{"product_id":"pulse-width-modulated-dc-dc-power-converters-isbn-9781119009542","title":"Pulse-Width Modulated DC-DC Power Converters","description":"\u003cp\u003ePWM DC-DC power converter technology underpins many energy conversion systems including renewable energy circuits, active power factor correctors, battery chargers, portable devices and LED drivers. \u003c\/p\u003e \u003cp\u003eFollowing the success of \u003ci\u003ePulse-Width Modulated DC-DC Power Converters\u003c\/i\u003e this second edition has been thoroughly revised and expanded to cover the latest challenges and advances in the field.\u003c\/p\u003e \u003cp\u003eKey features of \u003ci\u003e2nd edition\u003c\/i\u003e: \u003c\/p\u003e \u003cul\u003e \u003cli\u003eFour new chapters, detailing the latest advances in power conversion, focus on: small-signal model and dynamic characteristics of the buck converter in continuous conduction mode; voltage-mode control of buck converter; small-signal model and characteristics of the boost converter in the discontinuous conduction mode and electromagnetic compatibility EMC.\u003c\/li\u003e \u003cli\u003eProvides readers with a solid understanding of the principles of operation, synthesis, analysis and design of PWM power converters and semiconductor power devices, including wide band-gap power devices (SiC and GaN).\u003c\/li\u003e \u003cli\u003eFully revised Solutions for all end-of-chapter problems available to instructors via the book companion website.\u003c\/li\u003e \u003cli\u003eStep-by-step derivation of closed-form design equations with illustrations.\u003c\/li\u003e \u003cli\u003eFully revised figures based on real data. \u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eWith improved end-of-chapter summaries of key concepts, review questions, problems and answers, biographies and case studies, this is an essential textbook for graduate and senior undergraduate students in electrical engineering. Its superior readability and clarity of explanations also makes it a key reference for practicing engineers and research scientists. \u003c\/p\u003e \u003cp\u003eAbout the Author xxi\u003c\/p\u003e \u003cp\u003ePreface xxiii\u003c\/p\u003e \u003cp\u003eNomenclature xxv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Classification of Power Supplies 1\u003c\/p\u003e \u003cp\u003e1.2 Basic Functions of Voltage Regulators 3\u003c\/p\u003e \u003cp\u003e1.3 Power Relationships in DC–DC Converters 4\u003c\/p\u003e \u003cp\u003e1.4 DC Transfer Functions of DC–DC Converters 5\u003c\/p\u003e \u003cp\u003e1.5 Static Characteristics of DC Voltage Regulators 6\u003c\/p\u003e \u003cp\u003e1.6 Dynamic Characteristics of DC Voltage Regulators 9\u003c\/p\u003e \u003cp\u003e1.7 Linear Voltage Regulators 12\u003c\/p\u003e \u003cp\u003e1.7.1 Series Voltage Regulator 13\u003c\/p\u003e \u003cp\u003e1.7.2 Shunt Voltage Regulator 14\u003c\/p\u003e \u003cp\u003e1.8 Topologies of PWM DC–DC Converters 16\u003c\/p\u003e \u003cp\u003e1.9 Relationships Among Current, Voltage, Energy, and Power 18\u003c\/p\u003e \u003cp\u003e1.10 Summary 19\u003c\/p\u003e \u003cp\u003eReferences 19\u003c\/p\u003e \u003cp\u003eReview Questions 20\u003c\/p\u003e \u003cp\u003eProblems 21\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Buck PWM DC–DC Converter 22\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 22\u003c\/p\u003e \u003cp\u003e2.2 DC Analysis of PWM Buck Converter for CCM 22\u003c\/p\u003e \u003cp\u003e2.2.1 Circuit Description 22\u003c\/p\u003e \u003cp\u003e2.2.2 Assumptions 25\u003c\/p\u003e \u003cp\u003e2.2.3 Time Interval: 0 \u003ci\u003e\u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eDT \u003c\/i\u003e25\u003c\/p\u003e \u003cp\u003e2.2.4 Time Interval: \u003ci\u003eDT \u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eT \u003c\/i\u003e26\u003c\/p\u003e \u003cp\u003e2.2.5 Device Stresses for CCM 27\u003c\/p\u003e \u003cp\u003e2.2.6 DC Voltage Transfer Function for CCM 27\u003c\/p\u003e \u003cp\u003e2.2.7 Boundary Between CCM and DCM 29\u003c\/p\u003e \u003cp\u003e2.2.8 Capacitors 31\u003c\/p\u003e \u003cp\u003e2.2.9 Ripple Voltage in Buck Converter for CCM 33\u003c\/p\u003e \u003cp\u003e2.2.10 Switching Losses with Linear MOSFET Output Capacitance 39\u003c\/p\u003e \u003cp\u003e2.2.11 Switching Losses with Nonlinear MOSFET Output Capacitance 40\u003c\/p\u003e \u003cp\u003e2.2.12 Power Losses and Efficiency of Buck Converter for CCM 43\u003c\/p\u003e \u003cp\u003e2.2.13 DC Voltage Transfer Function of Lossy Converter for CCM 48\u003c\/p\u003e \u003cp\u003e2.2.14 MOSFET Gate-Drive Power 48\u003c\/p\u003e \u003cp\u003e2.2.15 Gate Driver 49\u003c\/p\u003e \u003cp\u003e2.2.16 Design of Buck Converter for CCM 50\u003c\/p\u003e \u003cp\u003e2.3 DC Analysis of PWM Buck Converter for DCM 52\u003c\/p\u003e \u003cp\u003e2.3.1 Time Interval: 0 \u003ci\u003e\u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eDT \u003c\/i\u003e56\u003c\/p\u003e \u003cp\u003e2.3.2 Time Interval: \u003ci\u003eDT \u0026lt; t \u003c\/i\u003e≤ (\u003ci\u003eD \u003c\/i\u003e+ \u003ci\u003eD\u003c\/i\u003e1)\u003ci\u003eT \u003c\/i\u003e58\u003c\/p\u003e \u003cp\u003e2.3.3 Time Interval: (\u003ci\u003eD \u003c\/i\u003e+ \u003ci\u003eD\u003c\/i\u003e1)\u003ci\u003eT \u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eT \u003c\/i\u003e58\u003c\/p\u003e \u003cp\u003e2.3.4 Device Stresses for DCM 59\u003c\/p\u003e \u003cp\u003e2.3.5 DC Voltage Transfer Function for DCM 59\u003c\/p\u003e \u003cp\u003e2.3.6 Maximum Inductance for DCM 62\u003c\/p\u003e \u003cp\u003e2.3.7 Power Losses and Efficiency of Buck Converter for DCM 63\u003c\/p\u003e \u003cp\u003e2.3.8 Design of Buck Converter for DCM 65\u003c\/p\u003e \u003cp\u003e2.4 Buck Converter with Input Filter 68\u003c\/p\u003e \u003cp\u003e2.5 Buck Converter with Synchronous Rectifier 68\u003c\/p\u003e \u003cp\u003e2.6 Buck Converter with Positive Common Rail 76\u003c\/p\u003e \u003cp\u003e2.7 Quadratic Buck Converter 76\u003c\/p\u003e \u003cp\u003e2.8 Tapped-Inductor Buck Converters 79\u003c\/p\u003e \u003cp\u003e2.8.1 Tapped-Inductor Common-Diode Buck Converter 79\u003c\/p\u003e \u003cp\u003e2.8.2 Tapped-Inductor Common-Transistor Buck Converter 81\u003c\/p\u003e \u003cp\u003e2.8.3 Watkins–Johnson Converter 82\u003c\/p\u003e \u003cp\u003e2.9 Multiphase Buck Converter 83\u003c\/p\u003e \u003cp\u003e2.10 Switched-Inductor Buck Converter 85\u003c\/p\u003e \u003cp\u003e2.11 Layout 85\u003c\/p\u003e \u003cp\u003e2.12 Summary 85\u003c\/p\u003e \u003cp\u003eReferences 87\u003c\/p\u003e \u003cp\u003eReview Questions 88\u003c\/p\u003e \u003cp\u003eProblems 88\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Boost PWM DC–DC Converter 90\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 90\u003c\/p\u003e \u003cp\u003e3.2 DC Analysis of PWM Boost Converter for CCM 90\u003c\/p\u003e \u003cp\u003e3.2.1 Circuit Description 90\u003c\/p\u003e \u003cp\u003e3.2.2 Assumptions 91\u003c\/p\u003e \u003cp\u003e3.2.3 Time Interval: 0 \u003ci\u003e\u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eDT \u003c\/i\u003e93\u003c\/p\u003e \u003cp\u003e3.2.4 Time Interval: \u003ci\u003eDT \u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eT \u003c\/i\u003e94\u003c\/p\u003e \u003cp\u003e3.2.5 DC Voltage Transfer Function for CCM 94\u003c\/p\u003e \u003cp\u003e3.2.6 Boundary Between CCM and DCM 95\u003c\/p\u003e \u003cp\u003e3.2.7 Ripple Voltage in Boost Converter for CCM 98\u003c\/p\u003e \u003cp\u003e3.2.8 Power Losses and Efficiency of Boost Converter for CCM 100\u003c\/p\u003e \u003cp\u003e3.2.9 DC Voltage Transfer Function of Lossy Boost Converter for CCM 102\u003c\/p\u003e \u003cp\u003e3.2.10 Design of Boost Converter for CCM 103\u003c\/p\u003e \u003cp\u003e3.3 DC Analysis of PWM Boost Converter for DCM 107\u003c\/p\u003e \u003cp\u003e3.3.1 Time Interval: 0 \u003ci\u003e\u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eDT \u003c\/i\u003e110\u003c\/p\u003e \u003cp\u003e3.3.2 Time Interval: \u003ci\u003eDT \u0026lt; t \u003c\/i\u003e≤ (\u003ci\u003eD \u003c\/i\u003e+ \u003ci\u003eD\u003c\/i\u003e1)\u003ci\u003eT \u003c\/i\u003e111\u003c\/p\u003e \u003cp\u003e3.3.3 Time Interval: (\u003ci\u003eD \u003c\/i\u003e+ \u003ci\u003eD\u003c\/i\u003e1)\u003ci\u003eT \u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eT \u003c\/i\u003e112\u003c\/p\u003e \u003cp\u003e3.3.4 Device Stresses for DCM 112\u003c\/p\u003e \u003cp\u003e3.3.5 DC Voltage Transfer Function for DCM 112\u003c\/p\u003e \u003cp\u003e3.3.6 Maximum Inductance for DCM 117\u003c\/p\u003e \u003cp\u003e3.3.7 Power Losses and Efficiency of Boost Converter for DCM 117\u003c\/p\u003e \u003cp\u003e3.3.8 Design of Boost Converter for DCM 120\u003c\/p\u003e \u003cp\u003e3.4 Bidirectional Buck and Boost Converters 127\u003c\/p\u003e \u003cp\u003e3.5 Synchronous Boost Converter 129\u003c\/p\u003e \u003cp\u003e3.6 Tapped-Inductor Boost Converters 129\u003c\/p\u003e \u003cp\u003e3.6.1 Tapped-Inductor Common-Diode Boost Converter 131\u003c\/p\u003e \u003cp\u003e3.6.2 Tapped-Inductor Common-Load Boost Converter 132\u003c\/p\u003e \u003cp\u003e3.7 Duality 133\u003c\/p\u003e \u003cp\u003e3.8 Power Factor Correction 134\u003c\/p\u003e \u003cp\u003e3.8.1 Power Factor 134\u003c\/p\u003e \u003cp\u003e3.8.2 Boost Power Factor Corrector 138\u003c\/p\u003e \u003cp\u003e3.8.3 Electronic Ballasts for Fluorescent Lamps 141\u003c\/p\u003e \u003cp\u003e3.9 Summary 141\u003c\/p\u003e \u003cp\u003eReferences 142\u003c\/p\u003e \u003cp\u003eReview Questions 143\u003c\/p\u003e \u003cp\u003eProblems 143\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Buck–Boost PWM DC–DC Converter 145\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 145\u003c\/p\u003e \u003cp\u003e4.2 DC Analysis of PWM Buck–Boost Converter for CCM 145\u003c\/p\u003e \u003cp\u003e4.2.1 Circuit Description 145\u003c\/p\u003e \u003cp\u003e4.2.2 Assumptions 146\u003c\/p\u003e \u003cp\u003e4.2.3 Time Interval: 0 \u003ci\u003e\u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eDT \u003c\/i\u003e146\u003c\/p\u003e \u003cp\u003e4.2.4 Time Interval: \u003ci\u003eDT \u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eT \u003c\/i\u003e148\u003c\/p\u003e \u003cp\u003e4.2.5 DC Voltage Transfer Function for CCM 149\u003c\/p\u003e \u003cp\u003e4.2.6 Device Stresses for CCM 150\u003c\/p\u003e \u003cp\u003e4.2.7 Boundary Between CCM and DCM 151\u003c\/p\u003e \u003cp\u003e4.2.8 Ripple Voltage in Buck–Boost Converter for CCM 152\u003c\/p\u003e \u003cp\u003e4.2.9 Power Losses and Efficiency of the Buck–Boost Converter for CCM 155\u003c\/p\u003e \u003cp\u003e4.2.10 DC Voltage Transfer Function of Lossy Buck–Boost Converter for CCM 158\u003c\/p\u003e \u003cp\u003e4.2.11 Design of Buck–Boost Converter for CCM 159\u003c\/p\u003e \u003cp\u003e4.3 DC Analysis of PWM Buck–Boost Converter for DCM 162\u003c\/p\u003e \u003cp\u003e4.3.1 Time Interval: 0 \u003ci\u003e\u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eDT \u003c\/i\u003e165\u003c\/p\u003e \u003cp\u003e4.3.2 Time Interval: \u003ci\u003eDT \u0026lt; t \u003c\/i\u003e≤ (\u003ci\u003eD \u003c\/i\u003e+ \u003ci\u003eD\u003c\/i\u003e1)\u003ci\u003eT \u003c\/i\u003e166\u003c\/p\u003e \u003cp\u003e4.3.3 Time Interval: (\u003ci\u003eD \u003c\/i\u003e+ \u003ci\u003eD\u003c\/i\u003e1)\u003ci\u003eT \u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eT \u003c\/i\u003e167\u003c\/p\u003e \u003cp\u003e4.3.4 Device Stresses of the Buck–Boost Converter in DCM 167\u003c\/p\u003e \u003cp\u003e4.3.5 DC Voltage Transfer Function of the Buck–Boost Converter for DCM 167\u003c\/p\u003e \u003cp\u003e4.3.6 Maximum Inductance for DCM 170\u003c\/p\u003e \u003cp\u003e4.3.7 Power Losses and Efficiency of the Buck–Boost Converter in DCM 172\u003c\/p\u003e \u003cp\u003e4.3.8 Design of Buck–Boost Converter for DCM 174\u003c\/p\u003e \u003cp\u003e4.4 Bidirectional Buck–Boost Converter 180\u003c\/p\u003e \u003cp\u003e4.5 Synthesis of Buck–Boost Converter 181\u003c\/p\u003e \u003cp\u003e4.6 Synthesis of Boost–Buck (ćuk) Converter 183\u003c\/p\u003e \u003cp\u003e4.7 Noninverting Buck–Boost Converters 184\u003c\/p\u003e \u003cp\u003e4.7.1 Cascaded Noninverting Buck–Boost Converters 184\u003c\/p\u003e \u003cp\u003e4.7.2 Four-Transistor Noninverting Buck–Boost Converters 184\u003c\/p\u003e \u003cp\u003e4.8 Tapped-Inductor Buck–Boost Converters 186\u003c\/p\u003e \u003cp\u003e4.8.1 Tapped-Inductor Common-Diode Buck–Boost Converter 186\u003c\/p\u003e \u003cp\u003e4.8.2 Tapped-Inductor Common-Transistor Buck–Boost Converter 187\u003c\/p\u003e \u003cp\u003e4.8.3 Tapped-Inductor