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
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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
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Outline
Introduction Problem Formulation Alleviation of Meander Segments Experimental Results Conclusion
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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
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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.
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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
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Alleviation of Meander Segments
Removal of dense meander segments Delete dense meander segment with width
smaller than a predefined value wt.
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Alleviation of Meander Segments
Growth of meander segments and space sharing
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Alleviation of Meander Segments
Modeling the patterns in a given free space
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Alleviation of Meander Segments The distance between horizontal wire segments
should always be larger than dm.
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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.
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Alleviation of Meander Segments
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Alleviation of Meander Segments
The maximum number of possible meander segments in a free space:
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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.
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Alleviation of Meander Segments
For the ith wire, the compensated length can be expressed as:
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Alleviation of Meander Segments
A group of wires has free spaces at both sides of it.
Push upwards
Push downwards
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Alleviation of Meander Segments
Modeling the sharing free space by multiple wire groups
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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
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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
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Alleviation of Meander Segments
The total compensated length for the jth wire can be computed as:
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Alleviation of Meander Segments
Try to maximize the compensated wirelength.
The objective function:
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Alleviation of Meander Segments
Binary search
Solve the ILP n times
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Experimental Results
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Experimental Results
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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.