Example of 100-ohm Differential Stripline

Length, l = 0.6 m (23.6 in.) (backplane application)

Conductor parameters: w = 152 m m (6 mil), t = 17.4 m m (1/2-oz. Cu), perimeter p = 2( w + t ) = 339 m m (13.35 mil)

Conductivity of signal conductor: s = 5.98 ·10 7 S/m

The critical dimension for non-TEM considerations is the separation between the planes b = 508 m m (20 mil)

Specification frequency for AC parameters: w = 2 p ·10 9

Characteristic impedance at w : Z = 100 ohms

Effective dielectric constant: R = 4.3

Effective loss tangent for FR-4 dielectric: tan q = 0.025

Proximity factor (see chapter on printed circuit traces ): k p = 3.2

Computed values

Propagation velocity above RC region: m/s ( t p = 175.7 ps/in.)

Differential inductance per meter: L = Z /v = 691 nH/m (17.6 nH/in.)

Differential capacitance per meter: C = 1/( Z v ) = 69.1 pF/m (1.76 pF/in.)

DC resistance: R DC = 2/( s wt ) = 12.64 W /m (0.321 W /in.)

AC resistance:

Lumped-Element Region

First check the critical distance test specified in [3.30] and [3.31]:

Equation 3.146

The trace length of l = 0.6 m falls short of the critical length. The exit from the lumped-element region will therefore fall along the curve prescribed by [3.27], proceeding directly into the LC region. There will be no observable RC region in this configuration.

Transitions into all the major regions are presented in Table 3.10 in units of Hz, which requires an adjustment by a factor of (1/2 p ) from the formulas presented previously in this chapter.

Table 3.10. Onset of Various Transmission Regions (Pcb Trace Example)

Onset of Region |
Formula for lower band edge |
Value |
Source |
---|---|---|---|

LC |
w LE = ( D /l)(LC) -1/2 |
9.58 MHz |
[3.27] |

Skin-effect |
w d = w ( R DC / R ) 2 |
27.1 MHz |
[3.104] |

Dielectric |
w q = (1/ w )[( v R )/( Z tan q )] 2 |
498 MHz |
[3.123] |

Waveguide (for stripline) |
w c = ( p v / b ) |
142 GHz |
[3.145] |

Operation of this differential stripline trace at frequencies less than 9.58 MHz may be successfully modeled using a one-stage pi network. Above 9.58 MHz a distributed LC model applies until the skin effect takes hold at 27.1 MHz. Above the skin-effect transition the loss grows (theoretically) in proportion to the square root of frequency until you reach the onset of the dielectric effect at 498 MHz. Because the spacing between the skin-effect onset and dielectric-loss onset is not very great in this example (a factor of only 18.4), you may expect that even at the lower band edge of the skin-effect region the dielectric effect will still be exerting noticeable influence. Figure 3.1 illustrates this stripline example as the topmost waveform in the figure. From the skin-effect onset at 27 MHz upwards, there is no clearly defined region with a loss slope of precisely 1/2. Instead, the skin and dielectric effects mush together over a broad band, gradually increasing the loss slope from 1/2 to 1 over the range from 27 to 1000 MHz.

Provided that the trace is shortened to reduce the overall trace loss to a manageable size, this stripline trace geometry may be successfully operated at frequencies up to nearly 142 GHz without fear of exciting any unusual non-TEM modes of propagation.

Example showing Belden type 8237 (RG-8) Coaxial Cable

Length, l = 2000 m (6561 ft)

Center cond. 7x#21AWG stranded Cu

DC resistance (including shield) R DC = 0.0103 W /m (3.14 m W /ft)

Critical dimension for non-TEM considerations = Shield diameter d 2 = 7.239 mm (0.285 in.)

Conductivity, s = 5.8 ·10 7 S/m

Specification frequency for AC parameters: w = 2 p ·10 7

Characteristic impedance at w : Z = 52 ohms

Effective dielectric constant: R = 2.29

Effective loss tangent for solid polyethylene dielectric: tan q = 0.00052

Proximity factor for 7-way stranded center conductor: k p = 1.07

Surface roughness factor for braided copper shield: k r = 1.8 (applies to frequencies above 10 MHz).

Computed Values

Effective diameter of center conductor: (0.077 in.)

Equation 3.147

Propagation velocity above RC region: ( t p =1.54 ns/ft)

Inductance per meter: L = Z / v = 253 nH/m (77.1 nH/ft)

Capacitance per meter: C = 1/( Z v ) = 101 pF/m (30.8 pF/ft)

Lumped-Element Region

Check the critical distance test specified in [3.30] and [3.31]:

**Equation 3.148 **

The cable length of l = 2000m well exceeds the critical length. The exit from the lumped-element region will therefore fall along the curve prescribed by [3.26], and the cable will at higher frequencies then proceed to the RC region. Had the length been less than 1262 meters , the cable would have exited the lumped-element region along the curve prescribed by [3.27], transitioning directly into some higher region and bypassing the RC region altogether.

Transitions into all the other major regions are presented in Table 3.11 in units of Hz, which requires an adjustment by a factor of (1/2 p ) from the formulas presented previously in this chapter.

Table 3.11. Onset of Various Transmission Regions (Coaxial Cable Example)

Onset of region |
Formula for lower band edge |
Value |
Source |
---|---|---|---|

RC |
w LE = ( D / l ) 2 ( R DC C ) “1 |
2.48 KHz |
[3.26] |

LC |
w LC = ( R DC /L ) |
6.24 KHz |
[3.53] |

Skin-effect |
w d = w ( R DC / R ) 2 |
24.1 KHz |
[3.104] |

Dielectric |
w q = (1/ w )[( v R )/( Z tan q )] 2 |
5.9 GHz |
[3.123] |

Waveguide (for coax) |
w c = 0.586( p v / d 2 ) |
8 GHz |
[3.145] |

Operation of this cable at frequencies less than 2.48 KHz may be successfully modeled using a one-stage p network. Above 2.48 KHz a distributed RC model applies until you reach the onset of the LC region at 6.24 KHz. From that point until the skin effect takes hold at 24.1 KHz, the cable response remains fairly flat. Above that the skin effect loss grows in proportion to the square root of frequency until you reach the onset of the dielectric effect at 5.9 GHz. Remember that the transition into the dielectric-loss-limited region is very broad, extending a factor of 100 either side of w q . Well above 5.9 GHz, the loss slope gradually increases until the loss in dB is growing in direct proportion to frequency.

The cable may be successfully operated at frequencies up to nearly 8 GHz without fear of exciting any unusual non-TEM modes of propagation.

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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