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Introduction to

Electronics

An Online Text

Bob Zulinski

Associate Professor

of Electrical Engineering

Michigan Technological University


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Introduction to Electronics ii

Dedication

Human beings are a delightful and complex amalgam of

the spiritual, the emotional, the intellectual, and the physical.

This is dedicated to all of them; especially to thosewho honor and nurture me with their friendship and love.


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Introduction to Electronics iii

Table of Contents

Preface xviPhilosophy of an Online Text . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi

Notes for Printing This Document . . . . . . . . . . . . . . . . . . . . . . . . xviii

Copyright Notice and Information . . . . . . . . . . . . . . . . . . . . . . . . xviii

Review of Linear Circuit Techniques 1Resistors in Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Resistors in Parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Product Over Sum 1

Inverse of Inverses 1

Ideal Voltage Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Ideal Current Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Real Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Voltage Dividers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Current Dividers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Superposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4A quick exercise 4

Whats missing from this review??? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Youll still need Ohms and Kirchoffs Laws 5

Basic Amplifier Concepts 6Signal Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Ground Terminal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

To work with (analyze and design) amplifiers . . . . . . . . . . . . . . . . . . . . . 7

Voltage Amplifier Model 8Si l S 8


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Power Supplies, Power Conservation, and Efficiency 11DC Input Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Conservation of Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Amplifier Cascades 13

Decibel Notation 14Power Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Cascaded Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Voltage Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Current Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Using Decibels to Indicate Specific Magnitudes . . . . . . . . . . . . . . . . . . . 15

Voltage levels: 15Power levels 16

Other Amplifier Models 17Current Amplifier Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Transconductance Amplifier Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Transresistance Amplifier Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Amplifier Resistances and Ideal Amplifiers 20Ideal Voltage Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Ideal Current Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Ideal Transconductance Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Ideal Transresistance Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Uniqueness of Ideal Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Frequency Response of Amplifiers 24Terms and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24


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Introduction to Electronics v

Differential Amplifiers 27Example: 27

Modeling Differential and Common-Mode Signals . . . . . . . . . . . . . . . . . 27 Amplifying Differential and Common-Mode Signals . . . . . . . . . . . . . . . . 28

Common-Mode Rejection Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Ideal Operational Amplifiers 29Ideal Operational Amplifier Operation . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Op Amp Operation with Negative Feedback . . . . . . . . . . . . . . . . . . . . . 30 Slew Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Op Amp Circuits - The Inverting Amplifier 31Voltage Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Input Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Output Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Op Amp Circuits - The Noninverting Amplifier 33Voltage Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Input and Output Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Op Amp Circuits - The Voltage Follower 34Voltage Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Input and Output Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Op Amp Circuits - The Inverting Summer 35Voltage Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Op Amp Circuits - Another Inverting Amplifier 36Voltage Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Op Amp Circuits Differential Amplifier 38


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Op Amp Circuits - Designing with Real Op Amps 42Resistor Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Source Resistance and Resistor Tolerances . . . . . . . . . . . . . . . . . . . . . 42

Graphical Solution of Simultaneous Equations 43

Diodes 46

Graphical Analysis of Diode Circuits 48Examples of Load-Line Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Diode Models 50

The Shockley Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Forward Bias Approximation 51Reverse Bias Approximation 51

At High Currents 51

The Ideal Diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 An Ideal Diode Example 53

Piecewise-Linear Diode Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 A Piecewise-Linear Diode Example 57

Other Piecewise-Linear Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Diode Applications - The Zener Diode Voltage Regulator 59Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Load-Line Analysis of Zener Regulators . . . . . . . . . . . . . . . . . . . . . . . . 59

Numerical Analysis of Zener Regulators . . . . . . . . . . . . . . . . . . . . . . . . 61Circuit Analysis 62

Zener Regulators with Attached Load . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Example - Graphical Analysis of Loaded Regulator 64

Diode Applications - The Half-Wave Rectifier 66


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Diode Applications - The Full-Wave Rectifier 72Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

1st(Positive) Half-Cycle 72

2nd(Negative) Half-Cycle 72

Diode Peak Inverse Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Diode Applications - The Bridge Rectifier 74

Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 741st(Positive) Half-Cycle 74

2nd(Negative) Half-Cycle 74

Peak Inverse Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Diode Applications - Full-Wave/Bridge Rectifier Features 75Bridge Rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Full-Wave Rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Filtered Full-Wave and Bridge Rectifiers . . . . . . . . . . . . . . . . . . . . . . . . 75

Bipolar Junction Transistors (BJTs) 76Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

Qualitative Description of BJT Active-Region Operation . . . . . . . . . . . . 77

Quantitative Description of BJT Active-Region Operation . . . . . . . . . . . 78

BJT Common-Emitter Characteristics 80Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Input Characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Output Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Active Region 81Cutoff 82

Saturation 82

The pnp BJT 83


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The n-Channel Junction FET (JFET) 86Description of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Equations Governing n-Channel JFET Operation . . . . . . . . . . . . . . . . . 89

Cutoff Region 89

Triode Region 89

Pinch-Off Region 89

The Triode - Pinch-Off Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

The Transfer Characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

Metal-Oxide-Semiconductor FETs (MOSFETs) 92The n-Channel Depletion MOSFET . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

The n-Channel Enhancement MOSFET . . . . . . . . . . . . . . . . . . . . . . . . 93

Comparison of n-Channel FETs 94

p-Channel JFETs and MOSFETs 96Cutoff Region 98

Triode Region 98

Pinch-Off Region 98

Other FET Considerations 99FET Gate Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

The Body Terminal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

Basic BJT Amplifier Structure 100Circuit Diagram and Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Load-Line Analysis - Input Side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Load-Line Analysis - Output Side . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

A Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

Basic FET Amplifier Structure 107


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Biasing BJTs - The Fixed Bias Circuit 113Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

For b = 100 113

For b = 300 113

Biasing BJTs - The Constant Base Bias Circuit 114Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

For b = 100 114For b = 300 114

Biasing BJTs - The Four-Resistor Bias Circuit 115Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Circuit Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

Bias Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 To maximize bias stability 117

Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 For b = 100 (and VBE= 0.7 V) 118

For b = 300 118

Biasing FETs - The Fixed Bias Circuit 119

Biasing FETs - The Self Bias Circuit 120

Biasing FETs - The Fixed + Self Bias Circuit 121

Design of Discrete BJT Bias Circuits 123Concepts of Biasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Design of the Four-Resistor BJT Bias Circuit . . . . . . . . . . . . . . . . . . . . 124

Design Procedure 124

Design of the Dual-Supply BJT Bias Circuit . . . . . . . . . . . . . . . . . . . . . 125 Design Procedure 125


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Bipolar IC Bias Circuits 129Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129The Diode-Biased Current Mirror . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

Current Ratio 130

Reference Current 131

Output Resistance 131

Compliance Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

Using a Mirror to Bias an Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

Wilson Current Mirror . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Current Ratio 133

Reference Current 134

Output Resistance 134

Widlar Current Mirror . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Current Relationship 135

Multiple Current Mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

FET Current Mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

Linear Small-Signal Equivalent Circuits 138

Diode Small-Signal Equivalent Circuit 139

The Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139The Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

Diode Small-Signal Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Notation 142

BJT Small-Signal Equivalent Circuit 143

The Common-Emitter Amplifier 145Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

Constructing the Small-Signal Equivalent Circuit . . . . . . . . . . . . . . . . . 146


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The Emitter Follower (Common Collector Amplifier) 149Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149Voltage Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

Input Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

Output Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

Review of Small Signal Analysis 153

FET Small-Signal Equivalent Circuit 154The Small-Signal Equivalent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

Transconductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

FET Output Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

The Common Source Amplifier 157The Small-Signal Equivalent Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

Voltage Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158



The Source Follower 159Small-Signal Equivalent Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

Voltage Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160



Review of Bode Plots 164Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

The Bode Magnitude Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

The Bode Phase Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

Single-Pole Low-Pass RC 167


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Coupling Capacitors 172Effect on Frequency Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Constructing the Bode Magnitude Plot for an Amplifier . . . . . . . . . . . . 174

