Page 375 - Engineering Electromagnetics, 8th Edition

CHAPTER 10 Transmission Lines 357

and reflected waves, which occur (in time) at each integer multiple of 2l/ν. So, when
moving up the axis, we add the voltages of both wavesto our total at each occurrence.
The voltage within each time interval is thus:
V R = V 0 + V 1 + = 40 V (0 < t < 2l/ν)
= V 0 + V + V + V 2 + =−20 V (2l/ν < t < 4l/ν)
+
−
1
1
= V 0 + V + V + V + V + V 3 + = 10 V (4l/ν < t < 6l/ν)
−
−
+
+
1
2
1
2
= V 0 + V + V + V + V + V + V + V 4 + =−5V (6l/ν < t < 8l/ν)
−
+
+
−
+
−
1
3
3
1
2
2
The resulting voltage plot over the desired time range is shown in Figure 10.28a.

Figure 10.28 Resistor voltage (a) and current (b)as
functions of time for the line of Figure 10.25, with values
as specified in Example 10.12.