Table Of Content

Switching Power Supplies A–Z This pageintentionallyleftblank Switching Power Supplies A–Z Sanjaya Maniktala AMSTERDAM(cid:129)BOSTON(cid:129)HEIDELBERG(cid:129)LONDON NEWYORK(cid:129)OXFORD(cid:129)PARIS(cid:129)SANDIEGO SANFRANCISCO(cid:129)SINGAPORE(cid:129)SYDNEY(cid:129)TOKYO NewnesisanimprintofElsevier NewnesisanimprintofElsevier TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UK 225WymanStreet,Waltham,MA02451,USA Copyrightr2012ElsevierLtd.Allrightsreserved Nopartofthispublicationmaybereproduced,storedinaretrievalsystemortransmittedinanyformorbyany meanselectronic,mechanical,photocopying,recordingorotherwisewithoutthepriorwrittenpermissionofthe publisher. 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TypesetbyMPSLimited,aMacmillanCompany,Chennai,India www.macmillansolutions.com PrintedinGreatBritain 11 12 13 14 15 10 9 8 7 6 5 4 Contents Preface.................................................................................................................xv Acknowledgments..................................................................................................xix Chapter 1: The Principles of Switching Power Conversion.......................................1 Introduction..................................................................................................................1 Overview and Basic Terminology...............................................................................4 Efficiency.........................................................................................................4 Linear Regulators............................................................................................5 Achieving High Efficiency through Switching..............................................7 Basic Types of Semiconductor Switches........................................................8 Semiconductor Switches Are Not “Perfect”.................................................10 Achieving High Efficiency through the Use of Reactive Components.......11 Early RC-Based Switching Regulators.........................................................12 LC-Based Switching Regulators...................................................................13 The Role of Parasitics...................................................................................14 Switching at High Frequencies.....................................................................16 Reliability, Life, and Thermal Management.................................................17 Stress Derating...............................................................................................19 Advances in Technology...............................................................................20 Understanding the Inductor........................................................................................21 Capacitors/Inductors and Voltage/Current....................................................21 The Inductor and Capacitor Charging/Discharging Circuits........................22 The Law of Conservation of Energy............................................................24 The Charging Phase and the Concept of Induced Voltage..........................24 The Effect of the Series Resistance on the Time Constant..........................26 The Inductor Charging Circuit with R50 and the “Inductor Equation”....28 The Duality Principle....................................................................................29 The “Capacitor Equation”.............................................................................30 The Inductor Discharge Phase......................................................................31 Flyback Energy and Freewheeling Current..................................................32 Current Must Be Continuous, Its Slope Need Not Be.................................32 The Voltage Reversal Phenomenon..............................................................34 v vi Contents A Steady State in Power Conversion and the Different Operating Modes........................................................................................35 The Voltseconds Law, Inductor Reset and Converter Duty Cycle..............39 Using and Protecting Semiconductor Switches............................................41 Evolution of Switching Topologies...........................................................................43 Controlling the Induced Voltage Spike by Diversion through a Diode.........................................................................................43 Achieving a Steady State and Deriving Useful Energy...............................45 The Buck-Boost Converter............................................................................46 Ground-Referencing Our Circuits.................................................................48 The Buck-Boost Configurations....................................................................48 The Switching Node......................................................................................49 Analyzing the Buck-Boost............................................................................50 Properties of the Buck-Boost........................................................................50 Why Three Basic Topologies Only?.............................................................52 The Boost Topology......................................................................................53 The Buck Topology.......................................................................................57 Advanced Converter Design.........................................................................59 Chapter 2:DC(cid:1)DC Converter Design and Magnetics..........................................61 DC Transfer Functions...............................................................................................62 The DC Level and the “Swing” of the Inductor Current Waveform........................63 Defining the AC, DC, and Peak Currents.................................................................66 Understanding the AC, DC, and Peak Currents........................................................68 Defining the “Worst-Case” Input Voltage.................................................................70 The Current Ripple Ratio “r”....................................................................................72 Relating r to the Inductance.......................................................................................73 The Optimum Value of r...........................................................................................74 Do We Mean Inductor? or Inductance?.....................................................................76 How Inductance and Inductor Size Depend on Frequency..........................77 How Inductance and Inductor Size Depend