Pulse-Width Modulated DC-DC Power Converters

Marian K. Kazimierczuk Wright State University, Dayton, Ohio, USA

• About the Author xxiPreface xxiiiNomenclature xxv1 Introduction 11.1 Classification of Power Supplies 11.2 Basic Functions of Voltage Regulators 31.3 Power Relationships in DC–DC Converters 41.4 DC Transfer Functions of DC–DC Converters 51.5 Static Characteristics of DC Voltage Regulators 61.6 Dynamic Characteristics of DC Voltage Regulators 91.7 Linear Voltage Regulators 121.7.1 Series Voltage Regulator 131.7.2 Shunt Voltage Regulator 141.8 Topologies of PWM DC–DC Converters 161.9 Relationships Among Current, Voltage, Energy, and Power 181.10 Summary 19References 19Review Questions 20Problems 212 Buck PWM DC–DC Converter 222.1 Introduction 222.2 DC Analysis of PWM Buck Converter for CCM 222.2.1 Circuit Description 222.2.2 Assumptions 252.2.3 Time Interval: 0 < t ≤ DT 252.2.4 Time Interval: DT < t ≤ T 262.2.5 Device Stresses for CCM 272.2.6 DC Voltage Transfer Function for CCM 272.2.7 Boundary Between CCM and DCM 292.2.8 Capacitors 312.2.9 Ripple Voltage in Buck Converter for CCM 332.2.10 Switching Losses with Linear MOSFET Output Capacitance 392.2.11 Switching Losses with Nonlinear MOSFET Output Capacitance 402.2.12 Power Losses and Efficiency of Buck Converter for CCM 432.2.13 DC Voltage Transfer Function of Lossy Converter for CCM 482.2.14 MOSFET Gate-Drive Power 482.2.15 Gate Driver 492.2.16 Design of Buck Converter for CCM 502.3 DC Analysis of PWM Buck Converter for DCM 522.3.1 Time Interval: 0 < t ≤ DT 562.3.2 Time Interval: DT < t ≤ (D + D1)T 582.3.3 Time Interval: (D + D1)T < t ≤ T 582.3.4 Device Stresses for DCM 592.3.5 DC Voltage Transfer Function for DCM 592.3.6 Maximum Inductance for DCM 622.3.7 Power Losses and Efficiency of Buck Converter for DCM 632.3.8 Design of Buck Converter for DCM 652.4 Buck Converter with Input Filter 682.5 Buck Converter with Synchronous Rectifier 682.6 Buck Converter with Positive Common Rail 762.7 Quadratic Buck Converter 762.8 Tapped-Inductor Buck Converters 792.8.1 Tapped-Inductor Common-Diode Buck Converter 792.8.2 Tapped-Inductor Common-Transistor Buck Converter 812.8.3 Watkins–Johnson Converter 822.9 Multiphase Buck Converter 832.10 Switched-Inductor Buck Converter 852.11 Layout 852.12 Summary 85References 87Review Questions 88Problems 883 Boost PWM DC–DC Converter 903.1 Introduction 903.2 DC Analysis of PWM Boost Converter for CCM 903.2.1 Circuit Description 903.2.2 Assumptions 913.2.3 Time Interval: 0 < t ≤ DT 933.2.4 Time Interval: DT < t ≤ T 943.2.5 DC Voltage Transfer Function for CCM 943.2.6 Boundary Between CCM and DCM 953.2.7 Ripple Voltage in Boost Converter for CCM 983.2.8 Power Losses and Efficiency of Boost Converter for CCM 1003.2.9 DC Voltage Transfer Function of Lossy Boost Converter for CCM 1023.2.10 Design of Boost Converter for CCM 1033.3 DC Analysis of PWM Boost Converter for DCM 1073.3.1 Time Interval: 0 < t ≤ DT 1103.3.2 Time Interval: DT < t ≤ (D + D1)T 1113.3.3 Time Interval: (D + D1)T < t ≤ T 1123.3.4 Device Stresses for DCM 1123.3.5 DC Voltage Transfer Function for DCM 1123.3.6 Maximum Inductance for DCM 1173.3.7 Power Losses and Efficiency of Boost Converter for DCM 1173.3.8 Design of Boost Converter for DCM 1203.4 Bidirectional Buck and Boost Converters 1273.5 Synchronous Boost Converter 1293.6 Tapped-Inductor Boost Converters 1293.6.1 Tapped-Inductor Common-Diode Boost Converter 1313.6.2 Tapped-Inductor Common-Load Boost Converter 