Digital Signal Processing Reference
In-Depth Information
65
Ω
61.25
Ω
, 1.873
×
10
8
m/s, 10 in
65
Ω
1.414 V
Figure 4-24
Equivalent modal circuit for the transmission-line pair in Example 4-4.
1
√
L
m
11
C
m
11
1
(
3
.
270
=
10
−
7
H
/
m
)(
8
.
718
10
−
11
F
/
m
)
×
×
ν
pm
=
1
1
√
L
m
22
C
m
22
(
3
.
914
10
−
7
H
/
m
)(
8
.
284
10
−
11
F
/
m
)
×
×
1
.
873
10
8
10
8
×
=
m
/
s
1
.
756
×
This gives us the information that we require to construct the modal circuit for
the odd mode, as shown in Figure 4-24.
Step 5: Transmission-line analysis
. Beginning with the low-to-high transition
at the voltage source, we use the odd-mode equivalent circuit in Figure 4-24
to calculate the voltage and current waves that are launched, assuming that the
rising edge occurs at time
t
=
1 ns.
61
.
25
61
.
25
v(t
=
1
,z
=
0
)
=
(
1
.
414 V
)
65
=
0
.
686 V
+
A
V
/
mA
A
v(t
=
0
,z
=
0
)
0
.
686 V
61
.
25
i(t
=
1
,z
=
0
)
=
=
=
11
.
20 mA
Z
m
The propagation delay to the far end (
z
=
l
=
0
.
254 m) is
10
9
ns
s
length
ν
pm,
odd
0
.
254 m
1
.
873
t
d,
odd
=
=
=
1
.
356 ns
10
8
m
/
s
×
The voltage reflection coefficient at the far end is
65
−
61
.
25
=
61
.
25
=
0
.
030
65
+
The voltage reflection coefficient at the source end is
65
−
61
.
25
=
61
.
25
=
0
.
030
65
+
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