Civil Engineering Reference
In-Depth Information
section can be extended to find the worst-case aggressor alignment, i.e., the
alignment that results in the worst-case delay.
Consider a victim with a rising waveform that is capacitively coupled to
several aggressors, each with a falling waveform, as illustrated in Figure 4.18(a).
At a node of interest on the victim, each aggressor will contribute a noise
waveform, The technique in [GARP98] uses a procedure similar to
waveform relaxation [LRSV83] to arrive at this solution. Each line is solved
separately using a Thevenin model for each driver, and its contribution
at the victim node is computed. Since this system uses a Thevenin equivalent
for each driver, it is purely linear, and the noise waveform can be found by
summing up the individual contributions
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The worst-case noise peak,
is achieved when the noise peaks of all of the aggressors are perfectly
aligned, as shown in Figure 4.18(b)
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. To determine the worst-case delay, this
composite noise pulse is aligned with the noise-free victim waveform to create
a worst-case scenario. This occurs when the noise peak is aligned with the time
at which the noise-free victim is at voltage Since the noise-free
waveform rises monotonically, the sum of the two waveforms has its minimum
at this time point, as shown in Figure 4.18(c).
Therefore, the process of determining the worst-case 50% delay at
for a
rising victim waveform consists of the following steps:
1.
The noise-free waveform is determined‚ as are the individual noise waveforms
from each aggressor.
2.
The peaks of the noise waveforms are all aligned to find
the noise wave-
form peak; note that
is negative since all of the aggressors sport falling
waveforms.
3.
The noise-free waveform‚ is now aligned with the noise signal in
such a way that the time at which the latter reaches
corresponds to the
time when
is at
An enhancement of this approach was proposed in [BSO03]. Firstly‚ it is
observed that the aggressor alignment strategy above uses the artifact of the
50% delay definition‚ which may not be very meaningful in practice. Specifi-
cally‚ when a noisy waveform is at the input to the victim receiver‚ the output
waveform is shown in Figure 4.19. In this case‚ the pulse propagates to the
output when the transient has already settled‚ and thus‚ the noise pulse does
not appreciably change the waveform at the victim output. Consequently‚ an
improved definition of the delay is necessary‚ whereby the worst-case aggressor
alignment is a function of the gate type‚ size‚ pmos/nmos ratio‚ and output
load on the victim receiver. An inexpensive precharacterization using a linear
fit was proposed to capture these effects in this work.
Secondly‚ [BSO03] noted that the Thevenin resistance that is valid over the
entire transition between 0 and is not identical to the resistance that is
seen for the noise transition‚ which has a much smaller range. Therefore‚ it
developed the concept of a
transient holding resistance
to capture this effect‚
