Advanced Signal Integrity for High-Speed Digital Designs

Preface xv

1. Introduction: The Importance of Signal Integrity 1

1.1 Computing Power: Past and Future 1

1.2 The Problem 4

1.3 The Basics 5

1.4 A New Realm of Bus Design 7

1.5 Scope of the Book 7

1.6 Summary 8

References 8

2. Electromagnetic Fundamentals for Signal Integrity 9

2.1 Maxwell’s Equations 10

2.2 Common Vector Operators 13

2.2.1 Vector 13

2.2.2 Dot Product 13

2.2.3 Cross Product 14

2.2.4 Vector and Scalar Fields 15

2.2.5 Flux 15

2.2.6 Gradient 18

2.2.7 Divergence 18

2.2.8 Curl 20

2.3 Wave Propagation 23

2.3.1 Wave Equation 23

2.3.2 Relation Between E and H and the Transverse Electromagnetic Mode 25

2.3.3 Time-Harmonic Fields 27

2.3.4 Propagation of Time-Harmonic Plane Waves 28

2.4 Electrostatics 32

2.4.1 Electrostatic Scalar Potential in Terms of an Electric Field 36

2.4.2 Energy in an Electric Field 37

2.4.3 Capacitance 40

2.4.4 Energy Stored in a Capacitor 41

2.5 Magnetostatics 42

2.5.1 Magnetic Vector Potential 46

2.5.2 Inductance 48

2.5.3 Energy in a Magnetic Field 51

2.6 Power Flow and the Poynting Vector 53

2.6.1 Time-Averaged Values 56

2.7 Reflections of Electromagnetic Waves 57

2.7.1 Plane Wave Incident on a Perfect Conductor 57

2.7.2 Plane Wave Incident on a Lossless Dielectric 60

References 62

Problems 62

3. Ideal Transmission-Line Fundamentals 65

3.1 Transmission-Line Structures 66

3.2 Wave Propagation on Loss-Free Transmission Lines 67

3.2.1 Electric and Magnetic Fields on a Transmission Line 68

3.2.2 Telegrapher’s Equations 73

3.2.3 Equivalent Circuit for the Loss-Free Case 76

3.2.4 Wave Equation in Terms of LC 80

3.3 Transmission-Line Properties 82

3.3.1 Transmission-Line Phase Velocity 82

3.3.2 Transmission-Line Characteristic Impedance 82

3.3.3 Effective Dielectric Permittivity 83

3.3.4 Simple Formulas for Calculating the Characteristic Impedance 85

3.3.5 Validity of the TEM Approximation 86

3.4 Transmission-Line Parameters for the Loss-Free Case 90

3.4.1 Laplace and Poisson Equations 91

3.4.2 Transmission-Line Parameters for a Coaxial Line 91

3.4.3 Transmission-Line Parameters for a Microstrip 94

3.4.4 Charge Distribution Near a Conductor Edge 100

3.4.5 Charge Distribution and Transmission-Line Parameters 104

3.4.6 Field Mapping 107

3.5 Transmission-Line Reflections 113

3.5.1 Transmission-Line Reflection and Transmission Coefficient 113

3.5.2 Launching an Initial Wave 116

3.5.3 Multiple Reflections 116

3.5.4 Lattice Diagrams and Over- or Underdriven Transmission Lines 118

3.5.5 Lattice Diagrams for Nonideal Topologies 121

3.5.6 Effect of Rise and Fall Times on Reflections 129

3.5.7 Reflections from Reactive Loads 129

3.6 Time-Domain Reflectometry 134

3.6.1 Measuring the Characteristic Impedance and Delay of a Transmission Line 134

3.6.2 Measuring Inductance and Capacitance of Reactive Structures 137

3.6.3 Understanding the TDR Profile 140

References 140

Problems 141

4. Crosstalk 145

4.1 Mutual Inductance and Capacitance 146

4.1.1 Mutual Inductance 147

4.1.2 Mutual Capacitance 149

4.1.3 Field Solvers 152

4.2 Coupled Wave Equations 153

4.2.1 Wave Equation Revisited 153

4.2.2 Coupled Wave Equations 155

4.3 Coupled Line Analysis 157

4.3.1 Impedance and Velocity 157

4.3.2 Coupled Noise 165

4.4 Modal Analysis 177

4.4.1 Modal Decomposition 178

4.4.2 Modal Impedance and Velocity 180

4.4.3 Reconstructing the Signal 180

4.4.4 Modal Analysis 181

4.4.5 Modal Analysis of Lossy Lines 192

4.5 Crosstalk Minimization 193

4.6 Summary 194

References 195

Problems 195

5. Nonideal Conductor Models 201

5.1 Signals Propagating in Unbounded Conductive Media 202

5.1.1 Propagation Constant for Conductive Media 202

5.1.2 Skin Depth 204

