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Crosstalk

Crosstalk. Calculation and SLEM. Topics. Crosstalk and Impedance Superposition Examples SLEM. Cross Talk and Impedance. Impedance is an electromagnetic parameter and is therefore effected by the electromagnetic environment as shown in the preceding slides.

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Crosstalk

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  1. Crosstalk Calculation and SLEM

  2. Topics • Crosstalk and Impedance • Superposition • Examples • SLEM Crosstalk Calculation

  3. Cross Talk and Impedance Impedance is an electromagnetic parameter and is therefore effected by the electromagnetic environment as shown in the preceding slides. In the this second half, we will focus on looking at cross talk as a function of impedance and some of the benefits of viewing cross talk from this perspective. Crosstalk Calculation

  4. Using Modal Impedance’s for Calculating Cross Talk • Any state can be described as a superposition of the system modes. • Points to Remember: • Each mode has an impedance and velocity associated with it. • In homogeneous medium, all the modal velocities will be equal. Crosstalk Calculation

  5. Odd Mode Switching Even Mode Switching Line 2 Line 1 ½ Even Mode V V 0.5 0.5 Time Time ½ Odd Mode V V 0.5 -0.5 Time Time Digital States that can occur in a 2 conductor system Total of 9 states = Single bit state 1.0 V V Time Time Super Positioning of Modes For a two line case, there are two modes + Crosstalk Calculation

  6. 50[inches] 30[Ohms] W=7mils S=10mils t=1.5 mils H=4.5 mils Er=4.5 Output? ? ? ? ? V V V V Line A Time Time Time Time Line B At Driver At Receiver Two Coupled Line Example Calculate the waveforms for two coupled lines when one is driven from the low state to the high and the other is held low. Input V Line A Time 1.0 V Line B Time Crosstalk Calculation

  7. 50[inches] 30[Ohms] W=7mils S=10mils t=1.5 mils H=4.5 mils Er=4.5 Two Coupled Line Example (Cont..) First one needs the [L] and [C] matrices and then I need the modal impedances and velocities. The following [L] and [C] matrices were created in HSPICE. • Sanity Check: • The odd and even velocities are the same Lo = 3.02222e-007 3.34847e-008 3.02222e-007 Co = 1.67493e-010 -1.85657e-011 1.67493e-010 Zodd 38.0 [Ohms] Vodd 1.41E+08 [m/s] Zeven 47.5 [Ohms] Veven 1.41E+08 [m/s] Crosstalk Calculation

  8. Line B Line A Case i Case ii ½ Even Mode This allows one to solve four easy problems and simply add the solutions together! Case iii Case iv V V 0.5 0.5 ½ Odd Mode Time Time V V 0.5 -0.5 Time Time 1.0 = Single bit state V V Time Time Line A Line B Two Coupled Line Example (Cont..) Now I deconvolve the the input voltage into the even and odd modes: Crosstalk Calculation

  9. 50[inches] 30[Ohms] V V 0.5 0.5 Time Time Driver (even) Receiver (even) 0.612[V] 0.612[V] 0.306[V] 0.306[V] 0.000[V] 0.000[V] 0.0[ns] 0.0[ns] 9.0[ns] 9.0[ns] Two Coupled Line Example (Cont..) Case i and Case ii are really the same: A 0.5[V] step into a Zeven=47.5[W] line: Line B Line A Case ii Case i Td=len*Veven=8.98[ns] Vinit=0.5[V]*Zeven/(Zeven+30[Ohms]) Vinit=.306[V] Vrcvr=2*Vinit=.612[V] Zodd 38.0 [Ohms] Vodd 1.41E+08 [m/s] Zeven 47.5 [Ohms] Veven 1.41E+08 [m/s] Crosstalk Calculation

  10. 50[inches] 30[Ohms] V Driver (odd) Receiver (odd) 0.558[V] 0.558[V] -0.5 Time 0.279[V] 0.279[V] 9.0[ns] 9.0[ns] 0.000[V] 0.000[V] -.279[V] -.279[V] -.558[V] -.558[V] Two Coupled Line Example (Cont..) Case iii is -0.5[V] step into a Zodd=38[W] line: Line A Case iii Td=len*Vodd=8.98[ns] Vinit=-0.5[V]*Zodd/(Zodd+30[Ohms]) Vinit=-.279[V] Vrcvr=2*Vinit=-.558[V] Zodd 38.0 [Ohms] Vodd 1.41E+08 [m/s] Zeven 47.5 [Ohms] Veven 1.41E+08 [m/s] Crosstalk Calculation

