CROSSTALK - Advanced Signal Integrity for High-Speed Digital Design - page 173

Noting again that the forward crosstalk is a function of the difference between
capacitive and inductive coupling, we see that the coupled pulse will have the
same polarity as the aggressor signal if there is more capacitive coupling than
inductive coupling in the system, and vice versa for the case where inductive
coupling dominates. Equation (4-60) also suggests that it is possible to have no
forward crosstalk if we can find a case where K C = K L . In fact, this is always
true for coupled lines in a homogeneous dielectric (proof is left for the reader as
Problem 4-9). On the other hand, for typical transmission lines in inhomogeneous
dielectrics, such as microstrip PCB traces, the inductive coupling is generally
greater than the capacitive coupling, so that the forward crosstalk pulse has the
opposite magnitude from that of the aggressor signal.
As we described earlier, the width of the forward crosstalk pulse is

=

t pw,f t r (4-61)

where t r is the rise time of the signal. Note that (4-60) and (4-61) are equally
applicable for a falling-edge transition.

Reverse Crosstalk To get an expression for the reverse (near-end) crosstalk, we
must take into account the fact that the coupling region travels in the direction
opposite to the coupled waved. The output wave at the left in Figure 4-17 is a
superposition of the waves coupled at earlier times that propagate and sum at the
near end. This requires that we integrate from z = 0to z = l while accounting

for the travel time of the wave:

l

K C + K L
2 ν p

dv(t − 2 z/ν p )

dt

v b = dz (4-62)

z = 0

After integration we have an expression for the coupled noise at the near end.

v 1 (t) − v 1 t −

K C + K L
4

2 l
ν p

v b (t) = (4-63)

The apparent reduction of the effect of the coupling coefficient after the inte-
gration of (4-62) is caused by the fact that the energy coupling of the backward
crosstalk is spread out over a pulse width of 2 l/v p . The width of the backward
coupled pulse is calculated with

t pw,b = 2 τ d l (4-64)

where τ d is the propagation delay per unit length and l is the coupled length.
Equations (4-63) and (4-64) assume that the backward crosstalk has saturated,
which is realistic for multi-Gb/s links.
Finally, we note that the equations that we derived in this section apply to
situation in which both lines are terminated at each end. Other configurations,
such as when the near end is not terminated, will have different equations to