### Fast Timing-Model Independent Buffered Clock

```Xin-Wei Shih and Yao-Wen Chang
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Introduction
Problem formulation
Algorithms
Experimental results
Conclusions
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Skew-minimized buffered clock-tree
synthesis plays an important role in highperformance VLSI designs for synchronous
circuits.
Due to the insufficient accuracy of existing
timing models for modern chip design,
embedding simulation process into a clocktree synthesis flow becomes inevitable.
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A possible way to improve the speed is
performing the clock construction by
structure optimization.
◦ Mesh
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In this paper, a novel timing-model
independent buffered clock tree synthesis
method is proposed.
◦ Buffering and wiring structures of all paths from the
clock source to its sinks are almost the same.
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Problem: Buffered Clock-Tree Synthesis (BCTS)
Instance: Given a set of clock sinks, a slewrate constraint, and a library of buffers.
Question: Construct a buffered clock tree to
minimize its skew, subject to no slew-rate
violation.
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The number of leaves (sinks) can be treated
as a multiplication sequence of branching.
◦ This multiplication sequence exactly forms a
factorization.
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Then, the BNP is arranged in the nonincreasing order1 of the factorization list.
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A top-down manner like [10] or a bottom-up
one like [7, 11], they can hardly apply to non
binary tree structures.
Therefore, we propose a novel partitioning
method, which can not only handle nonbinary tree structures, but also achieve good
quality in terms of the cluster diameter.
◦ cluster diameter : the maximum distance among
sub-trees within the same cluster.
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We borrow the idea of cake cutting, i.e.,
slicing a cake into pieces from the center of
the cake.
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Since the identical branch numbers at the same
level are required in the symmetrical structure, a
pseudo sink should be transformed into a
dangling wire to maintain the symmetry.
For partitioning, we relax that the sizes of
clusters in a partition can differ by at most one
for the first recursion.
For node embedding, we let the embedding
regions of pseudo sinks cover the entire chip.
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A top-down manner
◦ By tracing along the tree edges, once the slew rate
is about to violate the constraint, identical buffers
are inserted for all branches.
◦ Insert identical buffers in terms of the type and the
size at the same level.
◦ The slew rate is approximated by accumulated
capacitance starting from the latest inserted buffer.
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Implemented in the C++ programming
language on a 2.6 GHz AMD-64 workstation.
Four ISPD’09 Clock Network Synthesis
Contest benchmarks with no blockages [17]
and the IBM benchmarks [19].
Use ngspice [13] simulation based on the
45nm process technology [14] to evaluate the
quality.
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clock skew (skew)
clock-latency range(CLR)
total resource usage (usage)
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We have presented a fast timing-model
independent buffered clock tree synthesis
method to construct a symmetrical clock tree