Waves and Transmission Lines Wang C. Ng. Traveling Waves.
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Transcript of Waves and Transmission Lines Wang C. Ng. Traveling Waves.
![Page 1: Waves and Transmission Lines Wang C. Ng. Traveling Waves.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/1.jpg)
Wavesand
Transmission Lines
Wang C. Ng
![Page 2: Waves and Transmission Lines Wang C. Ng. Traveling Waves.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/2.jpg)
Traveling Waves
![Page 3: Waves and Transmission Lines Wang C. Ng. Traveling Waves.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/3.jpg)
Load
Envelop of a Standing Wave
![Page 4: Waves and Transmission Lines Wang C. Ng. Traveling Waves.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/4.jpg)
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.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/5.jpg)
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.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/6.jpg)
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.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/7.jpg)
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.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/8.jpg)
Load
![Page 9: Waves and Transmission Lines Wang C. Ng. Traveling Waves.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/9.jpg)
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.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/10.jpg)
Load
![Page 11: Waves and Transmission Lines Wang C. Ng. Traveling Waves.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/11.jpg)
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.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/12.jpg)
Traveling Waves
Load
![Page 13: Waves and Transmission Lines Wang C. Ng. Traveling Waves.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/13.jpg)
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.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/14.jpg)
Composite Waves
Load
![Page 15: Waves and Transmission Lines Wang C. Ng. Traveling Waves.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/15.jpg)
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.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/16.jpg)
Composite Waves
Load
![Page 17: Waves and Transmission Lines Wang C. Ng. Traveling Waves.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/17.jpg)
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.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/18.jpg)
Composite Waves
Load
![Page 19: Waves and Transmission Lines Wang C. Ng. Traveling Waves.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/19.jpg)
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.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/20.jpg)
Composite Waves
Load
![Page 21: Waves and Transmission Lines Wang C. Ng. Traveling Waves.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/21.jpg)
Smith Chart
Transmission Line
Calculator
![Page 22: Waves and Transmission Lines Wang C. Ng. Traveling Waves.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/22.jpg)
-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.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/23.jpg)
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.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/24.jpg)
-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.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/25.jpg)
-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.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/26.jpg)
-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.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649c7b5503460f9492f25f/html5/thumbnails/27.jpg)
| |
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