Foreword |
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xiii | |
Preface |
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xv | |
Acknowledgments |
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xvii | |
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Chapter 1 Basics of Loop Control |
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1 | (28) |
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1 | (3) |
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3 | (1) |
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1.2 The Necessity of Control---Closed-Loop Systems |
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4 | (2) |
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1.3 Notions of Time Constants |
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6 | (6) |
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1.3.1 Working with Time Constants |
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7 | (2) |
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1.3.2 The Proportional Term |
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9 | (1) |
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1.3.3 The Derivative Term |
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10 | (1) |
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11 | (1) |
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1.3.5 Combining the Factors |
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12 | (1) |
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1.4 Performance of a Feedback Control System |
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12 | (7) |
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1.4.1 Transient or Steady State? |
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13 | (2) |
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15 | (1) |
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1.4.3 The Sinusoidal Sweep |
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16 | (1) |
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17 | (2) |
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19 | (8) |
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1.5.1 The Laplace Transform |
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20 | (2) |
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1.5.2 Excitation and Response Signals |
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22 | (1) |
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23 | (2) |
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1.5.4 Combining Transfer Functions with Bode Plots |
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25 | (2) |
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27 | (2) |
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27 | (2) |
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Chapter 2 Transfer Functions |
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29 | (48) |
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2.1 Expressing Transfer Functions |
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29 | (3) |
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2.1.1 Writing Transfer Functions the Right Way |
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31 | (1) |
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2.1.2 The O-db Crossover Pole |
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32 | (1) |
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2.2 Solving for the Roots |
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32 | (7) |
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2.2.1 Poles and Zeros Found by Inspection |
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35 | (1) |
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2.2.2 Poles, Zeros, and Time Constants |
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36 | (3) |
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2.3 Transient Response and Roots |
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39 | (10) |
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2.3.1 When the Roots Are Moving |
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43 | (6) |
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2.4 S-Plane and Transient Response |
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49 | (7) |
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2.4.1 Roots Trajectories in the Complex Plane |
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54 | (2) |
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2.5 Zeros in the Right Half Plane |
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56 | (10) |
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2.5.1 A Two-Step Conversion Process |
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56 | (2) |
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2.5.2 The Inductor Current Slew-Rate Is the Limit |
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58 | (2) |
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2.5.3 An Average Model to Visualize RHP Zero Effects |
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60 | (2) |
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2.5.4 The Right Half Plane Zero in the Boost Converter |
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62 | (4) |
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66 | (11) |
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66 | (1) |
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Appendix 2A Determining a Bridge Input Impedance |
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67 | (2) |
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69 | (1) |
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Appendix 2B Plotting Evans Loci with Mathcad |
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70 | (1) |
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Appendix 2C Heaviside Expansion Formulas |
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71 | (3) |
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74 | (1) |
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Appendix 2D Plotting a Right Half Plane Zero with SPICE |
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74 | (3) |
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Chapter 3 Stability Criteria of a Control System |
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77 | (76) |
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3.1 Building An Oscillator |
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77 | (5) |
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79 | (3) |
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82 | (15) |
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3.2.1 Gain Margin and Conditional Stability |
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84 | (3) |
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3.2.2 Minimum Versus Nonminimum-Phase Functions |
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87 | (2) |
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89 | (2) |
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3.2.4 Extracting the Basic Information from the Nyquist Plot |
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91 | (2) |
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93 | (4) |
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3.3 Transient Response, Quality Factor, and Phase Margin |
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97 | (36) |
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3.3.1 A Second-Order System, the RLC Circuit |
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97 | (4) |
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3.3.2 Transient Response of a Second-Order System |
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101 | (9) |
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3.3.3 Phase Margin and Quality Factor |
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110 | (7) |
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3.3.4 Opening the Loop to Measure the Phase Margin |
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117 | (3) |
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3.3.5 The Phase Margin of a Switching Converter |
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120 | (2) |
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3.3.6 Considering a Delay in the Conversion Process |
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122 | (5) |
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3.3.7 The Delay in the Laplace Domain |
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127 | (3) |