1323.7 Duality 1333.8 Power Factor Correction 1343.8.1 Power Factor 1343.8.2 Boost Power Factor Corrector 1383.8.3 Electronic Ballasts for Fluorescent Lamps 1413.9 Summary 141References 142Review Questions 143Problems 1434 Buck–Boost PWM DC–DC Converter 1454.1 Introduction 1454.2 DC Analysis of PWM Buck–Boost Converter for CCM 1454.2.1 Circuit Description 1454.2.2 Assumptions 1464.2.3 Time Interval: 0 < t ≤ DT 1464.2.4 Time Interval: DT < t ≤ T 1484.2.5 DC Voltage Transfer Function for CCM 1494.2.6 Device Stresses for CCM 1504.2.7 Boundary Between CCM and DCM 1514.2.8 Ripple Voltage in Buck–Boost Converter for CCM 1524.2.9 Power Losses and Efficiency of the Buck–Boost Converter for CCM 1554.2.10 DC Voltage Transfer Function of Lossy Buck–Boost Converter for CCM 1584.2.11 Design of Buck–Boost Converter for CCM 1594.3 DC Analysis of PWM Buck–Boost Converter for DCM 1624.3.1 Time Interval: 0 < t ≤ DT 1654.3.2 Time Interval: DT < t ≤ (D + D1)T 1664.3.3 Time Interval: (D + D1)T < t ≤ T 1674.3.4 Device Stresses of the Buck–Boost Converter in DCM 1674.3.5 DC Voltage Transfer Function of the Buck–Boost Converter for DCM 1674.3.6 Maximum Inductance for DCM 1704.3.7 Power Losses and Efficiency of the Buck–Boost Converter in DCM 1724.3.8 Design of Buck–Boost Converter for DCM 1744.4 Bidirectional Buck–Boost Converter 1804.5 Synthesis of Buck–Boost Converter 1814.6 Synthesis of Boost–Buck (ćuk) Converter 1834.7 Noninverting Buck–Boost Converters 1844.7.1 Cascaded Noninverting Buck–Boost Converters 1844.7.2 Four-Transistor Noninverting Buck–Boost Converters 1844.8 Tapped-Inductor Buck–Boost Converters 1864.8.1 Tapped-Inductor Common-Diode Buck–Boost Converter 1864.8.2 Tapped-Inductor Common-Transistor Buck–Boost Converter 1874.8.3 Tapped-Inductor Common-Load Buck–Boost Converter 1884.8.4 Tapped-Inductor Common-Source Buck–Boost Converter 1914.9 Summary 192References 192Review Questions 193Problems 1935 Flyback PWM DC–DC Converter 1955.1 Introduction 1955.2 Transformers 1965.3 DC Analysis of PWM Flyback Converter for CCM 1975.3.1 Derivation of PWM Flyback Converter 1975.3.2 Circuit Description 1975.3.3 Assumptions 1995.3.4 Time Interval: 0 < t ≤ DT 2005.3.5 Time Interval: DT < t ≤ T 2015.3.6 DC Voltage Transfer Function for CCM 2035.3.7 Boundary Between CCM and DCM 2045.3.8 Ripple Voltage in Flyback Converter for CCM 2055.3.9 Power Losses and Efficiency of Flyback Converter for CCM 2075.3.10 DC Voltage Transfer Function of Lossy Converter for CCM 2105.3.11 Design of Flyback Converter for CCM 2115.4 DC Analysis of PWM Flyback Converter for DCM 2145.4.1 Time Interval: 0 < t ≤ DT 2175.4.2 Time Interval: DT < t ≤ (D + D1)T 2195.4.3 Time Interval: (D + D1)T < t ≤ T 2205.4.4 DC Voltage Transfer Function for DCM 2215.4.5 Maximum Magnetizing Inductance for DCM 2225.4.6 Ripple Voltage in Flyback Converter for DCM 2255.4.7 Power Losses and Efficiency of Flyback Converter for DCM 2265.4.8 Design of Flyback Converter for DCM 2285.5 Multiple-Output Flyback Converter 2325.6 Bidirectional Flyback Converter 2375.7 Ringing in Flyback Converter 2375.8 Flyback Converter with Passive Dissipative Snubber 2405.9 Flyback Converter with Zener Diode Voltage Clamp 2405.10 Flyback Converter with Active Clamping 2415.11 Two-Transistor Flyback Converter 2415.12 Summary 243References 244Review Questions 244Problems 2456 Forward PWM DC–DC Converter 2466.1 Introduction 2466.2 DC Analysis of PWM Forward Converter for CCM 2466.2.1 Derivation of Forward PWM Converter 