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2.6 Power Measurement 2 49

2.7 Series Resonance 2 50

2.8 Parallel Resonance 2 52

2.9 Problems 2 54

2.9.1 Problem 2 54

2.9.2 Problem 1: An Alternate Solution 2 58

2.9.3 Problem 2 2 61

2.9.4 Problem 3 2 63

2.9.5 Problem 4 2 65

2.9.6 Problem 5 2 69

2.9.7 Problem 6 2 71

2.9.8 Problem 7

2 73

CHAPTER 3

THREE PHASE A C CIRCUITS

3.1 Phasor Representation 2 77

3.2 Source/Load Connections 2 86

3.3 Solution of Balanced Three Phase Circuits 2 87

3.4 Solution of Unbalanced Three Phase Circuits 2 90

3.4.1 Use of Network Laws 2 90

3.4.2 Solution by Use of Symmetrical Components 2 96

3.5

l?E

Problems 2 98

3.5.1 Problem 2 98

3.5.2 Problem 2 2 101

3.5.3 Problem 3 2 103

3.5.4 Problem 4 2 106

3.5.5 Problem 5 2 108

3.5.6 Problem 6 2 110

3.5.7 Problem 7 2 113

3.5.8 Problem 8 2 117

APPENDIX A

SYMMETRICAL COMPONENTS

A.l Transformations 2A 1

A.2 Properties 2A 2

.3 Procedures 2A 5

A.4 Special Situations 2A 6

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APPENDIX B

THREE PHASE CAPACITOR BANK DESIGN

.l

Capacitor Unit Properties

2B 1

.2

Capacitor Unit Combinations

2B 2

.3

Design Procedure

2B 3

.3.1

Example Problem

2B 3

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.2 Transformer Application 3 18

.2.1 Connections 3 18

.2.2 Paralleling Transformers 3 28

.3 Tables 3 33

.4 Problems 3 35

.4.1 Problem 3 35

.4.2 Problem 2 3 37

.4.3 Problem 3 3 40

.4.4 Problem 4 3 42

.4.5 Problem 5 3 44

.4.6 Problem 6 3 47

.4.7 Problem 7 3 50

.4.8 Problem 8 3 52

.4.9 Problem 9 3 54

.4.10 Problem 10 3 56

.4.11 Problem

11

3 58

.4.12 Problem 12 3 60

.4.13 Problem 13 3 62

.4.14 Problem 14 3 64

CH PTER

ELECTRIC L MOTO RS

.1 Motor Application 3 67

.1.1 The Motor Load System 3 67

.1.2 The Energy Source 3 68

.1.3 Electrical Motors 3 69

.2 Theory of Motors 3 77

.2.1 A C Induction Motors 3 77

.2.2 A C Synchronous Motors 3 82

.2.3 D C Machines 3 88

3.3 Tables 3 90

3.4 Problems 3 98

.4.1 Problem 3 98

.4.2 Problem 2 3 101

.4.3 Problem 3 3 103

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3.4.4 Problem4

3.4.5 Problem5

3.4.6 Problem6

3.4.7 Problem7

.4.8 Problem 8

3.4.9 Problem 9

.4.10 Problem 10

.4.11 Practice Problem

CHAPTER

ELECTRIC GENERATORS

.1 Synchronous Gen erators

4.1.1 Model

4.1.2 Performance

4.1.3 Capacity/Loading

4.2 Induction Gen erators

.2.1 Model

.2.2 Performance

.3 Ge nera tor Application

4.4 Tables

4.5 Problems

4.5.1 Problem 3-127

4.5.2 Problem 2 3-130

4.5.3 Problem 3 3-132

CHAPTER

5

CIRCUIT BREAKERS

5.1 Ge nera l 3-135

5.1.1 Functions 3-135

5.1.2 Interru pters 3-136

5.1.3 Ope rating Mechan isms 3-136

5.1.4 Classification 3-136

5.2 Power Circuit Break ers 3-136

5.2.1 Packaging 3-136

5.2.2 Op erating Envelope 3-137

5.2.3 Application Proced ure 3-137

5.2.4 Th e Interruption Sequence 3-138

5.2.5 Perform ance Stand ards 3-138

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5.3 Mo lded Case Circuit Break ers 3-141

