On a two-wire transmission circuit, the difference between the instantaneous voltages a and b on the two wires is defined as the differential voltage d :

**Equation 6.2 **

where |
a and b are each measured with respect to a common arbitrary reference. |

On a two-wire transmission circuit, the average of the instantaneous voltages a and b on the two wires is called the common-mode voltage c :

**Equation 6.3 **

where |
a and b are each measured with respect to a common reference, usually a local earth ground, but sometimes a local reference plane or other local reference point. |

The differential and common-mode voltages comprise an alternate representation of the original signal, often called a decomposition of the original signal. Given the common-mode and differential voltages, you can reconstruct a and b . (The same decomposition applies to currents.)

**Equation 6.4 **

**Equation 6.5 **

In a good differential system one usually strives to limit the AC component of the common-mode signal. This is done because the common-mode portion of the transmitted signal does not enjoy any of the noise-canceling or radiation-preventing benefits of differential transmission. The common-mode and differential signals also propagate differently in most cabling systems, which can lead to peculiar skew or ringing problems if the common-mode component is an appreciable fraction of the overall signal amplitude, especially if those common-mode currents are accidentally converted into differential signals (see Section 6.8, "Differential to Common-Mode Conversion"). Intercabinet cabling, particularly, is extremely sensitive to the presence of high-frequency common-mode currents, which radiate quite efficiently from unshielded cabling.

Another decomposition of the two-wire transmission problem defines odd-mode and even-mode voltages and currents. These are similar to, but slightly different from, differential and common-mode voltages and currents.

An odd-mode signal is one that has amplitude x ( t ) on one wire and the opposite signal “ x ( t ) on the other wire. A signal with an odd-mode amplitude of x ( t ) has a differential amplitude of 2 x ( t ). If the signal x ( t ) takes on a peak-to-peak range of y , then the peak-to-peak odd-mode range is simply y , but the peak-to-peak differential amplitude is 2 y .

An even-mode signal is the same on both wires. An even-mode signal with a peak-to-peak range of y also has a peak-to-peak common-mode range of y . The even-mode amplitude and common-mode amplitude are one and the same thing.

Two-wire transmission systems sometimes send a signal voltage on one wire, but nothing on the other. In this case the differential-mode amplitude equals the signal amplitude on the first wire. The common-mode amplitude is half that value. In this case the odd-mode and even-mode amplitudes are the same and both equal to half the signal amplitude on the first wire.

Here are the translations between odd-mode and even-mode quantities . The same decomposition applies to currents.

**Equation 6.6 **

**Equation 6.7 **

**Equation 6.8 **

**Equation 6.9 **

where |
a and b represent the voltages on the two wires with respect to a common reference. |

The differential-and-common-mode decomposition and the even-and-odd mode decomposition share very similar definitions. The discrepancy between the two models has to do with the definition of the differential mode. The differential voltage is what you read with an electrical instrument when you put it across two wires. The odd-mode voltage is a mathematical construct that simplifies the bookkeeping in certain situations.

**Equation 6.10 **

**Equation 6.11 **

Any noise like external RF interference that equally affects both wires of a differential pair will induce a common-mode (even-mode) signal, but not a differential-mode (odd-mode) signal (Figure 6.8). A good differential receiver senses only the differential signal and is therefore immune to this type of noise.

Figure 6.8. A good differential receiver cancels any noise that affects both wires equally, such as external RFI.

POINTS TO REMEMBER

- Differential and common-mode signals are used to describe the voltages and currents on a two-wire transmission system.
- Odd-mode and even-mode signals are yet another way to describe the voltages and currents on a two-wire transmission system.
- Differential receivers cancel common-mode noise.

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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