Common-Load Buck–Boost Converter 188\u003c\/p\u003e \u003cp\u003e4.8.4 Tapped-Inductor Common-Source Buck–Boost Converter 191\u003c\/p\u003e \u003cp\u003e4.9 Summary 192\u003c\/p\u003e \u003cp\u003eReferences 192\u003c\/p\u003e \u003cp\u003eReview Questions 193\u003c\/p\u003e \u003cp\u003eProblems 193\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Flyback PWM DC–DC Converter 195\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 195\u003c\/p\u003e \u003cp\u003e5.2 Transformers 196\u003c\/p\u003e \u003cp\u003e5.3 DC Analysis of PWM Flyback Converter for CCM 197\u003c\/p\u003e \u003cp\u003e5.3.1 Derivation of PWM Flyback Converter 197\u003c\/p\u003e \u003cp\u003e5.3.2 Circuit Description 197\u003c\/p\u003e \u003cp\u003e5.3.3 Assumptions 199\u003c\/p\u003e \u003cp\u003e5.3.4 Time Interval: 0 \u003ci\u003e\u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eDT \u003c\/i\u003e200\u003c\/p\u003e \u003cp\u003e5.3.5 Time Interval: \u003ci\u003eDT \u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eT \u003c\/i\u003e201\u003c\/p\u003e \u003cp\u003e5.3.6 DC Voltage Transfer Function for CCM 203\u003c\/p\u003e \u003cp\u003e5.3.7 Boundary Between CCM and DCM 204\u003c\/p\u003e \u003cp\u003e5.3.8 Ripple Voltage in Flyback Converter for CCM 205\u003c\/p\u003e \u003cp\u003e5.3.9 Power Losses and Efficiency of Flyback Converter for CCM 207\u003c\/p\u003e \u003cp\u003e5.3.10 DC Voltage Transfer Function of Lossy Converter for CCM 210\u003c\/p\u003e \u003cp\u003e5.3.11 Design of Flyback Converter for CCM 211\u003c\/p\u003e \u003cp\u003e5.4 DC Analysis of PWM Flyback Converter for DCM 214\u003c\/p\u003e \u003cp\u003e5.4.1 Time Interval: 0 \u003ci\u003e\u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eDT \u003c\/i\u003e217\u003c\/p\u003e \u003cp\u003e5.4.2 Time Interval: \u003ci\u003eDT \u0026lt; t \u003c\/i\u003e≤ (\u003ci\u003eD \u003c\/i\u003e+ \u003ci\u003eD\u003c\/i\u003e1)\u003ci\u003eT \u003c\/i\u003e219\u003c\/p\u003e \u003cp\u003e5.4.3 Time Interval: (\u003ci\u003eD \u003c\/i\u003e+ \u003ci\u003eD\u003c\/i\u003e1)\u003ci\u003eT \u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eT \u003c\/i\u003e220\u003c\/p\u003e \u003cp\u003e5.4.4 DC Voltage Transfer Function for DCM 221\u003c\/p\u003e \u003cp\u003e5.4.5 Maximum Magnetizing Inductance for DCM 222\u003c\/p\u003e \u003cp\u003e5.4.6 Ripple Voltage in Flyback Converter for DCM 225\u003c\/p\u003e \u003cp\u003e5.4.7 Power Losses and Efficiency of Flyback Converter for DCM 226\u003c\/p\u003e \u003cp\u003e5.4.8 Design of Flyback Converter for DCM 228\u003c\/p\u003e \u003cp\u003e5.5 Multiple-Output Flyback Converter 232\u003c\/p\u003e \u003cp\u003e5.6 Bidirectional Flyback Converter 237\u003c\/p\u003e \u003cp\u003e5.7 Ringing in Flyback Converter 237\u003c\/p\u003e \u003cp\u003e5.8 Flyback Converter with Passive Dissipative Snubber 240\u003c\/p\u003e \u003cp\u003e5.9 Flyback Converter with Zener Diode Voltage Clamp 240\u003c\/p\u003e \u003cp\u003e5.10 Flyback Converter with Active Clamping 241\u003c\/p\u003e \u003cp\u003e5.11 Two-Transistor Flyback Converter 241\u003c\/p\u003e \u003cp\u003e5.12 Summary 243\u003c\/p\u003e \u003cp\u003eReferences 244\u003c\/p\u003e \u003cp\u003eReview Questions 244\u003c\/p\u003e \u003cp\u003eProblems 245\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Forward PWM DC–DC Converter 246\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 246\u003c\/p\u003e \u003cp\u003e6.2 DC Analysis of PWM Forward Converter for CCM 246\u003c\/p\u003e \u003cp\u003e6.2.1 Derivation of Forward PWM Converter 246\u003c\/p\u003e \u003cp\u003e6.2.2 Time Interval: 0 \u003ci\u003e\u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eDT \u003c\/i\u003e248\u003c\/p\u003e \u003cp\u003e6.2.3 Time Interval: \u003ci\u003eDT \u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eDT \u003c\/i\u003e+ \u003ci\u003etm \u003c\/i\u003e251\u003c\/p\u003e \u003cp\u003e6.2.4 Time Interval: \u003ci\u003eDT \u003c\/i\u003e+ \u003ci\u003etm \u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eT \u003c\/i\u003e253\u003c\/p\u003e \u003cp\u003e6.2.5 Maximum Duty Cycle 253\u003c\/p\u003e \u003cp\u003e6.2.6 Device Stresses 254\u003c\/p\u003e \u003cp\u003e6.2.7 DC Voltage Transfer Function for CCM 255\u003c\/p\u003e \u003cp\u003e6.2.8 Boundary Between CCM and DCM 255\u003c\/p\u003e \u003cp\u003e6.2.9 Ripple Voltage in Forward Converter for CCM 256\u003c\/p\u003e \u003cp\u003e6.2.10 Power Losses and Efficiency of Forward Converter for CCM 258\u003c\/p\u003e \u003cp\u003e6.2.11 DC Voltage Transfer Function of Lossy Converter for CCM 261\u003c\/p\u003e \u003cp\u003e6.2.12 Design of Forward Converter for CCM 262\u003c\/p\u003e \u003cp\u003e6.3 DC Analysis of PWM Forward Converter for DCM 269\u003c\/p\u003e \u003cp\u003e6.3.1 Time Interval: 0 \u003ci\u003e\u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eDT \u003c\/i\u003e269\u003c\/p\u003e \u003cp\u003e6.3.2 Time Interval: \u003ci\u003eDT \u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eDT \u003c\/i\u003e+ \u003ci\u003etm \u003c\/i\u003e272\u003c\/p\u003e \u003cp\u003e6.3.3 Time Interval: \u003ci\u003eDT \u003c\/i\u003e+ \u003ci\u003etm \u0026lt; t \u003c\/i\u003e≤ (\u003ci\u003eD \u003c\/i\u003e+ \u003ci\u003eD\u003c\/i\u003e1)\u003ci\u003eT \u003c\/i\u003e273\u003c\/p\u003e \u003cp\u003e6.3.4 Time Interval: (\u003ci\u003eD \u003c\/i\u003e+ \u003ci\u003eD\u003c\/i\u003e1)\u003ci\u003eT \u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eT \u003c\/i\u003e273\u003c\/p\u003e \u003cp\u003e6.3.5 DC Voltage Transfer Function for DCM 274\u003c\/p\u003e \u003cp\u003e6.3.6 Maximum Inductance for DCM 277\u003c\/p\u003e \u003cp\u003e6.3.7 Power Losses and Efficiency of Forward Converter for DCM 278\u003c\/p\u003e \u003cp\u003e6.3.8 Design of Forward Converter for DCM 280\u003c\/p\u003e \u003cp\u003e6.4 Multiple-Output Forward Converter 288\u003c\/p\u003e \u003cp\u003e6.5 Forward Converter with Synchronous Rectifier 288\u003c\/p\u003e \u003cp\u003e6.6 Forward Converters with Active Clamping 288\u003c\/p\u003e \u003cp\u003e6.7 Two-Switch Forward Converter 290\u003c\/p\u003e \u003cp\u003e6.8 Forward–Flyback Converter 291\u003c\/p\u003e \u003cp\u003e6.9 Summary 292\u003c\/p\u003e \u003cp\u003eReferences 293\u003c\/p\u003e \u003cp\u003eReview Questions 