on Load Current..................................77 How Vendors Specify the Current Rating of an Off-the-shelf Inductor and How to Select It..............................................................................................78 What Is the Inductor Current Rating We Need to Consider for a Given Application?........................................................................................79 The Spread and Tolerance of the Current Limit.......................................................83 Worked Example (1)..................................................................................................86 Current Limit Considerations in Setting r....................................................87 Continuous Conduction Mode Considerations in Fixing r...........................88 Setting r to Values Higher than 0.4 when Using Low-ESR Capacitors..................................................................................91 Setting r to Avoid Device “Eccentricities”..................................................91 Setting r to Avoid Subharmonic Oscillations...............................................93 Contents vii Quick Selection of Inductors Using “L3I” and “Load Scaling” Rules.................................................................................96 Worked Examples (2, 3, and 4).................................................................................97 The Current Ripple Ratio r in Forced Continuous Conduction Mode (“FCCM”)........................................................................................99 Basic Magnetic Definitions.........................................................................100 Worked Example (5) — When Not to Increase the Number of Turns..................103 The “Field Ripple Ratio”............................................................................104 The Voltage-Dependent Equation in Terms of Voltseconds (MKS Units)...................................................................104 CGS Units....................................................................................................105 The Voltage-Dependent Equation in Terms of Voltseconds (CGS Units)....................................................................105 Core Loss.....................................................................................................105 Worked Example (6) — Characterizing an Off-the-Shelf Inductor in a Specific Application......................................................................................106 Estimating Requirements............................................................................107 Current Ripple Ratio...................................................................................109 Peak Current................................................................................................110 Flux Density................................................................................................110 Copper Loss.................................................................................................111 Core Loss.....................................................................................................112 DC(cid:1)DC Converter Design and Magnetics.................................................113 Temperature Rise.........................................................................................113 Calculating “Other” Worst-case Stresses and their Selection Criteria...................114 Worst-case Core Loss..................................................................................114 Worst-case Diode Dissipation.....................................................................115 Note that the General Diode Selection Procedure is as Follows...............116 Worst-case Switch Dissipation....................................................................116 Note that the General Switch Selection Procedure is as Follows..............118 Worst-case Output Capacitor Dissipation...................................................118 Note that the General Output Capacitor Selection Procedure is as Follows.............................................................................................118 Worst-case Input Capacitor Dissipation.....................................................119 Note that the General Input Capacitor Selection Procedure is as Follows.............................................................................................120 Chapter 3: Off-Line Converter Design and Magnetics........................................123 Flyback Converter Magnetics..................................................................................124 Polarity of Windings in a Transformer.......................................................124 Transformer Action in a Flyback and Its Duty Cycle................................126 The Equivalent Buck-Boost Models...........................................................129 The Current Ripple Ratio for the Flyback..................................................131 The Leakage Inductance.............................................................................132 viii Contents Zener Clamp Dissipation.............................................................................132 Secondary-Side Leakages also Affect the Primary Side............................133 Measuring the Effective Primary-side Leakage Inductance.......................134 Worked Example (7) — Designing the Flyback Transformer...................135 Selecting the Wire Gauge and Foil Thickness...........................................142 Forward Converter Magnetics.....................................................................146 Duty Cycle...................................................................................................146 Worst-Case Input Voltage End...................................................................149 Window Utilization.....................................................................................151 Relating Core Size to Its Power Throughput..............................................152 Worked Example (8) — Designing the Forward Transformer..................154 Thermal Resistance.....................................................................................154 Chapter 4:The Topology FAQ........................................................................171 Questions and Answers............................................................................................171 Chapter 5:Advanced Magnetics: Optimal Core Selection...................................195 Part 1: Energy Transfer Principles...........................................................................195 Overview of Topologies..............................................................................195 The Energy Transfer