Digital Signal Processing Reference
In-Depth Information
2. At
t
200 ps the output of the pulse generator returns to 0V.
3. The pulse arrives at the load at
t
= 2 ns. Since
=
ρ
l
= +1, a 200-pS-wide reflec-
tion of 1.67V is created. From (11.4) the load voltage is the sum of the in-
cident and reflected voltages, noting that the load was previously 0V. This
makes the load voltage 3.34V.
4. The +1.67V reflection (and not the 3.34V load voltage) travels back down
the line and reaches the generator at
t
= 4 ns. Since
ρ
g
=
0.67, a 200-pS re-
1.12V is created from the +1.67V reflection impinging on the
generator (the output of which is 0V). From (11.4) the generator voltage
now becomes 0.55V.
5. The reflected
flection of
−
1.12V, 200-pS-wide pulse travels back up the line and at
t
= 6 ns arrives at the load where it sums with the
−
1.12V reflection created
by the open circuit. Because the load has returned to zero by the time this
reflection arrives, a total voltage of
−
−
2.24V is created.
6. The
1.12V, 200-pS-wide reflection travels down the line toward the gen-
erator, where it arrives at
t
= 8 ns.
7. When the
−
1.12V reflection reaches the generator, a +0.75V reflection is
produced which reaches the load at
t
= 10 ns. As the chart shows, this is
45% of the initial launched voltage of 1.67V. In fact, this is the product of
the percentages of all the proceeding reflections (1
−
0.67). This
observation can be used to find the voltage after any number of reflections
without resorting to constructing a reflection chart.
8. This process continues with the refl ection becoming smaller and changing
signs each time it rebounds from the generator impedance.
×
−
0.67
×
From the reflection chart it is apparent how it is the energy from the first
reflection that makes its way up and down the transmission line. Because each
subsequent reflection is multiplied by
(whose absolute value is never greater than
1), this means that, ignoring the effects of crosstalk, in a single pulse system the
subsequent reflections will never have a magnitude worse than the first reflection.
This knowledge is useful when setting up transmission line simulations and when
making laboratory measurements.
The chart suggests a difference between pulse and step excitation. If the signal
is a step longer than twice the round trip of the transmission line, the reflections
would add to the launched voltage to create the composite voltage,
V
ne
. For in-
stance, the near-end voltage at step 4 in the reflection chart (Figure 11.7) would
have become 2.22V (the sum of the reflections plus the 1.67V still present from the
generator) if the launched pulse was a step.
Reflection charts are no longer a practical design tool because even complex
networks can easily be modeled with modern circuit simulators. However, because
they show the behavior and characteristics of the reflected energy, they are a good
learning tool that the signal integrity engineer should master.
ρ