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3.3.8 Delay Margin versus Phase Margin |
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130 | (3) |
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3.4 Selecting the Crossover Frequency |
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133 | (17) |
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3.4.1 A Simplified Buck Converter |
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135 | (3) |
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3.4.2 The Output Impedance in Closed-Loop Conditions |
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138 | (4) |
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3.4.3 The Closed-Loop Output Impedance at Crossover |
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142 | (1) |
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3.4.4 Scaling the Reference to Obtain the Desired Output |
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143 | (6) |
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3.4.5 Increasing the Crossover Frequency Further |
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149 | (1) |
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150 | (3) |
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151 | (2) |
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153 | (100) |
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153 | (23) |
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4.1.1 The PID Expressions in the Laplace Domain |
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155 | (2) |
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4.1.2 Practical Implementation of a PID Compensator |
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157 | (4) |
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4.1.3 Practical Implementation of a PI Compensator |
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161 | (2) |
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4.1.4 The PID at Work in a Buck Converter |
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163 | (7) |
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4.1.5 The Buck Converter Transient Response with the PID Compensation |
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170 | (1) |
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4.1.6 The Setpoint Is Fixed: We Have a Regulator! |
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171 | (3) |
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4.1.7 A Peaky Output Impedance Plot |
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174 | (2) |
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4.2 Stabilizing the Converter with Poles-Zeros Placement |
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176 | (34) |
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4.2.1 A Simple Step-by-Step Technique |
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177 | (1) |
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4.2.2 The Plant Transfer Function |
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178 | (1) |
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4.2.3 Canceling the Static Error with an Integrator |
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179 | (3) |
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4.2.4 Adjusting the Gain with the Integrator: The Type 1 |
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182 | (1) |
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4.2.5 Locally Boosting the Phase at Crossover |
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183 | (2) |
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4.2.6 Placing Poles and Zeros to Create Phase Boost |
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185 | (4) |
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4.2.7 Create Phase Boost up to 90° with a Single Pole/Zero Pair |
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189 | (2) |
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4.2.8 Mid-Band Gain Adjustment with the Single Pole/Zero Pair: The Type 2 |
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191 | (1) |
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4.2.9 Design Example with a Type 2 |
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192 | (2) |
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4.2.10 Create Phase Boost up to 180° with a Double Pole/Zero Pair |
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194 | (3) |
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4.2.11 Mid-Band Gain Adjustment with the Double Pole/Zero Pair: The Type 3 |
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197 | (2) |
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4.2.12 Design Example with a Type 3 |
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199 | (1) |
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4.2.13 Selecting the Right Compensator Type |
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200 | (1) |
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4.2.14 The Type 3 at Work with a Buck Converter |
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201 | (9) |
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4.3 Output Impedance Shaping |
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210 | (11) |
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4.3.1 Making the Output Impedance Resistive |
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212 | (9) |
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221 | (32) |
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222 | (1) |
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Appendix 4A The Buck Output Impedance with Fast Analytical Techniques |
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222 | (5) |
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227 | (1) |
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Appendix 4B The Quality Factor from a Bode Plot with Group Delay |
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227 | (3) |
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Appendix 4C The Phase Display in Simulators or Mathematical Solvers |
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230 | (2) |
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232 | (2) |
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Accounting for the Quadrant |
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234 | (2) |
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Improving the Arctangent Function |
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236 | (1) |
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Phase Display in a SPICE Simulator |
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237 | (5) |
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242 | (1) |
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243 | (1) |
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Appendix 4D Impact of Open-Loop Gain and Origin Pole on Op Amp-Based Transfer Functions |
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243 | (5) |
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248 | (4) |
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Appendix 4E Summary of Compensator Configurations |
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252 | (1) |
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Chapter 5 Operational Amplifiers-Based Compensators |
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253 | (104) |
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5.1 Type 1: An Origin Pole |
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253 | (2) |
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255 | (2) |
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5.2 Type 2: An Origin Pole, plus a Pole/Zero Pair |
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257 | (3) |
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260 | (2) |
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5.3 Type 2a: An Origin Pole plus a Zero |
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262 | (1) |
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263 | (1) |
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5.4 Type 2b: Some Static Gain plus a Pole |
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264 | (2) |
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266 | (1) |
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5.5 Type 2: Isolation with an Optocoupler |
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267 | (2) |