Design Considerations for RC-Coupled Amplifiers 175

Low- & Mid-Frequency Performance of CE Amplifier 176Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

Midband Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

Design Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

The Effect of the Coupling Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . 179

The Effect of the Emitter Bypass Capacitor CE . . . . . . . . . . . . . . . . . . 180

The Miller Effect 183Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Deriving the Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

The Hybrid-p BJT Model 185The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

Effect of Cpand C m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

High-Frequency Performance of CE Amplifier 189The Small-Signal Equivalent Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

High-Frequency Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

The CE Amplifier Magnitude Response . . . . . . . . . . . . . . . . . . . . . . . . 192

Nonideal Operational Amplifiers 193Linear Imperfections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

Input and Output Impedance 193

Gain and Bandwidth 193


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DC Imperfections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

Input Offset Voltage, VIO195Input Currents 195

Modeling the DC Imperfections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

Using the DC Error Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

DC Output Error Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201Finding Worst-Case DC Output Error 201

Canceling the Effect of the Bias Currents . . . . . . . . . . . . . . . . . . . . . . 203

Instrumentation Amplifier 204Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204

Simplified Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

Noise 206Johnson Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

Johnson Noise Model 207

Shot Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

1/f Noise (Flicker Noise) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 Other mechanisms producing 1/f noise 209

Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

Amplifier Noise Performance 211Terms, Definitions, Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

Amplifier Noise Voltage 211

Amplifier Noise Current 212

Signal-to-Noise Ratio 212

Noise Figure 213

Noise Temperature 213Converting NF to/from Tn214

Adding and Subtracting Uncorrelated Quantities . . . . . . . . . . . . . . . . . 214

Amplifier Noise Calculations 215


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Noise - References and Credits 220

Introduction to Logic Gates 221The Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

The Ideal Case 221

The Actual Case 221

Manufacturers Voltage Specifications . . . . . . . . . . . . . . . . . . . . . . . . . 222

Noise Margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 Manufacturers Current Specifications . . . . . . . . . . . . . . . . . . . . . . . . . 223

Fan-Out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

Power Consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224Static Power Consumption 224

Dynamic Power Consumption 224

Rise Time, Fall Time, and Propagation Delay . . . . . . . . . . . . . . . . . . . 226

Speed-Power Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 TTL Logic Families & Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . 228

CMOS Logic Families & Characteristics . . . . . . . . . . . . . . . . . . . . . . . 229

MOSFET Logic Inverters 230NMOS Inverter with Resistive Pull-Up . . . . . . . . . . . . . . . . . . . . . . . . . 230

Circuit Operation 230Drawbacks 231

CMOS Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 Circuit Operation 232

Differential Amplifier 239Modeling Differential and Common-Mode Signals . . . . . . . . . . . . . . . . 239

Basic Differential Amplifier Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 Case #1 - Common-Mode Input 240

Case #2A - Differential Input 241

Case #2B - Differential Input 241


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Introduction to Electronics xv

Small-Signal Analysis of Differential Amplifier 246

Differential Input Only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 Analysis of Differential Half-Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

Differential Input Resistance 250

Differential Output Resistance 250

Common-Mode Input Only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251

Analysis of Common-Mode Half-Circuit . . . . . . . . . . . . . . . . . . . . . . . . 253Common-mode input resistance 253

Common-mode output resistance 253

Common-Mode Rejection Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254


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Introduction to Electronics xvi

Preface

Philosophy of an Online Text

I think of myself as an educator rather than an engineer. And it haslong seemed to me that, as educators, we should endeavor to bring

to the student not only as much information as possible, but weshould strive to make that information as accessible as possible,and as inexpensive as possible.

The technology of the Internet and the World Wide Web now allowsus to virtually give away knowledge! Yet, we dont, choosing

instead to write another conventional text book, and print, sell, anduse it in the conventional manner. The whys are undoubtedlyintricate and many; I offer only a few observations:

Anychange is difficult and resisted. This is true in the habits

we form, the tasks we perform, the relationships we engage.It is simply easier not to change than it is to change. Thoughchange is inevitable, it is not well-suited to the behavior of anyorganism.

The proper reward structure is not in place. Faculty are

supposedly rewarded for writing textbooks, thereby bringingfame and immortality to the institution of their employ.1 Therecognition and reward structure are simply not there for a textthat is simply posted on the web.


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Introduction to Electronics xvii

structure that allows allauthors to publish in this manner; thatallows students easy access to all such material, and that

rigorously ensures the material will exceed a minimumacceptable quality.

If I were to do this the way I think it ought to be done, I would haveprepared the course material in two formats. The first would be atext, identical to the textbooks with which you are familiar, butavailable online, and intended to be used in printed form. Thesecond would be a slide presentation, la CorelPresentations or MicrosoftPowerPoint , intended for use in the classroom or inan independent study.

But, alas, I am still on that journey, so what I offer you is a hybrid ofthese two concepts: an online text somewhat less verbose than aconventional text, but one that can also serve as classroomoverhead transparencies.

Other compromises have been made. It would be advantageous toproduce twoonline versions - one intended for use in printed form,and a second optimized for viewing on a computer screen. The twowould carry identical information, but would be formatted withdifferent page and font sizes. Also, to minimize file size, andtherefore download times, font selection and variations are

somewhat limited when compared to those normally encounteredin a conventional textbook.

You may also note that exercise problems are not included with thistext By their very nature problems quickly can become worn out


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Introduction to Electronics xviii

Notes for Printing This Document

This document can be printed directly from the AcrobatReader -see the AcrobatReader help files for details.

If you wish to print the entire document, do so in two sections, asmost printer drivers will only spool a maximum of 255 pages at onetime.

Copyright Notice and Information

This entire document is 1999 by Bob Zulinski. All rights reserved.

I copyrighted this online text because it required a lot of work, andbecause I hold a faint hope that I may use it to acquireimmeasurable wealth, thereby supporting the insatiable, salaciouslifestyle that Ive always dreamed of.

Thus, you will need my permission to print it. You may obtain thatpermission simply by asking: tell me who you are and what youwant it for. Route your requests via email to [email protected], or

by USPS mail to Bob Zulinski, Dept. of Electrical Engineering,Michigan Technological University, Houghton MI 49931-1295.

Generous monetary donations included with your request will belooked upon with great favor


19/272

Introduction to Electronics 1Review of Linear Circuit Techniques

R1

R2

Fig. 1.Rs in series.

R1 R2

Fig. 2.Rs in parallel.

R R R R total= + + +1 2 3 (1)

R R R

R Rtotal= +

1 2

1 2

(2)

R

R R R

total =+ + +

11 1 1

(3)

Review of Linear Circuit Techniques

Resistors in Series

This is the simple one!!!

Resistors mustcarry the same current !!!

Ls is series and Cs in parallel have same form.

Resistors in ParallelResistors musthave the same voltage !!!

Equation takes either of two forms:

Product Over Sum:

Onlyvalid for two resistors. Not calculator-efficient !!!

Inverse of Inverses:


20/272


+

-

+

-3 V 5 V

Fig. 3. Ideal voltagesources in parallel???

Fig. 4. Ideal current

sources in series???

v

i

ISC1/RTH

Ideal Voltage Sources

Cannotbe connected in parallel !!!

Real voltage sources include a seriesresistance (Thevenin equivalent), and can

be paralleled.

Ideal Current Sources

Cannotbe connected in series !!!

Real current sources include a parallelresistance (Norton equivalent), and can beconnected in series.

Real Sources

All sources we observe in nature exhibit adecreasing voltage as they supply increasingcurrent.

We presume that i-vrelationship to be linear,so we can write the equations:


21/272


+

-VOC = VTH

RTH +

-

v

i

Fig. 6. Theveninequivalent circuit.

ISC RTH

+

-

v

i

Fig. 7. Norton equivalentcircuit.

+

-

+

+

+

-

-

-VX

VA

VB

VC

RA

RB

RC

Fig. 8. Example of avoltage divider.

