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Sam Palermo
Analog & Mixed-Signal Center
Texas A&M University
ECEN689: Special Topics in High-Speed
Links Circuits and SystemsSpring 2012
Lecture 3: Time-Domain Reflectometry & S-Parameter Channel Models
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Announcements
• This Thursday lab time will be used for amake-up lecture
• No class next Monday
• Reference Material Posted on Website
• TDR theory application note
• S-parameter notes
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Agenda
• Interconnect measurement techniques• Time-domain reflectometry (TDR)
• Network analyzer
• S-parameters
• Cascading S-parameter models
• Full S-parameter channel model
• Transient simulations
• Impulse response generation
• Eye diagrams
• Inter-symbol interference
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Lecture References
• Majority of TDR material from DallyChapter 3.4, 3.6 - 3.7
• Majority of s-parameter material from Hall “Advanced Signal Integrity for High-SpeedDigital Designs” Chapter 9
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Interconnect Modeling
• Why do we need interconnect models?• Perform hand calculations and simulations (Spice, Matlab, etc…)
• Locate performance bottlenecks and make design trade-offs
• Model generation methods
• Electromagnetic CAD tools• Actual system measurements
• Measurement techniques
• Time-Domain Reflectometer (TDR)
•
Network analyzer (frequency domain)5
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Time-Domain Reflectometer (TDR)
• TDR consists of a fast step generator and a high-speedoscilloscope
• TDR operation
• Outputs fast voltage step onto channel
• Observe voltage at source, which includes reflections
• Voltage magnitude can be converted to impedance
• Impedance discontinuity location can be determined by delay
• Only input port access to characterize channel 6
[ Agilent]
[Dally]
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TDR Impedance Calculation
7
( ) ( ) ( )
( )
( ) ( )
( )( )( )
( )( )
V5.01If
21
1
STEP
000
0
0
=⇒=
−=
−
+
=
−
+
=
+
−==
i
ir i
r i
r
r T
T
T
i
r r
V V V
t V V
t V
Z t V V
t V V
Z t k
t k
Z t Z
Z t Z
Z t Z
V
t V t k
( ) ( )
( )
( )
==
−
=υ
xt Z x Z
t V V
t V Z t Z T T T
2
1
0
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TDR Waveforms (Open & Short)
• Open termination
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Input step at 1ns
2td
2td
• Short termination
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TDR Waveforms (Matched & Mismatched)
• Matched termination
9
• Mismatched termination 2tdZT > Z0
ZT < Z0
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TDR Waveforms (C & L Discontinuity)
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2td
2td
2
0C Z C =τ
02 Z
L L =τ
• Shunt C discontinuity
• Series L discontinuity
−
=
∆
−τ
τ r t
r
et V
V 1
Peak voltage spikemagnitude:
tr = 10ps
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TDR Rise Time and Resolution
• TDR spatial resolution is set by step risetime
• Step risetime degrades with propagation
through channel• Dispersion from skin-effect
• Lump discontinuities low-pass filter the step
• Causes difficulty in estimating L & C values• Channel filtering can actually compensate
for lump discontinuity spikes
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υ r t x >∆
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TDR Multiple Reflections
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TDR Waveforms (Multiple Discontinuities)
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A B C Load
A
B C
B AB ,CBC
B AC ,
CBCBC ,C AB
Note: Step comes at 1ns
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Time-Domain Transmission (TDT)
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• Can measure channel transfer function
• Hard to isolate impedance discontinuities, as they aresuperimposed on a single rising edge
( ) ( )
( )ω
ω
ω
jV
jV j H
1
2=
TDR TDT
[Dally]
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Network Analyzer
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• Stimulates network withswept-frequency source
• Measures network responseamplitude and phase
• Can measure transferfunction, scattering matrices,impedance, …
[Dally]
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Transfer Function & ImpedanceMeasurements
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[Dally]
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Scattering (S) Parameters
• Why S Parameters?• Easy to measure
• Y, Z parameters need open
and short conditions• S parameters are obtained
with nominal termination
• S parameters based on
incident and reflected waveratio
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[Dally]
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Formal S-Parameter Definitions
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[ Agilent]
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Cascading S-Parameters
• Network analysis allows cascading ofindependently characterized structures
• However, can’t directly cascade s-parameter matrices and multiply
