CROSSTALK - Advanced Signal Integrity for High-Speed Digital Design - page 168

t = 2 t d ⋅ I

Z 0

Z 0 , t d , l

Near-end × talk pulse at t = 2 t d ⋅ I

Z 0 Z 0

Z 0 , t d , l

Figure 4-20 Completion of the noise pulse at the near end (z = 0 ) .

the aggressor signal, as the figure illustrates. Even though additional energy is no
longer being coupled at this point, the backward crosstalk wave must still travel
back to the near end. This takes a full propagation delay ( t d = τ d l ) to complete
and is shown in Figure 4-20.
The shape of the near-end pulse depends on the electrical length of the coupled
lines relative to the transition time of the aggressor signal. Consider the case
for which the coupled length is less than one-half of the signal rise time. The
beginning of the signal transition will reach the far end before the rising edge at
the driving end has completed one-half of the transition. As the coupled noise
propagates back to the near end, the signal at the far end continues to change,
and therefore to couple more energy to the victim. Not until the rising-edge
transition has finished propagating all the way to the far end does coupling stop.
In that case, the near-end crosstalk pulse will have a similar shape (but different
amplitude) to the far-end pulse, as shown in Figure 4-21a.
On the other hand, if the coupled length is greater than one-half the signal rise
time, the near-end crosstalk pulse will reach maximum amplitude and will then
begin to spread in time, a phenomenon known as saturation , which is shown
in Figure 4-21b. To understand this effect, consider a case where the coupled
electrical length is equal to several rise times. For this situation, we can visualize
the signal edge as a traveling wave on the aggressor line. Recalling that the
lines couple only during the transition, we can imagine the backward crosstalk
as a train of pulses of equal magnitude with a width equal to the rise time that
propagate back to the near end. As a result, the backward noise does not grow in
magnitude, but instead, spreads out in time. Figure 4-22 illustrates the coupled
pulse propagation as just described.
As a final note, we must realize that the crosstalk pulse magnitudes and shapes
that we just described, and for which we will develop quantitative models in the
next section, are specific to the matched termination case. Terminating the lines
simplifies the analysis by eliminating the need to deal with reflected crosstalk
and crosstalk from reflected aggressor signals. In general, the characteristics of
the crosstalk noise are heavily dependent on the amount of coupling and the
termination. For cases with imperfect termination and/or complex topologies,
we recommend using a simulator to analyze the behavior of the system. Hall
et al. [2000] describe crosstalk shapes for some general nonperfect termination
schemes.