Top Banner
Waves and Transmission Lines Wang C. Ng
27

Waves and Transmission Lines Wang C. Ng. Traveling Waves.

Dec 14, 2015

Download

Documents

Saul Gobel
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

Wavesand

Transmission Lines

Wang C. Ng

Page 2: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

Traveling Waves

Page 3: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

Load

Envelop of a Standing Wave

Page 4: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

Waves in a transmission line

• Electrical energy is transmitted as waves in a transmission line.

• Waves travel from the generator to the load (incident wave).

• If the resistance of the load does not match the characteristic impedance of the transmission line, part of the energy will be reflected back toward the generator. This is called the reflected wave

Page 5: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

Reflection coefficient

• The ratio of the amplitude of the incident

wave (v+ ) and the amplitude the reflective

wave (v-) is called the reflection coefficient:

v

v

Page 6: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

Reflection coefficient

• The reflection coefficient can be determine from the load impedance and the characteristic impedance of the line:

0

0

ZZ

ZZ

L

L

Page 7: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

Short-circuited Load

• ZL = 0

= -1

• v - = - v + at the load

• As a result, vL = v + + v - = 0

Page 8: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

Load

Page 9: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

Open-circuited Load

• ZL = = +1

• v - = v + at the load

• As a result, vL = v + + v - = 2 v +

Page 10: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

Load

Page 11: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

Resistive Load

• ZL = Z0

= 0

• v - = 0 at the load

• As a result, vL = v +

Page 12: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

Traveling Waves

Load

Page 13: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

Resistive Load

• ZL = 0.5 Z0

= - 1/3

• v - = -0.333 v + at the load

• As a result, vL = v + + v - = 0.667 v +

Page 14: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

Composite Waves

Load

Page 15: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

Resistive Load

• ZL = 2 Z0

= + 1/3

• v - = 0.333 v + at the load

• As a result, vL = v + + v - = 1.333 v +

Page 16: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

Composite Waves

Load

Page 17: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

Reactive Load (Inductive)

• ZL = j Z0

= + j1

• v - = v +90 at the load

• As a result, vL = v + + v - = (1 + j1) v +

= 1.414 v +45

Page 18: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

Composite Waves

Load

Page 19: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

Reactive Load (Capacitive)

• ZL = -j Z0

= - j1

• v - = v +-90 at the load

• As a result, vL = v + + v - = (1 - j1) v +

= 1.414 v +-45

Page 20: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

Composite Waves

Load

Page 21: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

Smith Chart

Transmission Line

Calculator

Page 22: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

-j2

-j4

-j1

-j0.5

j0.5

j1

j4

j2

j0 0 0.5 1 2 4

ZL / Z0 = zL = 1 + j 2

Page 23: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

0 0.5 1

0.7 45

= 0.5 + j 0.5

real

imaginary

||

Page 24: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

-j2

-j 4

-j1

-j0.5

j0.5

j1

j4

j2

j 0 0 0.5 1 2 4

zL = 1 + j 2 0.7 45

||

||

re

im

Page 25: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

-j2

-j4

-j1

-j0.5

j0.5

j1

j4

j2

j0 0 0.5 1 2 4

zL = 1 + j 2

0.7 45

45

0

135

90

180

225

270

315

zL 1 j 2

zL 1

zL 1

0.5 0.5i

0.707

arg 45deg

Page 26: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

-j2

-j4

-j1

-j0.5

j0.5

j1

j4

j2

j0 0 0.5 1 2 4

zL = 0.5- j 0.5 0.45 -120

45

0

135

90

180

225

270

315

zL 0.5 j 0.5

zL 1

zL 1

0.2 0.4i

0.447

arg 116.565 deg

Page 27: Waves and Transmission Lines Wang C. Ng. Traveling Waves.

| |

0 0.5 1

-j2

-j4

-j1

-j0.5

j0.5

j1

j4

j2

j0

0 0.5 1 2 4

45

0

135

90

180

225

270

315

D C B E A

F

G

Re Im Mag AngleA 0 1 0 OpenB 2 0 1/3 0 Resistive = 2Z 0

C 1 0 0 0 Matched loadD 0.5 0 1/3 180° Resistive = Z 0/2E 0 0 1 180 Short F 0 1 1 90 Inductive = jZ 0

G 0 -1 1 -90° Capacitive = -jZ 0

zL Load