R VI

THOC

SC

= (5)

V R

R R RVB

B

A B C

X= + +(6)

The linear equations help us visualize what mightbe inside of a realsource:

Note that:

We can generalize this any linear resistive circuit can berepresented as in Figs. 6 and 7.

Voltage Dividers

Example - finding the voltage across RB :

Resistors must be in series, i.e., they mustcarry the same current!!!

(Sometimes we cheat a little and use the divider equation if the


22/272


RA RB RCIX

IB

Fig. 9. Example of a current divider.

+

-

I

Fig. 10. The totalresponse current I. . .

IA

Fig. 11. . . . is the sum ofthe response IA . . .

+

-

IB

Fig. 12. . . . and theresponse IB . . .

I R

R R R

IBB

A B C

X=+ +

1

1 1 1(7)

Current Dividers

Resistors must be in parallel, i.e.,have the same voltage!!!

Superposition

Superposition applies to any linear circuit - in fact, this is thedefinition of a linear circuit!!!

An example of finding a response using superposition:

A quick exercise:

Use superposition and voltage division to show that VX= 6 V:


23/272


Whats missing from this review???

Node voltages / mesh currents . . .

For the kinds of problems youll encounter in this course, I think youshould forgetabout these analysis methods !!!

If there is any other way to solve a circuit problem, do it that other

way . . . youll arrive at the answer more efficiently, and with more

insight.

Youll still need Ohms and Kirchoffs Laws:

KVL: Sum of voltages around a closed loop is zero.

Well more often use a different form:

Sum of voltages from point A to point B is the same

regardless of the path taken.

KCL: Sum of currents into a node (or area) is zero.

I wont insult you by repeating Ohms Law here . . .


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Introduction to Electronics 6Basic Amplifier Concepts

Signal

SourceAmplifier Loadvi (t) vo (t)

+ +

- -Ground

Fig. 14. Block diagram of basic amplifier.

vi

t

vo

t

vo

t

Basic Amplifier Concepts

Signal Source

A signal source is anything that provides the signal, e.g., . . .

. . . the carbon microphone in a telephone handset . . .

. . . the fuel-level sensor in an automobile gas tank . . .

Amplifier

An amplifier is a system that provides gain . . .

. . . sometimes voltage gain(illustrated below), sometimes currentgain, always power gain.


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Introduction to Electronics 7Basic Amplifier Concepts

Signal

SourceAmplifier Loadvi (t) vo (t)

+ +

- -Ground

Fig. 18. Block diagram of basic amplifier (Fig. 14 repeated).

Load

The load is anything we deliver the amplified signal to, e.g., . . .

. . . loudspeaker . . .

. . . the leg of lamb in a microwave oven . . .

Ground Terminal

Usually there is a groundconnection . . .

. . . usually common to input and output . . .

. . . maybe connected to a metal chassis . . .

. . . maybe connected to power-line ground . . .

. . . maybe connected to both . . .

. . . maybe connected to neither . . . use caution!!!

To work with (analyze and design) amplifiers


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Introduction to Electronics 8Voltage Amplifier Model

+ +- -

vs vi Avocvi vo+ +

- -

RS

RLRi

Roii io

Source Amplifier LoadFig. 19. Modeling the source, amplifier, and load with the emphasis on

voltage.

Voltage Amplifier Model

This is usually the one we have the most intuition about . . .

Signal Source

Our emphasis is voltage . . . source voltage decreases as sourcecurrent increases, as with any real source . . .

. . . so we use a Thevenin equivalent.

Amplifier Input

When the source is connected to the amplifier, current flows . . .

. . . the amplifier must have an input resistance, Ri .

Amplifier Output

Output voltage decreases as load current increases . . .


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+ +- -

vs vi Avocvi vo+ +

- -

RS

RLRi

Roii io

Source Amplifier Load

Fig. 20. Voltage amplifier model (Fig. 19 repeated).

Rii i

A v

vvoc

o

i RL

==

(8)

A v

vv

R

R RA v A A

R

R RV

o

i

oL

o L

voc i v voc L

o L

= =+

=+

(9)

Open-Circuit Voltage Gain

If we remove RL (i.e., with RL = ) the voltage of the Theveninsource in the amplifier output is the open-circuit output voltage ofthe amplifier. Thus, Avocis called the open-circuit voltage gain:

Voltage GainWith a load in place our concept of voltage gain changes slightly:

We can think of this as the amplifier voltage gain if the source wereideal:


28/272


+ +- -

vs vi Avocvi vo+ +

- -

RS

RLRi

Roii io


Fig. 22. Voltage amplifier model (Fig. 19 repeated).

A v

vv

R

R Rv A A

R

R R

R

R Rvs

o

s

ii

S i

s vs voc i

S i

L

o L

= =

+

=

+ +

(10)

A i

i

vR

vR

v

v

R

RA

R

Ri

o

i

o

L

i

i

o

i

i

L

vi

L

= = = = (11)

With our real source model we define another useful voltage gain:

Notice that Avand Avsare both less than Avoc , due to loading effects.

Current Gain

We can also define the amplifier current gain:

Power Gain

Because the amplifier input and load are resistances, we have


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Introduction to Electronics 11Power Supplies, Power Conservation, and Efficiency

+ +- -vs vi Avocvi vo+ +

- -

RS

RLR i

Roii io


V AA

-VBB

IA

IB

V AA

VBB

+

+

-

-

Fig. 23. Our voltage amplifier model showing power supply and ground connections.

P V I V I S AA A BB B= + (13)

Power Supplies, Power Conservation, and Efficiency

The signal power delivered to the load is converted from the dcpower provided by the power supplies.

DC Input Power

This is sometimes noted as PIN. Use care not to confuse this withthe signal input power Pi .

Conservation of Power

Signal power is delivered to the load Po

P i di i t d ithi th lifi h t P

I t d ti t El t i 12P S li P C ti d Effi i


30/272

Introduction to Electronics 12Power Supplies, Power Conservation, and Efficiency

+ +-

-

vs vi Avocvi vo+ +

- -

RS

RLR i

Roii io


V AA

-VBB

IA

IB

V AA

VBB

+

+

-

-

Fig. 24. Our voltage amplifier model showing power supply and ground connections(Fig. 23 repeated).

= PP

o

S

100% (15)

Efficiency

Efficiency is a figure of merit describing amplifier performance:

Introduction to Electronics 13Amplifier Cascades


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Introduction to Electronics 13Amplifier Cascades

+-

vi1Avoc1vi1

+-

Ri1

Ro1ii1

+-

vo1 = vi2Avoc2vi2

+-

Ri2

Ro2ii2 io2

vo2+-

Amplifier 1 Amplifier 2Fig. 25. A two-amplifier cascade.

A v

vv

o

i

11

1

= (16)

A v

v

v

vv

o

i

o

o

22

2

2

1

= = (17)

A v

v

v

vA Avoc

o

i

o

o

v v= =1

1

2

1

1 2 (18)

Amplifier Cascades

Amplifier stages may be connected together (cascaded) :

Notice that stage 1 is loaded by the input resistance of stage 2.

Gain of stage 1:

Gain of stage 2:

Gain of cascade:

We can replace the two models by a single model (remember, themodel is just a visualization of what mightbe inside):

Introduction to Electronics 14Decibel Notation


32/272


2 R

G GdB = 10log (19)

G G G G G G Gtotal dB dB dB, , ,log log log= = + = +10 10 101 2 1 2 1 2 (20)

Decibel Notation

Amplifier gains are often not expressed as simple ratios . . . ratherthey are mapped into a logarithmic scale.

The fundamental definition begins with a power ratio.

Power Gain

Recall that G = Po /Pi , and define:

GdBis expressed in units of decibels, abbreviated dB.

Cascaded Amplifiers

We know that Gtotal= G1 G2 . Thus:

Thus, the product of gains becomes the sumof gains in decibels.

