Digital Signal Processing Reference
In-Depth Information
describe the amplitudes and shapes of the crosstalk pulses. The modified crosstalk
equations can be derived by considering the effect of reflections as described in
Section 3.5.
Example 4-3
We now analyze the coupling from an active line to a quiet line
for the PCB transmission lines from Example 4-2. Recall that the lines had the
following inductances and capacitances:
3
.
592
10
−
7
10
−
7
10
−
8
×
3218
×
L
=
H
/
m
10
−
8
3218
×
3
.
592
×
10
−
11
10
−
11
10
−
12
8
.
501
×
−
2
.
173
×
C
=
F
/
m
10
−
12
−
2
.
173
×
8
.
533
×
The 0.2794-m-long traces have a typical (isolated) characteristic impedance of
approximately 65
and are terminated to ground in 65
at the far end. They
are driven by a 1-V 65-
source with a 100-ps rise time. Compare the analytical
results with those from a fully coupled simulation.
SOLUTION
Step 1
: We start by calculating the impedance and propagation velocity:
3
.
592
×
10
−
7
H
/
m
Z
0
,
isolated
=
10
−
11
F
/
m
=
65
.
0
8
.
501
×
1
ν
p,
isolated
=
3
.
592
×
10
−
7
H
/
m8
.
501
×
10
−
11
F
/
m
10
8
m
/
s
=
1
.
810
×
Step 2
: Since we plan to analyze the coupled noise, we need the coupling
coefficients.
10
−
11
F
/
m
2
.
173
×
K
C
=
10
−
11
F
/
m
=
0
.
0256
8
.
501
×
10
−
8
H
/
m
×
3
.
218
K
L
=
10
−
7
H
/
m
=
0
.
0896
3
.
593
×
Step 3
: Analysis for a rising edge:
Z
0
R
S
+
Z
0
V
S
=
65
.
0
65
+
v(t
=
0
,z
=
0
)
=
65
.
0
(
1V
)
=
0
.
500 V
v(t
=
0
,z
=
0
)
0
.
500 V
65
.
0
=
i(t
=
0
,z
=
0
)
=
=
7
.
69 mA
Z
0
R
S
−
Z
0
R
S
+
Z
0
65
−
65
.
0
(z
=
0
)
=
=
65
.
0
=
0
.
000
65
+
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