5.2 Classic Conductor Model for Transmission Lines 205

5.2.1 Dc Losses in Conductors 206

5.2.2 Frequency-Dependent Resistance in Conductors 207

5.2.3 Frequency-Dependent Inductance 213

5.2.4 Power Loss in a Smooth Conductor 218

5.3 Surface Roughness 222

5.3.1 Hammerstad Model 223

5.3.2 Hemispherical Model 228

5.3.3 Huray Model 237

5.3.4 Conclusions 243

5.4 Transmission-Line Parameters for Nonideal Conductors 244

5.4.1 Equivalent Circuit Impedance and Propagation Constant 244

5.4.2 Telegrapher’s Equations for a Real Conductor and a Perfect Dielectric 246

References 247

Problems 247

6. Electrical Properties of Dielectrics 249

6.1 Polarization of Dielectrics 250

6.1.1 Electronic Polarization 250

6.1.2 Orientational (Dipole) Polarization 253

6.1.3 Ionic (Molecular) Polarization 253

6.1.4 Relative Permittivity 254

6.2 Classification of Dielectric Materials 256

6.3 Frequency-Dependent Dielectric Behavior 256

6.3.1 Dc Dielectric Losses 257

6.3.2 Frequency-Dependent Dielectric Model: Single Pole 257

6.3.3 Anomalous Dispersion 261

6.3.4 Frequency-Dependent Dielectric Model: Multipole 262

6.3.5 Infinite-Pole Model 266

6.4 Properties of a Physical Dielectric Model 269

6.4.1 Relationship Between ε_ and ε__ 269

6.4.2 Mathematical Limits 271

6.5 Fiber-Weave Effect 274

6.5.1 Physical Structure of an FR4 Dielectric and Dielectric Constant Variation 275

6.5.2 Mitigation 276

6.5.3 Modeling the Fiber-Weave Effect 277

6.6 Environmental Variation in Dielectric Behavior 279

6.6.1 Environmental Effects on Transmission-Line Performance 281

6.6.2 Mitigation 283

6.6.3 Modeling the Effect of Relative Humidity on an FR4 Dielectric 284

6.7 Transmission-Line Parameters for Lossy Dielectrics and Realistic Conductors 285

6.7.1 Equivalent Circuit Impedance and Propagation Constant 285

6.7.2 Telegrapher’s Equations for Realistic Conductors and Lossy Dielectrics 291

References 292

Problems 292

7. Differential Signaling 297

7.1 Removal of Common-Mode Noise 299

7.2 Differential Crosstalk 300

7.3 Virtual Reference Plane 302

7.4 Propagation of Modal Voltages 303

7.5 Common Terminology 304

7.6 Drawbacks of Differential Signaling 305

7.6.1 Mode Conversion 305

7.6.2 Fiber-Weave Effect 310

Reference 313

Problems 313

8. Mathematical Requirements for Physical Channels 315

8.1 Frequency-Domain Effects in Time-Domain Simulations 316

8.1.1 Linear and Time Invariance 316

8.1.2 Time- and Frequency-Domain Equivalencies 317

8.1.3 Frequency Spectrum of a Digital Pulse 321

8.1.4 System Response 324

8.1.5 Single-Bit (Pulse) Response 327

8.2 Requirements for a Physical Channel 331

8.2.1 Causality 331

8.2.2 Passivity 340

8.2.3 Stability 343

References 345

Problems 345

9. Network Analysis for Digital Engineers 347

9.1 High-Frequency Voltage and Current Waves 349

9.1.1 Input Reflection into a Terminated Network 349

9.1.2 Input Impedance 353

9.2 Network Theory 354

9.2.1 Impedance Matrix 355

9.2.2 Scattering Matrix 358

9.2.3 ABCD Parameters 382

9.2.4 Cascading S-Parameters 390

9.2.5 Calibration and Deembedding 395

9.2.6 Changing the Reference Impedance 399

9.2.7 Multimode S-Parameters 400

9.3 Properties of Physical S-Parameters 406

9.3.1 Passivity 406

9.3.2 Reality 408

9.3.3 Causality 408

9.3.4 Subjective Examination of S-Parameters 410

References 413

Problems 413

10. Topics in High-Speed Channel Modeling 417

10.1 Creating a Physical Transmission-Line Model 418

10.1.1 Tabular Approach 418

10.1.2 Generating a Tabular Dielectric Model 419

10.1.3 Generating a Tabular Conductor Model 420

10.2 NonIdeal Return Paths 422

10.2.1 Path of Least Impedance 422

10.2.2 Transmission Line Routed Over a Gap in the Reference Plane 423

10.2.3 Summary 434