Voltage Gain

To derive the expression for voltage gain in decibels, we begin byrecalling from eq. (12) that G= Av

2(Ri /RL ). Thus:



33/272


A Av dB v = 20log (22)

A Ai dB i = 20log (23)

Even though Rimay not equal RLin most cases, we define:

Only when Ridoes equal RL , will the numerical values of GdBandAv dBbe the same. In all other cases they will differ.

From eq. (22) we can see that in an amplifier cascade the productof voltage gains becomes the sum of voltage gains in decibels.

Current Gain

In a manner similar to the preceding voltage-gain derivation, we canarrive at a similar definition for current gain:

Using Decibels to Indicate Specific Magnitudes

Decibels are defined in terms of ratios, but are often used toindicate a specific magnitude of voltage or power.

This is done by defining a reference and referring to it in the units

notation:

Voltage levels:

dBV decibels with respect to 1 V for example



34/272


5 10 5

6 99mW = mW

1 mWdBmlog .= (25)

5 23 0mW = 10log5 mW

1 WdbW= . (26)

Power levels:

dBm, decibels with respect to 1 mW . . . for example

dBW, decibels with respect to 1 W . . . for example

There is a 30 dB difference between the two previous examplesbecause 1 mW = - 30 dBW and 1 W = +30 dBm.

Introduction to Electronics 17Other Amplifier Models


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Introduction to Electronics 17O e p e ode s

+ +- -

vs vi Avocvi vo+ +

- -

RS

RLRi

Roii io

Source Amplifier LoadFig. 27. Modeling the source, amplifier, and load with the emphasis onvoltage (Fig. 19 repeated).

is RS RLRo

ii io

Source Current Amplifier Load

vi

+

- Riv

o

+

-Aiscii

Fig 28 Modeling the source amplifier and load with the emphasis on

Other Amplifier Models

Recall, our voltage amplifier model arose from our visualization ofwhat might be inside a real amplifier:

Current Amplifier Model

Suppose we choose to emphasize current. In this case we use

Norton equivalents for the signal source and the amplifier:



36/272

p

RLRo

ii io

Source Transconductance Amplifier Load

vi+-

Ri vo+-Gmscvi+-

vs

RS

Fig. 29. The transconductance amplifier model.

+

-vi Rmocii vo+ +

- -RLRi

Roii io

Source Transresistance Amplifier Load

is RS

G i

vmsc

o

i RL

== 0

(siemens, S) (28)

Transconductance Amplifier ModelOr, we could emphasize input voltageand output current:

The short-circuit transconductance gainis given by:

Transresistance Amplifier Model

Our last choice emphasizes input currentand output voltage:



37/272

Any of these four models can be used to represent what might beinside of a real amplifier.

Any of the four can be used to model the same amplifier!!!

Models obviously will be different inside the amplifier.

If the model parameters are chosen properly, they willbehave identically at the amplifier terminals!!!

We can change from any kind of model to any other kind:

Change Norton equivalent to Thevenin equivalent (ifnecessary).

Change the dependent sources variable of dependencywith Ohms Law vi= ii Ri (if necessary).

Try it!!! Pick some values and practice !!!

Introduction to Electronics 20Amplifier Resistances and Ideal Amplifiers


38/272

+ +- -

vs vi Avocvi vo+ +

- -

RS

RLRi

Roii io

Source Voltage Amplifier LoadFig. 31. Voltage amplifier model.

Amplifier Resistances and Ideal Amplifiers

Ideal Voltage Amplifier

Lets re-visit our voltage amplifier model:

Were thinking voltage, and were thinking amplifier . . . so how canwe maximize the voltage that gets delivered to the load ?

We can get the most voltage out of the signal source ifRi>> RS , i.e., if the amplifier can measure the signal voltagewith a high input resistance, like a voltmeter does.

In fact, if , we wont have to worry about the value ofRi RSat all!!!

We can get the most voltage out of the amplifier if Ro


39/272

+

-Avocvivi

+

-

Fig. 32. Ideal voltage amplifier. Signalsource and load are omitted for clarity.

is RS RLRo

ii io

Source Current Amplifier Load

vi+

-Ri vo

+

-Aiscii

Fig. 33. Current amplifier model (Fig. 28 repeated).

An ideal amplifier is only a concept; we cannot build one.

But an amplifier may approach the ideal, and we may use the

model, if only for its simplicity.

Ideal Current Amplifier

Now lets revisit our current amplifier model:

How can we maximize the current that gets delivered to the load ?



40/272

Aisciiii

Fig. 34. Ideal current amplifier.

Gmscvivi+

We can get the most current out of the amplifier if Ro>> R L ,i.e., if the amplifier can look as much like a current source aspossible.

In fact, if , we wont have to worry about the value ofRo RLat all!!!

This leads us to our conceptual ideal current amplifier:

Ideal Transconductance Amplifier

With a mixture of the previous concepts we can conceptualize anideal transconductance amplifier.

This amplifier ideally measures the input voltage and produces anoutput current:



41/272

Rmociiii+

-

Fig. 36. Ideal transresistance amplifier.

Ideal Transresistance AmplifierOur final ideal amplifier concept measures input current andproduces an output voltage:

Uniqueness of Ideal Amplifiers

Unlike our models of real amplifiers, ideal amplifier models cannot

be converted from one type to another(try it . . .).

Introduction to Electronics 24Frequency Response of Amplifiers


42/272

A V

V

V V

V VA Av

o

i

o o

i i

v v= =

= (30)

Frequency Response of Amplifiers

Terms and Definitions

In real amplifiers, gain changes with frequency . . .

Frequency implies sinusoidal excitation which, in turn, impliesphasors . . . using voltage gain to illustrate the general case:

Both |Av| and Avare functions of frequency and can be plotted.Magnitude Response:

A plot of |Av| vs. fis called the magnitude responseof the amplifier.

Phase Response:A plot of Avvs. fis called the phase response of the amplifier.

Frequency Response:

Taken together the two responses are called the frequency

response . . . though often in common usage the term frequencyresponse is used to mean only the magnitude response.

Amplifier Gain:



43/272

f (log scale)

|Av|dB

|Av mid|dB

3 dB

fH

Bandwidth, B

midband region

Fig. 37. Magnitude response of a dc-coupled, or direct-coupled amplifier.

f (log scale)

|Av|dB

|Av mid|dB

3 dB

fL fH

Bandwidth, B

midband region

Fig. 38. Magnitude response of an ac-coupled, or RC-coupled amplifier.

The Magnitude ResponseMuch terminology and measures of amplifier performance arederived from the magnitude response . . .

|A | is called the midband gain



44/272

+

-

+

-

Fig. 39. Two-stage amplifier model including straywiring inductance and stray capacitance betweenstages. These effects are also found within each

amplifier stage.

Causes of Reduced Gain at Higher FrequenciesStray wiring inductances . . .

Stray capacitances . . .

Capacitances in the amplifying devices (not yet included in our

amplifier models) . . .The figure immediately below provides an example:

Causes of Reduced Gain at Lower Frequencies

This decrease is due to capacitors placed between amplifier stages(in RC-coupled or capacitively-coupled amplifiers) . . .

This prevents dc voltages in one stage from affecting the next.

Signal source and load are often coupled in this manner also.

Introduction to Electronics 27Differential Amplifiers


45/272

+

-

+

-

+

-

+

-

vI1 vI2

vICMvID /2

vID /2

1

1

2

2

+-

Fig. 41. Representing two sources by their differentialandcommon-modecomponents.

Differential Amplifiers

Many desired signals are weak, differential signalsin the presenceof much stronger, common-mode signals.

Example:

Telephone lines, which carry the desired voice signal between the

green and red (called tip and ring) wires.

The lines often run parallel to power lines for miles along highwayright-of-ways . . . resulting in an induced 60 Hz voltage (as much as30 V or so) from each wire to ground.

We must extract and amplify the voltage difference between thewires, while ignoring the large voltage common to the wires.

