TABLE OF CONTENTS 1 Fundamentals Transmission Line Parameters... 29

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1 TABLE OF CONTENTS 1 Fundamentals Impedance of Linear, Time-Invariant, Lumped-Element Circuits Power Ratios Rules of Scaling Scaling of Physical Size Scaling Inductors Scaling Transmission-Line Dimensions Power Scaling Time Scaling Impedance Scaling with Constant Voltage Dielectric-Constant Scaling Partially Embedded Transmission Lines Magnetic Permeability Scaling The Concept of Resonance Extra for Experts: Maximal Linear System Response to a Digital Input Transmission Line Parameters Telegrapher s Equations So Good It Works on Barbed Wire The No-Storage Principle and Its Implications for Returning Signal Current Derivation of Telegrapher s Equations Definition of Characteristic Impedance ZC Changes in Characteristic Impedance Calculation of Impedance Zc From Parameters R, L, G, And C Definition of Propagation Coefficient γ Calculation of Propagation Coefficient γ from Parameters R, L, G, and C Ideal Transmission Line DC Resistance DC Conductance Skin Effect What Causes the Skin Effect, and What Does It Have to Do With Skin? Eddy Currents within a Conductor High and Low-Frequency Approximations for Series Resistance Skin-Effect Inductance... 66

2 2.8 Modeling Internal Impedance Practical Modeling of Internal Impedance Special Issues Concerning Rectangular Conductors Concentric-Ring Skin-Effect Model Modeling Skin Effect Regarding Modeling Skin Effect Proximity Effect Proximity Factor Proximity Effect for Coaxial Cables Proximity Effect for Microstrip and Stripline Circuits Last Words on Proximity Effect Proximity Effect II D Quasistatic Field Solvers Surface Roughness Severity of Surface Roughness Onset of Roughness Effect Roughness of Pcb Materials Controlling Roughness Dielectric Effects Dielectric Loss Tangent Rule of Mixtures Calculating the Loss Tangent for a Uniform Dielectric Mixture Calculating the Loss Tangent When You Don t Know q Causality and the Network Function Relations Finding er to Match a Measured Loss Tangent Kramers-Kronig Relations Complex Magnetic Permeability Impedance in Series with the Return Path Slow-Wave Mode On-Chip Performance Regions Signal Propagation Model Extracting Parameters for RLGC Simulators Hierarchy of Regions A Transmission Line Is Always a Transmission Line Necessary Mathematics: Input Impedance and Transfer Function Lumped-Element Region Boundary of Lumped-Element Region Pi Model Taylor-Series Approximation of H (Lumped-Element Region)

3 3.4.4 Input impedance (Lumped-Element Region) Transfer Function (Lumped-Element Region) Step Response (Lumped-Element Region) RC Region Boundary of RC Region Input Impedance (RC Region) Characteristic Impedance (RC Region) General Behavior within RC Region Propagation Coefficient (RC Region) Transfer Function (RC Region) Propagation Function of RC Line with Open-Circuited Load Propagation Function of RC Line with Matched End Termination Propagation Function of RC Line with Matched Source Termination Propagation Function of RC Line with Resistive End Termination Normalized Step Response (RC Region) Tradeoffs Between Distance and Speed (RC Region) Closed-Form Solution for Step Response (RC Region) Elmore Delay Estimation (RC Region) LC Region (Constant-Loss Region) Boundary of LC Region Characteristic Impedance (LC Region) Influence of Series Resistance on TDR Measurements Propagation Coefficient (LC Region) Possibility of Severe Resonance within the LC Region Alternate Interpretation of Equation [3.17] Practical Effect of Resonance Terminating an LC Transmission Line End Termination Source Termination Both-Ends Termination Subtle Differences Between Termination Styles Application of Termination Equations to Other Regions Tradeoffs Between Distance And Speed (LC Region) Mixed-Mode Operation (LC and RC Regions) Skin-Effect Region Boundary of Skin-Effect Region Characteristic Impedance (Skin-Effect Region) Influence of Skin-Effect on TDR Measurement Propagation Coefficient (Skin-Effect Region) Possibility of Severe Resonance within Skin-Effect Region

