Digital Signal Processing Reference
In-Depth Information
R
T
−
Z
0
65
−
65
.
0
(z
=
0
.
2794 m
)
=
=
65
.
0
=
0
.
000
R
T
+
Z
0
65
+
10
9
ns
s
l
ν
p
=
0
.
2794 m
1
.
810
t
d
=
=
1
.
544 ns
×
10
8
m
/
s
1
2
(K
C
−
K
L
)
l
ν
p
v
t
r
v
f
=
0
.
0896
)
1
2
(
0
.
0256
0
.
2794 m
1
.
820
=
−
10
8
m
/
s
×
0
.
500 V
100 ps
10
12
ps
s
×
=−
0
.
247 V
v(t)
−
v
t
−
K
C
+
K
L
4
2
l
ν
p
v
b
=
0
.
0256
(
0
.
500 V
)
=
+
0
.
0896
=
0
.
014 V
4
t
pw,f
=
t
r
=
100 ps
2
39
.
37 in
.
10
9
ns
11 in
.
m
t
pw,b
=
2
τ
d
l
=
1
.
810
×
10
8
m
/
s
s
=
3
.
088 ns
Since the reflection coefficients are zero, a lattice diagram is not necessary, as
we can construct the waveform directly from our calculations.
Step 4
: Comparison to simulation. Figure 4-23 compares our calculated results
with those from SPICE time-domain simulations. We see that although waveforms
nearly match, they are not identical. In particular, the rising edge of the active
signal in the SPICE simulation has grown to approximately 200 ps at the receiver
end of the transmission line. The degradation of the rising edge of the active
signal can be attributed to the crosstalk mechanism using an energy conservation
argument. To conserve energy, the active line must give up an amount of energy
that is equal to the amount coupled to the quiet line. Recall that the reactive
nature of the coupling mechanism means that energy is coupled to the quiet line
only during signal transition, so that the rising edge is degraded as a direct result
of the coupling. In addition, the increase in rise time at the receiver causes the
width of the crosstalk pulse at the receiver end to be approximately 200 ps rather
than the 100 ps predicted by our calculation.
As the example demonstrates, the crosstalk model presented here is an approxi-
mation. This model begins to break down when the coupled length is long enough
such that the difference in propagation delay between the even and odd modes
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