• Must first convert to an ABCD matrix (or Tmatrix)
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ABCD Parameters
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020202022
1
2
1
2
1
2
1
====
====vivi
i
i D
v
iC
i
v B
v
v A
2
21
i
v
DC
B A
i
v
i
•=
[Hall]
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Converting Between S & ABCD Parameters
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[Hall]
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Example: Cascaded Via & Transmission Line
• Taken from “Advanced Signal Integrity for High-Speed Digital Designs” by Hall
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Example: Cascaded Via & Transmission Line
• Taken from “Advanced Signal Integrity for High-Speed Digital Designs” by Hall
• Using conversion table:
• Can also use T matrixes to cascade
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S-Parameter Channel Example
24[Peters, IEEE Backplane Ethernet Task Force]
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S-Parameter Channel Example(4-port differential)
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−
=
=
0
0
44434241
34333231
24232221
14131211
4
3
2
1
44434241
34333231
24232221
14131211
4
3
2
1
v
v
S S S S
S S S S
S S S S
S S S S
a
a
a
a
S S S S
S S S S
S S S S
S S S S
b
b
b
b
( )
( )41234321
01
2
21
31133311
01
111
2
1
2
1
42
42
S S S S a
bS
S S S S a
bS
aad
d
dd
aad
d dd
−−+==
−−+==
==
==
[Hall]
Data from 50MHz to 15GHz in10MHz steps
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S-Parameter Channel Example
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S21
S11
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Impulse Response
• Channel impulse responses are used in• Time domain simulations
• Link analysis tools
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( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ){ }w H F t h
xt ht xt ht y
X H Y
1−
∞
∞−
=
−=∗=
=
∫ τ τ
ω ω ω
G i l f
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Generating an Impulse Response fromS-Parameters
• Perform the inverseFourier transform on thes-parameter of interest
• Step 1: For ifft, producenegative frequency valuesand append to s-parameter data in thefollowing manner
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( ) ( ){ }ω S F t h 1−=
( ) ( )∗=− f S f S
PositiveFrequency
NegativeFrequency
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Increasing Impulse Response Resolution
• Could perform ifft now,but will get an impulseresponse with timeresolution of
• To improve impulse
response resolutionexpand frequency axisand “zero pad”
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( ) ps3.33GHz152
1
2
1
max== f
zero padding
For 1ps resolution:zero pad to +/-500GHz
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Channel Impulse Response
• Now perform ifft toproduce impulse response
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• Can sanity check by doing anfft on impulse response andcomparing to measured data
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Impulse Response of Different Channels
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7” Desktop/0Conn
17” Refined BP/2Conn
17” Legacy BP/2Conn
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Channel Transient Response
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*
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Eye Diagrams
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[Walker]
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Eye Diagrams vs Data Rate
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Eye Diagrams vs Channel
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Inter-Symbol Interference (ISI)
• Previous bits residual state can distort the current bit,resulting in inter-symbol interference (ISI)
• ISI is caused by
• Reflections, Channel resonances, Channel loss (dispersion)
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Single Input Bit
Output Pulse
Response
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ISI Impact
• At channel input (TX output), eye diagram iswide open
• As data pulses propagate through channel, theyexperience dispersion and have significant ISI
• Result is a closed eye at channel output (RX input)
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Edge connector
Packaged SerDes
Line card trace
Backplane trace
Via stub
-100ps 100ps-50ps 0ps 50ps-500mV
500mV
-400mV
-300mV
-200mV
-100mV
-0.0mV
100mV
200mV
300mV
400mV
500mV
EyeFFE110.0Gb/s [OPEN,1e-8] NoXtalk
Time
DATA= RAND Tx 600mVpd AGCGain-5.48dBXTALK = NONE AGC 5.0GHz 0. 00dBPKG=0/0 TERM= 5050/5050 IC= 3/3
HSSCDR= 2.3.2-pre2IBMConfidentialDate= Sat 01/21/2006 12:00PMPLL=0F1V0S0,C16,N32,O1,L80FREQ=0.00ppm/0.00usFFE= [1.000, 0.000]
-100ps 100ps-50ps 0ps 50ps-500mV
500mV
-400mV
-300mV
-200mV
-100mV
-0.0mV
100mV
200mV
300mV
400mV
500mV
EyeFFE110.0Gb/s [OPEN,1e-8] NoXtalk
Time
DATA= RAND Tx 600mVpd AGCGain-6.02dBXTALK = NONE AGC 5.0GHz 0.00dBPKG=0/0 TERM= 5050/5050 IC= 3/3
HSSCDR= 2.3.2-pre2IBMConfidentialDate= Sat 01/21/2006 12:01PMPLL=0F1V0S0,C16,N32,O1,L80FREQ=0.00ppm/0.00usFFE= [1.000, 0.000]
INPUT
OUTPUT
[Meghelli (IBM) ISSCC 2006]