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5.5.1 Optocoupler and Op Amp: the Direct Connection, Common Emitter |
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269 | (2) |
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271 | (2) |
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5.5.3 Optocoupler and Op Amp: The Direct Connection, Common Collector |
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273 | (2) |
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5.5.4 Optocoupler and Op Amp: The Direct Connection Common Emitter and UC384X |
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275 | (1) |
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5.5.5 Optocoupler and Op Amp: Pull Down with Fast Lane |
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276 | (3) |
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279 | (1) |
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5.5.7 Optocoupler and Op Amp: Pull-Down with Fast Lane, Common Emitter, and UC384X |
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280 | (3) |
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5.5.8 Optocoupler and Op Amp: Pull Down Without Fast Lane |
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283 | (2) |
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285 | (3) |
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5.5.10 Optocoupler and Op Amp: A Dual-Loop Approach in CC-CV Applications |
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288 | (5) |
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293 | (6) |
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5.6 The Type 2: Pole and Zero are Coincident to Create an Isolated Type 1 |
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299 | (2) |
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301 | (2) |
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5.7 The Type 2: A Slightly Different Arrangement |
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303 | (5) |
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5.8 The Type 3: An Origin Pole, a Pole/Zero Pair |
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308 | (5) |
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313 | (2) |
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5.9 The Type 3: Isolation with an Optocoupler |
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315 | (1) |
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5.9.1 Optocoupler and Op Amp: The Direct Connection, Common Collector |
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315 | (2) |
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317 | (2) |
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5.9.3 Optocoupler and Op Amp: The Direct Connection, Common Emitter |
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319 | (2) |
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5.9.4 Optocoupler and Op Amp: The Direct Connection, Common Emitter, and UC384X |
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321 | (1) |
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5.9.5 Optocoupler and Op Amp: Pull-Down with Fast Lane |
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322 | (4) |
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326 | (2) |
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5.9.7 Optocoupler and Op Amp: Pull Down without Fast Lane |
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328 | (4) |
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332 | (3) |
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335 | (22) |
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335 | (1) |
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Appendix 5A Summary Pictures |
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335 | (5) |
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Appendix 5B Automating Components Calculations with k Factor |
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340 | (1) |
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340 | (1) |
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341 | (1) |
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342 | (2) |
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344 | (2) |
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Appendix 5C The Optocoupler |
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346 | (1) |
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346 | (1) |
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347 | (1) |
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348 | (2) |
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Extracting the Optocoupler Pole |
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350 | (1) |
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Watch for the LED Dynamic Resistance |
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351 | (3) |
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354 | (1) |
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355 | (2) |
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Chapter 6 Operational Transconductance Amplifier-Based Compensators |
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357 | (26) |
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6.1 The Type 1: An Origin Pole |
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358 | (1) |
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359 | (1) |
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6.2 The Type 2: An Origin Pole plus a Pole/Zero Pair |
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360 | (4) |
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364 | (1) |
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6.3 Optocoupler and OTA: A Buffered Connection |
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365 | (15) |
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368 | (2) |
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6.4 The Type 3: An Origin Pole and a Pole/Zero Pair |
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370 | (7) |
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377 | (3) |
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380 | (3) |
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Appendix 6A Summary Pictures |
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380 | (1) |
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381 | (2) |
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Chapter 7 TL431-Based Compensators |
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383 | (72) |
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7.1 A Bandgap-Based Component |
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383 | (7) |
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7.1.1 The Reference Voltage |
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385 | (2) |
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7.1.2 The Need for Bias Current |
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387 | (3) |
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7.2 Biasing the TL431: The Impact on the Gain |
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390 | (2) |
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7.3 Biasing the TL431: A Different Arrangement |
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392 | (3) |
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7.4 Biasing the TL431: Component Limits |
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395 | (1) |
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7.5 The Fast Lane Is the Problem |
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396 | (1) |
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7.6 Disabling the Fast Lane |
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397 | (34) |
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7.7 The Type 1: An Origin Pole, Common-Emitter Configuration |
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399 | (3) |
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402 | (1) |
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7.8 The Type 1: Common-Collector Configuration |
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403 | (1) |
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7.9 The Type 2: An Origin Pole plus a Pole/Zero Pair |
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403 | (4) |
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407 | (1) |
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7.10 The Type 2: Common-Emitter Configuration and UC384X |
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408 | (3) |