Modeling Differential and Common-Mode Signals

Introduction to Electronics 28Differential Amplifiers


46/272

+

-+

-

vo = Ad vid + Acm vic

vid /2

vid /2

+-Amplifier

+

-

vicm

Fig. 42. Amplifier with differential and common-mode input signals.

v v v v v v

ID I I ICM I I= = +

1 21 2

2and (33)

Solving these simultaneous equations for vIDand vICM :

Note that the differential voltage vID is the difference between the

signals vI1 and vI2 , while the common-mode voltage vICM is theaverage of the two (a measure of how they are similar).

Amplifying Differential and Common-Mode Signals

We can use superposition to describe the performance of an

amplifier with these signals as inputs:

A differential amplifieris designed so that Adis very large and Acmis very small, preferably zero.

Differential amplifier circuits are quite clever - they are the basicbuilding block of all operational amplifiers

Introduction to Electronics 29Ideal Operational Amplifiers


47/272

+

-

v+

v-

vO

vO = A0 (v+ -v- )Fig. 43. The ideal operational amplifier:

schematic symbol, input and output voltages,and input-output relationship.

Ideal Operational Amplifiers

The ideal operational amplifier is anideal differential amplifier:

A0= Ad= Acm= 0

Ri= Ro= 0

B=

The input marked + is called the noninverting input . . .

The input marked - is called the inverting input . . .The model, just a voltage-dependent voltage source with the gainA0 (v+ - v- ), is so simple that you should get used to analyzingcircuits with just the schematic symbol.

Ideal Operational Amplifier OperationWith A0= , we can conceive of three rules of operation:

1. If v+ > v- then voincreases . . .

2. If v+ < v- then vodecreases . . .

3. If v+ = v- then vodoes not change . . .

In a real op amp vocannot exceed the dc power supply voltages,which are not shown in Fig. 43.

Introduction to Electronics 30Ideal Operational Amplifiers


48/272

Op Amp Operation with Negative FeedbackConsider the effect of negative feedback:

If v+> v- then voincreases . . .

Because a fraction of vois applied to the inverting input,

v-increases . . .The gap between v+ and v- is reduced and will eventuallybecome zero . . .

Thus, votakes on the value that causes v + - v -= 0!!!

If v+< v- then vodecreases . . .

Because a fraction of vois applied to the inverting input,v-decreases . . .

The gap between v+ and v- is reduced and will eventually

become zero . . .Thus, votakes on the value that causes v + - v -= 0!!!

In either case, the output voltage takes on whatever value that

causes v+- v -= 0!!!

In analyzing circuits, then, we need only determine the value of vowhich will cause v+- v -= 0.

Slew Rate

Introduction to Electronics 31Op Amp Circuits - The Inverting Amplifier


49/272

+

-

+

vO

viR1 R2

i1 i2

0

Fig. 44. Inverting amplifier circuit.

v v R v R

R R

i o =

+

+

2 1

1 2

(35)

Op Amp Circuits - The Inverting Amplifier

Lets put our ideal op amp concepts to work in this basic circuit:

Voltage Gain

Because the ideal op amp has Ri= , the current into the inputswill be zero.

This means i1= i2 , i.e., resistors R1and R 2form a voltage dividerIII

Therefore, we can use superposition to find the voltage v- .

(Remember the quick exercise on p. 4 ??? This is the identicalproblem!!!):

Now, because there is negative feedback, v o takes on whatevervalue that causes v+- v = 0 , and v+ = 0 !!!

Introduction to Electronics 32Op Amp Circuits - The Inverting Amplifier


50/272

+

-

+

vO

viR1 R2

i1 i2

0

Fig. 45. Inverting amplifier circuit(Fig. 44 repeated).

i v

R R v

i

vR

iin

i iv

Ri

1

1 1

1

1= = = = (37)

Input Resistance

This means resistance seen by the signal source vi , not the inputresistance of the op amp, which is infinite.

Because v-= 0, the voltage across R1is vi . Thus:

Output Resistance

This is the Thevenin resistance which would be seen by a loadlooking back into the circuit (Fig. 45 does not show a load attached).

Our op amp is ideal; its Thevenin output resistance is zero:

Introduction to Electronics 33Op Amp Circuits - The Noninverting Amplifier


51/272

+

-

+vO

vi

R1 R2

i1 i2

0

Fig. 46. Noninverting amplifier circuit.

v v v R

R R

vi o= = =

++

1

1 2

(39)

v R R

Rv

R

Rv A

R

Ro i i v =

+= +

= +1 2

1

2

1

2

1

1 1 (40)

Op Amp Circuits - The Noninverting Amplifier

If we switch the vi and ground connections on the invertingamplifier, we obtain the noninverting amplifier:

Voltage Gain

This time our rules of operation and a voltage divider equation leadto:

from which:

Input and Output Resistance

The source is connected directly to the ideal op amp, so:

Introduction to Electronics 34Op Amp Circuits - The Voltage Follower


52/272

+

-

+vovi

Fig. 47. The voltage follower.

v v v v Ai o v= = = =+ 1 (43)

R Rin O= =and 0 (44)

Op Amp Circuits - The Voltage Follower

Voltage Gain

This one is easy:

i.e., the output voltage follows the input voltage.

Input and Output Resistance

By inspection, we should see that these values are the same as forthe noninverting amplifier . . .

In fact, the follower is just a special case of the noninvertingamplifier, with R1= and R2= 0 !!!

Introduction to Electronics 35Op Amp Circuits - The Inverting Summer


53/272

+

-

+

vO

vBRB RF

iA

iF+

v AR A iB

+ -

Fig. 48. The inverting summer.

i v

R

i v

R

AA

A

BB

B

= =and (45)

v v

Op Amp Circuits - The Inverting Summer

This is a variation of the inverting amplifier:

Voltage Gain

We could use the superposition approach as we did for thestandard inverter, but with three sources the equations becomeunnecessarily complicated . . . so lets try this instead . . .

Recall . . . vOtakes on the value that causes v-= v+ = 0 . . .

So the voltage across RAis vAand the voltage across RBis vB :

Because the current into the op amp is zero:

Introduction to Electronics 36Op Amp Circuits - Another Inverting Amplifier


54/272

+

-

+

vO

vi R1

R2i1 R4

R3i2

Fig. 49. An inverting amplifier with a resistive T-networkfor the feedback element.

Op Amp Circuits - Another Inverting Amplifier

If we want very large gains with the standard inverting amplifier ofFig. 44, one of the resistors will be unacceptably large orunacceptably small . . .

We solve this problem with the following circuit:

Voltage Gain

One common approach to a solution begins with a KCL equation atthe R2- R 3- R 4junction . . .

. . . well use the superposition & voltage divider approach, afterweapply some network reduction techniques.

Notice that R3 , R4and the op amp output voltage source can bereplaced with a Thevenin equivalent:

Introduction to Electronics 37Op Amp Circuits - Another Inverting Amplifier


55/272

v- = 0

vTH

REQ = R 2 + RTHR1vi

Fig. 51. Equivalent circuit to original amplifier.

v R

R Rv R R R TH O TH = +

=33 4

3 4and || (48)

v R

RvTH

EQi=

1

(49)

( )RR R

v R R R

Rv

R

R

R R

RvO i i

3

3 4

2 3 4

1

2

1

3 4

1+ =

+= +

|| ||(50)

The values of the Thevenin elements in Fig. 50 are:

With the substitution of Fig. 50 we can simplify the original circuit:

Again, vO , and therefore vTH, takes on the value necessary to makev+ - v-= 0 . . .