  11. 50[inches] 30[Ohms] V 0.5 Time Driver (odd) 0.558[V] 0.279[V] 0.000[V] 0.0[ns] 9.0[ns] Two Coupled Line Example (Cont..) Case iv is 0.5[V] step into a Zodd=38[W] line: Line B Case iv Td=len*Vodd=8.98[ns] Vinit=0.5[V]*Zodd/(Zodd+30[Ohms]) Vinit=.279[V] Vrcvr=2*Vinit=.558[V] Zodd 38.0 [Ohms] Vodd 1.41E+08 [m/s] Zeven 47.5 [Ohms] Veven 1.41E+08 [m/s] Receiver (odd) 0.558[V] 0.279[V] 0.000[V] 0.0[ns] 9.0[ns] Crosstalk Calculation

  12. Line A (Driver) Line A (Driver) Line B (Driver) Line B (Driver) .306+.279=.585[V] .306+.279=.585[V] .306-.279=.027[V] .306-.279=.027[V] 1.0[V] 1.0[V] 1.0[V] 1.0[V] 1.0[V] 1.0[V] 0.5[V] 0.5[V] 0.5[V] 0.5[V] 0.5[V] 0.5[V] 0.0[V] 0.0[V] 0.0[V] 0.0[V] 0.0[V] 0.0[V] 9.0[ns] 9.0[ns] 9.0[ns] 9.0[ns] 9.0[ns] 9.0[ns] -0.5[V] -0.5[V] -0.5[V] -0.5[V] -0.5[V] -0.5[V] -1.0[V] -1.0[V] -1.0[V] -1.0[V] -1.0[V] -1.0[V] Line A (Receiver) Line B (Receiver) Driver (odd) 6.12-.558= .0539[V] 0.558[V] Driver (odd) Driver (even) Driver (even) 0.279[V] 9.0[ns] 0.558[V] 0.612[V] 0.612[V] 0.000[V] 0.279[V] 0.306[V] 0.306[V] -.279[V] .612+.558=1.17[V] 0.000[V] 0.000[V] 0.000[V] -.558[V] 0.0[ns] 0.0[ns] 0.0[ns] 9.0[ns] 9.0[ns] 9.0[ns] Two Coupled Line Example (Cont..) Crosstalk Calculation

  13. Two Coupled Line Example (Cont..) Simulating in HSPICE results are identical to the hand calculation: Crosstalk Calculation

  14. Assignment1 • Use PSPICE and perform previous simulations Crosstalk Calculation

  15. W=7mils S=10mils t=1.5 mils H=4.5 mils Er=4.5 Super Positioning of Modes Continuing with the 2 line case, the following [L] and [C] matrices were created in HSPICE for a pair of microstrips: • Note: • The odd and even velocities are NOT the same Zodd=47.49243354 [Ohms] Vodd=1.77E+08[m/s] Zeven=54.98942739 [Ohms] Veven=1.64E+08 [m/s] Lo = 3.02222e-007 3.34847e-008 3.02222e-007 Co = 1.15083e-010 -4.0629e-012 1.15083e-010 Crosstalk Calculation

  16. Microstrip Example The solution to this problem follows the same approach as the previous example with one notable difference. The modal velocities are different and result in two different Tdelays: Tdelay (odd)= 7.19[ns] Tdelay (even)= 7.75[ns] This means the odd mode voltages will arrive at the end of the line 0.56[ns] before the even mode voltages Crosstalk Calculation

  17. Microstrip Cont.. HSPICE Results: Single Bit switching, two coupled microstrip example Crosstalk Calculation

  18. HSPICE Results of Microstrip The width of the pulse is calculated from the mode velocities. Note that the widths increases in 567[ps] increments with every transit Calculation Crosstalk Calculation 567[ps] 1134[ps] 1701[ps] 2268[ps]

  19. Assignment 2 and 3 • Use PSPICE and perform previous simulations Crosstalk Calculation

  20. Modal Impedance’s for more than 2 lines • So far we have looked at the two line crosstalk case, however, most practical busses use more than two lines. • Points to Remember: • For ‘N’ signal conductors, there are ‘N’ modes. • There are 3N digital states for N signal conductors • Each mode has an impedance and velocity associated with it. • In homogeneous medium, all the modal velocities will be equal. • Any state can be described as a superposition of the modes Crosstalk Calculation