293\u003c\/p\u003e \u003cp\u003eProblems 294\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Half-Bridge PWM DC–DC Converter 296\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 296\u003c\/p\u003e \u003cp\u003e7.2 DC Analysis of PWM Half-Bridge Converter for CCM 296\u003c\/p\u003e \u003cp\u003e7.2.1 Circuit Description 296\u003c\/p\u003e \u003cp\u003e7.2.2 Assumptions 299\u003c\/p\u003e \u003cp\u003e7.2.3 Time Interval: 0 \u003ci\u003e\u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eDT \u003c\/i\u003e299\u003c\/p\u003e \u003cp\u003e7.2.4 Time Interval: \u003ci\u003eDT \u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eT\u003c\/i\u003e∕2 301\u003c\/p\u003e \u003cp\u003e7.2.5 Time Interval: \u003ci\u003eT\u003c\/i\u003e∕2 \u003ci\u003e\u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eT\u003c\/i\u003e∕2 + \u003ci\u003eDT \u003c\/i\u003e303\u003c\/p\u003e \u003cp\u003e7.2.6 Time Interval: \u003ci\u003eT\u003c\/i\u003e∕2 + \u003ci\u003eDT \u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eT \u003c\/i\u003e304\u003c\/p\u003e \u003cp\u003e7.2.7 Device Stresses 304\u003c\/p\u003e \u003cp\u003e7.2.8 DC Voltage Transfer Function of Lossless Half-Bridge Converter for CCM 304\u003c\/p\u003e \u003cp\u003e7.2.9 Boundary Between CCM and DCM 305\u003c\/p\u003e \u003cp\u003e7.2.10 Ripple Voltage in Half-Bridge Converter for CCM 306\u003c\/p\u003e \u003cp\u003e7.2.11 Power Losses and Efficiency of Half-Bridge Converter for CCM 308\u003c\/p\u003e \u003cp\u003e7.2.12 DC Voltage Transfer Function of Lossy Converter for CCM 311\u003c\/p\u003e \u003cp\u003e7.2.13 Design of Half-Bridge Converter for CCM 312\u003c\/p\u003e \u003cp\u003e7.3 DC Analysis of PWM Half-Bridge Converter for DCM 315\u003c\/p\u003e \u003cp\u003e7.3.1 Time Interval: 0 \u003ci\u003e\u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eDT \u003c\/i\u003e315\u003c\/p\u003e \u003cp\u003e7.3.2 Time Interval: \u003ci\u003eDT \u0026lt; t \u003c\/i\u003e≤ (\u003ci\u003eD \u003c\/i\u003e+ \u003ci\u003eD\u003c\/i\u003e1)\u003ci\u003eT \u003c\/i\u003e320\u003c\/p\u003e \u003cp\u003e7.3.3 Time Interval: (\u003ci\u003eD \u003c\/i\u003e+ \u003ci\u003eD\u003c\/i\u003e1)\u003ci\u003eT \u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eT\u003c\/i\u003e∕2 322\u003c\/p\u003e \u003cp\u003e7.3.4 DC Voltage Transfer Function for DCM 322\u003c\/p\u003e \u003cp\u003e7.3.5 Maximum Inductance for DCM 326\u003c\/p\u003e \u003cp\u003e7.4 Summary 326\u003c\/p\u003e \u003cp\u003eReferences 327\u003c\/p\u003e \u003cp\u003eReview Questions 327\u003c\/p\u003e \u003cp\u003eProblems 328\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Full-Bridge PWM DC–DC Converter 330\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 330\u003c\/p\u003e \u003cp\u003e8.2 DC Analysis of PWM Full-Bridge Converter for CCM 330\u003c\/p\u003e \u003cp\u003e8.2.1 Circuit Description 330\u003c\/p\u003e \u003cp\u003e8.2.2 Assumptions 332\u003c\/p\u003e \u003cp\u003e8.2.3 Time Interval: 0 \u003ci\u003e\u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eDT \u003c\/i\u003e332\u003c\/p\u003e \u003cp\u003e8.2.4 Time Interval: \u003ci\u003eDT \u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eT\u003c\/i\u003e∕2 334\u003c\/p\u003e \u003cp\u003e8.2.5 Time Interval: \u003ci\u003eT\u003c\/i\u003e∕2 \u003ci\u003e\u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eT\u003c\/i\u003e∕2 + \u003ci\u003eDT \u003c\/i\u003e336\u003c\/p\u003e \u003cp\u003e8.2.6 Time Interval: \u003ci\u003eT\u003c\/i\u003e∕2 + \u003ci\u003eDT \u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eT \u003c\/i\u003e336\u003c\/p\u003e \u003cp\u003e8.2.7 Device Stresses 337\u003c\/p\u003e \u003cp\u003e8.2.8 DC Voltage Transfer Function of Lossless Full-Wave Converter for CCM 337\u003c\/p\u003e \u003cp\u003e8.2.9 Boundary Between CCM and DCM 338\u003c\/p\u003e \u003cp\u003e8.2.10 Ripple Voltage in Full-Bridge Converter for CCM 339\u003c\/p\u003e \u003cp\u003e8.2.11 Power Losses and Efficiency of Full-Bridge Converter for CCM 340\u003c\/p\u003e \u003cp\u003e8.2.12 DC Voltage Transfer Function of Lossy Converter for CCM 344\u003c\/p\u003e \u003cp\u003e8.2.13 Design of Full-Bridge Converter for CCM 345\u003c\/p\u003e \u003cp\u003e8.3 DC Analysis of PWM Full-Bridge Converter for DCM 351\u003c\/p\u003e \u003cp\u003e8.3.1 Time Interval: 0 \u003ci\u003e\u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eDT \u003c\/i\u003e351\u003c\/p\u003e \u003cp\u003e8.3.2 Time Interval: \u003ci\u003eDT \u0026lt; t \u003c\/i\u003e≤ (\u003ci\u003eD \u003c\/i\u003e+ \u003ci\u003eD\u003c\/i\u003e1)\u003ci\u003eT \u003c\/i\u003e353\u003c\/p\u003e \u003cp\u003e8.3.3 Time Interval: (\u003ci\u003eD \u003c\/i\u003e+ \u003ci\u003eD\u003c\/i\u003e1)\u003ci\u003eT \u0026lt; t \u003c\/i\u003e≤ \u003ci\u003eT\u003c\/i\u003e∕2 355\u003c\/p\u003e \u003cp\u003e8.3.4 DC Voltage Transfer Function for DCM 356\u003c\/p\u003e \u003cp\u003e8.3.5 Maximum Inductance for DCM 359\u003c\/p\u003e \u003cp\u003e8.4 Phase-Controlled Full-Bridge Converter 361\u003c\/p\u003e \u003cp\u003e8.5 Summary 362\u003c\/p\u003e \u003cp\u003eReferences 362\u003c\/p\u003e \u003cp\u003eReview Questions 362\u003c\/p\u003e \u003cp\u003eProblems 363\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Small-Signal Models of PWM Converters for CCM and DCM 365\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 365\u003c\/p\u003e \u003cp\u003e9.2 Assumptions 366\u003c\/p\u003e \u003cp\u003e9.3 Averaged Model of Ideal Switching Network for CCM 366\u003c\/p\u003e \u003cp\u003e9.4 Averaged Values of Switched Resistances 369\u003c\/p\u003e \u003cp\u003e9.5 Model Reduction 375\u003c\/p\u003e \u003cp\u003e9.6 Large-Signal Averaged Model for CCM 377\u003c\/p\u003e \u003cp\u003e9.7 DC and Small-Signal Circuit Linear Models of Switching Network for CCM 381\u003c\/p\u003e \u003cp\u003e9.7.1 Large-Signal Circuit Model of Switching Network for CCM 381\u003c\/p\u003e \u003cp\u003e9.7.2 Linearization of Switching Network Model for CCM 384\u003c\/p\u003e \u003cp\u003e9.8 Block Diagram of Small-signal Model of PWM DC–DC Converters 385\u003c\/p\u003e \u003cp\u003e9.9 Family of PWM Converter Models for CCM 386\u003c\/p\u003e \u003cp\u003e9.10 PWM Small-Signal Switch Model for CCM 389\u003c\/p\u003e \u003cp\u003e9.11 Modeling of