2466.2.2 Time Interval: 0 < t ≤ DT 2486.2.3 Time Interval: DT < t ≤ DT + tm 2516.2.4 Time Interval: DT + tm < t ≤ T 2536.2.5 Maximum Duty Cycle 2536.2.6 Device Stresses 2546.2.7 DC Voltage Transfer Function for CCM 2556.2.8 Boundary Between CCM and DCM 2556.2.9 Ripple Voltage in Forward Converter for CCM 2566.2.10 Power Losses and Efficiency of Forward Converter for CCM 2586.2.11 DC Voltage Transfer Function of Lossy Converter for CCM 2616.2.12 Design of Forward Converter for CCM 2626.3 DC Analysis of PWM Forward Converter for DCM 2696.3.1 Time Interval: 0 < t ≤ DT 2696.3.2 Time Interval: DT < t ≤ DT + tm 2726.3.3 Time Interval: DT + tm < t ≤ (D + D1)T 2736.3.4 Time Interval: (D + D1)T < t ≤ T 2736.3.5 DC Voltage Transfer Function for DCM 2746.3.6 Maximum Inductance for DCM 2776.3.7 Power Losses and Efficiency of Forward Converter for DCM 2786.3.8 Design of Forward Converter for DCM 2806.4 Multiple-Output Forward Converter 2886.5 Forward Converter with Synchronous Rectifier 2886.6 Forward Converters with Active Clamping 2886.7 Two-Switch Forward Converter 2906.8 Forward–Flyback Converter 2916.9 Summary 292References 293Review Questions 293Problems 2947 Half-Bridge PWM DC–DC Converter 2967.1 Introduction 2967.2 DC Analysis of PWM Half-Bridge Converter for CCM 2967.2.1 Circuit Description 2967.2.2 Assumptions 2997.2.3 Time Interval: 0 < t ≤ DT 2997.2.4 Time Interval: DT < t ≤ T∕2 3017.2.5 Time Interval: T∕2 < t ≤ T∕2 + DT 3037.2.6 Time Interval: T∕2 + DT < t ≤ T 3047.2.7 Device Stresses 3047.2.8 DC Voltage Transfer Function of Lossless Half-Bridge Converter for CCM 3047.2.9 Boundary Between CCM and DCM 3057.2.10 Ripple Voltage in Half-Bridge Converter for CCM 3067.2.11 Power Losses and Efficiency of Half-Bridge Converter for CCM 3087.2.12 DC Voltage Transfer Function of Lossy Converter for CCM 3117.2.13 Design of Half-Bridge Converter for CCM 3127.3 DC Analysis of PWM Half-Bridge Converter for DCM 3157.3.1 Time Interval: 0 < t ≤ DT 3157.3.2 Time Interval: DT < t ≤ (D + D1)T 3207.3.3 Time Interval: (D + D1)T < t ≤ T∕2 3227.3.4 DC Voltage Transfer Function for DCM 3227.3.5 Maximum Inductance for DCM 3267.4 Summary 326References 327Review Questions 327Problems 3288 Full-Bridge PWM DC–DC Converter 3308.1 Introduction 3308.2 DC Analysis of PWM Full-Bridge Converter for CCM 3308.2.1 Circuit Description 3308.2.2 Assumptions 3328.2.3 Time Interval: 0 < t ≤ DT 3328.2.4 Time Interval: DT < t ≤ T∕2 3348.2.5 Time Interval: T∕2 < t ≤ T∕2 + DT 3368.2.6 Time Interval: T∕2 + DT < t ≤ T 3368.2.7 Device Stresses 3378.2.8 DC Voltage Transfer Function of Lossless Full-Wave Converter for CCM 3378.2.9 Boundary Between CCM and DCM 3388.2.10 Ripple Voltage in Full-Bridge Converter for CCM 3398.2.11 Power Losses and Efficiency of Full-Bridge Converter for CCM 3408.2.12 DC Voltage Transfer Function of Lossy Converter for CCM 3448.2.13 Design of Full-Bridge Converter for CCM 3458.3 DC Analysis of PWM Full-Bridge Converter for DCM 3518.3.1 Time Interval: 0 < t ≤ DT 3518.3.2 Time Interval: DT < t ≤ (D + D1)T 3538.3.3 Time Interval: (D + D1)T < t ≤ T∕2 3558.3.4 DC Voltage Transfer Function for DCM 3568.3.5 Maximum Inductance for DCM 3598.4 Phase-Controlled Full-Bridge Converter 3618.5 Summary 362References 362Review Questions 362Problems 3639 Small-Signal Models of PWM Converters for CCM and DCM 3659.1 Introduction 3659.2 Assumptions 3669.3 Averaged Model of Ideal Switching Network for CCM 3669.4 Averaged Values of Switched Resistances 3699.5 Model