4 Subtle Differences Between Termination Styles Application of Termination Equations to Other Regions Step Response (Skin-Effect Region) Tradeoffs Between Distance and Speed (Skin-Effect Region) Dielectric Loss Region Boundary of Dielectric-Loss-Limited Region Characteristic Impedance (Dielectric-Loss-Limited Region) Influence of Dielectric Loss on TDR Measurement Propagation Coefficient (Dielectric-Loss-Limited Region) Possibility of Severe Resonance within Dielectric-Loss Limited Region Subtle Differences Between Termination Styles Application of Termination Equations to Other Regions Step Response (Dielectric-Loss-Limited Region) Tradeoffs Between Distance and Speed (Dielectric-Loss Region) Waveguide Dispersion Region Boundary of Waveguide-Dispersion Region Summary of Breakpoints Between Regions Equivalence Principle for Transmission Media Scaling Copper Transmission Media Scaling Multimode Fiber-Optic Cables Linear Equalization: Long Backplane Trace Example Adaptive Equalization: Accelerant Networks Transceiver Frequency-Domain Modeling Going Nonlinear Approximations to the Fourier Transform Discrete Time Mapping Other Limitations of the FFT Normalizing the Output of an FFT Routine Deriving the DFT Normalization Factors Useful Fourier Transform-Pairs Effect of Inadequate Sampling Rate Implementation of Frequency-Domain Simulation Embellishments What if a Large Bulk-Transport Delay Causes the Waveform to Slide Off the end of the Time-Domain Window? How Do I Transform an Arbitrary Data Sequence? How Do I Shift the Time-Domain Waveforms? What If I Want to Model a More Complicated System? What About Differential Modeling?

5 4.10 Checking the Output of Your FFT Routine Pcb (printed-circuit board) Traces Pcb Signal Propagation Characteristic Impedance and Delay Resistive Effects DC Resistance of Pcb Trace AC Resistance of Pcb Trace Calculation of Perimeter of Pcb Trace Very Low Impedance Pcb Trace Calculation of Skin-Effect Loss Coefficient for Pcb trace Popsicle-Stick Analysis Nickel-Plated Traces Dielectric Effects Estimating the Effective Dielectric Constant for a Microstrip Propagation Velocity Calculating the Effective Loss Tangent for a Microstrip Dielectric Properties of Laminate Materials (core and prepreg) Variations in Dielectric Properties with Temperature Passivation and Soldermask Dielectric Properties of Soldermask Materials Calculation of Dielectric Loss Coefficient for Pcb Trace Mixtures of Skin Effect and Dielectric Loss Non-TEM Modes Strange Microstrip Modes Simulation of Non-TEM Behavior Limits to Attainable Distance SONET Data Coding Pcb Noise and Interference Pcb: Reflections Both Ends Termination Pcb: Lumped-Element Reflections Potholes Inductive Potholes Who s Afraid of the Big, Bad Bend? Stubs and Vias Parasitic Pads How Close Is Close Enough? Placement of End Termination Making an Accurate Series Termination

6 Matching Pads Pcb Crosstalk Purpose of Solid Plane Layers Variations with Trace Geometry Directionality NEXT: Near-End or Reverse Crosstalk FEXT: Far-End or Forward Crosstalk Special Considerations Directionality of Crosstalk Pcb Connectors Mutual Understanding Through-Hole Clearances Measuring Connectors Tapered Transitions Straddle-Mount Connectors Cable Shield Grounding Modeling Vias Incremental Parameters of a Via Three Models for a Via Dangling Vias Capacitance Data Three-Layer Via Capacitance Effect of Back-Drilling Effect of Multiple Planes Inductance Data Through-Hole Via Inductance Via Crosstalk The Future of On-Chip Interconnections Differential Signaling Single-Ended Circuits Two-Wire Circuits Differential Signaling Differential and Common-Mode Voltages and Currents Differential and Common-Mode velocity Common-Mode Balance Common-Mode Range Differential to Common-Mode Conversion Differential Impedance Relation Between Odd-Mode and Uncoupled Impedance

7 6.9.2 Why the Odd-Mode Impedance Is Always Less Than the Uncoupled Impedance Differential Reflections Pcb Configurations Differential (Microstrip) Trace Impedance Edge-Coupled Stripline Breaking Up a Pair Broadside-Coupled Stripline Pcb Applications Matching to an External, Balanced Differential Transmission Medium Defeating ground bounce Reducing EMI with Differential Signaling Punching Through a Noisy Connector Differential Signaling (Through Connectors) Reducing Clock Skew Reducing Local Crosstalk A Good Reference about Transmission Lines Differential Clocks Differential Termination Differential U-Turn Your Layout Is Skewed Buying Time Intercabinet Applications Ribbon-Style Twisted-Pair Cables Immunity to Large Ground Shifts Rejection of External Radio-Frequency Interference (RFI) Differential Receivers Have Superior Tolerance to Skin Effect and Other High-Frequency Losses LVDS Signaling Output Levels Common-Mode Output Common-Mode Noise Tolerance Differential-Mode Noise Tolerance Hysteresis Impedance Control Trace Radiation Risetime Input Capacitance Skew Fail-Safe

