Digital Signal Processing Reference
In-Depth Information
tpd
tpd
t p
R
1
L
1
R
2
L
2
R
3
L
3
S
C
1
C
2
C
3
V
s
V
c
1
V
c
2
Figure 6.4
Applying voltage to transmission line causes inductors and capacitors to charge in a
wave-like manner.
We will start off by first assuming that the switch is off, that there is no current
flowing in the circuit, and that the capacitors have all been discharged. We will also
assume that the line is infinitely long and so there are no reflections.
Closing the switch causes current to flow through
L
1 and
R
1, charging capaci-
tor
C
1. However, the inductor and resistor prevent the capacitor from charging up
instantaneously. There is a time delay equal to
tpd
between the switch closing and
C
1 being charged.
Once the delay is over,
C
1 is fully charged and current can now pass through
L
2 and
R
2 to charge
C
2. After a delay of
tpd
seconds,
C
2 is fully charged and then
C
3 starts to charge. This process continues until all of the capacitors along the line
have been charged.
By measuring the voltage across each capacitor, it appears as if a voltage wave
is traveling from left to right in the figure. By monitoring the current through the
inductors, it appears that a current wave travels along with the voltage wave.
This description of line behavior is simplistic. Rather than waiting for
C
1 to
become fully charged, current begins to flow in
L
2 while
C
1 is still charging, and
C
2 can start to charge
C
3 before
C
2 is fully charged, and so on. This means that
the waveform gradually works its way down the line rather than doing so in steps
as we have described. However, if the segments are made small enough, the steps
become very small, and the observed behavior appears as a smooth wave traveling
down the line.