5.3.1 Com ponents 3-141

.3.2 Operating Envelope

3-141

5.4 Tables

3-143

5.5 Prob lems 3-148

5.5.1 Problem 3-148

CH PTER

B TTERIES

6.1 CellThe ory 3-151

6.1.1 Structure and Function 3-151

.1.2 Voltage 3-152

.1.3 Capacity 3-152

.1.4 Sh ort-circ uit Cu rrent 3-153

.1.5 Con tinuou s Cu rrent 3-153

.1.6 Cha rging 3-153

.1.7 Life-Exp ectancy 3-153

.2 Battery Theo ry 3-153

.2.1 Cell Combinations 3-153

.2.2 Battery Configurations 3-154

.3 Battery Design 3-154

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CHAPTER

FAULTED POWER SYSTEMS

2.1 Three Phase Faults 4 37

2.1.1 CurrentWoltage at the Fault 4 37

2.1.2 Fault Current Distribution 4 40

2.1.3 Phasor Representation 4 42

.2 Unbalanced Faults 4 43

2.2.1 Single Line to Ground Fault 4 44

.2.2 Line Line Fault 4 48

2.2.3 Double Line to Ground Fault 4 52

2.3 Tables 4 56

2.4 Problems 4 57

.4.1 Problem 4 57

.4.2 Problem 2 4 59

2.4.3 Problem 3 4 61

2.4.4 Problem 4 4 63

APPENDIX A

ONE LINE DIAGRAMS

APPENDIX

THE PER UNIT SYSTEM

B.1 The Equations 4B 1

B.2 Application 4B 3

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l E Electrical) License Review Manual. Volume

I1

2.6 Zener Diodes 16

2.7 Typical P E Problem 6 19

2.7.1

P E Problem ener Diode Analysis 6 19

2.8 Example Problems 6 19

2.8.1 Example Problem ener Diode Analysis 6 19

2.8.2 Example Problem 2 ener Diode 6 20

2.8.3 Example Problem 3 ener Regulator Design 6 20

2.8.4 Example Problem 4 ener Regulator Design 6 21

2.9 Clippers and Clampers 6 22

2.9.1 Clippers 22

2.9.2 Clampers 6 23

2.10 Typical

P.

E Problem 6 24

2.10.1

l E Problem arallel Biased Clipper 6 24

2.11 Example Problems 6 25

2.11.1 Example Problem arallel Biased Clipper 6 25

2.1 1.2 Example Problem 2 eries Biased Clipper 6 26

2.1 1.3 Example Problem 3 lamper Analysis 6 26

2.11.4 Example Problem 4 lamper Design 6 28

CH PTER 3

BIPOL R JUNCTION TR NSISTOR MPLIFIERS

.1 dc Transistor Circuits 6 29

.1.1 Bipolar Junction Transistors 6 29

3.1.2 Transistor Circuits 6 30

3.1.3 Transmitter Characteristics 6 31

3.1.4 Load Lines 6 33

3.1.5 Elimination of Bias Batteries 6 34

3.2 Typical l E Problems 35

3.2.1

P

E Problem c Biasing 6 35

3.2.2 P.E.Problem2 dcBiasing 6 35

3.3 Example Problem 6 36

3.3.1 Example Problem c Biasing 6 36

3.4 CE Amplifiers 37

3.4.1 Bypass and Coupling Capacitors 6 37

3.4.2 ac Load Lines 6 38

3.4.3 Maximum Undistorted Output 6 39

3.4.4 Common Emitter Design Equations 6 40

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Section 6 Electronic Circuits and Applications. Table of Contents

iii

ypical P. E Problems 6-43

.5.1

P E Problem E Amplifier Analysis

6-43

.5.2

l?E Problem 2 nalysis of CE Amplifier

6-45

xample Problems 6-46

.6.1 Example Problem E Amplifier Design 6-46

.6.2 Example Problem 2 E Amplifier Design 6-47

.6.3 Example Problem 3 E Amplifier Design 6-48

mitter Follower EF) Amplifiers 6-50

ypical P. E Problem

6-52

.8.1

l

E Problem F Amplifier Analysis

6-52


.9.1 Example Problem F Amplifier Analysis 6-54

.9.2 Example Problem 2 F Amplifier Design 6-55

.9.3 Example Problem 3 F Amplifier Design 6-56

B Amplifiers 6-57

.10.1 CB Amplifier Analysis 6-57

A0.2 CB Amplifier Design 6-57

ypical P E Problem

6-59

.11.1

l?