Reduction 3759.6 Large-Signal Averaged Model for CCM 3779.7 DC and Small-Signal Circuit Linear Models of Switching Network for CCM 3819.7.1 Large-Signal Circuit Model of Switching Network for CCM 3819.7.2 Linearization of Switching Network Model for CCM 3849.8 Block Diagram of Small-signal Model of PWM DC–DC Converters 3859.9 Family of PWM Converter Models for CCM 3869.10 PWM Small-Signal Switch Model for CCM 3899.11 Modeling of Ideal Switching Network for DCM 3919.11.1 Relationships Among DC Components for DCM 3919.11.2 Small-Signal Model of Ideal Switching Network for DCM 3959.12 Averaged Parasitic Resistances for DCM 3989.13 Summary 400References 402Review Questions 405Problems 40510 Small-Signal Characteristics of Buck Converter for CCM 40710.1 Introduction 40710.2 Small-Signal Model of the PWM Buck Converter 40710.3 Open-Loop Transfer Functions 40810.3.1 Open-Loop Control-to-Output Transfer Function 40910.3.2 Delay in Control-to-Output Transfer Function 41610.3.3 Open-Loop Input-to-Output Transfer Function 41810.3.4 Open-Loop Input Impedance 42010.3.5 Open-Loop Output Impedance 42310.4 Open-Loop Step Responses 42610.4.1 Open-Loop Response of Output Voltage to Step Change in Input Voltage 42610.4.2 Open-Loop Response of Output Voltage to Step Change in Duty Cycle 43110.4.3 Open-Loop Response of Output Voltage to Step Change in Load Current 43310.5 Open-Loop DC Transfer Functions 43410.6 Summary 436References 436Review Questions 437Problems 43811 Small-Signal Characteristics of Boost Converter for CCM 43911.1 Introduction 43911.2 DC Characteristics 43911.3 Open-Loop Control-to-Output Transfer Function 44011.4 Delay in Open-Loop Control-to-Output Transfer Function 44911.5 Open-Loop Audio Susceptibility 45111.6 Open-Loop Input Impedance 45511.7 Open-Loop Output Impedance 45711.8 Open-Loop Step Responses 46111.8.1 Open-Loop Response of Output Voltage to Step Change in Input Voltage 46111.8.2 Open-Loop Response of Output Voltage to Step Change in Duty Cycle 46411.8.3 Open-Loop Response of Output Voltage to Step Change in Load Current 46511.9 Summary 467References 467Review Questions 468Problems 46812 Voltage-Mode Control of PWM Buck Converter 47012.1 Introduction 47012.2 Properties of Negative Feedback 47112.3 Stability 47412.4 Single-Loop Control of PWM Buck Converter 47512.5 Closed-Loop Small-Signal Model of Buck Converter 47812.6 Pulse-Width Modulator 47812.7 Feedback Network 48312.8 Transfer Function of Buck Converter with Modulator and Feedback Network 48612.9 Control Circuits 48912.9.1 Error Amplifier 48912.9.2 Proportional Controller 49012.9.3 Integral Controller 49212.9.4 Proportional-Integral Controller 49312.9.5 Integral-Single-Lead Controller 49712.9.6 Loop Gain 50412.9.7 Closed-Loop Control-to-Output Voltage Transfer Function 50412.9.8 Closed-Loop Input-to-Output Transfer Function 50612.9.9 Closed-Loop Input Impedance 50812.9.10 Closed-Loop Output Impedance 50912.10 Closed-Loop Step Responses 51112.10.1 Response to Step Change in Input Voltage 51112.10.2 Response to Step Change in Reference Voltage 51312.10.3 Closed-Loop Response to Step Change in Load Current 51512.10.4 Closed-Loop DC Transfer Functions 51512.11 Summary 518References 519Review Questions 519Problems 52013 Voltage-Mode Control of Boost Converter 52113.1 Introduction 52113.2 Circuit of Boost Converter with Voltage-Mode Control 52113.3 Transfer Function of Modulator, Boost Converter Power Stage, and Feedback Network 52313.4 Integral-Double-Lead