/3 (m7tx) (n7tY)
    • -
    • o
    • ---- .4//2
    • ------- A
    • ,
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
• Page 406
  • 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.
  • Images
    • Image 1
    • Image 2
• Page 407
  • 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
  • Images
    • Image 1
    • Image 2
• Page 408
  • Images
    • Image 1
• Page 409
  • Titles
    • z=o
    • I-d-I
    • (Vim).
    • PROBLEMS
    • *
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
• Page 410
  • Titles
    • 4
    • \
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 411
  • Titles
    • ,.
    • -~
    • ...... I
    • A .. .::: •••
    • T
    • 1
    • fJr = I
    • ,-d-I
    • T
    • t
    • 1
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 412
  • Titles
    • ~
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 413
  • Images
    • Image 1
    • Image 2
• Page 414
  • Images
    • Image 1
• Page 415
  • Titles
    • Radiation and Antennas
    • R
    • E
    • T
    • Objectives
    • p
    • 9
    • A
    • H
    • c
    • Chapter Contents
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 416
  • Titles
    • 416
    • -
    • '" -' '-'
    • Incident
    • ~))
    • Wave launched
    • Overview
  • Images
    • Image 1
    • Image 2
• Page 417
  • Titles
    • ~
  • Images
    • Image 1
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    • Image 3
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    • Image 7
    • Image 8
    • Image 9
• Page 418
  • 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),
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 419
  • 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)
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 420
  • Titles
    • Dipole
    • 9-1.2 Power Density
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 421
  • Titles
    • F(8, ¢) = F(e) = sin2 a.
    • •..
    • F(e, ¢) = S(R. e. ¢)
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
• Page 422
  • Titles
    • y
    • ~CJ.)~t == ====,°=10 II I· • 1
    • Module 9.1
    • 9-2 Antenna Radiation Characteristics
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 423
  • Titles
    • = R2Smax f f F(8, ¢) sin e' de d¢
    • 9-2.1 Antenna Pattern
    • dA = R2 sin B dB d¢
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
• Page 424
  • Titles
    • o
    • ~
    • '2- -5
    • ~
    • ~
    • ~
    • ~
    • s
    • 9-2.2 Beam Dimensions
    • For an isotropic antenna with F (0. ¢) = 1 in all directions,
  • Images
    • Image 1
    • Image 2
• Page 425
  • Titles
    • 4~ ff F(8, ¢) dQ
    • 9-2.3 Antenna Directivity
    • o
    • co
    • .£
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    • ;.a -20
    • §
    • o
    • ~
    • -5 70
    • '5 80
  • Images
    • Image 1
    • Image 2
    • Image 3
  • Tables
    • Table 1
• Page 426
  • Titles
    • F(D,1')
    • Example 9-1: Antenna Radiation Properties
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
• Page 427
  • 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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    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
• Page 428
  • Titles
    • (dimensionless). (9.29) I
    • 9-2.5 Radiation Resistance
    • c 3 x 1O~
    • 47rR2 I57r/(~ (/)2 2 2 (1)2
    • I"" - 2
  • Images
    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
    • Image 7
• Page 429
  • Titles
    • 9-3 Half- Wave Dipole Antenna
    • ,
    • ~ ,/
    • 1
    • / = ..i12
    • L~-'/2
    • 1
    • /= ).12
    • 1
  • Images
    • Image 1
    • Image 2
• Page 430
  • 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=-·
  • Images
    • Image 1
    • Image 2
    • Image 3
• Page 431
  • Titles
    • I
    • T
    • ).14
    • l
    • II
    • 9-3.3 Quarter- Wave Monopole Antenna
    • 9-3.2 Radiation Resistance of 'A/2 Dipole
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    • 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
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    • Image 4
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    • Image 6
    • Image 7
    • Image 8
    • Image 9
• Page 439
  • Titles
    • R
    • 9-6 Friis Transmission Formula
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    • Image 1
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    • 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
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    • 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
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    • 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
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    • 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 )
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    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
    • Image 6
• Page 454
  • Titles
    • =
    • = 11 + ejYl2,
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    • Image 1
    • Image 2
    • Image 3
    • Image 4
    • Image 5
• Page 455
  • Titles
    • 9-10 N-ELEMENT ARRAY WITH UNIFORM PHASE DISTRIBUTION
    • z
    • 455
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    • Image 1
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    • Image 3
• Page 456
  • Titles
    • 9-11 Electronic Scanning of Arrays
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    • 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
    • Image 2
    • 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
    • Image 1
    • 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
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    • Image 1

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