10.3 Vias 434

10.3.1 Via Resonance 434

10.3.2 Plane Radiation Losses 437

10.3.3 Parallel-Plate Waveguide 439

References 441

Problems 442

11. I/O Circuits and Models 443

11.1 I/O Design Considerations 444

11.2 Push–Pull Transmitters 446

11.2.1 Operation 446

11.2.2 Linear Models 448

11.2.3 Nonlinear Models 453

11.2.4 Advanced Design Considerations 455

11.3 CMOS receivers 459

11.3.1 Operation 459

11.3.2 Modeling 460

11.3.3 Advanced Design Considerations 460

11.4 ESD Protection Circuits 460

11.4.1 Operation 461

11.4.2 Modeling 461

11.4.3 Advanced Design Considerations 463

11.5 On-Chip Termination 463

11.5.1 Operation 463

11.5.2 Modeling 463

11.5.3 Advanced Design Considerations 464

11.6 Bergeron Diagrams 465

11.6.1 Theory and Method 470

11.6.2 Limitations 474

11.7 Open-Drain Transmitters 474

11.7.1 Operation 474

11.7.2 Modeling 476

11.7.3 Advanced Design Considerations 476

11.8 Differential Current-Mode Transmitters 479

11.8.1 Operation 479

11.8.2 Modeling 480

11.8.3 Advanced Design Considerations 480

11.9 Low-Swing and Differential Receivers 481

11.9.1 Operation 481

11.9.2 Modeling 482

11.9.3 Advanced Design Considerations 483

11.10 IBIS Models 483

11.10.1 Model Structure and Development Process 483

11.10.2 Generating Model Data 485

11.10.3 Differential I/O Models 488

11.10.4 Example of an IBIS File 490

11.11 Summary 492

References 492

Problems 494

12. Equalization 499

12.1 Analysis and Design Background 500

12.1.1 Maximum Data Transfer Capacity 500

12.1.2 Linear Time-Invariant Systems 502

12.1.3 Ideal Versus Practical Interconnects 506

12.1.4 Equalization Overview 511

12.2 Continuous-Time Linear Equalizers 513

12.2.1 Passive CTLEs 514

12.2.2 Active CTLEs 521

12.3 Discrete Linear Equalizers 522

12.3.1 Transmitter Equalization 525

12.3.2 Coefficient Selection 530

12.3.3 Receiver Equalization 535

12.3.4 Nonidealities in DLEs 536

12.3.5 Adaptive Equalization 536

12.4 Decision Feedback Equalization 540

12.5 Summary 542

References 545

Problems 546

13. Modeling and Budgeting of Timing Jitter and Noise 549

13.1 Eye Diagram 550

13.2 Bit Error Rate 552

13.2.1 Worst-Case Analysis 552

13.2.2 Bit Error Rate Analysis 555

13.3 Jitter Sources and Budgets 560

13.3.1 Jitter Types and Sources 561

13.3.2 System Jitter Budgets 568

13.4 Noise Sources and Budgets 572

13.4.1 Noise Sources 572

13.4.2 Noise Budgets 579

13.5 Peak Distortion Analysis Methods 583

13.5.1 Superposition and the Pulse Response 583

13.5.2 Worst-Case Bit Patterns and Data Eyes 585

13.5.3 Peak Distortion Analysis Including Crosstalk 594

13.5.4 Limitations 598

13.6 Summary 599

References 599

Problems 600

14. System Analysis Using Response Surface Modeling 605

14.1 Model Design Considerations 606

14.2 Case Study: 10-Gb/s Differential PCB Interface 607

14.3 RSM Construction by Least Squares Fitting 607

14.4 Measures of Fit 615

14.4.1 Residuals 615

14.4.2 Fit Coefficients 616

14.5 Significance Testing 618

14.5.1 Model Significance: The F-Test 618

14.5.2 Parameter Significance: Individual t-Tests 619

14.6 Confidence Intervals 621

14.7 Sensitivity Analysis and Design Optimization 623

14.8 Defect Rate Prediction Using Monte Carlo Simulation 628

14.9 Additional RSM Considerations 633

14.10 Summary 633

References 634

Problems 635

Appendix A: Useful Formulas Identities Units and Constants 637

Appendix B: Four-Port Conversions Between T- and S-Parameters 641

Appendix C: Critical Values of the F-Statistic 645

Appendix D: Critical Values of the T-Statistic 647

Appendix E: Causal Relationship Between Skin Effect Resistance and Internal Inductance for Rough Conductors 649

Appendix F: Spice Level 3 Model for 0.25 μm MOSIS Process 653

Index 655