Civil Engineering Reference
In-Depth Information
the analysis in Section 4.5.3‚ it is adequate to explain the concept of timing
windows that is introduced in this section.
The use of a Miller capacitor transforms a coupled RC network into a set
of uncoupled RC trees‚ and the values of the capacitors‚ and hence the delays‚
in these trees depend on the switching characteristics of the neighboring wires.
Therein lies the complexity of the timing calculation procedure: the delays
depend on the Miller capacitance values‚ which in turn depend on the switching
times that are determined by the delays. This cyclic relationship makes the
task of timing analysis in coupled RC networks nontrivial.
In general‚ one can define a timing window as an interval (or most generally‚
a union of intervals) in time during which a node in a circuit may switch. Given
the timing windows for the aggressors and the victims at the driver inputs of
a set of coupled lines‚ it is possible to determine the timing windows at the
receivers driven by these drivers.
As an example‚ consider two wires that are laid out adjacent to each other‚
as shown in Figure 4.15(a). For purposes of illustration‚ let us use the sim-
plistic model in Figure 4.15(b)‚ where the capacitances to ground as well as
the coupling capacitance are all lumped; the analysis presented here will hold
even for more complex distributed or segmented wire models. If the input sig-
nals to driver of the two wires switch between times and
respectively‚ and if the delays required to propagate the
signal along the wires are in the range
and
re-
spectively‚ then the intervals during which the lines switch are
and
respectively‚ where
and
Therefore‚ the following relationship holds between the switching times and the
equivalent coupling capacitance‚
The first line of Table 4.2 corresponds to the case where the switching inter-
vals for the two lines overlap‚ and the value of
is accordingly chosen to be
either 0 or
depending on whether the signals switch in the same direction‚
