Linear Circuit I

Giáo trình chính thức sử dụng trong giảng dạy, học tập tại Đại học Bách khoa Hà Nội đối với học phần “Mạch tuyến tính I”, mã học phần EE3706E.

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