Post-Route Alleviation of Dense Meander Segments in High-Performance Printed Circuit Boards

1. Post-Route Alleviation of Dense Meander Segments in High-Performance Printed Circuit Boards T. Tseng, B. Li, T. Ho and U. Schlichtmann Technische Universitaet Muenchen Munich, Germany ICCAD 2013

2. Outline • Introduction • Problem Formulation • Alleviation of Meander Segments • Experimental Results • Conclusion

3. Introduction • Length-matching is an important technique to balance delays of bus signals in PCB routing. • Existing routers may generate dense meander segments with small distance. Meander segment

4. Introduction • This paper proposes a post-processing method to enlarge the width and the distance of meander segment so that the crosstalks can be reduced.

5. Problem Formulation • Input: • The original PCB routing • Given area constraints • Output: • A refined PCB routing • Objective: • Enlarge the widths of the dense meander segments as much as possible without changing the original wirelength or violating the given area constraints

6. Alleviation of Meander Segments • Removal of dense meander segments • Delete dense meander segment with width smaller than a predefined value wt.

7. Alleviation of Meander Segments • Growth of meander segments and space sharing

8. Alleviation of Meander Segments • Modeling the patterns in a given free space

9. Alleviation of Meander Segments • The distance between horizontal wire segments should always be larger than dm.

10. Alleviation of Meander Segments • The 0-1 variable ti,j defines whether a subordinate meander segments can exist in the final routing. • If a subordinate meander segment does not exist, the ones below it cannot be created to extend wirelength.

11. Alleviation of Meander Segments

12. Alleviation of Meander Segments • The maximum number of possible meander segments in a free space:

13. Alleviation of Meander Segments • Align the meander segments on different wires so that they can be formed into a group. • Force the solver to select the meander segments from the beginnings of the wires.

14. Alleviation of Meander Segments • For the ith wire, the compensated length can be expressed as:

15. Alleviation of Meander Segments • A group of wires has free spaces at both sides of it. Push upwards Push downwards

16. Alleviation of Meander Segments • Modeling the sharing free space by multiple wire groups

17. Alleviation of Meander Segments • Assign a 0-1 variable ci,j for the wire group pair (wgi, wgj) • If ci,j =1, wgi can pass wgj; otherwise, wgi is blocked by wgj. ci,j =1 ci,k =0 ci,j =0

18. Alleviation of Meander Segments • If (j-1)th wire group is below the jth wire group. If wgi is blocked by wgj from the left side, ci,j =0 If ci,j =1

19. Alleviation of Meander Segments • The total compensated length for the jth wire can be computed as:

20. Alleviation of Meander Segments • Try to maximize the compensated wirelength. • The objective function:

21. Alleviation of Meander Segments Solve the ILP n times Binary search

22. Experimental Results

23. Experimental Results

24. Conclusion • This paper addressed the delay speedup problem caused by dense meander segments in high-performance PCBs. • This paper proposed a post-processing framework modeling patterns in free space and area sharing using 0-1 variables.