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Sam Palermo
Analog & Mixed-Signal Center
Texas A&M University
ECEN689: Special Topics in High-Speed
Links Circuits and SystemsSpring 2010
Lecture 4: Transmission Line Examples
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Announcements
HW1 due 1/29 One page summary of recent link design paper
Current Reading
Chapter 3.3 3.4
For next time
Chapter 3.6 3.7
2
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Agenda
Transmission Lines Termination examples
Differential transmission lines
Majority of todays material from DallyChapter 3.3-3.4
3
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Reflections & Telegraphers Eq.
4
T
iT
ZZ
VI
+=
0
2
+
=
+=
=
0
0
0
00
2
ZZ
ZZ
Z
VI
ZZ
V
Z
VI
III
T
Tir
T
iir
Tfr
0
0
ZZ
ZZ
V
V
I
Ik
T
T
i
r
i
rr
+
===
Termination Current:
With a Thevenin-equivalent model of the line:
KCL at Termination:
Telegraphers Equation or
Reflection Coefficient
[Dally]
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Termination Examples - Ideal
5
RS = 50Z0 = 50, td = 1ns
RT = 50
05050
5050
05050
5050
5.05050
501
=+
=
=+
=
=
+=
rS
rT
i
k
k
VVV
in (step begins at 1ns)
source
termination
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Termination Examples - Open
6
RS = 50Z0 = 50, td = 1ns
RT ~ (1M)
05050
5050
150
50
5.05050
501
=+
=
+=+
=
=
+=
rS
rT
i
k
k
VVV
in (step begins at 1ns)
source
termination
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Termination Examples - Short
7
RS = 50Z0 = 50, td = 1ns
RT = 0
05050
5050
1500
500
5.05050
501
=+
=
=+
=
=
+=
rS
rT
i
k
k
VVV
in (step begins at 1ns)
source
termination
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Arbitrary Termination Example
8
RS = 400Z0 = 50, td = 1ns
RT = 600
778.050400
50400
846.050600
50600
111.050400
501
=+
=
=+
=
=
+=
rS
rT
i
k
k
VVV
in (step begins at 1ns)
sourcetermination
0.111V
0.205V
0.278V0.340
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Lattice Diagram
9
RS = 400
RT = 600
Z0 = 50, td = 1ns
in (step begins at 1ns)
Rings up to 0.6V(DC voltage division)
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Termination Reflection Patterns
10
RS = 25, RT = 25
krS & krT < 0
Voltages Converge
RS = 25, RT = 100
krS < 0 & krT > 0
Voltages Oscillate
RS = 100, RT = 25
krS > 0 & krT < 0
Voltages Oscillate
RS = 100, RT = 100
krS > 0 & krT < 0
Voltages Ring Up
source
termination
source
termination
source
termination
source
termination
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Termination Schemes
11
No Termination Little to absorb line energy
Can generate oscillatingwaveform
Line must be very short
relative to signal transition time n = 4 - 6
Limited off-chip use
Source Termination Source output takes 2 steps up
Used in moderate speed point-to-point connections
LCnlnTt triproundr 2=>
LCltporch 2
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Termination Schemes
12
Receiver Termination No reflection from receiver
Watch out for intermediateimpedance discontinuities
Little to absorb reflections at driver
Double Termination
Best configuration for minreflections
Reflections absorbed at both driverand receiver
Get half the swing relative tosingle termination
Most common termination schemefor high performance serial links
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Differential Transmission Lines
13
Differential signaling advantages Self-referenced
Common-mode noise rejection
Increased signal swing
Reduced self-induced power-supply noise
Requires 2x the number ofsignaling pins relative to single-ended signaling
But, smaller ratio of supply/signal(return) pins
Total pin overhead is typically 1.3-1.8x (vs 2x)
[Hall]
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Balanced Transmission Lines
Even (common) modeexcitation
Effective C = CC
Effective L = L + M Odd (differential) mode
excitation
Effective C = CC + 2Cd Effective L = L M
14
21
21
2
+
=
+=
dc
odd
c
even
CC
MLZ
C
MLZ
[Dally]
2,2 oddCMevenDIFF
ZZZZ ==
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PI-Termination
15
1RZeven =
2||2|| 221 RZRRZ evenodd ==
=
oddeven
evenodd
ZZ
ZZR 22
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T-Termination
16
12 2RRZodd +=
( )oddeven
odd
ZZR
RZ
=
=
2
11
2
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Next Time
Channel modeling Time domain reflectometer (TDR)
Network analysis
17