Transmission Lines

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Transmission Lines
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Water Wave Motion
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Speed of Voltage Wave
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Speed of Voltage Wave
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Transmission Line of Infinite Length
Assuming that the wire resistance is zero.
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Open Transmission Line of Finite Length
Assuming that the wire resistance is zero. 16.292
uS is the time it takes for the wave front to
travel 1 mile and be reflected back..
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Shorted Transmission Line of Finite Length
Assuming that the wire resistance is zero. 16.292
uS is the time it takes for the wave front to
travel 2 miles.
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Transmission Line Terminated with Characteristic
Impedance
Assuming that the wire resistance is zero.
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LC model of transmission line
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Propagation of voltage wave front
                                                
                         Propagate at speed of
light.
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(No Transcript)
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Characteristic Impedance
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Long and Short Transmission Lines

• In a short line, the propagation time is way less
  than ¼ of the period time of the RF on the line.
• In a long line, the propagation time is at least
  ¼ of the period time of the RF on the line.
• Thus long lines are at least ¼ wave length long.
  (775 miles for 60 Hz, 1.62 feet for 100 MHz))

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Reflected Wave
1
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Reflected Wave
2
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Reflected Wave
3
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Reflected Wave
4
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Reflected Wave
5
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Reflected Wave
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Reflected Wave
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Reflected Wave
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Reflected Wave
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Reflected Wave
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Reflected Wave
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Reflected Wave
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Reflection Coefficient

• The amount of reflected voltage

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The Reflected Voltage
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Maximum Voltage on the Line
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SWR
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Standing Wave
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Standing Wave Ratio if the Load is a resistor
only.
Whichever is Greater
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The Standing Wave

• Adding the reflected wave to the incident wave
  produces a standing wave.
• The standing wave is actually the ONLY voltage
  along the line.
• The standing wave oscillates in magnitude

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SWR

• A perfectly terminated line has SWR 1
• A line with high SWR acts like an antenna.
• High voltage nodes may stress the insulation of a
  transmission line.

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The Open Transmission Line
DC
RF
¼ l
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¼ Wave Open Transmission line
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½ Wave Open Transmission Line
1/2l
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¼ Wave Shorted Transmission Line
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Shorted Transmission Line
DC
RF
¼ l
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½ Wave Shorted Transmission Line
1/2l
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¼ Wave Transmission Line as an Impedance Matching
Transformer

• Find the necessary ZO
• From the cable specs get the velocity factor
• Calculate the length the wavelength
• Use a ¼ wave transmission line.

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Constant XL curves
Origin marked 1.0
Distance Scale
Resistive Axis
Constant XC curves
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Why use a Smith Chart?

• Design antenna matching networks
• Calculate input impedance of transmission lines
• Calculate SWR
• Express frequency-impedance relationships
  graphically
• Characterize the impedance of RF processors

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Smith Chart fun and games

• The origin represents the characteristic
  impedance of the processor (or transmission line)
• Normalization to the characteristic impedance
  makes the Smith Chart universal.

Do not plot this
Plot this
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Terminating Impedance
SWR