# ESE370: Circuit-Level for Digital Systems This Week Transmission

```ESE370:
Circuit-Level
This Week
Modeling, Design, and Optimization
for Digital Systems
Day 34: December 1, 2010
Transmission Lines
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Penn ESE370 Fall2010 -- DeHon
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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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Intuitive: Lossless
Transmission Line
•  Pulses travel as waves without
distortion
•  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
Impedance
Propagation
•
•  w=1/sqrt(LC)
–  Rate of propagation
–  Delay linear in length
•  V(x,t) = A+Be-(wt+x)
Be-(wt+x)=LCw2Be-(wt+x)
w=
•  Ici=CdVi/dt
•  Ici=wCBe-(wt+x)
•  Z0 = Vi/Ii ~Vi/Ici = 1/wC = 1/(C/sqrt(LC))
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LC
w=
•  CL = ε&micro;
c0
ε r &micro;r
€ r&micro;r)
–  w=1/sqrt(ε&micro;)=c0/sqrt(ε
–  Where c0=speed of light in vacuum=30cm/ns
Penn ESE370 Fall2010 -- DeHon
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Penn ESE370 Fall2010 -- DeHon
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–  (really Ii --- differs in phase)
Vi-1
Ii
Vi
Ii+1
Vi+1
Ici
Penn ESE370 Fall2010 -- DeHon
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End of Line Reflection
Infinite Lossless
Transmission Line
•  Transmission line looks like
Z0 =
L
C
Z0
€
⎛ R − Z 0 ⎞
Vi ⎜
⎟ = Vr
⎝ R + Z 0 ⎠
•  Input waveform travels down line at
velocity
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–  Without distortion
w=
LC
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Penn ESE370 Fall2010 -- DeHon
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Penn ESE370 Fall2010 -- DeHon
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⎛ 2R ⎞
Vi ⎜
⎟ = Vt
⎝ R + Z 0 ⎠
€
Back at Source?
R≠Z0
•  What happens at source?
•  What happens?
–  Depends on how terminated
–  Looks like at sink end
–  75 Ω termination on 50 Ω line
–  50 Ω termination on 75 Ω line
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Penn ESE370 Fall2010 -- DeHon
Penn ESE370 Fall2010 -- DeHon
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50Ω line, 75Ω termination
Simulation
•  For these, with direct drive from voltage
source
–  Source looks like short circuit
•  Source cannot be changed
Penn ESE370 Fall2010 -- DeHon
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⎛ R − Z 0 ⎞
⎛ 75 − 50 ⎞
Vr = Vi ⎜
⎟ = 0.2Vi
⎟ = Vi ⎜
⎝ 75 + 50 ⎠
Penn ESE370 Fall2010 -- DeHon ⎝ R + Z 0 ⎠
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€
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75Ω line, 50Ω termination
Series Termination
•  What happens here?
⎛ R − Z 0 ⎞
⎛ 50 − 75 ⎞
Vr = Vi ⎜
⎟ = −0.2Vi
⎟ = Vi ⎜
⎝ 50 + 75 ⎠
R
+
Z
Penn ESE370 Fall2010 -- DeHon⎝
0 ⎠
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Penn ESE370 Fall2010 -- DeHon
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Simulation
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
Penn ESE370 Fall2010 -- DeHon
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Penn ESE370 Fall2010 -- DeHon
Termination Cases
•  Parallel at Sink
•  Lab on Friday
–  Pix
–  Lecture Wednesday
•  Series at Source
–  pix
Penn ESE370 Fall2010 -- DeHon
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Penn ESE370 Fall2010 -- DeHon
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Idea (still working on)
•  Transmission lines
–  high-speed
–  high throughput
–  long-distance signaling
•  Termination
•  Signal quality
Penn ESE370 Fall2010 -- DeHon
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c0
=
LC
ε r &micro;r
L
Z0 =
C
w=
€
⎛ R − Z 0 ⎞
Vr = Vi ⎜
⎟
€ ⎝ R + Z 0 ⎠
19
€
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