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

Outline

Introduction Problem Formulation Alleviation of Meander Segments Experimental Results Conclusion

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

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.

Problem Formulation

Input: The original PCB routing Given area constraints

Output: A refined PCB routing

Objective: Enlarge the widths of the dense meander segme

nts as much as possible without changing the original wirelength or violating the given area constraints

Alleviation of Meander Segments

Removal of dense meander segments Delete dense meander segment with width

smaller than a predefined value wt.

Alleviation of Meander Segments

Growth of meander segments and space sharing

Alleviation of Meander Segments

Modeling the patterns in a given free space

Alleviation of Meander Segments The distance between horizontal wire segments

should always be larger than dm.

Alleviation of Meander Segments

The 0-1 variable ti,j defines whether a subordinate m

eander segments can exist in the final routing. If a subordinate meander segment does not exist, t

he ones below it cannot be created to extend wirelength.

Alleviation of Meander Segments

Alleviation of Meander Segments

The maximum number of possible meander segments in a free space:

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.

Alleviation of Meander Segments

For the ith wire, the compensated length can be expressed as:

Alleviation of Meander Segments

A group of wires has free spaces at both sides of it.

Push upwards

Push downwards

Alleviation of Meander Segments

Modeling the sharing free space by multiple wire groups

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 =0ci,j =1

ci,k =0

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

Alleviation of Meander Segments

The total compensated length for the jth wire can be computed as:

Alleviation of Meander Segments

Try to maximize the compensated wirelength.

The objective function:

Alleviation of Meander Segments

Binary search

Solve the ILP n times

Experimental Results

Experimental Results

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.