Sam PalermoAnalog & Mixed-Signal Center

Texas A&M University

ECEN689: Special Topics in High-Speed Links Circuits and Systems

Spring 2010

Lecture 7: Channel Time-Domain Response

Announcements

• HW2 due 2/5

• No class next week

• Reading• Will post some material on TDR and network

analyzers (S-parameters)• Link signaling papers

2

Agenda

• S-parameters revisited

• Impulse response generation

• Eye diagrams

• Inter-symbol interference (ISI)

3

Formal S-Parameter Definitions

4

[Agilent]

S-Parameters with Arbitrary Termination

5

(a2 ≠ 0)

(a1 ≠ 0)

• I believe this is what the network analyzer reports for s11and s22 when a matching network is not used

[Agilent]

S-Parameter Test Circuits & Meaning

6

( )

( )

( )

( )s

i

oo

ii

incidento

dtransmittei

s

so

oo

oo

incidento

reflectedo

s

o

ii

oo

incidenti

dtransmitteo

s

si

ii

ii

incidenti

reflectedi

VV

IRVIRV

VV

sS

VVV

IRVIRV

VV

sS

VV

IRVIRV

VV

sS

VVV

IRVIRV

VV

sS

=+−

==

−=

+−

==

=+−

==

−=

+−

==

0

0

,

,12

0

0

,

,22

0

0

,

,21

0

0

,

,11

[Sackinger]

• S11 = Input reflection coefficient• 1/S11 = Input return loss

• S21 = Forward transmission coefficient • Gain w/ input matching dependency

• S22 = Output reflection coefficient• 1/S22 = Output return loss

• S12 = Reverse transmission coefficient (isolation)

( ) ( )[ ] ( )gain voltageloaded is A(s) where

1 1121 sAsSsS +=

If a1 and a2 are not equal to zero for the appropriate measurements, these are “formally” s11

’ , s21’ , s22

’ , s12’

S-Parameter Channel Example

7

[Peters, IEEE Backplane Ethernet Task Force]

S-Parameter Channel Example (4-port differential)

8

−

=

=

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

9

S21

S11

Impulse Response

• Channel impulse responses are used in• Time domain simulations• Link analysis tools

10

( ) ( ) ( )

( ) ( ) ( ) ( ) ( )

( ) ( ){ }wHFth

xthtxthty

XHY

1−

∞

∞−

=

−=∗=

=

∫ ττ

ωωω

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

11

( ) ( ){ }ωSFth 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”

12

( ) ps3.33GHz1521

21

max

==f

zero padding

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

Channel Impulse Response

• Now perform ifft to produce impulse response

13

• Can sanity check by doing an fft on impulse response and comparing to measured data

Impulse Response of Different Channels

14

7” Desktop/0Conn

17” Refined BP/2Conn

17” Legacy BP/2Conn

Channel Transient Response

15

*

Eye Diagrams

16

[Walker]

Eye Diagrams vs Data Rate

17

Eye Diagrams vs Channel

18

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)

19

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)

20

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

500mVEye 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

500mVEye 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

21