a total magnitude on the line of V
i
+ V
i
. The reflected component will then travel back to the
source and possibly generate another reflection off the source. This reflection and
counterreflection continues until the line has reached a stable condition.
Figure 2.9: Incident signal being reflected from an unmatched load.
Figure 2.10
depicts special cases of the reflection coefficient. When the line is terminated in
a value that is exactly equal to its characteristic impedance, there is no discontinuity, and the
signal is terminated to ground with no reflections. With open and shorted loads, the reflection
is 100%, however, the reflected signal is positive and negative, respectively.
Figure 2.10: Reflection coefficient for special cases: (a) terminated in Z
o
; (b) short circuit;
(c) open circuit.
2.4.2. 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. When the reflected
signal reaches the source, another reflection will be generated if the source impedance does
not equal that of the transmission line. Subsequently, if an impedance discontinuity exists on
both sides of the transmission line, the signal will bounce back and forth between the driver
and receiver. The signal reflections will eventually reach steady state at the dc solution.
For example, consider
Figure 2.11
, which shows one example for a time interval of a few TD
(where TD is the time delay of the transmission line from source to load). When the source
transitions to V
s
, the initial voltage on the line, V
i
, is determined by the voltage divider V
i
=
V
s
Z
o
/(Z
o
+ R
s
). At time t = TD, the incident voltage V
i
arrives at the load R
t
. At this time a
reflected component is generated with a magnitude of
B
V
i
, which is added to the incident
voltage V
i
, creating a total voltage at the load of V
i
+
B
V
i
(
B
is the reflection coefficient
looking into the load). The reflected portion of the wave (
B
V
i
) then travels back to the source
and at time t = 2TD generates a reflection off the source determined by
A
B
V
i
(
A
is the
reflection coefficient looking into the source). At this time the voltage seen at the source will
be the previous voltage (V
i
) plus the incident transient voltage from the reflection (
B
V
i
) plus
the reflected wave (
A
B
V
i
). This reflecting and counter-reflecting will continue until the line
voltage has approached the steady-state dc value. As the reader can see, the reflections