Digital Signal Processing Reference
In-Depth Information
It is apparent from the example above that hand calculation of multiple reflec-
tions can be rather tedious. An easier way to predict the effect of reflections on
a signal is to use a lattice diagram.
3.5.4 Lattice Diagrams and Over- or Underdriven Transmission Lines
A
lattice diagram
(sometimes called a
bounce diagram
) is a graphical technique
used to solve the multiple reflections on a transmission line with linear loads.
Figure 3-30 shows a sample lattice diagram for the transmission line shown
in Figure 3-29. The left- and right-hand vertical lines represent the source end
(
z
=
0) and load end (
z
=
l
) of the transmission line. The diagonal lines contained
between the vertical lines represent the signal bouncing back and forth between
the source and the load. The diagram progressing from top to bottom represents
increasing time. Notice that the time increment is equal to the time delay
τ
d
of
the transmission line as calculated with (3-107), and the reflection coefficients
looking into the source and into the load are labeled at the top of the vertical bars.
The lowercase letters represent the magnitude of the reflected signal traveling on
the line. The uppercase letters represent the voltages seen at the source, and the
primed uppercase letters represent the voltage seen at the load end of the line.
For example, referring to Figure 3-30, the near end of the line will be held at
0
l
z
Γ
s
Γ
t
v
A
0
v
a
t
d
v
A
′
v
b
v
B
2
t
d
v
c
3
t
d
v
B
′
v
d
v
C
4
t
d
t
Figure 3-30
Structure of a lattice diagram for the transmission line in Figure 3-29.
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