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7.11 The Type 2: Common-Collector Configuration and UC384X |
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411 | (1) |
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7.12 The Type 2: Disabling the Fast Lane |
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411 | (2) |
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413 | (2) |
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7.13 The Type 3: An Origin Pole plus a Double Pole/Zero Pair |
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415 | (8) |
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423 | (1) |
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7.14 The Type 3: An Origin Pole plus a Double Pole/Zero Pair---No Fast Lane |
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424 | (5) |
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429 | (2) |
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7.15 Testing the Ac Responses on a Bench |
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431 | (3) |
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7.16 Isolated Zener-Based Compensator |
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434 | (7) |
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436 | (5) |
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7.17 Nonisolated Zener-Based Compensator |
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441 | (2) |
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7.18 Nonisolated Zener-Based Compensator: A Lower Cost Version |
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443 | (2) |
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445 | (10) |
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445 | (1) |
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Appendix 7A Summary Pictures |
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445 | (3) |
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Appendix 7B Second Stage LC Filter |
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448 | (1) |
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449 | (1) |
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450 | (4) |
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454 | (1) |
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Chapter 8 Shunt Regulator-Based Compensators |
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455 | (32) |
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8.1 The Type 2: An Origin Pole plus a Pole/Zero Pair |
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456 | (4) |
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460 | (6) |
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8.2 The Type 3: An Origin Pole plus a Double Pole/Zero Pair |
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466 | (2) |
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468 | (3) |
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8.3 The Type 3: An Origin Pole plus a Double Pole/Zero Pair---No Fast Lane |
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471 | (3) |
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474 | (2) |
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8.4 Isolated Zener-Based Compensator |
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476 | (7) |
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480 | (3) |
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483 | (4) |
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483 | (1) |
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Appendix 8A Summary Pictures |
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484 | (3) |
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Chapter 9 Measurements and Design Examples |
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487 | (78) |
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9.1 Measuring the Control System Transfer Function |
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487 | (75) |
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9.1.1 Opening the Loop with Bias Point Loss |
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488 | (4) |
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9.1.2 Power Stage Transfer Function without Bias Point Loss |
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492 | (1) |
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9.1.3 Opening the Loop in ac Only |
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493 | (3) |
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9.1.4 Voltage Variations at the Injection Points |
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496 | (8) |
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9.1.5 Impedances at the Injection Points |
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504 | (1) |
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505 | (4) |
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9.2 Design Example 1: A Forward dc-dc Converter |
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509 | (1) |
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509 | (2) |
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9.2.2 The Electrical Schematic |
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511 | (3) |
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9.2.3 Extracting the Power Stage Transfer Response |
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514 | (1) |
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9.2.4 Compensating the Converter |
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515 | (4) |
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9.3 Design Example 2: A Linear Regulator |
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519 | (1) |
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9.3.1 Extracting the Power Stage Transfer Function |
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520 | (1) |
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9.3.2 Crossover Frequency Selection and Compensation |
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521 | (6) |
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9.3.3 Testing the Transient Response |
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527 | (1) |
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9.4 Design Example 3: A CCM Voltage-Mode Boost Converter |
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528 | (1) |
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9.4.1 The Power Stage Transfer Function |
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529 | (4) |
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9.4.2 Compensating the Converter |
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533 | (2) |
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535 | (1) |
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535 | (2) |
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9.4.3 Plotting the Loop Gain |
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537 | (2) |
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9.5 Design Example 4: A Primary-Regulated Flyback Converter |
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539 | (1) |
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9.5.1 Deriving the Transfer Function |
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540 | (4) |
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9.5.2 Verifying the Equations |
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544 | (1) |
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9.5.3 Stabilizing the Converter |
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545 | (7) |
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9.6 Design Example 5: Input Filter Compensation |
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552 | (1) |
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9.6.1 A Negative Incremental Resistance |
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553 | (1) |
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9.6.2 Building an Oscillator |
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554 | (2) |
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9.6.3 Taming the Oscillations |
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556 | (6) |
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562 | (3) |
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562 | (3) |
Conclusion |
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565 | (2) |
Appendix |
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567 | (4) |
About the Author |
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571 | |