lemar: a novel length matching routing algorithm for analog and mixed signal circuits h. yao, y. cai...
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LEMAR: A Novel Length Matching Routing Algorithm for Analog and Mixed Signal Circuits
H. Yao, Y. Cai and Q. Gao
EDA Lab, Department of CS, Tsinghua University, Beijing, China
ASPDAC 2012
Outline
Introduction Problem Formulation and Overall Flow Tile-based Detouring Tile Path Searching and Detouring Experimental Results Conclusions
Introduction
The design automation for analog and mixed signal circuit components in SOCs is attracting increasing interests.
Mismatches in electrical characteristics (e.g., parasitic capacitance and resistance) between two matching nets will cause circuit malfunctions.
It is very important to enforce the matching constraint on certain analog signals.
Introduction
Problem Formulation
This paper focused on the single-layer length matching routing problem for two nets.
Given: A single-layer routing area R with a set of routing obstacles O an
d two nets n1 and n2. Find:
Routing paths p1 and p2 for nets n1 and n2 to minimize the total wirelength.
Subject to: The routing obstacles in O are avoided. There are no design rule violations. p1 and p2 are of the same length.
Overall Flow
Tile-Based Detouring
Partitioning of the routing area Expand obstacles by WSmin/2 called obstacle tiles. Represent the source and target pins as rectangular tiles
called pin tiles. The routing area is partitioned by the boundaries of all the
pin tiles and obstacle tiles.
Tile-Based Detouring
There is a special type of space tiles called tiny tiles, whose width or height is smaller than a pitch.
pitch = WSmin + WWmin. During the partitioning of the routing area, merge th
e tiny tiles into the adjacent tiles.
Tile-Based Detouring
Estimation of the detouring length Nets can make detours in the free tiles. The detouring length Ld can be calculated as follows:
Sa: the area of the original tile
S: the area of the wasted region
Tile-Based Detouring
Transformation of Different Tiles According to the entrance and exit points within the tile,
free tiles can be classified into two categories: Entrance and exit are on the diagonal corners. Entrance and exit are on the same edge.
The two different cases can be transformed into single type of tile by some operations.
All the free tiles are transformed into a single case, where entrance and exit are on the bottom left and top right corners of tile.
Tile-Based Detouring
Transformation of Different Tiles
Tile-Based Detouring
Detouring Pattern To obtain maximum detouring length, adopt two detouring
patterns according to the geometric shape of a free tile: Narrow pattern: width or height of a tile < 4 X pitch Standard pattern: width and height of a tile > 4 X pitch
Narrow pattern Standard pattern
Tile Path Searching and Detouring A*-Search Algorithm for tile path
Terminate condition
Backtrack strategy
costF = costG + costH
costG: cost from ts to tcur
costH: Manhattan distance from tnew to tt.
Tile Path Searching and Detouring
The backtrack strategy is used in the tile searching process.
If tcur is tt, but the max length from ts to tt of the curre
nt tile path is smaller then Lobj, the algorithm would s
et tcur free.
tcur would be equal to a neighbor tile of tt, and expan
d to tt again.
This would force tile path to detour around the tt to i
ncrease the detouring length.
Tile Path Searching and Detouring
Minimum Length and Maximum Length If there is not a turn at tcur, the relative position of source p
oint in tnew is the same as tcur.
curt
Tile Path Searching and Detouring
Minimum Length and Maximum Length If the first turn of tile path is at tcur, the width or height of tcur
is pitch.
Tile Path Searching and Detouring
Detouring after Searching The routing path is detoured in the tiles one by one from tt
to ts.
The desired wirelength in each tile can be calculated as follows:
The maximum detour length of each tile: Lmaxt
The detouring length Ld of each tile:
Tile Path Searching and Detouring
Adjust the height of some detouring parts
Experimental Results
Experimental Results
Experimental Results
Conclusions
This paper presents a novel detailed routing algorithm for length matching problem.
Future work includes extending the algorithm for matching more than two nets simultaneously and evenly distributed detouring wires to avoid local congestion.