Digital Signal Processing Reference
In-Depth Information
Since
i
2
0, port 2 is open. Therefore, the voltage at port 2 will have an incident
and a reflected component. For convenience, the total voltage at port 2 is set
equal to 1:
=
=
v
+
+
v
−
=
v
2
1
v
+
=
v
−
=
1
2
The voltage at port 1 is calculated using equation (6-49) with
z
=−
l
.
e
γl
+
e
−
γl
2
=
v(z
=−
l)
=
v
+
e
γl
+
v
−
e
−
γl
v
1
=
The ratio of
v
1
and
v
2
is used to calculate
A
:
+
e
−
γl
2
e
γl
A
=
=
cosh
γl
(9-42a)
The term
C
is also calculated with
i
2
=
0.
i
2
=
0
i
1
v
2
C
=
The current
i
1
is calculated at
z
=−
l
using the characteristics impedance.
e
γl
−
e
−
γl
2
1
Z
0
v
+
e
γl
1
Z
0
v
−
e
−
γl
1
Z
0
i
1
=
i(z
=
l)
=
−
=
The ratio of
i
1
and
v
2
is used to calculate
C
:
−
e
−
γl
2
e
γl
1
Z
0
1
Z
0
sinh
γl
C
=
=
(9-42b)
Terms
B
and
D
are calculated with
v
2
=
0:
v
2
=
0
v
1
i
2
B
=
Since
v
2
=
0, port 2 is shorted:
1
2
−
1
2
=
=
v
+
+
v
−
=
v
2
0
v
+
Z
0
v
−
Z
0
−
−
1
/
2
Z
0
1
/
2
Z
0
1
Z
0
i
2
=
−
=
=
−
e
−
γl
2
e
γl
=
v(z
=−
l)
=
v
+
e
γl
+
v
−
e
−
γl
v
1
=
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