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ELE1110C Tutorial 5. 7-10-2006 Luk Chun Pong. Reminder Midterm date and time: 6-11-2006, 12:30--1:10pm 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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ELE1110C Tutorial 5

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ELE1110C Tutorial 5

7-10-2006

Luk Chun Pong


Reminder

Midterm date and time:

6-11-2006, 12:30--1:10pm

Today’s tutorial outline

-Transmission Line

-Examples

-Past midterm exam questions


In previous chapters…

  • We assume that:

    • Signal propagation is instantaneous

    • Signal received at the receiver = signal at the transmitter

    • The length of the wires connecting the circuit can be ignored

  • But this may not be true in transmission line


RS

Ir

Ii

Z0

+

Vi

Vr

RL

VS

-

Transmission Line

Simple model of transmission line


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

  • So… there must be reflected wave, ohm’s law must be agreed

    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


About ρ…

  • 0 <= ρ <= 1

  • Reflect wave can never greater than Incident wave

  • Reflected wave can be negative

  • ZL = 0, ρ = -1

  • ZL = infinity, ρ = 1

  • ZL = Z0, ρ = 0

  • ρ < 0, reduce the incident wave

  • ρ > 0, reinforce the incident wave


RS

Ir

Ii

Z0

+

Vi

Vr

RL

VS

-

Sink

Source

Transmission Line

Vi

Vr =

Vr’ =

Note that only reflected voltage is reflected


If ρ = 0…

  • No reflected signal…

  • So, to eliminate reflected signal, we can “matched at load” or “matched at source”

  • For t -> infinity… so voltage at load eventually meet..

Vs


Problem set 4

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 10-11F/m, L = 5 X 10-7 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,

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.


Q2 Answer

  • 5V

  • (a) 5 V

    (b) 5 x 10-7s = 0.5μs

    (c) 0

    (d) 5V

    (e) 0

    (f) 5

    (g)

5V


(iii) (a) 7.5V

(b) -1/3

(c) 7.5V

(d) -2.5V

(e) 5V

(f)

7.5V

5V

1s


(iv) (a) 10V

(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


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