Charts........................................................................203 Peak Energy Storage Requirements............................................................210 Calculating Inductance Based on Desired Current Ripple.........................214 Part 2: Energy to Core Sizes....................................................................................217 Magnetic Circuits and the Effective Length of Gapped Cores..................217 Stored Energy in Gapped Cores and the z-Factor......................................219 Energy of a Gapped Core in Terms of the Volume of the Core...............223 Part 3: Toroids to E-Cores.......................................................................................226 Part 4: More on AC(cid:1)DC Flyback Transformer Design.........................................229 Part 5: More on AC(cid:1)DC Forward Converter Transformer Design.......................233 Chapter 6:Component Ratings, Stresses, Reliability, and Life ............................241 Introduction..............................................................................................................241 Stresses and Derating...............................................................................................242 Part 1: Ratings and Derating in Power Converter Applications.............................245 Operating Environments..............................................................................246 Component Ratings and Stress Factors in Power Supplies........................250 Mechanical Stresses.....................................................................................263 Part 2: MTBF, Failure Rate, Warranty Costs, and Life..........................................264 MTBF...........................................................................................................264 Warranty Costs............................................................................................268 Life Expectancy and Failure Criteria..........................................................269 Reliability Prediction Methods...................................................................270 Demonstrated Reliability Testing (DRT)....................................................272 Accelerated Life Testing.............................................................................273 Part 3: Life Prediction of Aluminum Electrolytic Capacitors................................275 Contents ix Chapter 7:Optimal Power Components Selection..............................................281 Overview..................................................................................................................281 The Key Stresses in Power Converters....................................................................281 Waveforms and Peak Voltage Stresses for Different Topologies...........................282 The Importance of RMS and Average Currents......................................................288 Calculation of RMS and Average Currents for Diode, FET, and Inductor............289 Calculation of RMS and Average Currents for Capacitors.....................................292 The Stress Spiders....................................................................................................298 Stress Reduction in AC(cid:1)DC Converters................................................................302 RCD Clamps versus RCD Snubbers........................................................................304 Chapter 8: Conduction and Switching Losses.....................................................311 Switching a Resistive Load......................................................................................312 Switching an Inductive Load...................................................................................316 Switching Losses and Conduction Loss..................................................................319 A Simplified Model of the MOSFET for Studying Inductive Switching Losses..................................................................................................320 The Parasitic Capacitances Expressed in an Alternate System..............................322 Gate Threshold Voltage...........................................................................................324 The Turn-On Transition...........................................................................................324 The Turn-Off Transition..........................................................................................328 Gate Charge Factors.................................................................................................330 Worked Example......................................................................................................332 Turn-On.......................................................................................................333 Turn-Off.......................................................................................................335 Applying the Switching Loss Analysis to Switching Topologies...........................336 Worst-Case Input Voltage for Switching Losses....................................................337 How Switching Losses Vary with the Parasitic Capacitances................................338 Optimizing Driver Capability vis-a`-vis MOSFET Characteristics.........................340 Chapter 9: Discovering New Topologies............................................................343 Part 1: Fixed-Frequency Synchronous Buck Topology..........................................343 Using a FET (Safely) Instead of Diode......................................................343 Birth of Dead Time.....................................................................................346 CdV/dt-Induced Turn-On............................................................................347 Counting on the Body-Diode......................................................................347 External (Paralleled) Schottky Diode.........................................................348 Synchronous (Complementary) Drive........................................................350 Part 2: Fixed-Frequency Synchronous Boost Topology.........................................351 Part 3: Current-Sensing Categories and General Techniques.................................357 DCR Sensing...............................................................................................359 The Inductorless Buck Cell.........................................................................365 Lossless Droop Regulation and Dynamic Voltage Positioning.................367 Part 4: The Four-Switch Buck-Boost......................................................................369 Part 5: Auxiliary Rails and Composite Topologies.................................................375