lecture3 ee689 tdr spar

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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



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

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 DallyChapter 3.4, 3.6 - 3.7

• Majority of s-parameter material from Hall “Advanced Signal Integrity for High-SpeedDigital 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-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]



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



TDR Waveforms (Open & Short)

• Open termination

8

Input step at 1ns

2td

2td

• Short termination



TDR Waveforms (Matched & Mismatched)

• Matched termination

9

• Mismatched termination 2tdZT > Z0

ZT < Z0



TDR Waveforms (C & L Discontinuity)

10

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



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 r t x >∆



TDR Multiple Reflections

12



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



Time-Domain Transmission (TDT)

14

• 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]



Network Analyzer

15

• Stimulates network withswept-frequency source

• Measures network responseamplitude and phase

• Can measure transferfunction, scattering matrices,impedance, …

[Dally]



Transfer Function & ImpedanceMeasurements

16

[Dally]



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

17

[Dally]



Formal S-Parameter Definitions

18

[ Agilent]



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)

19



ABCD Parameters

20

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]



Converting Between S & ABCD Parameters

21

[Hall]



22

Example: Cascaded Via & Transmission Line

• Taken from “Advanced Signal Integrity for High-Speed Digital Designs” by Hall



23

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

24[Peters, IEEE Backplane Ethernet Task Force]



S-Parameter Channel Example(4-port differential)

25

−

=

=

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



S-Parameter Channel Example

26

S21

S11



Impulse Response

• Channel impulse responses are used in• Time domain simulations

• Link analysis tools

27

( ) ( ) ( )

( ) ( ) ( ) ( ) ( )

( ) ( ){ }w H F t h

xt ht xt ht y

X H Y

1−

∞

∞−

=

−=∗=

=

∫ τ τ

ω ω ω

G i l f



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

28

( ) ( ){ }ω S F t h 1−=

( ) ( )∗=− f S f S

PositiveFrequency

NegativeFrequency



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”

29

( ) ps3.33GHz152

1

2

1

max== f

zero padding

For 1ps resolution:zero pad to +/-500GHz



Channel Impulse Response

• Now perform ifft toproduce impulse response

30

• Can sanity check by doing anfft on impulse response andcomparing to measured data



Impulse Response of Different Channels

31

7” Desktop/0Conn

17” Refined BP/2Conn

17” Legacy BP/2Conn



Channel Transient Response

32

*



Eye Diagrams

33

[Walker]



Eye Diagrams vs Data Rate

34



Eye Diagrams vs Channel

35



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)

36

Single Input Bit

Output Pulse

Response



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)

37

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]



Next Time

• Channel pulse response model

• Modulation schemes

lecture3 ee689 tdr spar

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