E Problem B Amplifier Analysis 6-59


.12.1 Example Problem B Amplifier Analysis 6-61

.12.2 Example Problem 2 B Amplifier Design 6-62

.12.3 Example Problem 3 B Amplifier Design 6-63

ultistage Amplifiers 6-64

.13.1 Types of Amplifier Coupling 6-64

.13.2 Direct Coupled Amplifiers 6-64

ypicalP E Problem

6-66

.14.1

P E

Problem c Coupled Amplifier Analysis

6-66


.15.1 Example Problem c Coupled Amplifier 6-68

3.15.2

Example Problem 2 apacitive Coupled

mplifier Analysis 6-69

CH PTER

FIELD

EFFECT

TR NSISTOR MPLIFIERS

.1 CS Amplifiers 6-71

.1.1 FET Transistors 6-71

.1.2 FET Advantages and Disadvantages 6-72

.1.3 FET Characteristics and Construction 6-73

.1.4 CS Amplifier

....

6-75

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F

E Electrical) License Review Manual. Volume

I

.2 Typical P. E Problems 6-78

.2.1

P E Problem S Amplifier Analysis

6-78

4.2.2

P.

E Problem 2 S Amplifier Analysis 6-79

.3 Example Problems 6-81

4.3.1 Example Problem S Amplifier Analysis 6-81

4.3.2 Example Problem 2 S Amplifier Design 6-82

4.3.3 Example Problem

3

S Amplifier Design 6-83

.4 Common Drain CD) Amplifiers 6-84


4.5.1 Example Problem D Analysis 6-86

4.5.2 Example Problem 2 D Amplifier Design 6-87

CH PTER

POWER MPLIFIERS

.1 Introduction to Power Amplifiers 6-89

5.1.1 Classes of Amplifiers 6-89

.1.2 Class B Power Amplifier 6-90

5.1.3 Complimentary Symmetry Diode

ompensated Amplifier CSDC) 6-92


.2.1 Example Problem 1 SDC Amplifier 6-94

.2.2 Example Problem 2 SDC Amplifier 6-94

5.2.3 Example Problem 3 ower Amplifier Used in Regulator 6-95

.3 Darlington Pairs 6-97


5.4.1

Example Problem E Amplifier Using Darlington Pairs

6-99

5.4.2

Example Problem 2 F Amplifier Using Darlington Pairs 6-101

CH PTER 6

FREQUENCY RESPONSE

6.1 Frequency Response of CE Amplifiers 6-103

6.1.1 Low Frequency Response of CE AMplifiers 6-103

6.1.2 High Frequency Response of CE Amplifiers 6-105

.2 Typical P. E Problems 6-106

6.2.1 P E Problem Analysis of CE Low Frequency Response 6-106

6.2.2

P. E

Problem 2 nalysis of CE High Frequency Response 6-108

6.2.3

P E Problem 3 nalysis of CE High Frequency Response 6-110

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Section 6. Electronic Circuits and Applications. Table of Contents

.3 Example Problems 6 112

6.3.1

Example Problem esign of CE Low

requency Response 6 112

6.3.2

Example Problem 2 esign of CE Low


.4 CS Amplifiers 6 115

6.4.1 Low Frequency Response of CS Amplifiers 6 115

.4.2 High Frequency Response of CS Amplifiers 6 117

.5 mi ca 1 P E Problems 6 119

6.5.1

P E Problem nalysis of CS Low Frequency Response

6 119

6.5.2

F E Problem 2 nalysis of CS High Frequency Response

6 121

6.5.3

F E Problem 3 requency Analysis of CS Amplifier

6 122


6.6.1

Example Problem esign of CS Low


6.6.2

Example Problem 2 esign of CS Low


CHAPTER

SPECIAL CIRCUITS NEEDED FOR OP AMPS

.1 Op Amp Circuits 6 127

.1.1 Discussion of Op Amps 6 127

.1.2 Fixed Biased Transistor Current Source 6 128

.1.3 Simple Current Source 6 129

.1.4 Widlar Current Source 6 129

.1.5 Wilson Current Source 6 130

.2 Typical P

E

Problem 6 131

7.2.1

P E Problem nalysis of Simple Current Source 6 131


7.3.1

Example Problem nalysis of Fixed Biased

urrent Source 6 132

7.3.2

Example Problem 2 esign of Fixed Biased

urrent Source 6 133

7.3.3 Example Problem 3 esign of Simple Current Source 6 134

.3.4

Example Problem 4 esign of Widlar Current Source

6 135

7.3.5

Example Problem 5 esign of Wilson Current Source 6 135

.4 Differential Amplifiers 6 136

.5 Typical

P E

Problems 6 138

7.5.1

P E Problem nalysis of Differential Amplifier 6 138

7.5.2

P

E Problem 2 nalysis of Differential Amplifier 6 139

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I? Electrical) License Review Man ual. Volume I

