Digital Signal Processing Reference
In-Depth Information
V
Z
0
R
R
∼
Z
in
=
Z
11
(a)
V
R
∼
Z
in
Z
in
−
R
Z
in
S
11
=
R
+
(b)
Figure 9-9
Return loss for the more general case where the network is not perfectly
terminated in its characteristic impedance: (a) input impedance looking into the network;
(b) equivalent circuit for the return loss.
contributions from both the impedance discontinuity at the source and at the
far-end termination. This means that the input impedance looking into the network
from the source will be dependent on frequency. The return loss for a nonperfectly
terminated structure such as the circuit shown in Figure 9-9a is calculated as
Z
in
(f )
−
R
Z
in
(f )
+
R
S
11
(f )
=
(9-20)
where
Z
in
(f )
is calculated for a transmission line with equation (9-5) for the
general case. An intuitive understanding of the return loss can be achieved by
constructing a simple equivalent circuit as shown in Figure 9-9b. Since
Z
in
(or
Z
11
) is dependent on both the propagating delay and the impedance of the struc-
ture, both can be calculated from
S
11
, as demonstrated in Example 9-4.
Example 9-4
Using the measured return loss of a transmission line shown in
Figure 9-10, calculate the characteristic impedance and the propagation delay.
Assume that the source and termination impedance values are 50
.
SOLUTION
Step 1:
Determine the propagation delay. This is easily calculated from the
periodic behavior of
S
11
using equation (9-4). The distance between peaks is
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