Controller 52713.5 Design of Integral-Double-Lead Controller 53213.6 Loop Gain 53613.7 Closed-Loop Control-to-Output Voltage Transfer Function 53713.8 Closed-Loop Audio Susceptibility 53913.9 Closed-Loop Input Impedance 53913.10 Closed-Loop Output Impedance 54213.11 Closed-Loop Step Responses 54413.11.1 Closed-Loop Response to Step Change in Input Voltage 54413.11.2 Closed-Loop Response to Step Change in Reference Voltage 54713.11.3 Closed-Loop Response to Step Change in Load Current 54813.12 Closed-Loop DC Transfer Functions 54913.13 Summary 552References 552Review Questions 552Problems 55314 Current-Mode Control 55414.1 Introduction 55414.2 Principle of Operation of PWM Converters with Peak CMC 55514.3 Relationship Between Duty Cycle and Inductor-Current Slopes 55914.4 Instability of Closed-Current Loop 56014.5 Slope Compensation 56414.5.1 Analysis of Slope Compensation in Time Domain 56414.5.2 Boundary of Slope Compensation for Buck and Buck–Boost Converters 56914.5.3 Boundary Slope Compensation for Boost Converter 57014.6 Sample-and-Hold Effect on Current Loop 57014.6.1 Natural Response of Inductor Current to Small Perturbation in Closed-Current Loop 57214.6.2 Forced Response of Inductor Current to Step Change in Control Voltage in Closed-Current Loop 57514.6.3 Relationship Between s-Domain and z-Domain 57714.6.4 Transfer Function of Closed-Current Loop in z-Domain 57814.7 Closed-Loop Control Voltage-to-Inductor Current Transfer Function in s-Domain 58014.7.1 Approximation of Hicl by Rational Transfer Function 58214.7.2 Step Responses of Closed-Inner Loop 58814.8 Loop Gain of Current Loop 58814.8.1 Loop Gain of Inner Loop in z-Domain 58814.8.2 Loop Gain of Inner Loop in s-Domain 59014.9 Gain-Crossover Frequency of Inner Loop 59514.10 Phase Margin of Inner Loop 59614.11 Maximum Duty Cycle for Converters without Slope Compensation 59814.12 Maximum Duty Cycle for Converters with Slope Compensation 60014.13 Minimum Slope Compensation for Buck and Buck–Boost Converter 60514.14 Minimum Slope Compensation for Boost Converter 60714.15 Error Voltage-to-Duty Cycle Transfer Function 61014.16 Closed-Loop Control Voltage-to-Duty Cycle Transfer Function of Current Loop 61414.17 Alternative Representation of Current Loop 61814.18 Current Loop with Disturbances 61814.18.1 Modified Approximation of Current Loop 61914.19 Voltage Loop of PWM Converters with Current-Mode Control 62414.19.1 Control-to-Output Transfer Function for Buck Converter 62414.19.2 Block Diagram of Power Stages of PWM Converters 62714.19.3 Closed-Voltage Loop Transfer Function of PWM Converters with Current-Mode Control 62814.19.4 Closed-Loop Audio Susceptibility of PWM Converters with Current-Mode Control 62814.19.5 Closed-Loop Output Impedance of PWM Converters with Current-Mode Control 63014.20 Feedforward Gains in PWM Converters with Current-Mode Control without Slope Compensation 63114.21 Feedforward Gains in PWM Converters with Current-Mode Control and Slope Compensation 63414.22 Control-to-Output Voltage Transfer Function of Inner Loop with Feedforward Gains 63614.23 Audio-Susceptibility of Inner Loop with Feedforward Gains 63714.24 Closed-Loop Transfer Functions with Feedforward Gains 63814.25 Slope Compensation by Adding a Ramp to Inductor Current Waveform 63814.26 Relationships for Constant-Frequency Current-Mode On-Time Control 63914.27 Summary 639References 640Review Questions 644Problems 64414.28 Appendix: Sample-and-Hold Modeling 64514.28.1 