Sam PalermoAnalog & Mixed-Signal Center
Texas A&M University
ECEN720: High-Speed Links Circuits and Systems
Spring 2021
Lecture 3: Time-Domain Reflectometry & S-Parameter Channel Models
Announcements• Lab 1 report and Prelab 2 due Feb 3
• Reference Material Posted on Website• TDR theory application note • S-parameter notes
2
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
3
Lecture References• Majority of TDR material from Dally
Chapter 3.4, 3.6 - 3.7
• Majority of s-parameter material from Hall “Advanced Signal Integrity for High-Speed Digital Designs” Chapter 9
4
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
Time-Domain Reflectometer (TDR)
• TDR consists of a fast step generator and a high-speed oscilloscope
• 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 channel6
[Agilent]
[Dally]
TDR Impedance Calculation
7
V5.01 If21
1
STEP
000
0
0
i
iri
ri
r
rT
T
T
i
rr
VVVtVV
tVZtVVtVVZ
tktkZtZ
ZtZZtZ
VtVtk
xtZxZ
tVVtVZtZ TTT
2 10
TDR Waveforms (Open & Short)• Open termination
8
Input step at 1ns
2td
2td
• Short termination
TDR Waveforms (Matched & Mismatched)
• Matched termination
9
• Mismatched termination 2td ZT > Z0ZT < Z0
TDR Waveforms (C & L Discontinuity)
10
2td
2td
20CZ
C
02ZL
L
• Shunt C discontinuity
• Series L discontinuity
rt
r
etV
V 1Peak voltage spike magnitude:
tr = 10ps
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
rtx
TDR Multiple Reflections
12
TDR Waveforms (Multiple Discontinuities)
13
A B C Load
A
B C
BAB,CBC
BAC,CBCBC,CAB
Note: Step comes at 1ns
Time-Domain Transmission (TDT)
14
• Can measure channel transfer function• Hard to isolate impedance discontinuities, as they are
superimposed on a single rising edge
jVjVjH
1
2
TDR TDT
[Dally]
• Stimulates network with swept-frequency source• Measures network response amplitude and phase• Can measure transfer function, scattering
matrices, impedance, …• Test set is configured differently for each kind of
measurement to be performed
Network Analyzer
15
[Dally]
• Test sets in high-frequency network analyzers make use of 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 ZA to be proportional to the forward traveling wave and the voltage across ZB to be proportional to any reflected wave
Directional Coupler
16
[Dally]
Transfer Function & Impedance Measurements
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[Dally]
• Transfer function measurement• The input signal is from a directional coupler which samples the forward
traveling wave• The network output serves as the output
• Impedance measurement• The input signal is from a directional coupler which samples the forward
traveling wave• The reflected wave from the network is compared with this input to
characterize the impedance over frequency
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 wave ratio
18
[Dally]
Formal S-Parameter Definitions
19
[Agilent]
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 T matrix)
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ABCD Parameters
21
020202022
1
2
1
2
1
2
1
vivi i
iDviC
ivB
vvA
2
21
iv
DCBA
iv
i
[Hall]
Converting Between S & ABCD Parameters
22
[Hall]
23
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
S-Parameter Channel Example
25[Peters, IEEE Backplane Ethernet Task Force]
S-Parameter Channel Example (4-port differential)
26
0
0
44434241
34333231
24232221
14131211
4
3
2
1
44434241
34333231
24232221
14131211
4
3
2
1
v
v
SSSSSSSSSSSSSSSS
aaaa
SSSSSSSSSSSSSSSS
bbbb
4123432101
221
3113331101
111
21
21
42
42
SSSSabS
SSSSabS
aad
ddd
aad
ddd
[Hall]
Data from 50MHz to 15GHz in 10MHz steps
S-Parameter Channel Example
27
S21
S11
Impulse Response• Channel impulse responses are used in
• Time domain simulations• Link analysis tools
28
wHFth
xthtxthty
XHY
1
Generating an Impulse Response from S-Parameters• Perform the inverse
Fourier transform on the s-parameter of interest
• Step 1: For ifft, produce negative frequency values and append to s-parameter data in the following manner
29
SFth 1
fSfS
Positive Frequency
Negative Frequency
Increasing Impulse Response Resolution• Could perform ifft now,
but will get an impulse response with time resolution of
• To improve impulse response resolution expand frequency axis and “zero pad”
30
ps3.33GHz1521
21
max
f
zero padding
For 1ps resolution: zero pad to +/-500GHz
Channel Impulse Response• Now perform ifft to
produce impulse response
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• Can sanity check by doing an fft on impulse response and comparing to measured data
Impulse Response of Different Channels
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7” Desktop/0Conn
17” Refined BP/2Conn
17” Legacy BP/2Conn
Channel Transient Response
33
*
Eye Diagrams
34
[Walker]
Eye Diagrams vs Data Rate
35
Eye Diagrams vs Channel
36
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)
37
Single Input Bit
Output Pulse Response
ISI Impact• At channel input (TX output), eye diagram is
wide open
• As data pulses propagate through channel, they experience dispersion and have significant ISI• Result is a closed eye at channel output (RX input)
38
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
Eye FFE1 10.0Gb/s [OPEN,1e-8] No Xtalk
Time
Sign
al A
mpl
itude
Vpd
DATA = RAND Tx 600mVpd AGC Gain -5.48dBXTALK = NONE AGC 5.0GHz 0.00dBPKG=0/0 TERM = 5050/5050 IC = 3/3
HSSCDR = 2.3.2-pre2 IBM ConfidentialDate = Sat 01/21/2006 12:00 PMPLL=0F1V0S0,C16,N32,O1,L80 FREQ=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
Eye FFE1 10.0Gb/s [OPEN,1e-8] No Xtalk
Time
Sign
al A
mpl
itude
Vpd
DATA = RAND Tx 600mVpd AGC Gain -6.02dBXTALK = NONE AGC 5.0GHz 0.00dBPKG=0/0 TERM = 5050/5050 IC = 3/3
HSSCDR = 2.3.2-pre2 IBM ConfidentialDate = Sat 01/21/2006 12:01 PMPLL=0F1V0S0,C16,N32,O1,L80 FREQ=0.00ppm/0.00usFFE = [1.000, 0.000]
INPUT
OUTPUT
[Meghelli (IBM) ISSCC 2006]
Next Time• Channel pulse response model
• Modulation schemes
39
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