ELE1110C Tutorial 5. 7102006 Luk Chun Pong. Reminder Midterm date and time: 6112006, 12:301:10pm Today’s tutorial outline Transmission Line Examples Past midterm exam questions. In previous chapters…. We assume that: Signal propagation is instantaneous
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Midterm date and time:
6112006, 12:301:10pm
Today’s tutorial outline
Transmission Line
Examples
Past midterm exam questions
RS
Ii
Z0
+
Vi
…
RL
VS

First we set RLnot equal to Z0…
Let’s think about that… at t = 0, what’s Z0?
Z0 = Vi / li
But what happen when the signal propagate to the load…?
RL should be Vi / li but RLnot equal to Z0…
RS
Ii
Ir
Z0
IL
IL = Ii – Ir
VL = Vi + Vr
+
Vi
Vr
VL
RL
VS

For the proof, please check the lecture notes
u = speed of the signal
L = Inductance and C = Capacitance
Z0 = Characteristic Impedance
L = Inductance and C = Capacitance
Reflecting coefficient at the load
Reflecting coefficient at the source
ρ= Vr/Vi
RS
Ir
Ii
Z0
+
Vi
Vr
RL
VS

Sink
Source
Transmission Line
Vi
Vr =
Vr’ =
Note that only reflected voltage is reflected
Vs
Q1. If the signal propagation speed of a cable is 2 x 108 m/s, and the cable impedance is 100 Ohm, find the inductance and capacitance per unit length of the cable.
Using the formulas with Z0 = 100 ohm and u = 2 x 108 m/s
Ans: C = 5 X 1011F/m, L = 5 X 107 H/m
Q2. Suppose the signal propagation speed of the following cable is , the cable impedance is Z0, and the time for the signal to reach the load be tL.If the switch is closed at time t=0, answer the following questions.
i) If the length of the cable is very short so that its effect can be ignored, what is the voltage at the load (50ohm)? .
ii) If Z0=50ohm
a) At t=0, what is the voltage at z=0?
b) How long does it take for the signal to travel to z=100m?
c) What is the reflection coefficient of the load (50ohm)?
d) What is the incident voltage wave at the load?
e) What is the reflected wave at the load?
f) What is the voltage at the load at t= tL?
g) Plot the voltage waveform at z=0 from t=0 to t=1.5ms.
iii) If Z0=100ohm, effect can be ignored, what is the voltage at the load (50ohm)? .
a) At t=0, what is the voltage at z=0?
b) What is the reflection coefficient of the load (50ohm)?
c) What is the incident voltage wave at the load?
d) What is the reflected wave at the load?
e) What is the voltage at the load at t= tL?
f) Plot the voltage waveform at z=0 from t=0 to t=1.5ms.
iv) If Z0=200ohm,
a) At t=0, what is the voltage at z=0?
b) What is the reflection coefficient of the load (50ohm)?
c) What is the incident voltage wave at the load?
d) What is the reflected wave at the load?
e) What is the voltage at the load at at t= tL?
f) What is the reflection coefficient at the source?
g) What is the reflected voltage at the source?
h) What is the voltage at the source at t=2tL?
i) What is the voltage at the load at t=3tL?
j) Find the voltage at z=50m at t=0, 0.5tL, tL, 1.5tL, 2tL, and 2.5tL.
(b) 5 x 107s = 0.5μs
(c) 0
(d) 5V
(e) 0
(f) 5
(g)
5V
(iii) (a) 7.5V effect can be ignored, what is the voltage at the load (50ohm)? .
(b) 1/3
(c) 7.5V
(d) 2.5V
(e) 5V
(f)
7.5V
5V
1s
(iv) (a) 10V effect can be ignored, what is the voltage at the load (50ohm)? .
(b) 0.6
(c) 10
(d) 6
(e) 4V
(f) 0.3333…
(g) 2V
(h) 6V
(i) 4.8V
(j) t = 0: 0V, t=0.5tL,1tL: 10V,
t=1.5tL, 2tL: 4V, t=2.5tL: 6V