Whenever you alter the path of current, you alter the inductance. Because the skin effect modifies the distribution of current within the conductor, it must also change the inductance of that conductor. You can observe this in very careful measurements of transmission-line inductance at high and low frequencies.

At frequencies well above the skin-effect onset frequency w d the current in a transmission line distributes itself in whatever way minimizes the overall inductance of the circuit (current follows the path of least inductance). The least-inductive distribution for a transmission line concentrates current around the periphery of the conductors, with little or no flux interior to the conductors. The value of inductance so obtained is called the external inductance of the transmission line L e .

The external inductance is defined at a frequency sufficiently high that the skin depth shrinks to much less than the wire thickness , but also sufficiently low that the wire still operates in a TEM mode (or for microstrips, a quasi-TEM mode ”see "Non-TEM Modes" in Section 5.1.5). The name external inductance applies because the definition assumes the skin effect has expunged all magnetic flux from the interior of each conductor; thus the circuit responds only to magnetic flux appearing external to the conductors themselves . The external inductance is the value of series inductance, in Henries per meter, computed by a 2-D field solver under the assumption that current rides on the surface of each conductor without penetrating deeply into the body of any of the conductors.

At frequencies well below w d , current in a transmission line redistributes itself to minimize the resistance of the circuit (current follows the path of least resistance). Because this distribution is not the same as the least-inductive distribution, the value of low-frequency inductance must by definition be higher than the minimum inductance L e . The difference in inductance between low and high frequency values is called the internal inductance of the transmission line, L i . It carries this name to remind you that the shift in inductance has to do with the penetration of flux internal to the conducting elements of the line.

The redistribution of current within the conductors at low frequencies affects their inductance, but not their capacitance. The creation of an analogous "internal capacitance " would require that electric fields penetrate the body of the conductors, something that does not happen for good metallic conductors at any reasonable operating frequency. When working with metallic conductors you may assume that charge remains bound to the surfaces at all frequencies of interest to digital designers. Around the skin-effect onset frequency there is no change in capacitance.

If a material of very low conductivity violates the assumption s >> w e , then electric fields will penetrate the conductor. Above a certain frequency w c = s / e , there will develop an electric-field skin effect accompanied by changes in capacitance somewhat analogous to the changes in internal inductance caused by the magnetic skin effect. The partial penetration of electric fields into a lightly doped silicon substrate is the root cause of the slow-wave effect (see Section 2.14, " Slow-Wave Mode On-Chip").

Models for predicting the series resistance and inductance of conductors are presented in the next section.

POINTS TO REMEMBER

- The distribution of current at high frequencies minimizes inductance.
- At DC, the path of least DC resistance creates a slightly higher inductance.
- Good models for skin effect take into account changes in both resistance and inductance with frequency.

Fundamentals

- Impedance of Linear, Time-Invariant, Lumped-Element Circuits
- Power Ratios
- Rules of Scaling
- The Concept of Resonance
- Extra for Experts: Maximal Linear System Response to a Digital Input

Transmission Line Parameters

- Transmission Line Parameters
- Telegraphers Equations
- Derivation of Telegraphers Equations
- Ideal Transmission Line
- DC Resistance
- DC Conductance
- Skin Effect
- Skin-Effect Inductance
- Modeling Internal Impedance
- Concentric-Ring Skin-Effect Model
- Proximity Effect
- Surface Roughness
- Dielectric Effects
- Impedance in Series with the Return Path
- Slow-Wave Mode On-Chip

Performance Regions

- Performance Regions
- Signal Propagation Model
- Hierarchy of Regions
- Necessary Mathematics: Input Impedance and Transfer Function
- Lumped-Element Region
- RC Region
- LC Region (Constant-Loss Region)
- Skin-Effect Region
- Dielectric Loss Region
- 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

- 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
- Useful Fourier Transform-Pairs
- Effect of Inadequate Sampling Rate
- Implementation of Frequency-Domain Simulation
- Embellishments
- Checking the Output of Your FFT Routine

Pcb (printed-circuit board) Traces

- Pcb (printed-circuit board) Traces
- Pcb Signal Propagation
- Limits to Attainable Distance
- Pcb Noise and Interference
- Pcb Connectors
- Modeling Vias
- The Future of On-Chip Interconnections

Differential Signaling

- 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
- Pcb Configurations
- Pcb Applications
- Intercabinet Applications
- LVDS Signaling

Generic Building-Cabling Standards

- 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

100-Ohm Balanced Twisted-Pair Cabling

- 100-Ohm Balanced Twisted-Pair Cabling
- UTP Signal Propagation
- UTP Transmission Example: 10BASE-T
- UTP Noise and Interference
- UTP Connectors
- Issues with Screening
- Category-3 UTP at Elevated Temperature

150-Ohm STP-A Cabling

- 150-Ohm STP-A Cabling
- 150- W STP-A Signal Propagation
- 150- W STP-A Noise and Interference
- 150- W STP-A: Skew
- 150- W STP-A: Radiation and Safety
- 150- W STP-A: Comparison with UTP
- 150- W STP-A Connectors

Coaxial Cabling

- Coaxial Cabling
- Coaxial Signal Propagation
- Coaxial Cable Noise and Interference
- Coaxial Cable Connectors

Fiber-Optic Cabling

- Fiber-Optic Cabling
- Making Glass Fiber
- Finished Core Specifications
- Cabling the Fiber
- Wavelengths of Operation
- Multimode Glass Fiber-Optic Cabling
- Single-Mode Fiber-Optic Cabling

Clock Distribution

- Clock Distribution
- Extra Fries, Please
- Arithmetic of Clock Skew
- Clock Repeaters
- Stripline vs. Microstrip Delay
- Importance of Terminating Clock Lines
- Effect of Clock Receiver Thresholds
- Effect of Split Termination
- Intentional Delay Adjustments
- Driving Multiple Loads with Source Termination
- Daisy-Chain Clock Distribution
- The Jitters
- Power Supply Filtering for Clock Sources, Repeaters, and PLL Circuits
- Intentional Clock Modulation
- Reduced-Voltage Signaling
- Controlling Crosstalk on Clock Lines
- Reducing Emissions

Time-Domain Simulation Tools and Methods

- Ringing in a New Era
- Signal Integrity Simulation Process
- The Underlying Simulation Engine
- IBIS (I/O Buffer Information Specification)
- IBIS: History and Future Direction
- IBIS: Issues with Interpolation
- IBIS: Issues with SSO Noise
- Nature of EMC Work
- Power and Ground Resonance

Points to Remember

Appendix A. Building a Signal Integrity Department

Appendix B. Calculation of Loss Slope

Appendix C. Two-Port Analysis

- Appendix C. Two-Port Analysis
- Simple Cases Involving Transmission Lines
- Fully Configured Transmission Line
- Complicated Configurations

Appendix D. Accuracy of Pi Model

Appendix E. erf( )

Notes

High-Speed Signal Propagation[c] Advanced Black Magic

ISBN: 013084408X

EAN: N/A

EAN: N/A

Year: 2005

Pages: 163

Pages: 163

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