.6 Example Problem 6 141

.6.1 Example Problem esign of Differential Amplifier 6 141

.7 Level Shifters 6 143

.8 Typical P E Problem 6 145

7.8.1 P E Problem nalysis of Level Shifter 6 145

.9 Example Problem 6 146

7.9.1 Example Problem esign of Level Shifter 6 146

CH PTER

OPER TION L MPLIFIERS

.1 Ideal Op Amps 6 149

.1.1 Discussion of Ideal Op Amps 6 149

.1.2 Analysis of Ideal Op Amps 6 15

.1.3 Design of Op Amp Circuits 6 154

.2 Typical l? E Problems 6 156

8.2.1 P E

Problem nalysis of Op Amp Circuits 6 156

8.2.2

P E Problem 2 nalysis of Op Amp Circuits 6 157

8.2.3 P E Problem 3 nalysis of Op Amp Circuits 6 158


8.3.1 Example Problem esign of Op Amp Circuit 6 159

8.3.2 Example Problem 2 esign of an Op Amp Circuit 6 160

.4 Non Ideal Operational Amplifier 6 162

.4.1 Analysis of Op Amp Circuits 6 162

.4.2 Design of Multiple Op Amp Circuits 6 165

.5 Typical

l?

E Problems 6 166

8.5.1 P E Problem nalysis of Single Op Amp 6 166

8.5.2

F E Problem 2 nalysis of Multiple Op Amp Circuit 6 168

8.5.3

E Problem 3 esign of Op Amp Circuit 6 170

8.5.4 P E Problem 4 esign of Hybrid Op Amp Circuit 6 171


8.6.1

Example Problem esign of Multiple Op Amp Circuit 6 173

8.6.2

Example Problem 2 esign of Multiple Op Amp circuit 6 175

CH PTER 9

CTIVE FILTERS

.1 Introduction to Active Filters 6 177

.2 Typical P E Problems 6 179

9.2.1

P E Problem esign of High Pass Filter

6 179

9.2.2

F E Problem 2 nalysis of Amplifiers 6 181

9.2.3

P E Problem 3 nalysis and Design of Two

Transistor Circuit 6 183

9.2.4

P

E

Problem 4 nalysis of Filter Circuit 6 185

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Section 6. Electronic Circuits and Applications. Table of Contents

