Civil Engineering Reference
In-Depth Information
capacitor associated with each segment is converted to the corresponding Miller
capacitance‚ depending on the direction in which the coupled wires switch.
4.5.3 Accurate coupling models and aggressor alignment
The use of the Miller capacitance is only a simple first-order approximation
that can be used to extend the existing circuit analysis machinery for RC trees
using Elmore delay computations‚ AWE‚ and the like. The primary advantage
of this approximation is that it alters a coupled interconnect system to a set of
uncoupled systems‚ each of which can be solved using the methods described
earlier.
A more accurate picture of reality is illustrated for a pair of simultaneously
switching coupled lines in Figure 4.14. The line of interest is the victim line‚
and the aggressor line influences it through a set of coupling capacitances that
are not explicitly shown in the figure.
There are two sources of noise on a wire
A noise bump at the input to a gate may propagate to its output‚ typically
in an attenuated form. Extremely fast noise transitions at a gate input may
not be sent through at all‚ since a gate acts as a low pass filter.
The voltage on the aggressor line results in the injection of a noise voltage
pulse on node of the victim‚ as shown in
Processing the effects of the first of these components exactly requires a topo-
logical traversal of the entire circuit to trace the noise propagation [SNR99]‚
since the combinational stage at the input to a given stage must be processed
prior to the current stage. To avoid the complications associated with such sce-
narios‚ which may result in cyclical dependencies when a topologically earlier
stage is coupled to a topologically later stage‚ one may often impose a constraint
that limits the propagated noise bump to be lower than a peak value and pes-
simistically assume the propagated noise to be at this peak value on each net.
This yields the advantage that each net can be processed independently.
These two components add up to contribute to a noise voltage waveform at
node on the victim. Since the interconnect net‚ when driven by a Thevenin
equivalent for the driver‚ is a linear system‚ the composite waveform at can
be obtained by adding the noise-free waveform‚ shown by the uppermost graph
in Figure 4.14(c)‚ with this noise bump. The exact time at which the noise is
injected depends on the transition time of the aggressor‚ relative to that of the
victim; this is referred to as the
aggressor alignment.
The second and third
graphs in Figure 4.14(c) show the noise bump waveforms corresponding to two
different aggressor alignments.
Note that the noise-free waveform‚ has a delay of in
the figure‚ while the two different aggressor alignments have delays of and
respectively‚ and the latter corresponds to the worst-case delay at over all
alignments. The task of delay computation in a coupled system involves the
determination of aggressor alignments that result in the worst-case delay(s) at
the nodes(s) of interest.
Figure 4.14(b)
4
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