Digital Signal Processing Reference
In-Depth Information
t
r
Driven signal
t
d
⋅
I
Near-end crosstalk
t
r
Far-end crosstalk
t
r
(a)
t
r
Driven signal
t
d
⋅
I
Near-end crosstalk
Far-end
crosstalk
t
r
2
t
d
⋅
I
(b)
Figure 4-21
Forward- and backward-coupled noise pulses: (a) nonsaturated; (b) sat-
urated.
Quantitative Development
Having developed an intuitive understanding of
crosstalk and the characteristics of crosstalk noise, we now derive the equations
for noise at each end of a quiet transmission line (line 2 in Figure 4-17) that
is induced by coupling from an adjacent coupled line (line 1) that is actively
driven. Noise will be coupled from line 1 to line 2 through the mutual inductance
L
M
dz
and mutual capacitance
C
M
dz
. Line 1, whose characteristic impedance
is
Z
0
, has an incident pulse of magnitude
v
1
(voltage) and
i
1
(current), and is
terminated in its characteristic impedance at both ends. We want to come up
with expressions for the backward (
v
b
) and forward (
v
f
) noise pulses on
line 2, which also has a characteristic impedance of
Z
0
with termination at both
ends. Our derivation follows the method presented by Seraphim et al. [1989].
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