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List of Principal Symbols |
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xi | |
Preface |
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xiii | |
Authors |
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xv | |
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1 | (10) |
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1.1 Evolution of Power Electronics |
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1 | (1) |
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1.2 Analysis of Power Electronic Circuits |
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2 | (5) |
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1.2.1 Fourier Series Technique |
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4 | (1) |
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1.2.2 Laplace Transform Method |
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4 | (1) |
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1.2.3 Existence Function Technique |
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5 | (1) |
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1.2.4 State Variable Method |
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5 | (1) |
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1.2.5 Averaging Technique |
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6 | (1) |
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1.2.6 z-Transform Analysis |
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6 | (1) |
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1.2.7 Other Methods of Analysis |
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6 | (1) |
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1.3 Search for a New Method of Analysis |
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7 | (4) |
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8 | (3) |
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2 An Alternative Class of Orthogonal Functions |
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11 | (36) |
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2.1 Orthogonal Functions and Their Properties |
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11 | (2) |
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13 | (2) |
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2.3 Rademacher and Walsh Functions |
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15 | (7) |
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2.3.1 Representation of a Function Using Walsh Functions |
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21 | (1) |
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2.4 Block Pulse Functions and Their Applications |
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22 | (5) |
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2.4.1 Representation of a Function as a Linear Combination of BPFs |
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25 | (2) |
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27 | (1) |
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2.6 Delayed Unit Step Functions |
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28 | (2) |
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2.7 General Hybrid Orthogonal Functions |
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30 | (1) |
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2.8 Sample-and-Hold Functions |
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30 | (2) |
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32 | (2) |
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2.10 Hybrid Function: A Combination of SHF and TF |
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34 | (2) |
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2.11 Applications of Walsh Functions |
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36 | (11) |
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40 | (7) |
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3 Walsh Domain Operational Method of System Analysis |
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47 | (42) |
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3.1 Introduction to Operational Matrices |
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47 | (15) |
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3.1.1 Operational Matrix for Integration |
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48 | (7) |
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3.1.1.1 Representation of Integration of a Function Using Operational Matrix for Integration |
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55 | (3) |
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3.1.2 Operational Matrix for Differentiation |
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58 | (1) |
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3.1.2.1 Representation of Differentiation of a Function Using Operational Matrix for Differentiation |
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59 | (3) |
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3.2 Time Scaling of Operational Matrices |
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62 | (3) |
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3.2.1 Time-Scaled Operational Matrix for Integration |
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63 | (2) |
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3.2.2 Time-Scaled Operational Matrix for Differentiation |
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65 | (1) |
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3.3 Philosophy of the Proposed Walsh Domain Operational Technique |
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65 | (4) |
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3.4 Analysis of a First-Order System with Step Input |
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69 | (3) |
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3.5 Analysis of a Second-Order System with Step Input |
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72 | (1) |
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3.6 Oscillatory Phenomenon in Walsh Domain System Analysis |
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73 | (13) |
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3.6.1 Oscillatory Phenomenon in a First-Order System |
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74 | (1) |
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3.6.2 Analytical Study of the Oscillatory Phenomenon |
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75 | (11) |
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86 | (3) |
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86 | (3) |
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4 Analysis of Pulse-Fed Single-Input Single-Output Systems |
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89 | (42) |
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4.1 Analysis of a First-Order System |
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90 | (4) |
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90 | (2) |
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92 | (1) |
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4.1.3 Alternating Double-Pulse Input |
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92 | (2) |
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4.2 Analysis of a Second-Order System |
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94 | (3) |
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94 | (1) |
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95 | (1) |
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4.2.3 Alternating Double-Pulse Input |
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95 | (2) |
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4.3 Pulse-Width Modulated Chopper System |
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97 | (30) |
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4.3.1 Case I: Stepwise PWM |
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97 | (1) |
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4.3.1.1 Walsh Function Representation of Significant Current Variables |
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97 | (3) |
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4.3.1.2 Determination of Normalized Average and rms Currents through Load and Semiconductor Components |
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100 | (3) |
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4.3.1.3 Determination of Exact Normalized Average and rms Current Equations Considering Switching Transients |
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103 | (4) |
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4.3.2 Case II: Continuous PWM |
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107 | (4) |
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4.3.2.1 Mathematical Operations |
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111 | (1) |
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4.3.2.2 Simulation of an Ideal Continuously Pulse-Width Modulated DC Chopper System |
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112 | (1) |
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4.3.2.3 Determination of Normalized Average and rms Currents through Load and Semiconductor Components |
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113 | (7) |
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4.3.2.4 Simulation of an Ideal Chopper-Fed DC Series Motor |
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120 | (7) |
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127 | (4) |
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128 | (3) |
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5 Analysis of Controlled Rectifier Circuits |
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131 | (34) |
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5.1 Representation of a Sine Wave by Walsh Functions |
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132 | (2) |
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5.2 Conventional Analysis of Half-Wave Controlled Rectifier |
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134 | (3) |
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5.3 Walsh Domain Analysis of Half-Wave Controlled Rectifier |
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137 | (8) |
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5.3.1 Computational Algorithm |
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140 | (5) |
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5.4 Walsh Domain Analysis of Full-Wave Controlled Rectifier |
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145 | (17) |
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5.4.1 Single-Phase Full-Wave Controlled Rectifier |
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146 | (1) |
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5.4.2 Representation of the Load Voltage by Walsh Functions |
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147 | (4) |
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5.4.3 Determination of Normalized Average and rms Currents |
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151 | (1) |
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5.4.3.1 Exact Equations for Phase-Controlled Rectifier |
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152 | (8) |
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5.4.4 Computational Algorithm |
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160 | (2) |
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162 | (3) |
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163 | (2) |
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6 Analysis of Inverter Circuits |
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165 | (16) |
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6.1 Voltage Control of a Single-Phase Inverter |
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166 | (9) |
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6.1.1 Single-Pulse Modulation |
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168 | (1) |
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6.1.1.1 Walsh Function Representation of Single-Pulse Modulation |
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169 | (3) |
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6.1.1.2 Computation of Normalized Average and rms Load Currents for Single--Pulse Modulation |
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172 | (3) |
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6.2 Analysis of an RL Load Fed from a Typical Three-Phase Inverter Line-to-Neutral Voltage |
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175 | (4) |
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179 | (2) |
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179 | (2) |
Appendix A Introduction to Linear Algebra |
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181 | (10) |
Appendix B Selected Matlab® Programs |
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191 | (84) |
Index |
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275 | |