Sampler of the Control Voltage 64514.28.2 Zero-Order Hold of Inductor Current 64814.28.3 Approximations of esTs 65015 Current-Mode Control of Boost Converter 65315.1 Introduction 65315.2 Open-Loop Small-Signal Transfer Functions 65315.2.1 Open-Loop Duty Cycle-to-Inductor Current Transfer Function 65315.2.2 High-Frequency Open-Loop Duty Cycle-to-Inductor Current Transfer Function 65915.2.3 Open-Loop Input Voltage-to-Inductor Current Transfer Function 66015.2.4 Open-Loop Inductor-to-Output Current Transfer Function 66515.3 Open-Loop Step Responses of Inductor Current 66715.3.1 Open-Loop Response of Inductor Current to Step Change in Input Voltage 66715.3.2 Open-Loop Response of the Inductor Current to Step Change in the Duty Cycle 67015.3.3 Open-Loop Response of Inductor Current to Step Change in Load Current 67215.4 Closed-Current-Loop Transfer Functions 67515.4.1 Forward Gain 67515.4.2 Loop Gain of Current Loop 67515.4.3 Closed-Loop Gain of Current Loop 67515.4.4 Control-to-Output Transfer Function 67715.4.5 Input Voltage-to-Duty Cycle Transfer Function 68415.4.6 Load Current-to-Duty Cycle Transfer Function 68815.4.7 Output Impedance of Closed-Current Loop 69015.5 Closed-Voltage-Loop Transfer Functions 69515.5.1 Control-to-Output Transfer Function 69515.5.2 Control Voltage-to-Feedback Voltage Transfer Function 69515.5.3 Loop Gain of Voltage Loop 69715.5.4 Closed-Loop Gain of Voltage Loop 70115.5.5 Closed-Loop Audio Susceptibility with Integral Controller 70315.5.6 Closed-Loop Output Impedance with Integral Controller 70415.6 Closed-Loop Step Responses 70615.6.1 Closed-Loop Response of Output Voltage to Step Change in Input Voltage 70615.6.2 Closed-Loop Response of Output Voltage to Step Change in Load Current 70815.6.3 Closed-Loop Response of Output Voltage to Step Change in Reference Voltage 70815.7 Closed-Loop DC Transfer Functions 71015.8 Summary 711References 711Review Questions 712Problems 71216 Open-Loop Small-Signal Characteristics of PWM Boost Converter for DCM 71316.1 Introduction 71316.2 Small-Signal Model of Boost Converter for DCM 71316.3 Open-Loop Control-to-Output Transfer Function 71616.4 Open-Loop Input-to-Output Voltage Transfer Function 71916.5 Open-Loop Input Impedance 72416.6 Open-Loop Output Impedance 72516.7 Step Responses of Output Voltage of Boost Converter for DCM 72816.7.1 Response of Output Voltage to Step Change in Input Voltage 72816.7.2 Response of Output Voltage to Step Change in Duty Cycle 73016.7.3 Response of Output Voltage to Step Change in Load Current 73016.8 Open-Loop Duty Cycle-to-Inductor Current Transfer Function 73116.9 Open-Loop Input Voltage-to-Inductor Current Transfer Function 73516.10 Open-Loop Output Current-to-Inductor Current Transfer Function 73516.11 Step Responses of Inductor Current of Boost Converter for DCM 73816.11.1 Step Response of Inductor Current to Step Change in Input Voltage 73816.11.2 Step Response of Inductor Current to Step Change in Duty Cycle 74016.11.3 Step Response of Inductor Current to Step Change in Load Current 74116.12 DC Characteristics of Boost Converter for DCM 74216.12.1 DC-to-DC Voltage Transfer Function of Lossless Boost Converter for DCM 74216.12.2 DC-to-DC Voltage Transfer Function of Lossy Boost Converter for DCM 74316.12.3 Efficiency of Boost Converter for DCM 74516.13 Summary 745References 745Review Questions 746Problems 74617 Silicon and Silicon-Carbide Power Diodes 74717.1 Introduction 74717.2 Electronic Power Switches 74717.3 Atom 