Civil Engineering Reference
In-Depth Information
tails‚ the reader is referred to [KR95‚ Fri95‚ CHKM96]. As we will see‚ hybrid
tree/mesh structures are also commonly used in high-performance design.
9.2.1 H-tree-like approaches
Early methods for clock tree design attempted to achieve zero-skew by bal-
ancing the wire length to each sink. H-trees [FK82]‚ illustrated in Figure 9.4
and so named because of their structure‚ were recognized for years as a tech-
nique to help reduce the skew in synchronous systems. The H-tree ensured‚
by construction‚ that all sinks of the clock tree are equidistant from the clock
source. For regular structures such as systolic arrays‚ the H-tree works well to
reduce skew‚ but in the general case‚ asymmetric distributions of clock pins are
common and a symmetric H-tree may not be effective for clock routing. To
address this issue‚ the method of recursive geometric matching [KCR91] and
the method of means and medians [JSK90] were proposed; these extend the
H-tree idea to structures with a smaller degree of regularity.
Nevertheless‚ H-trees have still been used very widely because of their regular
structure‚ which makes it easy to account for routing resource utilization. It
is common in high-performance design to build a backbone structure that is
based on an H-tree and to size the wires suitably so as to achieve zero skew
[PMP93‚ PMOP93].
9.2.2
Exact zero-skew clock routing
Early H-tree based methods used symmetric structures‚ and simplified the prob-
lem of equalizing the clock delays into the geometric problem of equalizing the