Weve now solved this problem twice before (the quick exercise on

p. 4, and the standard inverting amplifier analysis of p. 31):

Substituting for vTHand REQ , and solving for vOand Av :

Introduction to Electronics 38Op Amp Circuits - The Differential Amplifier


56/272

+

-

+

vO

v1R1 R2

i1 i2

+

R1

R2v2

+ -

Fig. 52. The differential amplifier.

v R

R Rv v+ = + =2

1 2

2 (52)

( )i v v

RvR

RR R R

v i11

1

1

1

2

1 1 2

2 2= = + = (53)

( )v i R R

R v R R

R R RvR2 2 2

2

11

2 2

1 1 22= = +

(54)

Op Amp Circuits - Differential Amplifier

The op amp is a differential amplifier to begin with, so of coursewecan build one of these!!!

Voltage Gain

Again, vO takes on the valuerequired to make v+ = v- .Thus:

We can now find the currenti1 , which must equal thecurrent i2 :

Knowing i2 , we can calculate the voltage across R2 . . .

Th lt i t th t t t i l

Introduction to Electronics 39Op Amp Circuits - The Differential Amplifier


57/272

( ) ( ) ( )R

R Rv

R R

R R Rv

R R

R R Rv

R R

R R Rv2

1 2

22 2

1 1 2

21 2

1 1 2

22 2

1 1 2

2+ +

+ =

+ +

+(56)

( )( )( )

= ++

= ++

=R R R R R R R

v R R RR R R

v RR

v1 2 2 2

1 1 2

22 1 2

1 1 2

22

1

2 (57)

( )v R

Rv

R

Rv

R

Rv vO = + =

2

1

12

1

22

1

2 1 (58)

Working with just the v2terms from eq. (55) . . .

And, finally, returning the resulting term to eq. (55):

So, under the conditions that we can have identical resistors (andan ideal op amp) we truly have a differential amplifier!!!

Introduction to Electronics 40Op Amp Circuits - Integrators and Differentiators


58/272

+

-

vO

viR C

iR iC

+

+ -

Fig. 53. Op amp integrator.

i v

RiR

iC= = (59)

( )vC

i dtC

i dt v C C

t

C C

t

= = +

1 10

0

(60)

( ) ( )vC

v

R

dt v

RC

v dt v Oi

t

C i C

t

= + = +

10

10

0 0

(61)

Op Amp Circuits - Integrators and Differentiators

Op amp circuits are not limited to resistive elements!!!

The Integrator

From our rules and previous

experience we know that v-= 0and iR= iC , so . . .

From the i-v relationship of acapacitor:

Combining the two previous equations, and recognizing thatvO= - vC :

Normally vC (0) = 0 (but not always). Thus the output is the integralof in erted and scaled b 1/RC

Introduction to Electronics 41Op Amp Circuits - Integrators and Differentiators


59/272

+

-

vO

vi RC

iRiC

+

+ -

Fig. 54. The op amp differentiator.

i Cdv

dtC

dv

dtiC

C iR= = = (62)

v v i R RC dv

dtO R R

i= = = (63)

The Differentiator

This analysis proceeds in thesame fashion as the previousanalysis.

From our rules and previousexperience we know that v-= 0and iC= iR . . .

From the i-vrelationship of a capacitor:

Recognizing that vO= - vR :

Introduction to Electronics 42Op Amp Circuits - Designing with Real Op Amps

O A Ci i D i i i h R l O A


60/272

+

-

+

vO

vi

R1

RL

iLiF

+

-R2

Fig. 55. Noninverting amplifier with load.

+

-

+

vO

viR1 R2

i1 i2

RS

Op Amp Circuits - Designing with Real Op Amps

Resistor Values

Our ideal op amp can supply unlimited current; real ones cant . . .

To limit iF + iL to a reasonable

value, we adopt the rule ofthumb that resistances shouldbe greater than approx. 100 .

Of course this is highly

dependent of the type of op amp

to be used in a design.Larger resistances render circuits more susceptible to noise andmore susceptible to environmental factors.

To limit these problems we adopt the rule of thumb thatresistances should be less than approximately 1 M.

Source Resistance and Resistor Tolerances

In some designs RS will

affect desired gain.

Resistor tolerances willalso affect gain.

Introduction to Electronics 43Graphical Solution of Simultaneous Equations

G hi l S l ti f Si lt E ti


61/272

y x y= =and 4 (64)

Fig. 57. Simple example of obtaining the solution to simultaneousequations using a graphical method.

Graphical Solution of Simultaneous Equations

Lets re-visit some 7th-grade algebra . . .we can find the solution oftwo simultaneous equations by plotting them on the same set ofaxes.

Heres a trivial example:

We plot both equations:

Introduction to Electronics 44Graphical Solution of Simultaneous Equations


62/272

yx

x=

0), current flows easily.When we apply an external voltage that opposes this combination,(a reversevoltage, vD< 0), current flow is essentially zero.

Introduction to Electronics 47Diodes


65/272

Fig. 61. PSpice-generated i-vcharacteristic for a 1N750 diode showing the various regions ofoperation.

Thus, the typical diode i-v characteristic:

VFis called the forward knee voltage, or simply, the forward voltage.

It is typically approximately 0.7 V, and has a temperature

coefficient of approximately -2 mV/KVBis called the breakdown voltage.

It ranges from 3.3 V to kV, and is usually given as a positive

Introduction to Electronics 48Graphical Analysis of Diode Circuits

Graphical Analysis of Diode Circuits


66/272

iD

+

-vD

+

-

R

VS

Fig. 62. Example circuit to illustrategraphical diode circuit analysis.

v

+

-

(=R)

VOC

i

+

-(=VS)

RTH

Fig. 63. Thevenin eq. ofFig. 62 identified.

ISC

i=iD

v V iR i I v

ROC TH SC

TH

= = or (69)

Graphical Analysis of Diode Circuits

We can analyze simple diode circuits using the graphical methoddescribed previously:

We need two equations to find thetwo unknowns iD and vD .

The first equation is provided bythe diode i-v characteristic.

The second equation comes fromthe circuit to which the diode is

connected.

This is just a standard Theveninequivalent circuit . . .

. . . and we already know its i-v

characteristic . . . from Fig. 5 and eq.(4) on p. 2:

. . . where VOCand ISCare the open-circuit voltage and the short-circuitcurrent respectively

Introduction to Electronics 49Graphical Analysis of Diode Circuits

Examples of Load-Line Analysis


67/272

iD

+

-vD

+

-

R

VS

Fig. 65. Example circuit(Fig. 62 repeated).

Case 3: VOC= VS= 10 V ISC= 10 V / 1 k = 10 mA

VOCnot on scale, use slope:

Examples of Load Line Analysis

Case 1: VS= 2.5 V and R= 125

Case 2: VS= 1 V and R= 25

Case 3: VS= 10 V and R= 1 k

Case 1: VOC= VS= 2.5 V and ISC= 2.5 V / 125 = 20 mA.

We locate the intercepts, and draw the line.

The solution is at vD 0.71 V, iD 14.3 mA

Case 2: VOC= VS= 1 V and ISC= 1 V / 25 = 40 mA

ISCis not on scale, so we use the slope: 125 40 200 5 = =mAV mAV.

The solution is at vD 0.70 V, iD 12.0 mA

Introduction to Electronics 50Diode Models

Diode Models


68/272

i I vnV

D SD

T

=

exp 1 (70)

v nV i

ID T

D

S

= +

ln 1 (71)

V kT

qT = (72)

Diode Models

Graphical solutions provide insight, but neither convenience noraccuracy . . . for accuracy, we need an equation.

The Shockley Equation

or conversely

where,

ISis the saturation current, 10 fA for signal diodes

ISapprox. doubles for every 5 K increase in temp.

n is the emission coefficient, 1 n 2

n= 1 is usually accurate for signal diodes ( iD< 10 mA)

VTis the thermal voltage,

k, Boltzmanns constant, k= 1.38 (10-23

) J/KT. temperature in kelvins

q, charge of an electron, q= 1.6 (10 -19) C



69/272

i I v

nVD S

D

T

exp (75)

i ID S (76)

v nV i

Ii RD T

D

S

D S= +

+ln 1 (77)

i I v

nVD S

D

T

=

exp 1 (73)

v nV

i

ID TD

S= +

ln 1(74)

Repeating the two forms of the Shockley equation:

Forward Bias Approximation:

For vDgreater than a few tenths of a volt, exp( vD /nVT ) >> 1, and:

Reverse Bias Approximation:

For vDless than a few tenths (negative), exp( vD /nVT )


70/272

+ -iD

vD

fwd bias (ON)

rev bias (OFF)

Fig. 67. Ideal diode i-vcharacteristic.

