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

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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

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)

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• 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

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[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

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[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

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[Dally]

Formal S-Parameter Definitions

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[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

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[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)

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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

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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

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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”

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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

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[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)

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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)

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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

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