1. Worst Case Crosstalk Noise for Nonswitching Victims in High-Speed Buses
Jun Chen and Lei He

2. Outline Introduction Preliminaries WCN without timing constraint
WCN problem with timing window constraints
Conclusion

3. Outline Introduction Preliminaries WCN without timing constraint
WCN problem with timing window constraints
Conclusion

4. Introduction
The coupling-induced crosstalk noise gains growing importance in deep-submicrometer circuits and circuits with higher clock frequency
Crosstalk noise may cause variation of delay and logic failure of a victim net
In multigigahertz designs, the inductive crosstalk noise can no longer be ignored

5. Introduction (cont.)
Worst case delay (WCD): the maximum possible delay caused by crosstalk noise
Worst case noise (WSN): the maximum possible crosstalk noise
For the RC model, the WCN problem is formulated as finding the alignment of switching times for multiple aggressors such that WCN is reached

6. Introduction (cont.)
With the consideration of inductance, the WCN problem becomes much more complicated:
Switching patterns, alignment, and switching direction
Coupling between both adjacent and nonadjacent interconnects
Routing direction

7. Outline Introduction Preliminaries WCN without timing constraint
WCN problem with timing window constraints
Conclusion

8. Preliminaries victim types: quiet, noisy, or switching
Only non-switching victims are considered
Arbitrary switching patterns for aggressors
Assume all drivers(receivers) have a uniform size and are cascaded inverters
Assume all wires have uniform width and spacing

9. Preliminaries (cont.)
Only coupling capacitance between adjacent wires are considered
Full partial element equivalent circuit(PEEC):
Self-inductance for each wire segment
Mutual inductance between any pair of wire segments

10. Outline Introduction Preliminaries WCN without timing constraint
WCN problem with timing window constraints
Conclusion

11. WCN under RC model No resonance in the noise waveform
The problem can be reduced as the alignment of aggressor switching times
Simultaneous switching(SS)
Superposition(SP)
Aligned switching(AS)

12. Impact of shielding for RLC model
Assume there are shield at both edges of the bus structure

13. Impact of switching pattern for RLC model
The waveform may have resonance due to inductance under the RLC model

14. Impact on routing direction for RLC model
Signals are routed either from left(top) to right(down) or from right(down) to left(top)

15. Algorithms for the quiet victim
SS: All aggressors switch simultaneously in the same direction.
SP: Find the maximum noise peak for each aggressor when only this aggressor switches
AS: Obtain the individual noise waveform by simulating the interconnect structure with only one aggressor switching for each time
PP alignment
NN alignment
PN alignment
Simulated annealing(SA) and genetic algorithm(GA)

16. New algorithm
SS + AS: WCN is approximated by the larger one between the results obtained by SS and AS

17. Time complexity

18. Experiments with the quiet victim
Aligned bus
Different routing direction
Unaligned bus

19. Aligned bus

20. Different routing direction

21. Unaligned bus

22. Noisy victim
SS:

23. Noisy victim (cont.)
SP: Sum of all peak noise values and the peak value of the propagated noise
AS: Treat the propagated noise as an individual noise waveform of an extra aggressor

24. Noisy victim (cont.)

25. Outline Introduction Preliminaries WCN without timing constraint
WCN problem with timing window constraints
Conclusion

26. WCN problem with timing window constraints
Each aggressor has the switching timing window
The victim has the sampling timing window at the far end
Both timing windows should be considered in the algorithm

27. AS Algorithm
For PN alignment:

28. Expansion of noise waveform

29. SS Algorithm
Determine all the overlapped regions for the timing windows of all the aggressors
For each such regions, find the simultaneous switching noise within the sampling window
The largest noise among the simultaneous switching noise of all the overlapped regions is the WCN

30. Experiments
The timing windows and routing directions are randomly generated
Aligned bus structure
The driver size is 100X
The victim is quiet

31. Experimental results

32. Comparison of WCN under RLC and RC
Aggressor switching windows size = 20(ps)
Victim sampling windows size = 10(ps)

33. Comparison of WCN under RLC and RC
Aggressor switching windows size = 30(ps)
Victim sampling windows size = 15(ps)

34. Comparison of WCN under RLC and RC
Aggressor switching windows size = 50(ps)
Victim sampling windows size = 25(ps)

35. Outline Introduction Preliminaries WCN without timing constraint
WCN problem with timing window constraints
Conclusion

36. Conclusion
Both switching time and switching logic pattern of aggressors affect the WCN under the RLC model and the routing direction also impacts WCN significantly under RLC model
A new SS + AS with linear time complexity has proposed, which has an average underestimation of 3%