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Library of Congress Cataloging-in-Publication Data:
Hall, Stephen H.
Advanced signal integrity for high-speed digital designs / Stephen H. Hall, Howard
L. Heck.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-470-19235-1 (cloth)
1. Digital electronics. 2. Logic designs. I. Heck, Howard L. II. Title.
TK7868.D5H298 2009
621
.381—dc22
2008027977
Printed in the United States of America

CONTENTS
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
v
vi CONTENTS
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
CONTENTS vii
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
viii CONTENTS
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
CONTENTS ix
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
x CONTENTS
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
CONTENTS xi
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
xii CONTENTS
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
CONTENTS xiii
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

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