1. Escape Routing of Mixed-Pattern Signals Based on Staggered-Pin- Array PCBs K. Wang, H. Wang and S. Dong Department of Computer Science & Technology, Tsinghua University, China ISPD 2013

2. Outline Introduction Preliminaries Problem Formulation The Mixed-Pattern Escape Routing Algorithm Experimental Results Conclusion

3. Introduction High speed PCB routing has become more and more difficult for manual design due to increased pin count and dwindling routing resource. Pin array  Grid pin array (GPA)  Staggered pin array (SPA) SPA can increase pin density greatly under the same area.

4. Introduction GPA Single-pattern escape routing SPA Single-pattern escape routing SPA Mixed-pattern escape routing

5. Introduction Solve differential-pair routing and single-signal routing separately Optimize both differential-pair and single-signal routing

6. Preliminaries Tile network Staggered pin arrayTile network

7. Problem Formulation Given  An mxn staggered pin array  Differential pairs and single signals to be routed to the boundary  Design rules including wire length matching of differential pairs, non-crossing rules  Capacity constraints Objective  Escape all marked pins to the array boundary with minimized total wire length.  No design rule is violated.

8. The mixed-pattern escape routing algorithm

9. Differential Pair Pre-conditioning Different from single signals, the pins of differential pairs have more constraints  The routing of differential pairs should satisfy the length- matching rule.  Differential pair protection constraint: In order to avoid signal crosstalk, before the two wires from the two pins of differential pair meet with each other, no other signal is allowed to be close to.

10. Differential Pair Pre-conditioning illegallegal

11. Median point searching algorithm Case 1: y a =y b Case 2: x a =x b |y a -y b | is not multiple of 4 Case 3: x a =x b |y a -y b | is multiple of 4

12. Median point searching algorithm

14. Simultaneously median point and shortest pin-median-point path determination The differential pairs can be classified into K groups according to the crossing possibility of path candidates.

15. Routing Network S0S0 S SDSD Median point StSt 1 1 |T D | |P S | |T D |+|P S | 1

16. ILP formulation Source constraint Sink constraint

17. ILP formulation DP flow conservation constraint Single signals flow conservation constraint Capacity constraint DP protection constraint

18. Slice-based MPER Algorithm

19. Partition into apartNum regions DPs and single signals are classified into each region Generate routing network for each region and solve the ILP Failed signals will be redistributed into nearby region which has the most routing resource

20. Experimental Results

22. Conclusion This paper proposed an algorithm for escape routing of simultaneously differential pairs and single signals on staggered pin array based PCB. Experimental results show that the proposed method can solve both single-pattern and mixed- pattern effectively.