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