Preface

1 Waveforms

Structure, Behavior, and Function 1

Waveform Parameters 1

Average and RMS Power 4

Sinusoidal Power 8

Waveform Phasing 9

Current Waveforms 11

Average and RMS Values of Added Waveforms 15

Waveform Performance Parameters 17

Ripple Characterization 19

2 Transductors

Quantities of Electricity and Magnetism 22

Maxwell’s Equations 23

Faraday’s Law 23

Ampere’s Law 25

Gauss’s Electric Law 25

Gauss’s Magnetic Law 26

Magnetic Reference Frames 27

Magnetic-Electric Analogs 29

Magnetic Ohm’s Law 29

Magnetic Kirchhoff’s Laws 29

Inductance From Geometry 31

Solenoid Inductance 31

Toroid Inductance 32

Terminology 34

AC and DC 34

Electric and Magnetic Quantity Names 35

Mutual Inductance 37

Transductor Circuit Models 41

Transductor Model from Measurements 44

Isolated Transductor Circuit Model 45

Transductor Circuit Transforms 46

Three-Terminal Configurations 50

3 Magnetic Design

Magnetic Energy 52

Energy Transfer and Ripple 55

Magnetic Saturation 57

Magnetic Saturation Approximation 63

Magnetic Power Loss 65

Square-Wave Magnetic Power Loss 69

Magnetic Core Materials 71

Magnetic Energy Density of Cores 74

Core Power-Loss Density Estimation 75

Thermal Shape Factor 80          

Rectangular Toroid Power-Loss Density 82

Round Toroid Power-Loss Density 84

EE Core Power-Loss Density 85

ETD Core Power-Loss Density 86

Pot Core Power-Loss Density 87

Core-Shape Thermal Performance 89

Thermal Advantage of Distributed Cores 90

4 Electrical Design

Wire Size 92

Conductor Ampacity 94

Wire Fusing Current 95

Etched Circuit Board Traces 98

Wire Packing Factor 99

            Wire Packing Factor - Mathcad Listing 106

            Innovatia Wire Table 108

Bundled Strands of Wire 109

Winding Turn Length: Round Window 120

Winding Turn Length: Square Window 121

Winding Area: Round Window 123

Winding Area: Square Window 126

Toroid Turn Length 127

            Example 132

Toroid Window Fill Factor 132

Wound Toroid Volume 133

Skin Effect 135

Frequency-Dependent Resistance 142

Proximity Effect 143

Equivalent Foil, Square and Round Wire 145

Dowell’s Equation 150

Fr and Minimum Winding Resistance 153

FR Approximation 161

Approximate Minimum Rw for Foil 162

Approximate Minimum Rw for Wire 163

Winding Design Example 165

Winding Loss from Waveshape 166

Foil, ECB Traces, and Winding Shape 170

Aluminum or Copper Wire 171

Winding Sequence 174

Leakage Inductance Reduction 175

Leakage Inductance in Winding Window 176

Leakage Inductance FL Effects 177

Single-Bundle Multifilar Windings 178

Bundle Layer Approximation 184

Unibundle Eddy-Current Effects 186

Layering and Interlayer Capacitance 191

            Distributed Capacitance and Voltage 192

            Charge on Distributed Capacitance 193

            Interlayer Voltage from Field Energy 196

Unidirectional Winding Technique 198

Concentric Winding Sequencing 198

Capacitance of Two Loops 200

Bifilar Strand Capacitance 202

Capacitance of Adjacent Layers 204

Toroid Concentric Winding Capacitance 207

Winding Resonance 210

Common-Mode Transformer Capacitance 211

Forward Converter Interwinding Capacitance 213

Flyback & IsoCuk Interwinding Capacitance 214

Flyback Switching & Interwinding Capacitance 216

5 Optimization

Maximum Core Utilization 220

Optimal Turns 221

Winding Window Turns Limitation 225

Optimal Ripple Factor 226

Resistance-Matching Circuit and Field 229

Optimal Turns from Nλ and Ni  233

Core Volume Minimization 234

Transfer Power for Multiple Windings 236

Maximized Transfer and Utilization 238

Transductor Design Optimization 240

Air Gap Optimization of Magnetic Path 243

Optimal Ferrite Core Operating-Point 245

Maximum Power with Large Ripple 247

Transformer Optimization 251

Frequency Optimization 255

Optimal Core Geometry 260

Area-Product Core Selection 264

One-Sided Power-Loss Circuit Models 265

Maximum Output Power 269

Maximum Power Transfer 270

Circuit Equations for Pc = Pw 273

Secondary Maximum η(Is) and η(Vs) 275

            Secondary Max-η(Vp’) with Voltage-Source Load 279

            Secondary Max-η(Vs) with Current-Source Load 281

            Primary Max-η(Vs’) with Voltage-Source Load 283

            Primary Max-η(Vp) with Voltage-Source Load 285

            Primary Max-η(Vs’) with Current-Source Load 286

Generalized η and ψ Equations 288

General Power-Transfer Circuit Model 289

            Efficiency 291

            Core and Winding Power Loss 292

            Power-Loss Ratio 295

            Optimal Voltage and Power-Loss Ratios 297

            βmax and Optimal Rw 300

Minimum-Power-Loss Optimization 302

            Minimum Power Loss with Voltage- and Current-Source Loads 304

            Minimum-Loss Turns 307

Winding Optimization 308

            Winding Geometry 309

Optimal Strands Under Static Condition 311

Eddy-Current Effects and Winding Geometry 313

            Minimum-Fr Mv(rcw) 315

            Constant-Area MA(rcw) 317

            Constant-Strands MN(rcw) 318

            Winding Design Constraints Compared 319

            Dowell's Equation - Design Optimization - Mathcad Listing 323       

            Optimal Window Aspect Ratio 335

            Linear Layering in a Closed Winding Window 336

            Toroid Winding Design 337

6 Design Procedures & Examples

Simple Linear Inductor Design 352

Simple Nonlinear Inductor Design 353

            Example Inductor Design 355

Transductor Board Assembly 356

Design Power for a Vg Range 357

Power Flows 358

Input Port Power 359

Inductor Power 360

Inductor Design Power 363

Transformer Waveforms and Power 368

Primary Winding and Input Power 369

Transformer Design Power 369

Core Sizing 374

Ferrite Designs 375

Iron-Powder Designs 377

Transductor Design Procedure 379

Transductor Specification 379

Core Material, Frequency, and Size 380

Magnetic Operating-Point 381

Optimal Ripple Factor, Nw, and L Range 381

Optimal Turns, Inductance, and Power 383

Core Power Loss 384

Winding Configuration 385

Winding Design Procedure 387

Design Example: Ćuk Transductor 390

            Specifications 390

Ćuk Converter Transductor Behavior 392

            EE Core: EE2425 or E25/10/6 3C90 393

                        Magnetic Design 393

                        Electric Design 396

            Planar E Core: E18/4/10/R 3F3 401

                        Magnetic Design 401

                        Electric Design 404

            Toroids: Fe-Powder 2 T80B 20 mm 410

                        Magnetic Design 411

                        Electric Design 413

            FeSiAl Design: 7705x 12.7 mm Toroid 416

            NiFeMo Design: 550xx 12.7 mm Toroid 417

            NiFe Design: 12.7 mm Toroid 419

            FeSi Design: E12.7/6.4/3.6 420

Design Example: Buck Inductor 422

Design Example: Battery Converter 425

            Transformer Design 427

            Inductor Design 435

Closure 439

Index

A - W 440

Symbols 451

Materials 455

Tables and Mathcad Programs 455

 

456 numbered pages

465 total nonblank pages

466 total pages

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