Digital Signal Processing Reference
In-Depth Information
R
S
N1
N2
TX
TT1
T2
T3
T4
T5
C
L
1
C
L
2
C
L
3
Figure 12.15
Stubs
T
4 and
T
5 connect the load capacitances to the main transmission line (
T
1
-
T
3).
For instance, if the signal rise time is 1 ns, transmission lines
T
4 and
T
5 would
appear to be long if their electrical lengths were 0.5 ns or greater.
If the electrical length of
T
4 and
T
5 is small, then the capacitance of the stub
is found with (12.8) and is added to the load capacitance as we did in the previous
section. This increases the load capacitance and creates a larger impedance discon-
tinuity at the point where the load connects to the line. However, because the stub
is short, incident and reflected waves will not appear along its length.
12.8.1 Branches
When the trace connecting the load to the main transmission line is electrically long,
it acts as a branch rather than a stub. The branch is then in parallel with the main
transmission line, which lowers the impedance where the branch connects. Figure
12.15 is redrawn as Figure 12.16 to emphasize this parallel connection. The net can
be series- or parallel-terminated.
It is evident from Figure 12.16 how an incident wave exiting
T
1 would simulta-
neously send energy down the parallel combination of
T
2 and
T
4. In this particular
case
T
2 and
T
4 are each 50
Ω
, so the impedance experienced by the incident wave
when it reaches
N
1 is 25
. Unless terminated at the load, the wave launched down
T
4 will reflect when it reaches load capacitor
C
L
1
. That reflection will be rere-
flected when it reaches node
N
1, because from the point of view of this wave, the
50
Ω
transmission lines
T
1 and
T
2 are in parallel, and node
N
1 has an impedance
of 25
Ω
. This same process occurs at node
N
2 with transmission lines
T
3 and
T
5.
Depending on the relative lengths of
T
2 through
T
4, the reflected energy can create
complex-looking waveforms at the loads, and the waveforms at each of the loads
can be quite different.
We can see from this how ineffectual series termination will be at controlling
these reflections. In fact, the best signal integrity will occur when each of the loads
is individually terminated, but even so, the impedance mismatch between the 50
Ω
Ω
transmission line
T
1 and the apparent 25
impedance appearing at node
N
1 (and
node
N
2) will still give rise to reflected energy.
This can be solved by lowering the impedance of
T
1 to 25
Ω
, matching
T
1 to
the impedance at
N
1, and eliminating any reflections from the incident wave when
Ω
