Digital Signal Processing Reference
In-Depth Information
If the impedance discontinuity is shorted to ground, as shown in Figure 3-28b,
the signal propagating on transmission line
A
will also be reflected 100%, but
the reflected wave will be out of phase from the incident by 180
◦
, yielding
short
=−
1
(3-105)
The reason for the phase shift is explained in Section 2.7.1, for a plane wave
incident on a perfect conductor.
3.5.2 Launching an Initial Wave
When a driver launches a signal onto a transmission line, the magnitude of the
initial voltage (
v
i
) seen on the transmission line at
0 will be governed by
the voltage divider between the source resistance and the line impedance (see
Figure 3-29):
t
=
Z
0
v
i
=
v
s
(3-106)
Z
0
+
R
s
If the end of the transmission line is terminated with an impedance that exactly
matches the characteristic impedance of the line, the signal with amplitude
v
i
will be terminated to ground and the voltage
v
i
will remain on the line until the
signal source switches again. If the end of the transmission line is terminated
with a resistance different than the characteristic impedance of the line, a portion
of the signal will be terminated to ground and the remainder of the signal will
be reflected back down the transmission line toward the source.
3.5.3 Multiple Reflections
As described above, when a signal is reflected from an impedance discontinuity
at the end of the line, a portion of the signal will be reflected back toward
the source. The amount of signal reflected back is determined by the reflection
coefficient between the transmission-line impedance (
Z
0
) and the termination
resistance (
R
t
) and calculated with (3-102), where
Z
02
=
R
t
. When the incident
wave hits the termination,
R
t
, a portion of the signal,
v
i
t
,isreflected back
l
υ
s
R
s
R
t
z
o
V
i
v
i
Γ
t
t
=
0
t
= t
d
v
(
t
= τ
d
)
=
v
i
+
v
i
Γ
t
v
i
Γ
t
Γ
s
t
=
2
t
d
v
(
t
=
2
t
d
)
=
v
i
+
v
i
Γ
t
+
v
i
Γ
t
Γ
s
Figure 3-29
Initial voltage launched onto a transmission line and subsequent reflections.
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