Ideal Switching Network for DCM 391\u003c\/p\u003e \u003cp\u003e9.11.1 Relationships Among DC Components for DCM 391\u003c\/p\u003e \u003cp\u003e9.11.2 Small-Signal Model of Ideal Switching Network for DCM 395\u003c\/p\u003e \u003cp\u003e9.12 Averaged Parasitic Resistances for DCM 398\u003c\/p\u003e \u003cp\u003e9.13 Summary 400\u003c\/p\u003e \u003cp\u003eReferences 402\u003c\/p\u003e \u003cp\u003eReview Questions 405\u003c\/p\u003e \u003cp\u003eProblems 405\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Small-Signal Characteristics of Buck Converter for CCM 407\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 407\u003c\/p\u003e \u003cp\u003e10.2 Small-Signal Model of the PWM Buck Converter 407\u003c\/p\u003e \u003cp\u003e10.3 Open-Loop Transfer Functions 408\u003c\/p\u003e \u003cp\u003e10.3.1 Open-Loop Control-to-Output Transfer Function 409\u003c\/p\u003e \u003cp\u003e10.3.2 Delay in Control-to-Output Transfer Function 416\u003c\/p\u003e \u003cp\u003e10.3.3 Open-Loop Input-to-Output Transfer Function 418\u003c\/p\u003e \u003cp\u003e10.3.4 Open-Loop Input Impedance 420\u003c\/p\u003e \u003cp\u003e10.3.5 Open-Loop Output Impedance 423\u003c\/p\u003e \u003cp\u003e10.4 Open-Loop Step Responses 426\u003c\/p\u003e \u003cp\u003e10.4.1 Open-Loop Response of Output Voltage to Step Change in Input Voltage 426\u003c\/p\u003e \u003cp\u003e10.4.2 Open-Loop Response of Output Voltage to Step Change in Duty Cycle 431\u003c\/p\u003e \u003cp\u003e10.4.3 Open-Loop Response of Output Voltage to Step Change in Load Current 433\u003c\/p\u003e \u003cp\u003e10.5 Open-Loop DC Transfer Functions 434\u003c\/p\u003e \u003cp\u003e10.6 Summary 436\u003c\/p\u003e \u003cp\u003eReferences 436\u003c\/p\u003e \u003cp\u003eReview Questions 437\u003c\/p\u003e \u003cp\u003eProblems 438\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Small-Signal Characteristics of Boost Converter for CCM 439\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 439\u003c\/p\u003e \u003cp\u003e11.2 DC Characteristics 439\u003c\/p\u003e \u003cp\u003e11.3 Open-Loop Control-to-Output Transfer Function 440\u003c\/p\u003e \u003cp\u003e11.4 Delay in Open-Loop Control-to-Output Transfer Function 449\u003c\/p\u003e \u003cp\u003e11.5 Open-Loop Audio Susceptibility 451\u003c\/p\u003e \u003cp\u003e11.6 Open-Loop Input Impedance 455\u003c\/p\u003e \u003cp\u003e11.7 Open-Loop Output Impedance 457\u003c\/p\u003e \u003cp\u003e11.8 Open-Loop Step Responses 461\u003c\/p\u003e \u003cp\u003e11.8.1 Open-Loop Response of Output Voltage to Step Change in Input Voltage 461\u003c\/p\u003e \u003cp\u003e11.8.2 Open-Loop Response of Output Voltage to Step Change in Duty Cycle 464\u003c\/p\u003e \u003cp\u003e11.8.3 Open-Loop Response of Output Voltage to Step Change in Load Current 465\u003c\/p\u003e \u003cp\u003e11.9 Summary 467\u003c\/p\u003e \u003cp\u003eReferences 467\u003c\/p\u003e \u003cp\u003eReview Questions 468\u003c\/p\u003e \u003cp\u003eProblems 468\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Voltage-Mode Control of PWM Buck Converter 470\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 470\u003c\/p\u003e \u003cp\u003e12.2 Properties of Negative Feedback 471\u003c\/p\u003e \u003cp\u003e12.3 Stability 474\u003c\/p\u003e \u003cp\u003e12.4 Single-Loop Control of PWM Buck Converter 475\u003c\/p\u003e \u003cp\u003e12.5 Closed-Loop Small-Signal Model of Buck Converter 478\u003c\/p\u003e \u003cp\u003e12.6 Pulse-Width Modulator 478\u003c\/p\u003e \u003cp\u003e12.7 Feedback Network 483\u003c\/p\u003e \u003cp\u003e12.8 Transfer Function of Buck Converter with Modulator and Feedback Network 486\u003c\/p\u003e \u003cp\u003e12.9 Control Circuits 489\u003c\/p\u003e \u003cp\u003e12.9.1 Error Amplifier 489\u003c\/p\u003e \u003cp\u003e12.9.2 Proportional Controller 490\u003c\/p\u003e \u003cp\u003e12.9.3 Integral Controller 492\u003c\/p\u003e \u003cp\u003e12.9.4 Proportional-Integral Controller 493\u003c\/p\u003e \u003cp\u003e12.9.5 Integral-Single-Lead Controller 497\u003c\/p\u003e \u003cp\u003e12.9.6 Loop Gain 504\u003c\/p\u003e \u003cp\u003e12.9.7 Closed-Loop Control-to-Output Voltage Transfer Function 504\u003c\/p\u003e \u003cp\u003e12.9.8 Closed-Loop Input-to-Output Transfer Function 506\u003c\/p\u003e \u003cp\u003e12.9.9 Closed-Loop Input Impedance 508\u003c\/p\u003e \u003cp\u003e12.9.10 Closed-Loop Output Impedance 509\u003c\/p\u003e \u003cp\u003e12.10 Closed-Loop Step Responses 511\u003c\/p\u003e \u003cp\u003e12.10.1 Response to Step Change in Input Voltage 511\u003c\/p\u003e \u003cp\u003e12.10.2 Response to Step Change in Reference Voltage 513\u003c\/p\u003e \u003cp\u003e12.10.3 Closed-Loop Response to Step Change in Load Current 515\u003c\/p\u003e \u003cp\u003e12.10.4 Closed-Loop DC Transfer Functions 515\u003c\/p\u003e \u003cp\u003e12.11 Summary 518\u003c\/p\u003e \u003cp\u003eReferences 519\u003c\/p\u003e \u003cp\u003eReview Questions 519\u003c\/p\u003e \u003cp\u003eProblems 520\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Voltage-Mode Control of Boost Converter 521\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 521\u003c\/p\u003e \u003cp\u003e13.2 Circuit of Boost Converter with Voltage-Mode Control 521\u003c\/p\u003e \u003cp\u003e13.3 Transfer Function of Modulator, Boost Converter Power Stage, and Feedback Network 523\u003c\/p\u003e \u003cp\u003e13.4 Integral-Double-Lead Controller 527\u003c\/p\u003e \u003cp\u003e13.5 Design of Integral-Double-Lead Controller 532\u003c\/p\u003e \u003cp\u003e13.6 Loop Gain 536\u003c\/p\u003e \u003cp\u003e13.7 Closed-Loop Control-to-Output Voltage Transfer Function 537\u003c\/p\u003e \u003cp\u003e13.8 Closed-Loop Audio Susceptibility 539\u003c\/p\u003e \u003cp\u003e13.9 Closed-Loop Input Impedance 539\u003c\/p\u003e \u003cp\u003e13.10 Closed-Loop Output Impedance 542\u003c\/p\u003e \u003cp\u003e13.11 Closed-Loop Step Responses 544\u003c\/p\u003e \u003cp\u003e13.11.1 Closed-Loop Response to Step Change in Input Voltage 544\u003c\/p\u003e \u003cp\u003e13.11.2 Closed-Loop Response to Step Change in Reference Voltage 547\u003c\/p\u003e \u003cp\u003e13.11.3 Closed-Loop Response to Step Change in Load Current 548\u003c\/p\u003e \u003cp\u003e13.12 Closed-Loop DC Transfer Functions 549\u003c\/p\u003e \u003cp\u003e13.13 Summary 552\u003c\/p\u003e \u003cp\u003eReferences 552\u003c\/p\u003e \u003cp\u003eReview Questions 552\u003c\/p\u003e \u003cp\u003eProblems 553\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Current-Mode Control 554\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction 554\u003c\/p\u003e \u003cp\u003e14.2 Principle of Operation of PWM Converters with Peak CMC 555\u003c\/p\u003e \u003cp\u003e14.3 Relationship Between Duty Cycle and Inductor-Current Slopes 559\u003c\/p\u003e \u003cp\u003e14.4 Instability of Closed-Current Loop 560\u003c\/p\u003e \u003cp\u003e14.5 Slope Compensation 564\u003c\/p\u003e \u003cp\u003e14.5.1 Analysis of Slope Compensation in Time Domain 564\u003c\/p\u003e \u003cp\u003e14.5.2 Boundary of Slope Compensation for Buck and Buck–Boost Converters 569\u003c\/p\u003e \u003cp\u003e14.5.3 Boundary Slope Compensation for Boost Converter 570\u003c\/p\u003e \u003cp\u003e14.6 Sample-and-Hold Effect on Current Loop 570\u003c\/p\u003e \u003cp\u003e14.6.1 Natural Response of Inductor Current to Small Perturbation in Closed-Current Loop 572\u003c\/p\u003e \u003cp\u003e14.6.2 Forced Response of Inductor Current to Step Change in Control Voltage in Closed-Current Loop 575\u003c\/p\u003e \u003cp\u003e14.6.3 Relationship Between \u003ci\u003es\u003c\/i\u003e-Domain and \u003ci\u003ez\u003c\/i\u003e-Domain 577\u003c\/p\u003e \u003cp\u003e14.6.4 Transfer Function of Closed-Current Loop in \u003ci\u003ez\u003c\/i\u003e-Domain 578\u003c\/p\u003e \u003cp\u003e14.7 Closed-Loop Control Voltage-to-Inductor Current Transfer Function in \u003ci\u003es\u003c\/i\u003e-Domain 580\u003c\/p\u003e \u003cp\u003e14.7.1 Approximation of \u003ci\u003eH\u003csub\u003eicl \u003c\/sub\u003e\u003c\/i\u003eby Rational Transfer Function 582\u003c\/p\u003e \u003cp\u003e14.7.2 Step Responses of Closed-Inner Loop 588\u003c\/p\u003e \u003cp\u003e14.8 Loop Gain of Current Loop 588\u003c\/p\u003e \u003cp\u003e14.8.1 Loop Gain of Inner Loop in \u003ci\u003ez\u003c\/i\u003e-Domain 588\u003c\/p\u003e \u003cp\u003e14.8.2 Loop Gain of Inner Loop in \u003ci\u003es\u003c\/i\u003e-Domain 590\u003c\/p\u003e \u003cp\u003e14.9 Gain-Crossover Frequency of Inner Loop 595\u003c\/p\u003e \u003cp\u003e14.10 Phase Margin of Inner Loop 596\u003c\/p\u003e \u003cp\u003e14.11 Maximum Duty Cycle for Converters without Slope Compensation 598\u003c\/p\u003e \u003cp\u003e14.12 Maximum Duty Cycle for Converters with Slope Compensation 600\u003c\/p\u003e \u003cp\u003e14.13 Minimum Slope Compensation for Buck and Buck–Boost Converter 605\u003c\/p\u003e \u003cp\u003e14.14 Minimum Slope Compensation for Boost Converter 607\u003c\/p\u003e \u003cp\u003e14.15 Error Voltage-to-Duty Cycle Transfer Function 610\u003c\/p\u003e \u003cp\u003e14.16 Closed-Loop Control Voltage-to-Duty Cycle Transfer Function of Current Loop 614\u003c\/p\u003e \u003cp\u003e14.17 Alternative Representation of Current Loop 618\u003c\/p\u003e \u003cp\u003e14.18 Current Loop with Disturbances 618\u003c\/p\u003e \u003cp\u003e14.18.1 Modified Approximation of Current Loop 619\u003c\/p\u003e \u003cp\u003e14.19 Voltage Loop of PWM Converters with Current-Mode Control 624\u003c\/p\u003e \u003cp\u003e14.19.1 Control-to-Output Transfer Function for Buck Converter 624\u003c\/p\u003e \u003cp\u003e14.19.2 Block Diagram of Power Stages of PWM Converters 627\u003c\/p\u003e \u003cp\u003e14.19.3 Closed-Voltage Loop Transfer Function of PWM Converters with Current-Mode Control 628\u003c\/p\u003e \u003cp\u003e14.19.4 Closed-Loop Audio Susceptibility of PWM Converters with Current-Mode Control 628\u003c\/p\u003e \u003cp\u003e14.19.5 Closed-Loop Output Impedance of PWM Converters with Current-Mode Control 630\u003c\/p\u003e \u003cp\u003e14.20 Feedforward Gains in PWM Converters with Current-Mode Control without Slope Compensation 631\u003c\/p\u003e \u003cp\u003e14.21 Feedforward Gains in PWM Converters with Current-Mode Control and Slope Compensation 634\u003c\/p\u003e \u003cp\u003e14.22 Control-to-Output Voltage Transfer Function of Inner Loop with Feedforward Gains 636\u003c\/p\u003e \u003cp\u003e14.23 Audio-Susceptibility of Inner Loop with Feedforward Gains 637\u003c\/p\u003e \u003cp\u003e14.24 Closed-Loop Transfer Functions with Feedforward Gains 638\u003c\/p\u003e \u003cp\u003e14.25 Slope Compensation by Adding a Ramp to Inductor Current Waveform 638\u003c\/p\u003e \u003cp\u003e14.26 Relationships for Constant-Frequency Current-Mode On-Time Control 639\u003c\/p\u003e \u003cp\u003e14.27 Summary 639\u003c\/p\u003e \u003cp\u003eReferences 640\u003c\/p\u003e \u003cp\u003eReview Questions 644\u003c\/p\u003e \u003cp\u003eProblems 644\u003c\/p\u003e \u003cp\u003e14.28 Appendix: Sample-and-Hold Modeling 645\u003c\/p\u003e \u003cp\u003e14.28.1 Sampler of the Control Voltage 645\u003c\/p\u003e \u003cp\u003e14.28.2 Zero-Order Hold of Inductor Current 648\u003c\/p\u003e \u003cp\u003e14.28.3 Approximations of \u003ci\u003ee\u003csup\u003esTs \u003c\/sup\u003e\u003c\/i\u003e650\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Current-Mode Control of Boost Converter 653\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Introduction 653\u003c\/p\u003e \u003cp\u003e15.2 Open-Loop Small-Signal Transfer Functions 653\u003c\/p\u003e \u003cp\u003e15.2.1 Open-Loop Duty Cycle-to-Inductor Current Transfer Function 653\u003c\/p\u003e \u003cp\u003e15.2.2 High-Frequency Open-Loop Duty Cycle-to-Inductor Current Transfer Function 659\u003c\/p\u003e \u003cp\u003e15.2.3 Open-Loop Input Voltage-to-Inductor Current Transfer Function 660\u003c\/p\u003e \u003cp\u003e15.2.4 Open-Loop Inductor-to-Output Current Transfer Function 665\u003c\/p\u003e \u003cp\u003e15.3 Open-Loop Step Responses of Inductor Current 667\u003c\/p\u003e \u003cp\u003e15.3.1 Open-Loop Response of Inductor Current to Step Change in Input Voltage 667\u003c\/p\u003e \u003cp\u003e15.3.2 Open-Loop Response of the Inductor Current to Step Change in the Duty Cycle 670\u003c\/p\u003e \u003cp\u003e15.3.3 Open-Loop Response of Inductor Current to Step Change in Load Current 672\u003c\/p\u003e \u003cp\u003e15.4 Closed-Current-Loop Transfer Functions 675\u003c\/p\u003e \u003cp\u003e15.4.1 Forward Gain 675\u003c\/p\u003e \u003cp\u003e15.4.2 Loop Gain of Current Loop 675\u003c\/p\u003e \u003cp\u003e15.4.3 Closed-Loop Gain of Current Loop 675\u003c\/p\u003e \u003cp\u003e15.4.4 Control-to-Output Transfer Function 677\u003c\/p\u003e \u003cp\u003e15.4.5 Input Voltage-to-Duty Cycle Transfer Function 684\u003c\/p\u003e \u003cp\u003e15.4.6 Load Current-to-Duty Cycle Transfer Function 688\u003c\/p\u003e \u003cp\u003e15.4.7 Output Impedance of Closed-Current Loop 690\u003c\/p\u003e \u003cp\u003e15.5 Closed-Voltage-Loop Transfer Functions 695\u003c\/p\u003e \u003cp\u003e15.5.1 Control-to-Output Transfer Function 695\u003c\/p\u003e \u003cp\u003e15.5.2 Control Voltage-to-Feedback Voltage Transfer Function 695\u003c\/p\u003e \u003cp\u003e15.5.3 Loop Gain of Voltage Loop 697\u003c\/p\u003e \u003cp\u003e15.5.4 Closed-Loop Gain of Voltage Loop 701\u003c\/p\u003e \u003cp\u003e15.5.5 Closed-Loop Audio Susceptibility with Integral Controller 703\u003c\/p\u003e \u003cp\u003e15.5.6 Closed-Loop Output Impedance with Integral Controller 704\u003c\/p\u003e \u003cp\u003e15.6 Closed-Loop Step Responses 706\u003c\/p\u003e \u003cp\u003e15.6.1 Closed-Loop Response of Output Voltage to Step Change in Input Voltage 706\u003c\/p\u003e \u003cp\u003e15.6.2 Closed-Loop Response of Output Voltage to Step Change in Load Current 708\u003c\/p\u003e \u003cp\u003e15.6.3 Closed-Loop Response of Output Voltage to Step Change in Reference Voltage 708\u003c\/p\u003e \u003cp\u003e15.7 Closed-Loop DC Transfer Functions 710\u003c\/p\u003e \u003cp\u003e15.8 Summary 711\u003c\/p\u003e \u003cp\u003eReferences 711\u003c\/p\u003e \u003cp\u003eReview Questions 712\u003c\/p\u003e \u003cp\u003eProblems 712\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Open-Loop Small-Signal Characteristics of PWM Boost Converter for DCM 713\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction 713\u003c\/p\u003e \u003cp\u003e16.2 Small-Signal Model of Boost Converter for DCM 713\u003c\/p\u003e \u003cp\u003e16.3 Open-Loop Control-to-Output Transfer Function 716\u003c\/p\u003e \u003cp\u003e16.4 Open-Loop Input-to-Output Voltage Transfer Function 719\u003c\/p\u003e \u003cp\u003e16.5 Open-Loop Input Impedance 724\u003c\/p\u003e \u003cp\u003e16.6 Open-Loop Output Impedance 725\u003c\/p\u003e \u003cp\u003e16.7 Step Responses of Output Voltage of Boost Converter for DCM 728\u003c\/p\u003e \u003cp\u003e16.7.1 Response of Output Voltage to Step Change in Input Voltage 728\u003c\/p\u003e \u003cp\u003e16.7.2 Response of Output Voltage to Step Change in Duty Cycle 730\u003c\/p\u003e \u003cp\u003e16.7.3 Response of Output Voltage to Step Change in Load Current 730\u003c\/p\u003e \u003cp\u003e16.8 Open-Loop Duty Cycle-to-Inductor Current Transfer Function 731\u003c\/p\u003e \u003cp\u003e16.9 Open-Loop Input Voltage-to-Inductor Current Transfer Function 735\u003c\/p\u003e \u003cp\u003e16.10 Open-Loop Output Current-to-Inductor Current Transfer Function 735\u003c\/p\u003e \u003cp\u003e16.11 Step Responses of Inductor Current of Boost Converter for DCM 738\u003c\/p\u003e \u003cp\u003e16.11.1 Step Response of Inductor Current to Step Change in Input Voltage 738\u003c\/p\u003e \u003cp\u003e16.11.2 Step Response of Inductor Current to Step Change in Duty Cycle 740\u003c\/p\u003e \u003cp\u003e16.11.3 Step Response of Inductor Current to Step Change in Load Current 741\u003c\/p\u003e \u003cp\u003e16.12 DC Characteristics of Boost Converter for DCM 742\u003c\/p\u003e \u003cp\u003e16.12.1 DC-to-DC Voltage Transfer Function of Lossless Boost Converter for DCM 742\u003c\/p\u003e \u003cp\u003e16.12.2 DC-to-DC Voltage Transfer Function of Lossy Boost Converter for DCM 743\u003c\/p\u003e \u003cp\u003e16.12.3 Efficiency of Boost Converter for DCM 745\u003c\/p\u003e \u003cp\u003e16.13 Summary 745\u003c\/p\u003e \u003cp\u003eReferences 745\u003c\/p\u003e \u003cp\u003eReview Questions 746\u003c\/p\u003e \u003cp\u003eProblems 746\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Silicon and Silicon-Carbide Power Diodes 747\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Introduction 747\u003c\/p\u003e \u003cp\u003e17.2 Electronic Power Switches 747\u003c\/p\u003e \u003cp\u003e17.3 Atom 748\u003c\/p\u003e \u003cp\u003e17.4 Electron and Hole Effective Mass 749\u003c\/p\u003e \u003cp\u003e17.5 Semiconductors 750\u003c\/p\u003e \u003cp\u003e17.6 Intrinsic Semiconductors 751\u003c\/p\u003e \u003cp\u003e17.7 Extrinsic Semiconductors 756\u003c\/p\u003e \u003cp\u003e17.7.1 n-Type Semiconductor 756\u003c\/p\u003e \u003cp\u003e17.7.2 p-Type Semiconductor 759\u003c\/p\u003e \u003cp\u003e17.7.3 Maximum Operating Temperature 761\u003c\/p\u003e \u003cp\u003e17.8 Wide Band Gap Semiconductors 762\u003c\/p\u003e \u003cp\u003e17.9 Physical Structure of Junction Diodes 764\u003c\/p\u003e \u003cp\u003e17.9.1 Formation of Depletion Layer 765\u003c\/p\u003e \u003cp\u003e17.9.2 Charge Transport 767\u003c\/p\u003e \u003cp\u003e17.10 Static \u003ci\u003eI\u003c\/i\u003e–\u003ci\u003eV \u003c\/i\u003eDiode Characteristic 768\u003c\/p\u003e \u003cp\u003e17.11 Breakdown Voltage of Junction Diodes 772\u003c\/p\u003e \u003cp\u003e17.11.1 Depletion-Layer Width 773\u003c\/p\u003e \u003cp\u003e17.11.2 Electric Field Intensity Distribution 775\u003c\/p\u003e \u003cp\u003e17.11.3 Avalanche Breakdown Voltage 779\u003c\/p\u003e \u003cp\u003e17.11.4 Punch-Through Breakdown Voltage 781\u003c\/p\u003e \u003cp\u003e17.11.5 Edge Terminations 782\u003c\/p\u003e \u003cp\u003e17.12 Capacitances of Junction Diodes 784\u003c\/p\u003e \u003cp\u003e17.12.1 Junction Capacitance 784\u003c\/p\u003e \u003cp\u003e17.12.2 Diffusion Capacitance 787\u003c\/p\u003e \u003cp\u003e17.13 Reverse Recovery of pn Junction Diodes 789\u003c\/p\u003e \u003cp\u003e17.13.1 Qualitative Description 789\u003c\/p\u003e \u003cp\u003e17.13.2 Reverse Recovery in Resistive Circuits 790\u003c\/p\u003e \u003cp\u003e17.13.3 Charge-Continuity Equation 793\u003c\/p\u003e \u003cp\u003e17.13.4 Reverse Recovery in Inductive Circuits 796\u003c\/p\u003e \u003cp\u003e17.14 Schottky Diodes 798\u003c\/p\u003e \u003cp\u003e17.14.1 Static \u003ci\u003eI\u003c\/i\u003e–\u003ci\u003eV \u003c\/i\u003eCharacteristic of Schottky Diodes 801\u003c\/p\u003e \u003cp\u003e17.14.2 Breakdown Voltages of Schottky Diodes 802\u003c\/p\u003e \u003cp\u003e17.14.3 Junction Capacitance of Schottky Diodes 802\u003c\/p\u003e \u003cp\u003e17.14.4 Switching Characteristics of Schottky Diodes 