Problem 2.75 Generate a bounce diagram for the voltage V (z,t) for a 1-m–long
lossless line characterized by Z0 = 50 Ω and up = 2c/3 (where c is the velocity of
light) if the line is fed by a step voltage applied at t = 0 by a generator circuit with
Vg = 60 V and Rg = 100 Ω. The line is terminated in a load RL = 25 Ω. Use the
bounce diagram to plot V (t) at a point midway along the length of the line from t = 0
to t = 25 ns.
Solution:
Rg − Z0 100 − 50
50
1
=
=
= ,
Rg + Z0 100 + 50 150 3
ZL − Z0 25 − 50 −25 −1
=
=
=
.
ΓL =
ZL + Z0 25 + 50
75
3
Γg =
From Eq. (2.149b),
V1+ =
Vg Z0
60 × 50
=
= 20 V.
Rg + Z0 100 + 50
Also,
T=
l
3
l
=
=
= 5 ns.
up 2c/3 2 × 3 × 108
The bounce diagram is shown in Fig. P2.75(a) and the plot of V (t) in Fig. P2.75(b).
Voltage
Γ = Γg = 1
3
z=0
Γ = ΓL = - 1
3
z = 0.5 m
z=1m
V1+ = 20V
5 ns
-6.67 V
10 ns
-2.22 V
15 ns
0.74 V
20 ns
0.25 V
25 ns
-0.08 V
t
t
Figure P2.75: (a) Bounce diagram for Problem 2.75.
V(0.5 m, t)
20 V
20 V
13.34 V
5
10
11.12 V
11.86 V
12.10 V
15
20
25
Figure P2.75: (b) Time response of voltage.
t (ns)