Civil Engineering Reference
In-Depth Information
earliest and latest switching time‚ and assume that a switching event is permis-
sible at any intermediate time. In practice‚ this is a pessimistic argument‚ and
the true switching windows could be a union of disjoint windows. For instance‚
consider the example shown in Figure 4.16‚ where and are primary inputs
that switch at time 0. Assuming that the delay of each gate is 1‚ the minimum
and maximum delays at nodes and the inputs to gate
G‚
can easily be seen
to be 0 and 2 units‚ respectively. Accordingly‚ adding to this the unit delay of
gate
G‚
the switching window at can be set to the interval [1‚ 3]. However‚
in reality‚ a switching event at can only occur at this node at time 1‚ due to
path or at time 3‚ due to path or and not
at any arbitrary time in this interval (e.g.‚ at time 2). Therefore‚ the choice of
the entire interval [1‚ 3] may enable some nonexistent simultaneous switching
events‚ which will result in pessimistic calculations for both the maximum and
minimum delays at the output of
G.
4.5.5 Extending the effective capacitance method to coupled RC lines
We will illustrate the concept of computations from [DP97] on a pair of
RC coupled lines‚ shown in Figure 4.17‚ but the idea can be extended to RC
coupled trees with an arbitrary number of coupled nets. In the two-line case
considered here‚ the first step is to replace each driver by a Thevenin model‚ as
in Section 4.4.3; in this explanation‚ a Norton equivalent is used instead. This
is characterized by the parameters and for the first line and and
for the second‚ and these must be calculated‚ in addition to the resistors
and
Two effective capacitances‚ and one for each driver‚ and the
four Thevenin parameters for the two driver models are computed as follows:
An initial guess for the
values is chosen.
Considering this system as a two-port‚ the linear system is solved to find
the voltage at each of the driving point nodes. Effectively‚ this method is
identical to that considered for the RC line case‚ except for the addition of
an extra current source in the load driven by each Thevenin equivalent.
Next‚ for each line‚ the average voltage at the driving point for the coupled
load is equated with that injected into the effective capacitance load. In
