Digital Signal Processing Reference
In-Depth Information
The total inductance was calculated in (5-20):
L
total
=
L
internal
+
L
external
(5-20)
indicating that the series impedance contribution from the inductance is
simply
jω(L
internal
+
L
external
)
. To calculate the total series impedance of a
transmission-line segment, the resistive component is added:
=
R
ac
+
jω(L
internal
+
L
external
)
Z
series
=
R
ac
+
jωL
total
ohms
(5-68)
leading to the equivalent circuit for a transmission line with a conductor of finite
conductivity, as shown in Figure 5-27, where
N
s
is the number of segments,
C
z
=
z C
and
L
z
=
z L
total
, as calculated in Section 3.2.3, and
R
z
=
z R
ac
, where
z
is the length of the differential section of transmission line
and
C
,
L
total
, and
R
ac
are the capacitance, inductance, and resistance per unit
length.
The characteristic impedance, which was defined in equation (3-33), can be
calculated by dividing the series impedance as defined by (5-68) by the parallel
admittance of the capacitance,
Y
shunt
=
jωC
, for a short section of transmission
line of length
z
.
Z
series
Y
shunt
R
AC
+
jωL
total
jωC
Z
0
=
=
ohms
(5-69)
Note that the units in (5-69) are
√
ohms
/(
1
/
ohms
)
=
(
ohms
)
2
=
ohms.
L
z
∆
R
∆
z
C
z
∆
(a)
N
s
1
2
L
L
L
∆
z
∆
z
∆
z
R
R
R
∆
z
∆
z
∆
z
C
C
C
∆
z
∆
z
∆
z
(b)
Figure 5-27
(a) Model for a differential element of a transmission line; (b) full model.
Search WWH ::
Custom Search