8 7 Generic Building-Cabling Standards Generic Cabling Architecture SNR Budgeting Glossary of Cabling Terms Preferred Cable Combinations FAQ: Building-Cabling Practices Crossover Wiring Plenum-Rated Cables Laying cables in an Uncooled Attic Space FAQ: Older Cable Types Ohm Balanced Twisted-Pair Cabling UTP Signal Propagation UTP Modeling Adapting the Metallic-Transmission Model UTP Transmission Example: 10BASE-T UTP Noise and Interference UTP: Far-End Reflections UTP: Near-End Reflections UTP: (Structural) Return Loss Modeling Structural Return Loss UTP: Hybrid Circuits UTP: Near-End Crosstalk UTP: Alien crosstalk UTP: Far-End Crosstalk Power sum NEXT and ELFEXT UTP: Radio-Frequency Interference UTP: Radiation UTP Connectors Issues with Screening Category-3 UTP at Elevated Temperature Ohm STP-A Cabling Ω STP-A Signal Propagation Ω STP-A Noise and Interference Ω STP-A: Skew Ω STP-A: Radiation and Safety Ω STP-A: Comparison with UTP Ω STP-A Connectors

9 10 Coaxial Cabling Coaxial Signal Propagation Stranded Center-Conductors Why 50 Ohms? Ohm Mailbag Coaxial Cable Noise and Interference Coax: Far-End Reflected Noise Coax: Radio Frequency Interference Coax: Radiation Coaxial Cable: Safety Issues Coaxial Cable Connectors Fiber-Optic Cabling Making Glass Fiber Finished Core Specifications Cabling the Fiber Wavelengths of Operation Multimode Glass Fiber-Optic Cabling Multimode Signal Propagation Why Is Graded-Index Fiber Better than Step-Index? Standards for Multimode Fiber What Considerations Govern the Use of 50-micron Fiber? Multimode Optical Performance Budget Multimode Dispersion Budget Multimode Attenuation Budget Jitter Multimode Fiber-Optic Noise and Interference Multimode Fiber Safety Multimode Fiber with Laser Source VCSEL Diodes Multimode Fiber-Optic Connectors Single-Mode Fiber-Optic Cabling Single-Mode Signal Propagation Single-Mode Fiber-Optic Noise and Interference Single-Mode Fiber Safety Single-Mode Fiber-Optic Connectors Clock Distribution Extra Fries, Please Arithmetic of Clock Skew

10 12.3 Clock Repeaters Active Skew Correction Zero-Delay Clock Repeaters Compensating for Line Length Stripline vs. Microstrip Delay Importance of Terminating Clock Lines Effect of Clock Receiver Thresholds Effect of Split Termination Intentional Delay Adjustments Fixed Delay Adjustable Delays Automatically Programmable Delays Serpentine Delays Switchback Coupling Driving Multiple Loads with Source Termination To Tee or Not To Tee Driving Two Loads Daisy-Chain Clock Distribution Case Study of Daisy-Chained Clock The Jitters When Clock Jitter Matters Clock Jitter Rarely Matters within the Boundaries of a Synchronous State Machine Clock Jitter Propagation Variance of the Tracking Error Clock Jitter in FIFO-Based Architectures What Causes Jitter Random and Deterministic Jitter Measuring Clock Jitter Jitter Measurement Jitter and Phase Noise Power Supply Filtering for Clock Sources, Repeaters, and PLL Circuits Healthy Power Clean Power Intentional Clock Modulation Signal Integrity Mailbag Jitter-Free Clocks Reduced-Voltage Signaling Controlling Crosstalk on Clock Lines

11 12.16 Reducing Emissions Time-Domain Simulation Tools and Methods Ringing in a New Era Signal Integrity Simulation Process How Much Modeling Do You Need? What Happens After Parameter Extraction? A Word of Caution The Underlying Simulation Engine Evolving Forward Pitfalls of SPICE-Like Algorithms Transmission Lines Interpreting Your Results Using SPICE Intelligently IBIS (I/O Buffer Information Specification) What Is IBIS? Who Created IBIS? What Is Good About IBIS? What s Wrong with IBIS? What You Can Do to Help IBIS: History and Future Direction IBIS Historical Overview Comparison to SPICE Future Directions IBIS: Issues with Interpolation IBIS: Issues with SSO Noise Nature of EMC Work EMC Simulation Power and Ground Resonance Collected References Points to Remember Appendix A - Building a Signal Integrity Department Appendix B - Calculation of Loss Slope Appendix C - Two-Port Analysis Simple Cases Involving Transmission Lines Fully Configured Transmission Line Complicated Configurations

12 Appendix D - Accuracy of Pi Model Pi-Model Operated in the LC Region Appendix E - erf( )