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The switching function analysis of power electronic circuits
IET 2008
سرفصلها
Part 1 The switching function 1
1 The switching function: Application and properties 3
1.1 Introduction 3
1.2 Application of the switching function technique 3
1.3 Properties of the switching function 6
2 Voltage–current relations in switched circuits 17
2.1 Single switch 18
2.2 Parallel switches 19
2.3 Parallel switched-resistors 20
2.4 Switched-inductors 21
2.5 Parallel switched-capacitors 24
2.6 Kirchoff’s First Law (current law) 27
2.7 Kirchoff’s Second Law (voltage) 27
2.8 Superposition theorem in switched circuits 29
2.9 Current sharing in a parallel RC switched network 31
3 Pulse width modulation 35
3.1 Sinusoidally modulated PWM signal – unipolar 36
3.2 The rectified sine-wave PWM signal 39
3.3 The PWM signal of a composite function 43
3.4 PWM sine-wave – bipolar square wave modulation 45
Part 2 AC to DC conversion 49
4 Analysis of the single phase ac to dc phase controlled converter
with R–L load 51
4.1 Introduction 51
4.2 Mathematical modelling 51
4.3 Analysis 55
5 The single phase full-wave diode rectifier – RC load 65
5.1 Introduction 65
5.2 Mathematical modelling 65
vi Contents
5.3 Analysis 72
5.4 Neutral current in three phase systems 77
6 The three-phase half-wave phase controlled converter 83
6.1 Introduction 83
6.2 Mathematical modelling of the three-phase half-wave
phase controlled converter 83
6.3 Analysis 91
6.4 Results 98
7 The three-phase full-wave phase controlled rectifier 101
7.1 Introduction 101
7.2 The mathematical modelling of the three-phase
full-wave controlled rectifier circuit 101
7.3 Analysis of three-phase full-wave phase controlled
rectifier 111
8 Overlap in ac to dc three-phase converters 121
8.1 Introduction 121
8.2 Operation and modes 122
8.3 Analysis 132
Part 3 DC to DC converters 135
9 The step down converter 137
9.1 Introduction 137
9.2 Mathematical modelling of the step down converter 137
10 The step up or boost converter 145
10.1 Introduction 145
10.2 Mathematical modelling of the dc to dc step up
(boost) converter 145
10.3 Analysis 152
11 The buck boost dc to dc converter 163
11.1 Introduction 163
11.2 Mathematical modelling of the buck boost converter 164
11.3 Analysis of the buck boost converter 168
12 The CUK dc to dc converter 175
12.1 Introduction 175
12.2 Mathematical modelling of the CUK dc to dc
converter 175
12.3 Analysis of the CUK dc to dc converter 180
13 The PWM full bridge dc to dc converter 187
13.1 Introduction 187
13.2 Operation and modes of the PWM full bridge dc to dc
converter: bipolar operation 188
13.3 Analysis of the PWM full bridge dc to dc converter:
bipolar operation 189
13.4 Operation and modes of the PWM full bridge
dc to dc converter: unipolar operation 193
Contents vii
13.5 Analysis of the PWM full bridge dc to dc converter:
unipolar operation 197
Part 4 Frequency changers 203
14 Three by three matrix converter 205
14.1 Introduction 205
14.2 Operation and mathematical model 206
14.3 The modes of operation and the switching functions 208
14.4 Analysis of the matrix converter as a three-phase to
three-phase system 211
14.5 The matrix converter as an ac to dc voltage converter 218
15 The single pulse PWM inverter 223
15.1 Introduction 223
15.2 Operation and modes of the circuit 223
15.3 The mathematical model and analysis 229
16 The sinusoidally PWM inverter 235
16.1 Introduction 235
16.2 Mathematical modelling 235
16.3 Analysis 241
17 The envelope cyclo-converter 245
17.1 Introduction 245
17.2 The mathematical model 245
17.3 The switching functions 246
Part 5 Active filters 249
18 The thyristor-controlled reactor 251
18.1 Introduction 251
18.2 The single reactor arrangement 251
18.3 The two reactor arrangement 257
19 The switched capacitor active filters 263
19.1 Introduction 263
19.2 The general model for the switched-capacitor active
filters 263
19.3 The switching functions 265
19.4 The line current 266
19.5 The double-switch double-capacitor 266
19.6 Reactive power generation 266
20 The inverter configuration active filter 271
20.1 Introduction 271
20.2 Operation and analysis 271
21 Single phase rectification with active line shaping 275
21.1 Mathematical modelling of the active shaping circuit 275
Discussion 289
References 291
Index 293
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The switching function analysis of power electronic circuits 