Lets stop and review . . .

Graphical solutions provide insight, not accuracy.

The Shockley equation provides accuracy, not convenience.

But we can approximate the diode i-v characteristic to provideconvenience, and reasonable accuracy in many cases . . .

The Ideal Diode

This is the diode wed liketo have.

We normally ignore the breakdownregion (although we could model this,too).

Both segments are linear . . . if weknew the correct segment we could

use linear analysis!!!

In general we dontknow which line segment is correct . . .so wemust guess , and then determine if our guess is correct.

If we guess ON, we know that vD= 0, and that iDmust turn out tobe positive if our guess is correct.

If OFF k th t i 0 d th t t t t t



71/272

10 V 10 V

+

+ +

-

- -

4 k

6 k 3 k

7 kvDiD

Fig. 68.Circuit for an ideal diode example.

10 V 10 V

+

+ +

- -

4 k

6 k 3 k

7 kvD -

Fig. 69.Equivalent circuit if the diode is OFF.

10 V 10 V

+

+ +

- -

4 k

6 k 3 k

7 kvD -

6 V 3 V+ +

- -

Fig. 70.Calculating vDfor the OFF diode.

10 V 10 V

+ +

- -

4 k

6 k 3 k

7 kiD

Fig. 71.Equivalent circuit if the diode is ON.

An Ideal Diode Example:

We need first toassume a diode state,i.e., ON or OFF.

Well arbitrarily chooseOFF.

If OFF, iD = 0, i.e., thediode is an open circuit.

We can easily find vDusing voltage divisionand KVL vD = 3 V.

vD is not negative, sodiode must be ON.

If ON, vD = 0, i.e., thediode is a short circuit.


L t i th t h i l d i l i id l di d


72/272

+ -iD

vD

fwd bias (ON)

rev bias (OFF)

Fig. 73. Ideal diode i-vcharacteristic.

(Fig. 67 repeated)

Lets review the techniques, or rules, used in analyzing ideal diodecircuits. These rules apply even to circuits with multiple diodes:

1. Make assumptions about diode states.

2. Calculate vD for all OFF diodes, and iDfor all ON diodes.

3. If all OFF diodes have vD < 0, and allON diodes have iD > 0,the initial assumption was correct. If not make newassumption and repeat.


Pi i Li Di d M d l


73/272

VX

-V X /RX

1/RX

i

v

Fig. 74. A piecewise-linear segment.+ +- -

VX RX

v

i

Fig. 75. Circuit producing eq. (?).

v V iR X X= + (78)

Piecewise-Linear Diode Models

This is a generalization of the ideal diode concept.

Piecewise-linear modeling uses straight line segments toapproximate various parts of a nonlinear i-v characteristic.

The line segment at left has theequation:

The same equation is providedby the following circuit:

Thus, we can use the line segments of Fig. 74 to approximateportions of an elements nonlinear i-v characteristic . . .

and use the equivalent circuits of Fig 75 to represent the


A complete piecewise linear diode model looks like this:


74/272

iD

vDVF

1/RFVZ

1/RZ

Fig. 76. A diode i-vcharacteristic (red) andits piecewise-linear equivalent (blue).

A complete piecewise-linear diode model looks like this:

In the forward bias region . . .

. . . the approximating segment is characterized by the forwardvoltage, VF , and the forward resistance, RF .

In the reverse bias region . . .

. . . the approximating segment is characterized by iD= 0, i.e.,an open circuit


A Piecewise Linear Diode Example:


75/272

5 V

500

+ +

--vD

iD

Fig. 77. Circuit for piecewise-linear example.

5 V

500

+

+

-

-

vD

+

-0.5 V

10

Fig. 78. Equivalent circuit in forwardbi i

iD=

+ =5 0 5

500 108 82

V VmA

..

(79)

( )( )vD= +=

0 5 8 82 100588. ..

V mAV

(80)

A Piecewise-Linear Diode Example:

We have modeled a diode using piecewise-linear segments with:

VF= 0.5 V, RF= 10 , and VZ= 7.5 V, RZ= 2.5

Let us find iDand vDin the following circuit:

We need to guess a line segment.

Because the 5 V source would tend toforce current to flow in a clockwisedirection, and that is the direction of

forward diode current, let us choose theforward bias region first.

Our equivalent circuit for the forward biasregion is shown at left. We have

and


Other Piecewise Linear Models


76/272

+ -iD

vD

fwd bias (ON)

rev bias (OFF)

Fig. 79. Ideal diode i-vcharacteristic.(Fig. 67 repeated)

+-

iD

vDVF

fwd bias (ON)

rev bias (OFF)

Fig. 80. I-vcharacteristic of constant voltagedrop diode model.

Other Piecewise-Linear Models

Our ideal diode model is aspecial case . . .

. . . it has VF= 0, RF= 0 in theforward bias region . . .

. . . it doesnt have abreakdown region.

The constant voltage drop

diode model is also a specialcase . . .

. . . it has RF= 0 in the forwardbias region . . .

. . . VFusually 0.6 to 0.7 V . . .

. . . it doesnt have abreakdown region

Introduction to Electronics 59The Zener Diode Voltage Regulator

Diode Applications - The Zener Diode Voltage Regulator


77/272

+

+

+

-

-

-

VTH

RTH = 500

vD vOUT

iD7.5 V to 10 V

Introduction

This application uses diodes in the breakdown region . . .

For VZ< 6 V the physical breakdown phenomenon is called zenerbreakdown (high electric field). It has a negative temperature

coefficient.For VZ> 6 V the mechanism is called avalanche breakdown (highkinetic energy). It has a positive temperature coefficient.

For VZ 6 V the breakdown voltage has nearly zerotemperaturecoefficient, and a nearly vertical i-v char. in breakdown region, i.e.,

a very small RZ .

These circuits can produce nearly constant voltages when usedwith voltage supplies that have variable or unpredictable outputvoltages. Hence, they are called voltage regulators.

Load-Line Analysis of Zener Regulators

Note: when intended for useas a zener diode, theschematic symbol changes

slightly . . .

With VTH positive, zenercurrent can flow only if the


RTH = 500 Note that vOUT = - vD Fig 83


78/272

+

+

+

-

-

-

VTHvD vOUT

iD7.5 V to 10 V

Fig. 82. Thevenin equivalent source withunpredictable voltage and zener diode.

(Fig. 81 repeated)

Note that vOUT vD . Fig. 83

below shows the graphicalconstruction.

Because the zener is upside-downthe Thevenin equivalent load lineis in the 3rdquadrant of the diode

characteristic.

As VTHvaries from 7.5 V to 10 V, the load line moves from its blueposition, to its green position.

As long as the zener remains in breakdown, vOUT remains nearly

constant, at 4.7 V.As long as the minimum VTH is somewhat greater than VZ(in thiscase VZ= 4.7 V) the zener remains in the breakdown region.

If were willing to give up some output voltage magnitude, in return

we get a very constant output voltage.


Numerical Analysis of Zener Regulators


79/272

Fig. 84. Zener i-vcharacteristic of Fig. 83 withpiecewise-linear segment.

+

VTH

RTH = 500

vOUT

8 +

Numerical Analysis of Zener Regulators

To describe line voltage regulation numerically we use linear circuitanalysis with a piecewise-linear model for the diode.

To obtain the model we draw a tangent to the curve in the vicinityof the operating point:

From the intercept and slope of the piecewise-linear segment weobtain VZ= 4.6 V and RZ= 8 . Our circuit model then becomes:


R = 500


80/272

+

-

VTH

RTH

500

vOUT

7.5 V to 10 V

8

4.6 V+

-

+

-

Fig. 86. Regulator with diode model(Fig. 85 repeated).