  21. Three Conductor Considerations There are 3N digital states for N signal conductors Crosstalk Calculation

  22. S=10mils S=10mils t=1.5 mils H=4.5 mils W=7mils Er=4.5 Three Coupled Microstrip Example From HSPICE: Lo = 3.02174e-007 3.32768e-008 3.01224e-007 9.01613e-009 3.32768e-008 3.02174e-007 Co = 1.15088e-010 -4.03272e-012 1.15326e-010 -5.20092e-013 -4.03272e-012 1.15088e-010 Crosstalk Calculation

  23. Three Coupled Microstrip Example Actual modal info: Using the approximations gives: Z[1,1,1]=59.0[Ohms] Z[1,-1,1]=44.25[Ohms] Modal velocities The three mode vectors The Approx. impedances and velocities are pretty close to the actual, but much simpler to calculate. Crosstalk Calculation

  24. Three Coupled Microstrip ExampleSingle Bit Example: HSPICE Result Crosstalk Calculation

  25. Points to Remember • The modal impedances can be used to hand calculate crosstalk waveforms • Any state can be described as a superposition of the modes • For ‘N’ signal conductors, there are ‘N’ modes. • There are 3N digital states for N signal conductors • Each mode has an impedance and velocity associated with it. • In homogeneous medium, all the modal velocities will be equal. Crosstalk Calculation

  26. Crosstalk Trends • Key Topics: • Impedance vs. Spacing • SLEM • Trading Off Tolerance vs. Spacing Crosstalk Calculation

  27. Impedance vs Line Spacing • As we have seen in the preceding sections, • 1) Cross talk changes the impedance of the line • 2) The further the lines are spaced apart the the less the impedance changes Crosstalk Calculation

  28. Single Line Equivalent Model(SLEM) • SLEM is an approximation that allows some cross talk effects to be modeled without running fully coupled simulations • Why would we want to avoid fully coupled simulations? • Fully coupled simulations tend to be time consuming and dependent on many assumptions Crosstalk Calculation

  29. Zo=90[W] Zo=40[W] 30[Ohms] 30[Ohms] Single Line Equivalent Model(SLEM) • Using the knowledge of the cross talk impedances, one can change a single transmission line’s impedance to approximate: • Even, Odd, or other state coupling Equiv to Even State Coupling Equiv to Odd State Coupling Crosstalk Calculation

  30. V1 Time V2 Time V3 Time Single Line Equivalent Model(SLEM) • Limitations of SLEM • SLEM assumes the transmission line is in a particular state (odd or even) for it’s entire segment length • This means that the edges are in perfect phase • It also means one can not simulate random bit patterns properly with SLEM (e.g. Odd -> Single Bit -> Even state) The edges maybe in phase here, but not here 1 2 3 1 2 3 Three coupled lines, two with serpentining Crosstalk Calculation

  31. Vinit=Vin(Zstate/(Rin+Zstate)) Single Line Equivalent Model(SLEM) • How does one create a SLEM model? • There are a few ways • Use the [L] and [C] matrices along with the approximations • Use the [L] and [C] matrices along with Weimin’s MathCAD program • Excite the coupled simulation in the desired state and back calculate the equivalent impedance (essentially TDR the simulation) Crosstalk Calculation

  32. Trading Off Tolerance vs. Spacing • Ultimately in a design you have to create guidelines specifying the trace spacing and specifying the tolerance of the motherboard impedance • i.e. 10[mil] edge to edge spacing with 10% impedance variation • Thinking about the spacing in terms of impedance makes this much simpler Crosstalk Calculation

  33. Trading Off Tolerance vs. Spacing • Assume you perform simulations with no coupling and you find a solution space with an impedance range of • Between ~35[W] to ~100[W] • Two possible 65[W] solutions are • 15[mil] spacing with 15% impedance tolerance • 10[mil] spacing with 5% impedance tolerance Crosstalk Calculation

  34. Reducing Cross Talk • Separate traces farther apart • Make the traces short compared to the rise time • Make the signals out of phase • Mixing signals which propagate in opposite directions may help or hurt (recall reverse cross talk!) • Add Guard traces • One needs to be careful to ground the guard traces sufficiently, otherwise you could actually increase the cross talk • At GHz frequency this becomes very difficult and should be avoided • Route on different layers and route orthogonally Crosstalk Calculation

  35. In Summary: • Cross talk is unwanted signals due to coupling or leakage • Mutual capacitance and inductance between lines creates forward and backwards traveling waves on neighboring lines • Cross talk can also be analyzed as a change in the transmission line’s impedance • Reverse cross talk is often the dominate cross talk in a design • (just because the forward cross talk is small or zero, does not mean you can ignore cross talk!) • A SLEM approach can be used to budget impedance tolerance and trace spacing Crosstalk Calculation

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