Civil Engineering Reference
In-Depth Information
into node
where
is the voltage at node
This is illustrated by the example
in Figure 3.10.
This modified network now consists entirely of resistors and current sources.
Taking the input node‚ which is at voltage of 1 after
as the datum‚ its
nodal equations for
may be written as
In other words‚
where the vector‚
1
‚ has all entries equal to 1.
Since‚ from Equation (3.8)‚ the Elmore delay at node
is given by
we can write
3.4.2 A closed-form Elmore delay expression for RC trees
In general‚ inverting
G
is a tedious and computationally expensive procedure.
However‚ in the case of an RC tree‚
admits a closed form‚ and the Elmore
delay at node
can be written down by inspection as follows. Let
be the
unique path from the input node
to some internal node
of the tree‚ and
for any two nodes
and
in the tree‚ we will denote
as the
portion of the path between
and
that is common to the path between
and
The set of the resistances in the path
are referred to as the
upstream resistances
for node
The Elmore delay to node
in the RC tree is then given by the expression