( )V88

500 8 7 5 4 6 45 67

= + =. . .V V mV (81)

VO = + =46 45 67 464567. . .V mV V (82)

( )V88

500 810 4 6 85 04

=+

=V V V. . (83)

Important: The model above is valid only if zener is inbreakdown region !!!

Circuit Analysis:

The 500 and 8 resistors are in series, forming a voltage divider.

For VTH= 7.5 V:

For VTH= 10 V:


Zener Regulators with Attached Load


81/272

+

+-

-

vD vOUT

iD

+

-VSS

RS

RL

Fig. 87. Zener regulator with load.

+

+ -

-

vDvOUT

iD

+

-VSS

RS

RL

Fig. 88. Regulator drawn with zener andload in reversed positions.

+

+ -

-

vDvOUT

iD

+

-VTH

RTH

Fig. 89. Regulator of Fig. 87 with VSS , RS ,and RLreplaced by Thevenin eq.

g

Now lets add a load to our regulator circuit . . .

Only the zener is nonlinear, so we approach this problem by findingthe Thevenin equivalent seen by the diode:

The resulting circuit is topologically identical to the circuit we justanalyzed!!!


Example - Graphical Analysis of Loaded Regulator


82/272

+

+-

-

vD vOUT

iD

+

-

RS= 500

RL10 VVSS

Fig. 90. Example of loaded zener regulator forgraphical analysis.

V VOC TH = = + =

10

50010 9 52

k

10 kV V

. (85)

I V

RSC

SS

S

= = =10 20V

500mA

(86)

V VOC TH= = 1

10k

V = 6.67 V

(87)

Lets examine graphically the behavior of a loaded zener regulator.

Let VSS= 10 V, RS= 500 and,

(a) RL= 10 k (b) RL= 1 k (c) RL= 100

We find the load lines in each case by calculating the open-circuit(Thevenin) voltage and the short-circuit current:

(a)

(b)


100 (c)


83/272

V VOC TH = = + =100 500 10 167 V V. (89)

Fig. 91. Load line analysis for the loaded zener regulator.

I V

RSC

SS

S

= = =10

20V

500mA

(90)

The three load lines are plotted on the zener characteristic below:

As long as RL(and therefore VTH ) is large enough so that the zenerremains in breakdown, the output voltage is nearly constant !!!

Introduction to Electronics 66The Half-Wave Rectifier

Diode Applications - The Half-Wave Rectifier


84/272

vO

vD

Vm sin tvS++

+

--

-

RL

Fig. 92. The half-wave rectifier circuit.

t

vS

T

Vm

-Vm

Fig. 93. Waveform of voltage source.

t

vO

T

Vm

Fig. 94. Output voltage waveform.

vD

Introduction

This diode application changesac into dc. The voltage source ismost often a sinusoid (but can beanything).

Well assume the diode is idealfor our analysis.

During positive half-cycle . . .

. . . diode conducts (ON)

. . . vD = 0

. . . vO= vS

During negative half-cycle . . .. . . diode OFF

. . . iD= 0, vO= 0

. . . vD = vS

Peak Inverse Voltage, PIV:

A th t f b kd


A Typical Battery Charging Circuit


85/272

Rtotal D

VBATTERY+

-

A

110 Vrms Vm sin t+

-

Fig. 96. A circuit typical of most battery chargers.

t

Vm

T

VBATT

Chargingcurrent

vS

In the figure above . . .

. . . VBATTERY

represents the battery to be charged . . .

. . . Rtotalincludes all resistance (wiring, diode, battery, etc.) reflectedto the transformer secondary winding.

Charging current flows only when Vm sin t > VBATTERY. . .

. . . inertia of meter movement allows indication of average current.


The Filtered Half-Wave Rectifier


86/272

vS (t) C RL vL (t)

iD (t) iL (t)

++

--

Fig. 98. Filtered half-wave rectifier.

vL(t)

Vm

Ripple voltage, Vr

Also called a peak rectifier, a half-wave rectifier with a smoothingcapacitor, or a half-wave rectifier with a capacitor-input filter.

We create it by placing a capacitor in parallel with the rectifier load(creating a low-pass filter):

Analysis of this circuitwith a nonlinear elementis very difficult . . .

. . . so we will use theideal diode model.

A lot happens in this circuit!!! Lets look at the load voltage:


vL(t)Ri l lt V


87/272

t

Vm

Ripple voltage, Vr

ondiode off

T Tonon diode off

Fig. 100. Load voltage waveform (Fig. 99 repeated).

We let vS (t) = Vm sin t. . . and assume steady-state . . .

1. When vS> vL (shown in blue), the diode is on, and the voltage

source charges the capacitor.(Because the diode and source are ideal, vS can only beinfinitesimally greater than vL )

2. When vS< vL( shown in red), the diode is off, and Cdischargesexponentially through RL .

3. We define peak-to-peak ripple voltage, Vr ,as the total changein vLover one cycle.


vL(t)Ri l lt V


88/272

t

Vm

Ripple voltage, Vr

ondiode off

T Tonon diode off


Q I T V

RT

V

fRL

m

L

m

L

= (91)

Q V Cr= (92)

Relating Capacitance to Ripple Voltage

Because the diode is off for nearly the entire period, T, the capacitormust supply the dc load current during this interval.

The charge taken from the capacitor in this interval is:

The capacitor voltage decreases by Vr in this interval, whichrequires a decrease in the charge stored in the capacitor:


Because allof the charge supplied to the load must come from the

l h th di d i ON i b l


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t

vL(t)

Vm

Ripple voltage, Vr

ondiode off

T Tonon diode off


i(t)

iD(t)

iL(t)

iD PEAK

source only when the diode is ON, iD PEAK can be very large, asillustrated below..

Introduction to Electronics 72The Full-Wave Rectifier

Diode Applications - The Full-Wave Rectifier

The full wave rectifiermakes use of a center tapped transformerto


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vS (t)

vL (t)

iL (t)

+

-

vS (t)

vin (t)

+

+-

-

vA (t)

vB (t)

D A

DBRL

Fig. 104. The full-wave rectifier.

vS vL

The full-wave rectifiermakes use of a center-tapped transformertoeffectively create twoequal input sources:

Operation

Note that the upper half of the transformer secondary voltage hasits negative reference at ground, while the lower half of thesecondary voltage has its positive reference at ground.

1st(Positive) Half-Cycle:

Current flows from upper source, through DA

and RL

, returning toupper source via ground. Any current through DB would be inreverse direction, thus DBis off.

2nd(Negative) Half-Cycle:

Current flows from lower source, through DBand RL, returning to

lower source via ground. Any current through DA would be inreverse direction, thus DAis off.

Introduction to Electronics 73The Full-Wave Rectifier

+

vA (t)


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vS (t)

vL (t)

iL (t)

+

-

vS (t)vin (t)

+

+-

-

vB (t)

D A

DBRL

Fig. 107. The full-wave rectifier (Fig. 104 repeated).

t

vA

-2Vm

Fig. 108. Voltage across diode DA .

t

vB

-2Vm

Fig. 109. Voltage across diode DB .

Diode Peak Inverse Voltage

When DAis on, DBis off . . . a KVL path around the outside loop ofthe transformer secondary shows that DBmust withstand a voltage

of 2vS .When DB is on, DAis off . . . now a KVL path shows that DBmustwithstand 2vS .

Thus the diode PIV rating must be 2Vm . Diode voltage waveforms

are shown below . . .

Introduction to Electronics 74The Bridge Rectifier

Diode Applications - The Bridge Rectifier

The bridge rectifier is also a full wave rectifier but uses a diode


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vL (t)

iL (t)

+

-

vin (t) vS (t)

D1+

-D2D3

D4

Fig. 110. The bridge rectifi

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