vii


9.3.1

Example Problem esign of Low Pass Filter 6-187

9.3.2

Example Problem 2 esign of Low Pass Filter 6-189

9.3.3

Example Problem 3 eneral First Order Filters 6-190

9.3.4

Example Problem 4 econd Order Single Amplifier

ow-Pass Filter with Gain 6-191

9.3.5

Example Problem

5

econd Order Single Amplifier

igh-Pass Filters with Gain 6-192

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l

E

Electrical) License Review M anual. Volum e

I1

.5.4 Second Translation Shifting) Property 7-8

.5.5 Inverse of a Derivative 7-9

.5.6 Inverse of Integrals 7-9

.5.7 Multiplication by s 7-10

.5.8 Division by s 7-10

.6 The Method of Partial Fraction Expansion 7-11

.7 Examples of Partial Fraction Expansion 7-12

.7.1 Example 1 epeated Roots 7-12

1.7.2 Example 2

umerator Power Equals Denominator Power 7-12

.7.3 Example 3 elay Terms 7-13

.7.4 Example 4 omplex Roots 7-14

.8 Laplace Transform Solution of Differential Equations 7-14

.9 Examples of Laplace Transform Solution of Differential Equations 7-14

.9.1 Example

1

econd Order Differential Equation 7-14

.9.2 Example 2 imultaneous Differential Equations 7-15

.9.3 Example 3 ntegral Differential Equations 7-16

.10 Initial and Final Value Theorems 7-16

11 Laplace Transform in Network Analysis 7-17

.12 Examples of Laplace Transform in Network Analysis 7-17

.12.1 Example 1 L Network 7-17

.12.2 Example 2 LC Network 7-19

.13 Proofs of Laplace Transform Properties 7-20

.13.1 First Translation Shifting) Property 7-20

.13.2 Real Differentiation 7-20

.13.3 Real Integration 7-20

.13.4 Change of Scale 7-21

.13.5 Multiplication by tn 7-21

.13.6 Division by t 7-22

.13.7 Second Translation Shifting) Property 7-22

.13.8 Periodic Functions 7-22

.14 Homework 7-23

.15 Solutions to Selected Homework Problems on Laplace Transform 7-29

CH PTER

CONTR OL SYSTEMS ND TERMINOLOGY

.1 Block Diagrams 7-33

.2 Electrical Networks 7-34

.3 Translational Mechanical Networks 7-34

.4 Relational Mechanical Networks 7-35

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Section

7.

Control Systems. Table of Contents

CH PTER

BLOCK DI GR M LGEBR ND SEC OND ORDER SYSTEMS

.1 Canonical Form 7-37

.2 Block Diagram Transformation Theorems 7-38

.3 Example of Block Diagram Transformation 7-40

.4 Reduction of Multiple.Input. Multiple-Output Diagrams 7-42

.5 Single Flow Graphs 7-44

.6 Mason s Gain Rule 7-44

3.6.1

Example ransfer Function Evaluation

sing Mason s Gain Rule 7-44

.7 Second Order Systems 7-45

.7.1 Rise time Tr 7-48

.7.2 Peak time Tp 7-48

.7.3 Setting Time Ts 7-48

.7.4 Peak Response Mpt 7-48

.7.5 Percent Overshoot PO 7-49


3.8.1

Example valuation of Frequency and Damping of

econd Order Systems 7-49

3.8.2 Example 2 valuation of Frequency and Damping of

econd Order Systems 7-49

3.8.3

Example 3 valuation of P.O., Rise Time

nd Settling Time 7-49

.8.4 Example 4 djustable Gain Calculation 7-49

.8.5 Example 5 Adjustable Gain Calculation 7-50

CH PTER 4

ST BILITY N LYSIS

.1 Definition 7-51

.2 Routh Stability Criterion 7-55

.3 Adjustable Systems 7-56

.4 Examples 7-56

.4.1 Example econd Order System 7-56

.4.2 Example 2 -Fourth Order System 7-57

.5 Example Problems pecial Cases 7-57

.5.1 Example ow of Zeroes 7-57

.5.2 Example

2

eroes in First Column 7-58

.5.3 Example 3 nstable System 7-59

.5.4 Example 4 inding Imaginary Axis Crossing 7-59

.5.5 Example 5 nstable Systems 7-60

.5.6 Example 6 egative Gain 7-60

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Section

7

Control Systems Table of Contents

v

.2 Gain Crossover 7-95

.3 Phase Margin 7-95

.4 Phase Crossover 7-95

.5 Gain Margin 7-96

.6 Nyquist Diagram 7-97

.7 Typical P E Problems 7-98

7.7.1

P E Problem requency Response

7-98

7.7.2

P E Problem 2 ain MarginIPhase Margin

7-99

7.7.3

P E Problem 3 requency Response 7-101

CH PTER

SELECTED CONTROL SYSTEMS PROBLEMS

.1 Typical

P

E Problems 7-107

8.1.1

P

E

Problem inding Gain Rise Time P.O. and Phase 7-107

8.1.2

P E Problem 2 ind Gain and Phase Margins 7-109

.1.3

P E Problem 3 teady State Errors

7-111

8.1.4

F .E Problem 4 ind Gain. Given P.O. and Peak Times 7-112

P E Problem 5 ind Parameters Given w

Z;

and

teady State Error 7-114

P E Problem 6 ind Parameters Given and w 7-115

P E Problem 7 tate Variable Description 7-116

P

E

Problem 8 ind Damping PO. T . Ts. w from

ole Locations 7-118

P E Problem 9 etermine Stability and Steady State Error 7-120

P E Problem 10 perational Amplifier 7-122

P E Problem igital Control System

7-125

P

E Problem 12 igital Control System 7-127

F .E Problem 13 igital Control System

7-128

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P E. Electrical) License Review Manual, Volume

I

.12 Microwave Path Calculation 8-32

1.12.1 Problem 8-32

.13 Microwave System Design 8-33

1.13.1 Problem 8-36

1.14 Microwave Transmitter 8-39

.14.1 Problem 8-39

.14.2 Problem 2 8-43

.14.3 Problem 3 8-44

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