1. Crosstalk Calculation and SLEM

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

3. 3 Crosstalk Calculation 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.

4. 4 Crosstalk Calculation 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.

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

6. 6 Crosstalk Calculation 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. H=4.5 mils t=1.5 mils W=7mils Er=4.5 S=10mils 30[Ohms] 50[inches] Input V Time V 1.0 Line A Line B Output? V Time ? V ? Line A Line B At DriverAt Receiver V Time ? V ?

7. 7 Crosstalk Calculation 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. Lo = 3.02222e-007 3.34847e-008 3.02222e-007 Co = 1.67493e-010 -1.85657e-011 1.67493e-010 Zodd38.0 [Ohms] Vodd1.41E+08 [m/s] Zeven47.5 [Ohms] Veven1.41E+08 [m/s] H=4.5 mils t=1.5 mils W=7mils Er=4.5 S=10mils Sanity Check: The odd and even velocities are the same 30[Ohms] 50[inches]

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

9. 9 Crosstalk Calculation Two Coupled Line Example (Cont..) Zodd38.0 [Ohms] Vodd1.41E+08 [m/s] Zeven47.5 [Ohms] Veven1.41E+08 [m/s] 30[Ohms] 50[inches] Case i and Case ii are really the same: A 0.5[V] step into a Zeven=47.5[  ] line: Line A Line B 0.5 V Time 0.5 V Time Case i Case ii Td=len*Veven=8.98[ns] Vinit=0.5[V]*Zeven/(Zeven+30[Ohms]) Vinit=.306[V] Vrcvr=2*Vinit=.612[V] 0.000[V] Driver (even) 0.0[ns] 9.0[ns] 0.306[V] 0.612[V] 0.000[V] Receiver (even) 0.0[ns] 9.0[ns] 0.306[V] 0.612[V]

10. 10 Crosstalk Calculation Two Coupled Line Example (Cont..) Zodd38.0 [Ohms] Vodd1.41E+08 [m/s] Zeven47.5 [Ohms] Veven1.41E+08 [m/s] 30[Ohms] 50[inches] Case iii is -0.5[V] step into a Zodd=38[  ] line: Line A Td=len*Vodd=8.98[ns] Vinit=-0.5[V]*Zodd/(Zodd+30[Ohms]) Vinit=-.279[V] Vrcvr=2*Vinit=-.558[V] Driver (odd) 0.000[V] 9.0[ns] 0.279[V] 0.558[V] -.558[V] -.279[V] Receiver (odd) 0.000[V] 9.0[ns] 0.279[V] 0.558[V] -.558[V] -.279[V] -0.5 V Time Case iii

11. 11 Crosstalk Calculation Two Coupled Line Example (Cont..) Zodd38.0 [Ohms] Vodd1.41E+08 [m/s] Zeven47.5 [Ohms] Veven1.41E+08 [m/s] 30[Ohms] 50[inches] Case iv is 0.5[V] step into a Zodd=38[  ] line: Td=len*Vodd=8.98[ns] Vinit=0.5[V]*Zodd/(Zodd+30[Ohms]) Vinit=.279[V] Vrcvr=2*Vinit=.558[V] 0.000[V] Driver (odd) 0.0[ns] 9.0[ns] 0.279[V] 0.558[V] 0.000[V] Receiver (odd) 0.0[ns] 9.0[ns] 0.279[V] 0.558[V] 0.5 V Time Line B Case iv

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

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

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

15. 15 Crosstalk Calculation 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: Lo = 3.02222e-007 3.34847e-008 3.02222e-007 Co = 1.15083e-010 -4.0629e-012 1.15083e-010 Zodd=47.49243354 [Ohms] Vodd=1.77E+08[m/s] Zeven=54.98942739 [Ohms] Veven=1.64E+08 [m/s] H=4.5 mils t=1.5 mils W=7mils Er=4.5 S=10mils Note: The odd and even velocities are NOT the same

16. 16 Crosstalk Calculation 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

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

18. 18 Crosstalk Calculation 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 567[ps]1134[ps]1701[ps]2268[ps] Calculation

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

20. 20 Crosstalk Calculation 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 3 N 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

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

22. 22 Crosstalk Calculation Three Coupled Microstrip Example H=4.5 mils t=1.5 mils W=7mils Er=4.5 S=10mils 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

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

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

25. 25 Crosstalk Calculation 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 3 N 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.

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

27. 27 Crosstalk Calculation 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

28. 28 Crosstalk Calculation 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

29. 29 Crosstalk Calculation 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 30[Ohms] Zo=90[  ] 30[Ohms] Zo=40[  ] Equiv to Even State Coupling Equiv to Odd State Coupling

30. 30 Crosstalk Calculation 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 Three coupled lines, two with serpentining V2 Time V1 Time V3 Time 123123 123123

31. 31 Crosstalk Calculation 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 ) Vinit=Vin(Zstate/(Rin+Zstate))

32. 32 Crosstalk Calculation 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

33. 33 Crosstalk Calculation 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[  ] to ~100[  ] Two possible 65[  ] solutions are 15[mil] spacing with 15% impedance tolerance 10[mil] spacing with 5% impedance tolerance

34. 34 Crosstalk Calculation 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

35. 35 Crosstalk Calculation 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