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Sam Palermo
Analog & Mixed-Signal Center
Texas A&M University
ECEN720: High-Speed Links
Circuits and SystemsSpring 2013
Lecture 3: Time-Domain Reflectometry & S-Parameter Channel Models
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Announcements
• The first lab is today in ZACH 203•Prelab 1 is due on Wednesday
• 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
( )( ) ( )
( )
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( )( )
V5.01If
21
1
STEP
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i
iri
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r T
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=υ
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tVZtZ T T T
2
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0
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TDR Waveforms (Open & Short)
• Open termination
8
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
20CZ
C =τ
02Z
LL =τ
• Shunt C discontinuity
• Series L discontinuity
−
=
∆
−τ
τ rt
r
etV
V1
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
11
υ rtx>∆
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TDR Multiple Reflections
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TDR Waveforms (Multiple Discontinuities)
13
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 jH
1
2=
TDR TDT
[Dally]
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• Stimulates network with swept-frequency source
• Measures network response amplitude and phase
• Can measure transfer function, scatteringmatrices, impedance, …
• Test set is configured differently for each kind of measurement to be performed
Network Analyzer
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[Dally]
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• Test sets in high-frequency network analyzers make useof directional couplers
• Directional couplers are two transmission lines coupled
over a short distance• If the short line is properly terminated, it allows for the
voltage across Z A to be proportional to the forwardtraveling wave and the voltage across ZB to be
proportional to any reflected wave
Directional Coupler
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[Dally]
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Transfer Function & ImpedanceMeasurements
17
[Dally]
• Transfer function measurement
• The input signal is from a directional coupler which samples the forwardtraveling wave
• The network output serves as the output• Impedance measurement
• The input signal is from a directional coupler which samples the forwardtraveling wave
• The reflected wave from the network is compared with this input to
characterize the impedance over frequency
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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 of independently 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
iD
v
iC
i
vB
v
vA
2
21
i
v
DC
BA
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
25[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
SSSSSSSS
SSSS
SSSS
aa
a
a
SSSSSSSS
SSSS
SSSS
bb
b
b
( )
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01
2
21
31133311
01
111
2
1
2
1
42
42
SSSSa
bS
SSSSa
bS
aad
d
dd
aad
ddd
−−+==
−−+==
==
==
[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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( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ){ }wHFth
xthtxthty
XH Y
1−
∞
∞−
=
−=∗=
=
∫ τ τ
ω ω ω
G i I l R 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 SFth 1−=
( ) ( )∗=− f Sf 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
EyeFF E110.0Gb/s [OPEN,1e-8]No Xtalk
Time
DATA =RAND Tx600mVpd AGC Gain-5.48dBXTALK =NONE AGC 5.0GHz 0. 00dBPKG=0/0 TERM=5050/5050 IC =3/3
HSSCDR =2.3.2-pre2IBM ConfidentialDate=Sat 01/21/2006 12:00P MPLL=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
EyeF FE1 10.0Gb/s [OPEN,1e-8]No Xtalk
Time
DATA =RAND Tx600mVpd AGC Gain-6.02dBXTALK =NONE AGC 5.0GHz 0.00dBPKG=0/0 TE RM=5050/5050 IC =3/3
HSSCDR =2.3.2-pre2IBM ConfidentialDate=Sat 01/21/2006 12:01P MPLL=0F1V0S0,C16,N32,O1,L80FREQ=0.00ppm/0.00usFFE =[1.000, 0.000]
INPUT
OUTPUT
[Meghelli (IBM) ISSCC 2006]
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Next Time
• Channel pulse response model
• Modulation schemes