74817.4 Electron and Hole Effective Mass 74917.5 Semiconductors 75017.6 Intrinsic Semiconductors 75117.7 Extrinsic Semiconductors 75617.7.1 n-Type Semiconductor 75617.7.2 p-Type Semiconductor 75917.7.3 Maximum Operating Temperature 76117.8 Wide Band Gap Semiconductors 76217.9 Physical Structure of Junction Diodes 76417.9.1 Formation of Depletion Layer 76517.9.2 Charge Transport 76717.10 Static I–V Diode Characteristic 76817.11 Breakdown Voltage of Junction Diodes 77217.11.1 Depletion-Layer Width 77317.11.2 Electric Field Intensity Distribution 77517.11.3 Avalanche Breakdown Voltage 77917.11.4 Punch-Through Breakdown Voltage 78117.11.5 Edge Terminations 78217.12 Capacitances of Junction Diodes 78417.12.1 Junction Capacitance 78417.12.2 Diffusion Capacitance 78717.13 Reverse Recovery of pn Junction Diodes 78917.13.1 Qualitative Description 78917.13.2 Reverse Recovery in Resistive Circuits 79017.13.3 Charge-Continuity Equation 79317.13.4 Reverse Recovery in Inductive Circuits 79617.14 Schottky Diodes 79817.14.1 Static I–V Characteristic of Schottky Diodes 80117.14.2 Breakdown Voltages of Schottky Diodes 80217.14.3 Junction Capacitance of Schottky Diodes 80217.14.4 Switching Characteristics of Schottky Diodes 80217.15 Solar Cells 80617.16 Light-Emitting Diodes 80917.17 SPICE Model of Diodes 81017.18 Summary 811References 815Review Questions 816Problems 81718 Silicon and Silicon-Carbide Power MOSFETs 81918.1 Introduction 81918.2 Integrated MOSFETs 81918.3 Physical Structure of Power MOSFETs 81918.4 Principle of Operation of Power MOSFETs 82418.4.1 Cutoff Region 82418.4.2 Formation of MOSFET Channel 82418.4.3 Linear Region 82418.4.4 Saturation Region 82518.4.5 Antiparallel Diode 82518.5 Derivation of Power MOSFET Characteristics 82618.5.1 Ohmic Region 82618.5.2 Pinch-off Region 82918.5.3 Channel-Length Modulation 83018.6 Power MOSFET Characteristics 83118.7 Mobility of Charge Carriers 83318.7.1 Effect of Doping Concentration on Mobility 83418.7.2 Effect of Temperature on Mobility 83618.7.3 Effect of Electric Field on Mobility 84018.8 Short-Channel Effects 84618.8.1 Ohmic Region 84618.8.2 Pinch-off Region 84718.9 Aspect Ratio of Power MOSFETs 84818.10 Breakdown Voltage of Power MOSFETs 85018.11 Gate Oxide Breakdown Voltage of Power MOSFETs 85218.12 Specific On-Resistance 85218.13 Figures-of-Merit of Semiconductors 85518.14 On-Resistance of Power MOSFETs 85718.14.1 Channel Resistance 85718.14.2 Accumulation Region Resistance 85718.14.3 Neck Region Resistance 85818.14.4 Drift Region Resistance 85918.15 Capacitances of Power MOSFETs 86218.15.1 Gate-to-Source Capacitance 86218.15.2 Drain-to-Source Capacitance 86418.15.3 Gate-to-Drain Capacitance 86418.16 Switching Waveforms 87518.17 SPICE Model of Power MOSFETs 87718.18 IGBTs 87918.19 Heat Sinks 88018.20 Summary 886References 888Review Questions 888Problems 88919 Electromagnetic Compatibility 89119.1 Introduction 89119.2 Definition of EMI 89119.3 Definition of EMC 89219.4 EMI Immunity 89219.5 EMI Susceptibility 89319.6 Classification of EMI 89319.7 Sources of EMI 89519.8 Safety Standards 89619.9 EMC Standards 89619.10 Near Field and Far Field 89719.11 Techniques of EMI Reduction 89719.12 Insertion Loss 89819.13 EMI Filters 89819.14 Feed-Through Capacitors 90019.15 EMI Shielding 90019.16 Interconnections 90219.17 Summary 903References 903Review Questions 903Problem 904A Introduction to SPICE 907B Introduction to MATLAB® 910C Physical Constants 915Answers to Problems 917Index 925