802\u003c\/p\u003e \u003cp\u003e17.15 Solar Cells 806\u003c\/p\u003e \u003cp\u003e17.16 Light-Emitting Diodes 809\u003c\/p\u003e \u003cp\u003e17.17 SPICE Model of Diodes 810\u003c\/p\u003e \u003cp\u003e17.18 Summary 811\u003c\/p\u003e \u003cp\u003eReferences 815\u003c\/p\u003e \u003cp\u003eReview Questions 816\u003c\/p\u003e \u003cp\u003eProblems 817\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Silicon and Silicon-Carbide Power MOSFETs 819\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Introduction 819\u003c\/p\u003e \u003cp\u003e18.2 Integrated MOSFETs 819\u003c\/p\u003e \u003cp\u003e18.3 Physical Structure of Power MOSFETs 819\u003c\/p\u003e \u003cp\u003e18.4 Principle of Operation of Power MOSFETs 824\u003c\/p\u003e \u003cp\u003e18.4.1 Cutoff Region 824\u003c\/p\u003e \u003cp\u003e18.4.2 Formation of MOSFET Channel 824\u003c\/p\u003e \u003cp\u003e18.4.3 Linear Region 824\u003c\/p\u003e \u003cp\u003e18.4.4 Saturation Region 825\u003c\/p\u003e \u003cp\u003e18.4.5 Antiparallel Diode 825\u003c\/p\u003e \u003cp\u003e18.5 Derivation of Power MOSFET Characteristics 826\u003c\/p\u003e \u003cp\u003e18.5.1 Ohmic Region 826\u003c\/p\u003e \u003cp\u003e18.5.2 Pinch-off Region 829\u003c\/p\u003e \u003cp\u003e18.5.3 Channel-Length Modulation 830\u003c\/p\u003e \u003cp\u003e18.6 Power MOSFET Characteristics 831\u003c\/p\u003e \u003cp\u003e18.7 Mobility of Charge Carriers 833\u003c\/p\u003e \u003cp\u003e18.7.1 Effect of Doping Concentration on Mobility 834\u003c\/p\u003e \u003cp\u003e18.7.2 Effect of Temperature on Mobility 836\u003c\/p\u003e \u003cp\u003e18.7.3 Effect of Electric Field on Mobility 840\u003c\/p\u003e \u003cp\u003e18.8 Short-Channel Effects 846\u003c\/p\u003e \u003cp\u003e18.8.1 Ohmic Region 846\u003c\/p\u003e \u003cp\u003e18.8.2 Pinch-off Region 847\u003c\/p\u003e \u003cp\u003e18.9 Aspect Ratio of Power MOSFETs 848\u003c\/p\u003e \u003cp\u003e18.10 Breakdown Voltage of Power MOSFETs 850\u003c\/p\u003e \u003cp\u003e18.11 Gate Oxide Breakdown Voltage of Power MOSFETs 852\u003c\/p\u003e \u003cp\u003e18.12 Specific On-Resistance 852\u003c\/p\u003e \u003cp\u003e18.13 Figures-of-Merit of Semiconductors 855\u003c\/p\u003e \u003cp\u003e18.14 On-Resistance of Power MOSFETs 857\u003c\/p\u003e \u003cp\u003e18.14.1 Channel Resistance 857\u003c\/p\u003e \u003cp\u003e18.14.2 Accumulation Region Resistance 857\u003c\/p\u003e \u003cp\u003e18.14.3 Neck Region Resistance 858\u003c\/p\u003e \u003cp\u003e18.14.4 Drift Region Resistance 859\u003c\/p\u003e \u003cp\u003e18.15 Capacitances of Power MOSFETs 862\u003c\/p\u003e \u003cp\u003e18.15.1 Gate-to-Source Capacitance 862\u003c\/p\u003e \u003cp\u003e18.15.2 Drain-to-Source Capacitance 864\u003c\/p\u003e \u003cp\u003e18.15.3 Gate-to-Drain Capacitance 864\u003c\/p\u003e \u003cp\u003e18.16 Switching Waveforms 875\u003c\/p\u003e \u003cp\u003e18.17 SPICE Model of Power MOSFETs 877\u003c\/p\u003e \u003cp\u003e18.18 IGBTs 879\u003c\/p\u003e \u003cp\u003e18.19 Heat Sinks 880\u003c\/p\u003e \u003cp\u003e18.20 Summary 886\u003c\/p\u003e \u003cp\u003eReferences 888\u003c\/p\u003e \u003cp\u003eReview Questions 888\u003c\/p\u003e \u003cp\u003eProblems 889\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Electromagnetic Compatibility 891\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 Introduction 891\u003c\/p\u003e \u003cp\u003e19.2 Definition of EMI 891\u003c\/p\u003e \u003cp\u003e19.3 Definition of EMC 892\u003c\/p\u003e \u003cp\u003e19.4 EMI Immunity 892\u003c\/p\u003e \u003cp\u003e19.5 EMI Susceptibility 893\u003c\/p\u003e \u003cp\u003e19.6 Classification of EMI 893\u003c\/p\u003e \u003cp\u003e19.7 Sources of EMI 895\u003c\/p\u003e \u003cp\u003e19.8 Safety Standards 896\u003c\/p\u003e \u003cp\u003e19.9 EMC Standards 896\u003c\/p\u003e \u003cp\u003e19.10 Near Field and Far Field 897\u003c\/p\u003e \u003cp\u003e19.11 Techniques of EMI Reduction 897\u003c\/p\u003e \u003cp\u003e19.12 Insertion Loss 898\u003c\/p\u003e \u003cp\u003e19.13 EMI Filters 898\u003c\/p\u003e \u003cp\u003e19.14 Feed-Through Capacitors 900\u003c\/p\u003e \u003cp\u003e19.15 EMI Shielding 900\u003c\/p\u003e \u003cp\u003e19.16 Interconnections 902\u003c\/p\u003e \u003cp\u003e19.17 Summary 903\u003c\/p\u003e \u003cp\u003eReferences 903\u003c\/p\u003e \u003cp\u003eReview Questions 903\u003c\/p\u003e \u003cp\u003eProblem 904\u003c\/p\u003e \u003cp\u003eA Introduction to SPICE 907\u003c\/p\u003e \u003cp\u003eB Introduction to MATLAB\u003csup\u003e®\u003c\/sup\u003e 910\u003c\/p\u003e \u003cp\u003eC Physical Constants 915\u003c\/p\u003e \u003cp\u003eAnswers to Problems 917\u003c\/p\u003e \u003cp\u003eIndex 925\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eMarian K. Kazimierczuk\u003c\/b\u003e \u003ci\u003eWright State University, Dayton, Ohio, USA\u003c\/i\u003e   \u003c\/p\u003e\u003cp\u003e\u003cb\u003ePulse-Width Modulated DC-DC Power Converters\u003c\/b\u003e Second Edition \u003c\/p\u003e\u003cp\u003ePWM DC–DC power converter technology underpins many energy conversion systems including renewable energy circuits, active power factor correctors, battery chargers, portable devices, and LED drivers. \u003c\/p\u003e\u003cp\u003eFollowing the success of \u003ci\u003ePulse-Width Modulated DC–DC Power Converters\u003c\/i\u003e, this second edition has been thoroughly revised and expanded to cover the latest challenges and advances in the field. \u003c\/p\u003e\u003cp\u003eKey features of second edition: \u003c\/p\u003e\u003cul\u003e \u003cli\u003eFour new chapters, detailing the latest advances in power conversion, focus on: small-signal model and dynamic characteristics of the buck converter in continuous conduction mode; voltage-mode control of buck converter; small-signal model and characteristics of the boost converter in the discontinuous conduction mode and electromagnetic compatibility EMC.\u003c\/li\u003e \u003cli\u003eProvides readers with a solid understanding of the principles of operation,\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989890154725,"sku":"NP9781119009542","price":169.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119009542.jpg?v=1761785808","url":"https:\/\/k12savings.com\/es\/products\/pulse-width-modulated-dc-dc-power-converters-isbn-9781119009542","provider":"K12savings","version":"1.0","type":"link"}