Digital Signal Processing Reference
In-Depth Information
H
E
Figure 4-1
Coupled PCB transmission lines.
onto the victim line in proportion to the rate of change of voltage on the driven
line:
dv
dt
i
C
=
C
M
(4-2)
In equation (4-2),
i
C
is the amount of current coupled through the mutual
capacitance
C
M
, when driven by the voltage signal
v
.
I/O circuit rise and fall times decrease as data transfer rates increase, so (4-1)
and (4-2) predict that both inductive and capacitive crosstalk will play a signif-
icant role in high-speed digital applications. Thus, we must account for mutual
capacitance and inductance in our modeling and analysis of coupled systems, and
we now proceed to examine each in more detail.
4.1.1 Mutual Inductance
We start our discussion of mutual inductance by studying the simple inductive
circuit shown in Figure 4-2. Given transient currents
i
1
and
i
2
injected into on
lines 1 and 2, respectively, we can write expressions for
v
1
and
v
2
from Faraday's
law,
=
L
0
di
1
dt
+
L
M
di
2
v
1
(4-3)
dt
=
L
0
di
2
dt
+
L
M
di
1
v
2
(4-4)
dt
where
L
0
is the self-inductance and
L
M
is the mutual inductance between lines
1 and 2. From (4-3) and (4-4) we note that the potential differences
v
1
and
v
2
depend on both input currents and on the self- and mutual inductances. We can
better understand the impact of mutual inductance by analyzing the situations
where the input currents are equal (
i
1
=
−
i
2
). In the equal-current case we assume that their transition times are equal,
so that
di
1
/t
=
di
2
/dt
=
di/dt
. Applying these signals leads to
=
i
2
) and where they are opposite (
i
1
di
dt
v
1
=
v
2
=
(L
0
+
L
M
)
(4-5)
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