Chapter 1 Basic Concepts 1
1.1 Introduction 1
1.1.1 Functioning of Transistors 1
1.1.2 What Are the Problems with Power Delivery? 4
1.1.3 Importance of Power Delivery in Microprocessors and ICs 5
1.1.4 Power Delivery Network 6
1.1.5 Transients on the Power Supply 8
1.2 Simple Relationships for Power Delivery 10
1.2.1 Core Circuits 10
1.2.2 I/O Circuits 14
1.2.3 Delay Due to SSN 15
1.2.4 Timing and Voltage Margin Due to SSN 16
1.2.5 Relationship between Capacitor and Current 17
1.3 Design of PDNs 17
1.3.1 Target Impedance 20
1.3.2 Impedance and Noise Voltage 22
1.4 Components of a PDN 24
1.4.1 Voltage Regulator 24
1.4.2 Bypass or Decoupling Capacitors 28
1.4.3 Package and Board Planes 37
1.4.4 On-Chip Power Distribution 42
1.4.5 PDN with Components 45
1.5 Analysis of PDNs 45
1.5.1 Single-Node Analysis 48
1.5.2 Distributed Analysis 55
1.6 Chip-Package Antiresonance:An Example 61
1.7 High-Frequency Measurements 65
1.7.1 Measurement of Impedance 66
1.7.2 Measurement of Self-Impedance 68
1.7.3 Measurement of Transfer Impedance 70
1.7.4 Measurement of Impedance by Completely Eliminating Probe Inductance 70
1.8 Signal Lines Referenced to Planes 71
1.8.1 Signal Lines as Transmission Lines 72
1.8.2 Relationship between Transmission-Line Parameters and SSN 74
1.8.3 Relationship between SSN and Return Path Discontinuities 75
1.9 PDN Modeling Methodology 77
1.10 Summary 79
Chapter 2 Modeling of Planes 83
2.1 Introduction 83
2.2 Behavior of Planes 84
2.2.1 Frequency Domain 84
2.2.2 Time Domain 86
2.2.3 Two-Dimensional Planes 88
2.3 Lumped Modeling Using Partial Inductances 89
2.3.1 Extracting the Inductance and Resistance Matrices 90
2.4 Distributed Circuit-Based Approaches 94
2.4.1 Modeling Using Transmission Lines 94
2.4.2 Transmission Matrix Method(TMM) 97
2.4.3 Frequency-Dependent Behavior of Unit-Cell Elements 104
2.4.4 Modeling of Gaps in Planes 113
2.5 Discretization-Based Plane Models 117
2.5.1 Finite-Difference Method 117
2.5.2 Finite-Difference Time-Domain Method 128
2.5.3 Finite-Element Method 132
2.6 Analytical Methods 133
2.6.1 Cavity Resonator Method 133
2.6.2 Network Representation of the Cavity Resonator Model 135
2.7 Multiple Plane Pairs 138
2.7.1 Coupling through the Vias 141
2.7.2 Coupling through the Conductors 154
2.7.3 Coupling through the Apertures 158
2.8 Summary 169
Chapter 3 Simultaneous Switching Noise 175
3.1 Introduction 175
3.1.1 Methods for Modeling SSN 175
3.2 Simple Models 177
3.2.1 Modeling of Output Buffers 180
3.3 Modeling of Transmission Lines and Planes 185
3.3.1 Microstrip Configuration 186
3.3.2 Stripline Configuration 189
3.3.3 Conductor-Backed Coplanar Waveguide Configuration 205
3.3.4 Summary of Modal Decomposition Methods 207
3.4 Application of Models in Time-Domain Analysis 209
3.4.1 Plane Bounce from Return Currents 209
3.4.2 Microstrip-to-Microstrip Via Transition 217
3.4.3 Split Planes 222
3.5 Application of Models in Frequency-Domain Analysis 226
3.5.1 Stripline between a Power and a Ground Plane 226
3.5.2 Microstrip-to-Stripline Via Transition 228
3.5.3 Reduction of Noise Coupling Using Thin Dielectrics 231
3.6 Extension of M-FDM to Incorporate Transmission Lines 233
3.6.1 Analysis of a Complex Board Design 236
3.7 Summary 239
Chapter 4 Time-Domain Simulation Methods 243
4.1 Introduction 243
4.2 Rational Function Method 244
4.2.1 Basic Theory 244
4.2.2 Interpolation Schemes 246
4.2.3 Properties of Rational Functions 252
4.2.4 Passivity Enforcement 257
4.2.5 Integration in a Circuit Solver 283
4.2.6 Disadvantages 291
4.3 Signal Flow Graphs 295
4.3.1 Cau'sality 296
4.3.2 Transfer-Function Causality 296
4.3.3 Minimum Phase 296
4.3.4 Delay Extraction from Frequency Response 300
4.3.5 Causal Signal Flow Graphs 302
4.3.6 Computational Aspects in SFG 303
4.3.7 Fast Convolution Methods 307
4.3.8 Cosimulation of Signal and Power Using SFGs 312
4.4 Modified Nodal Analysis(MNA) 317
4.4.1 What Is MNA? 317
4.4.2 Frequency Domain 318
4.4.3 Time Domain 320
4.4.4 MNA Formulation with S-Parameters 322
4.5 Summary 327
Chapter 5 Applications 333
5.1 Introduction 333
5.2 High-Speed Servers 334
5.2.1 Core PDN Noise 336
5.2.2 I/O PDN Noise 345
5.2.3 Summary 349
5.3 High-Speed Differential Signaling 349
5.3.1 Test Vehicle Description 350
5.3.2 Plane Modeling 352
5.3.3 Modeling of Master and Slave Islands 358
5.3.4 Rational Function Modeling 361
5.3.5 Modal Decomposition and Noise Simulation 361
5.3.6 Summary 364
5.4 Analysis of IC Packages 365
5.4.1 Simulation of a Multilayered Package Using M-FDM 366
5.4.2 Causal Simulation of HyperBGA Package 368
5.4.3 Summary 372
5.5 Extraction of Dielectric Constant and Loss Tangent 372
5.5.1 Problem Definition 373
5.5.2 Corner-to-Corner Plane-Probing Method 378
5.5.3 Causal Model Development 386
5.5.4 Summary 391
5.6 Embedded Decoupling Capacitors 392
5.6.1 Embedded Individual Thin-or Thick-Film Capacitors 394
5.6.2 Why Embed Individual Capacitors 395
5.6.3 Design of an Embedded Thick-Film Capacitor Array 395
5.6.4 Integration of Embedded Capacitors into IBM Package 400
5.6.5 Embedded Planar Capacitors 404
5.6.6 Summary 415
5.7 Electromagnetic Bandgap(EBG)Structures 415
5.7.1 Basic Theory 416
5.7.2 Response of EBG Structures 417
5.7.3 Dispersion-Diagram Analysis 420
5.7.4 Modification of M-FDM Using Fringe and Gap Fields 424
5.7.5 Scalable Design of EBG Structures for Power Plane Isolation 430
5.7.6 Digital-RF Integration 434
5.7.7 ADC Load-Board Design 436
5.7.8 Issues with EBG Structures for Digital Systems 439
5.7.9 Summary 442
5.8 Future Challenges 443
Appendix A 451
A.1 Multiport Networks 451
A.2 Matrix Representation of Transmission Lines 453
A.3 Spectrum of Digital Signals 454
Appendix B Software list 459
Index 461