Linear Circuit I

TABLE OF CONTENTS

PREFACE.............................................................................................................3

CHAPTER 1. BASIC CONCEPTS ..................................................................27
1.1. Introduction ............................................................................................27
1.2. System of units ........................................................................................29
1.3. Charge and current ................................................................................30
1.4. Voltage.....................................................................................................32
1.5. Power and energy ...................................................................................33
1.6. Circuit elements......................................................................................35
1.6.1. Independent sources .........................................................................35
1.6.2. Dependent sources............................................................................36
1.7. Summary .................................................................................................37
1.8. Problems..................................................................................................38

CHAPTER 2. BASIC LAWS ............................................................................41
2.1. Ohm’s law ...............................................................................................41
2.2. Nodes, branches, and loops....................................................................45
2.3. Kirchhoff’s laws......................................................................................46
2.3.1. Kirchhoff’s current law ....................................................................46
2.3.2. Kirchhoff’s voltage law....................................................................49
2.4. Series connection ....................................................................................50
2.4.1. Series resistors and voltage division.................................................51
2.4.2. Series voltage sources ......................................................................53
2.4.3. Series current sources.......................................................................54
2.5. Parallel connection .................................................................................54
2.5.1. Parallel resistors and current division...............................................55
2.5.2. Parallel current sources ....................................................................58
2.5.3. Parallel voltage sources....................................................................59
2.6. Wye – delta transformation................................................................... 59
2.6.1. Delta to wye conversion................................................................... 61
2.6.2. Wye to delta conversion................................................................... 63
2.7. Summary ................................................................................................. 68
2.8. Problems.................................................................................................. 70

CHAPTER 3. METHODS OF ANALYSIS..................................................... 73
3.1. Branch current method.......................................................................... 73
3.2. Node voltage method.............................................................................. 83
3.3. Mesh current method............................................................................. 94
3.4. Which method should we choose?....................................................... 104
3.5. Summary ............................................................................................... 117
3.6. Problems................................................................................................ 117

CHAPTER 4. CIRCUIT THEOREMS.......................................................... 122
4.1. Linear property .................................................................................... 122
4.2. Superposition ........................................................................................ 127
4.2.1. How to turn off an independent voltage source ............................. 127
4.2.2. How to turn off an independent current source.............................. 127
4.2.3. Superposition.................................................................................. 128
4.3. Source transformation ......................................................................... 139
4.3.1. Source transformation .................................................................... 139
4.3.2. Millman’s theorem ......................................................................... 141
4.4. Thevenin’s theorem.............................................................................. 145
4.5. Norton’s theorem.................................................................................. 160
4.6. What method should we choose? ........................................................ 172
4.7. Maximum power transfer.................................................................... 175
4.8. Summary ............................................................................................... 192
4.9. Problems................................................................................................ 192

CHAPTER 5. OPERATIONAL AMPLIFIERS ........................................... 196
5.1. Operational amplifiers ......................................................................... 196
5.2. Ideal op amp..........................................................................................200
5.3. Inverting amplifier ...............................................................................204
5.4. Noninverting amplifier.........................................................................207
5.5. Summing amplifier...............................................................................211
5.6. Difference amplifier..............................................................................212
5.7. Cascaded op amp circuits ....................................................................215
5.8. Analysis of circuits with op amps........................................................217
5.8.1. Equivalent dependent sources of op amp .......................................217
5.8.2. Branch current method ...................................................................218
5.8.3. Node voltage method......................................................................224
5.8.4. Mesh current method......................................................................229
5.8.5. Which one should we use? .............................................................238
5.9. Applications ..........................................................................................245
5.9.1. Comparator.....................................................................................245
5.9.2. Instrumentation amplifier...............................................................245
5.10. Summary .............................................................................................246
5.11. Problems..............................................................................................247

CHAPTER 6. CAPACITORS AND INDUCTORS ......................................251
6.1. Capacitors .............................................................................................251
6.2. Series and parallel capacitors..............................................................257
6.3. Inductors ...............................................................................................262
6.4. Series and parallel inductors ...............................................................270
6.5. Analysis of circuits with capacitors and inductors............................272
6.6. Op amp circuits with capacitors..........................................................280
6.6.1. Integrator ........................................................................................280
6.6.2. Differentiator..................................................................................282
6.7. Applications ..........................................................................................283
6.8. Summary ...............................................................................................283
6.9. Problems................................................................................................284

CHAPTER 7. FIRST-ORDER CIRCUITS ................................................... 289
7.1. The source-free RC circuit................................................................... 289
7.2. The source-free RL circuit ................................................................... 298
7.3. Singularity functions ............................................................................ 306
7.3.1. The unit step function..................................................................... 306
7.3.2. The unit impulse function .............................................................. 308
7.3.3. The unit ramp function................................................................... 309
7.4. Step response of an RC circuit............................................................. 310
7.5. Step response of an RL circuit............................................................. 322
7.6. First-order op amp circuits.................................................................. 335
7.7. Applications .......................................................................................... 343
7.8. Summary ............................................................................................... 343
7.9. Problems................................................................................................ 345

CHAPTER 8. SECOND-ORDER CIRCUITS .............................................. 349
8.1. Initial values.......................................................................................... 349
8.2. The source-free series RLC circuit...................................................... 359
8.3. The source-free parallel RLC circuit .................................................. 367
8.4. Step response of a series RLC circuit.................................................. 373
8.5. Step response of a parallel RLC circuit .............................................. 377
8.6. General second-order circuits ............................................................. 380
8.7. Second-order op amp circuits.............................................................. 395
8.8. Applications .......................................................................................... 402
8.9. Summary ............................................................................................... 406
8.10. Problems.............................................................................................. 406

BIBLIOGRAPHY............................................................................................ 411