Transcript ppt

ESE370:
Circuit-Level
Modeling, Design, and Optimization
for Digital Systems
Day 34: December 1, 2010
Transmission Lines
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Penn ESE370 Fall2010 -- DeHon
This Week
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General wire formulation
Lossless Transmission Line
End of Transmission Line?
Termination
Where arise?
Implications
Discuss Lossy
See in action in lab
Penn ESE370 Fall2010 -- DeHon
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Transmission Line
• When resistance is negligible
– Have LC wire = Lossless Transmission Line
– More typical of Printed Circuit Board wires
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Penn ESE370 Fall2010 -- DeHon
Intuitive: Lossless
• Pulses travel as waves without
distortion
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Penn ESE370 Fall2010 -- DeHon
Propagation
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Be-(wt+x)=LCw2Be-(wt+x)
w=1/sqrt(LC)
Rate of propagation
Delay linear in length
w=
1
LC
w=
• CL = em
c0
e r mr
 rmr)
– w=1/sqrt(em)=c0/sqrt(e
– Where c0=speed of light in vacuum=30cm/ns
Penn ESE370 Fall2010 -- DeHon

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Impedance
• V(x,t) = A+Be-(wt+x)
• Ici=CdVi/dt
• Ici=wCBe-(wt+x)
• Z0 = Vi/Ii ~Vi/Ici = 1/wC = 1/(C/sqrt(LC))
– (really Ii --- differs in phase)
Vi-1
Ii
Vi
Ii+1
Vi+1
Ici
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Penn ESE370 Fall2010 -- DeHon
Infinite Lossless
Transmission Line
• Transmission line looks like
resistive load
L
Z0 =
C
Z0

• Input waveform travels down line at
velocity
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– Without distortion
Penn ESE370 Fall2010 -- DeHon
w=
LC
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End of Line Reflection
R  Z 0 
Vi 
= Vr
R  Z0 
 2R 
Vi 
= Vt
R  Z 0 
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Penn ESE370 Fall2010 -- DeHon
Back at Source?
• What happens at source?
– Depends on how terminated
– Looks like at sink end
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Penn ESE370 Fall2010 -- DeHon
R≠Z0
• What happens?
– 75 W termination on 50 W line
– 50 W termination on 75 W line
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Penn ESE370 Fall2010 -- DeHon
Simulation
• For these, with direct drive from voltage
source
– Source looks like short circuit
• Source cannot be changed
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50W line, 75W termination
R  Z0  75  50 
Vr = Vi
= 0.2Vi
= Vi 
75  50 
Penn ESE370 Fall2010 -- DeHon R  Z 
0
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75W line, 50W termination
R  Z 0 
50  75 
Vr = Vi 
= 0.2Vi
= Vi 
50  75 
Penn ESE370 Fall2010 -- DeHonR  Z 
0
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Series Termination
• What happens here?
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Simulation
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Penn ESE370 Fall2010 -- DeHon
Series Termination
• Rseries = Z0
• Initial voltage divider
– Half voltage pulse down line
• End of line open circuit
– sees single transition to full voltage
• Reflection returns to source and sees
termination Rseries = Z0
• No further reflections
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Penn ESE370 Fall2010 -- DeHon
Termination Cases
• Parallel at Sink
– Pix
• Series at Source
– pix
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Penn ESE370 Fall2010 -- DeHon
Admin
• Lab on Friday
– Lecture Wednesday
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Penn ESE370 Fall2010 -- DeHon
Idea (still working on)
• Transmission lines
– high-speed
– high throughput
– long-distance signaling
• Termination
• Signal quality
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c0
w=
=
LC
e r mr
L
Z0 =
C
R  Z 0 
Vr = Vi 

 R  Z 0 

Penn ESE370 Fall2010 -- DeHon
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