Transcript EE 3760 chapter 7 - Seattle Pacific University

Transmission Lines
Kevin Bolding
Electrical Engineering
Seattle Pacific University
Seattle Pacific University
Transmission Lines
No. 1
Transmission Lines
• Long electrical wires are known
as transmission lines
• In short lines, it is safe to
assume that wires have the
same voltage and current at all
points
• In transmission lines, the
voltage and current may vary
along the length of the line
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How long is “long”?
Wires longer than1/10 of
the wavelength of the
signal applied. (Assume
travelling at the speed of
light, 3.0x108 m/s)
At 1MHz, this is 30m.
At 3GHz, this is 1cm.
Transmission Lines
No. 2
Transmission Line Thought Experiments
3,000,000,000 m
i
5V
5
+
-
When the switch is closed, what current flows?
What if the switch is closed for 1 second, then opened?
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Transmission Lines
No. 3
Transmission Line Model
Infinitely Long
i
5V
+
-
• Any wire has resistance… but let’s pretend it doesn’t
• Any pair of wires has some capacitance between them
• Charging the capacitors will take current.
• Any wire has inductance
• Inductors oppose changes in current
• A balance will be reached, with some resultant current, i
• This implies an resistance, R = V/i
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Transmission Lines
No. 4
Characteristic Impedance
• A transmission line appears to have a resistance that is
related to the distributed capacitance and inductance
Characteristic Impedance – Z0
Apparent resistance seen at the input of a transmission line.
Determined primarily by the capacitance and inductance of the
line, especially for high frequency signals.
Applies to infinitely long lines, but also to lines with AC inputs if
the line is “long” compared with the AC wavelength.
• Z0 cannot be measured in traditional ways
• If we put an Ohmmeter on an open transmission line, it will measure
“open” or high resistance because we’re making a DC
measurement
• An Ohmmeter would work if we had an infinite line…
• AC instruments (scopes) can be used
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Transmission Lines
No. 5
Factors affecting Characteristic Impedance
5V
+
-
• Z0 depends on C, L, and R per length
• Higher C  Lower Z0 (More ability to “soak up” charge)
• C ↑  Z0 ↓
• Higher L  Higher Z0 (More opposition to current)
• L ↑  Z0 ↑
• Higher R  Higher Z0 (Duh!)
• R ↑  Z0 ↑
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Transmission Lines
No. 6
Factors affecting Characteristic Impedance
Conductors
Dielectric Insulator
d
r
• Capacitance per length depends on:
• Conductor spacing – d – Larger spacing means less capacitance
• d ↑  C ↓, but C ↑  Z0 ↓, thus d ↑  Z0 ↑
• Relative permittivity of the dielectric separating the conductors
• Inductance per length depends on:
• Conductor radius – r – Larger radius means less inductance
• r ↑  L ↓, but L↑  Z0 ↑, thus r ↑  Z0 ↓
• Conductor spacing – d – When conductors are close together, the
magnetic fields cancel out
• d ↑  L ↑, and L↑  Z0 ↑, thus d ↑  Z0 ↑
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Transmission Lines
No. 7
Determining Characteristic Impedance
Conductors
Dielectric Insulator
with relative permittivity k
d
r
• For two parallel wires:
276
d
Z0 
log10
r
k
Looking for k?
Try “relative static permittivity” on
wikipedia.
d2
• For coaxial cable:
138
d1
Z0 
log10
d2
k
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Dielectric Insulator
with relative permittivity k
d1 (inside diameter of outer conductor)
Signal Propagation
speed (c = speed of
light in vacuum):
Transmission Lines
1
vc
k
No. 8
Z0 and Resistance
• Characteristic Impedance looks like a resistance, but it isn’t!
•
•
•
•
Composed of C’s and L’s: No resistance (ideally)
Z0 doesn’t convert electrical energy into heat like a resistance
Z0 does not contribute to attenuation
Z0 does not vary with the length of the line
Conductors
Dielectric Insulator
with relative permittivity k
• Real transmission lines have real resistance
d
r
• Loss due to metal resistance - proportional to square root of
frequency; goes up with line length
• Loss due to dielectric resistance – proportional to frequency; goes
up with line length
• It is these two resistances that are the primary causes of attenuation
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Transmission Lines
No. 9
The end of the line
NOT Infinitely Long
i
5V
open
shorted
+
-
• After switch is closed, a wave travels down the t-line
• What happens when it hits the open end?
• What if the end is shorted?
• Open or shorted t-lines will cause (unwanted) reflections.
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Transmission Lines
No. 10
Termination
NOT Infinitely Long
i
5V
R = Z0
+
-
• Place a resistor of value Z0 at the end of the line
• What happens when the wave hits the terminated end?
• A properly terminated line will appear to be an infinite line
and have no reflections
• Any impedance change will cause reflections
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Transmission Lines
No. 11
Why we dislike Reflections
• Reflections can mess up values on the line in locations
between the source and end
• If a periodic signal is applied to an un-terminated
transmission line, the reflections will set up a standing
wave pattern
• The amplitude of the standing wave may be very large and will
radiate power away
• This is great if we’re building an antenna, but we’re not!
• Un-terminated lines are a major source of Electromagnetic
Interference (EMI)
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Transmission Lines
No. 12
Creating Reflections – Things to Avoid
• Obviously, un-terminated t-lines
• Remember, a line should be treated as a t-line if it is longer than 1/10 of
the wavelength of the applied signal
• Any change in impedance of the line will create reflections
•
•
•
•
Change of cable type
Change of the separation between conductors
Change in the width of conductors
Change in the dielectric between conductors
• Use of standard cable with standard connectors avoids
problems
• Match the impedance of the cable to the equipment being used
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Transmission Lines
No. 13
Creating Reflections – Things to Avoid
• Printed Circuit Boards (PCBs) present a challenge
signal
ground
signal
ground
signal
ground
If the spacing between conductors
changes, the impedance changes!
If the width of the conductors
changes, the impedance changes!
Square corners not only change the
spacing between conductors, but
the width of the conductors too!
Ground planes help a lot because the signal’s return path will follow
directly underneath the signal. However, the impedance of the line will
depend on the thickness and type of material in the PCB.
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Transmission Lines
No. 14