The loss slope, for the purposes of this discussion, is defined as the slope, using a log-log plot, of attenuation a , in dB, versus frequency f , in Hz.

**Equation B.1 **

Notice that since a , in dB, is already the logarithm of signal amplitude v in Volts, the loss-slope definition is making use of a double-logarithm. The next equation shows the relation between loss slope and signal amplitude.

**Equation B.2 **

As an example, let's determine the loss slope for a signal amplitude v that varies exponentially with some power h of frequency.

**Equation B.3 **

The attenuation a in dB is base-10-logarithmically related to the signal amplitude.

**Equation B.4 **

Substitute [B.3] for v , and simplify using the relation log( e x ) = x /ln(10).

**Equation B.5 **

And the log of attenuation is what we display in the loss-slope graph.

**Equation B.6 **

The loss slope is defined as d (log a )/ d (log f ). Let u = log f , and evaluate the loss slope as d (log a )/ du using [B.6] for the definition of log a .

**Equation B.7 **

Inside the square brackets the right-hand term remains constant and so contributes nothing to the derivative. In the left-hand term the expression log( f ) may be changed to u , producing this:

**Equation B.8 **

In conclusion, given a linear system whose attenuation in dB varies with f h , the loss slope is h .

In the skin-effect limited region the transmission-line attenuation in dB varies with the square root of f, producing a loss slope of 1/2. In the dielectric-loss region the attenuation varies directly with f, producing a loss slope of 1.

In a dispersion-limited transmission system the loss slope indicates the severity of the tradeoff between transmission distance and operating speed.

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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