Fast Eye-Diagram Analysis

吳瑞北, Ruey-Beei Wu

Rm. 340, Department of Electrical Engineering

E-mail: rbwu@ew.ee.ntu.edu.tw

url: http://cc.ee.ntu.edu.tw/~rbwu

S. H. Hall & H. L. Heck, High-Speed Digital Designs, ch. 13.

R. B. Wu

Contents

• Introduction

• Peak Distortion Analysis

• Diffusion in RC Line

• Fast Lossy Line Characterization

• Arbitrary Tx-Line Systems

R. B. Wu January 4, 2017 Peak Distortion Analysis

Ideal sampling positionTiming skew

Jitter

Ideal reference point

Voltage offset

Voltage Noise and

required comparator

input

Margin Calculation

R. B. Wu January 4, 2017 Peak Distortion Analysis

Ideal sampling position Timing skew Jitter

Ideal sampling position

Voltage offset

Voltage Noise and

required comparator

inputVoltage margin

Time margin

Margin Calculation (zoomed)

R. B. Wu January 4, 2017 Peak Distortion Analysis

• Eye diagrams are generally calculated empirically

– Convolve random data with pulse response of channel

– Pulse response is derived by convolving the impulse reponse with the transmitted symbol

• For eye diagrams to represent the worst-case, a large set of random data must be used

– Low probability of hitting worst case data transitions

– Computationally inefficient

• An analytical method of producing the worst-case eye diagram exists

– Computationally efficient algorithm

Worst-case eye calculation

Peak Distortion Analysis

Ref.: J. G. Proakis, Digital Communications, 3rd

ed., Singapore: McGraw-Hill, 1995, pp. 602-603

(not much detailed info here)

January 4, 2017 Peak Distortion Analysis

R. B. Wu January 4, 2017 Peak Distortion Analysis

• Point to point differential desktop topology

10” μstrip

• Differential, edge-coupled microstrip (10” @ 55Ω)

socket socket

• 2 Sockets

pkg pkg

• 2 Packages (2” @ 45Ω)

• 1pF pad capacitance

• 50Ω single-ended termination

Interconnect Model

R. B. Wu

Differential S Parameters

January 4, 2017 Peak Distortion Analysis

R. B. Wu

Eye diagram (100 bits @5Gb/s)

January 4, 2017 Peak Distortion Analysis

Random data eye (100 bits) ---

Random data eye (1000 bits) ---

R. B. Wu

cursorprecursor postcursor

ISI+ ISI-

Sample pulse response

R. B. Wu

0 1 1 0 1 0 0 1 0 0 0 0 0

ISIV 0WC

Worst-case 0

R. B. Wu

0 1 0 1 1 0 0 0 0 0

ISIcursorV 1WC

Worst-case 1

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1 1 0 1 0 0 1

0 0 1 0 1 1 0

Worst-case 0

Worst-case 1

Worst-case Patterns

R. B. Wu

• Given S Parameters and the corresponding

pulse response, the worst case eye shape can

be determined analytically

• Worst-case co-channel interference can also

be determined analytically

• Advantages – objective, exact, and

computationally efficient

Summary

Diffusion in RC Line

R. B. Wu

Diffusion (RC line, i.e., L=G=0)

t

VRC

z

tzV

t

tzVC

z

tzItzIR

z

tzV

2

2 ),(

),(),( );,(

),(

BdyeAtzut

u

Dz

u Dtzy

4

02

22

),( 1

equationDiffusion

BdyeAtzV

ztRCy

4

0

2

),(

where A and B should be determined by boundary conditions.

R. B. Wu

Diffusion in a Semi-infinitely Long Line

0(0,0 ) ;

( , ) 0 for 0

V V

V t t

20

0 00

yA e dy B V B V

24

0 00

2( , ) 1 erfc 4

RC t zyV z t V e dy V z RC t

20

0 00

2 0 0

2

y VA e dy V A V A

R. B. Wu

Pulse Response

• Input: a rectangular pulse2

2

( , )RC line

V z t VRC

z t

Features:

. Delay is proportional to t2

. Long tail causes significant

inter symbol interference

Ref.: N. N. Rao, Elements of Engineering Electromagnetics, 6th Ed., Sec. 7.5

zttRC

ztRC

y

ttRC

tRC

tt

o

dyeV

zVzVtzV

)(4

40

)(4040

2

00

2

erfcerfc),(

Fast Eye-Diagram Analysis for Lossy Tx-Line

Ref.: W.-D. Guo, J.-H. Lin, C.-M. Lin, T.-W. Huang, & R.-B. Wu, “Fast methodology for

determining eye-diagram characteristics of lossy transmission lines,” IEEE Trans. Adv. Packag.,

Feb. 2009.

(Best Paper Award)

19

R. B. Wu 20

Matched Lossy Tx-Line Systems

PRBS :

5Gbps, and

tr = 50ps. 5mil (H)

Rx

Rin ≈ ∞

VO

Metal : Copper

εr = 4.4tan δ = 0.02

8mil (W)2mil (T)

Microstrip line( Z0 ≈ 50Ω, Length : l )

+ VS

RS=50Ω

Tx ГS ГL

RL=

50Ω

Step Input

Signal

Vo

lta

ge

Time

Low

High

Monotonic Step Response

Lift up to the “High” level

Bit Period

If the tail is too wide, serious inter-symbol

interference (ISI) will be induced.

R. B. Wu 21

Worst-Case Eye-Diagram

0 50 100 150 2000

0.1

0.2

0.3

0.4

Tim e (ns )

Vo

lta

ge

(V

)

p

Lower Bound

0 50 100 150 2000

0.1

0.2

0.3

0.4

Tim e (ns )

Vo

lta

ge

(V

)

p

Lower Bound

0 50 100 150 2000

0.1

0.2

0.3

0.4

Time (ns )

Vo

lta

ge

(V

)

p

Upper Bound

0 50 100 150 2000

0.1

0.2

0.3

0.4

Time (ns )

Vo

lta

ge

(V

)

p

Upper Bound

degraded by ISI

Initial state 0

Initial state 1

30”-Long Line

0 2 4 6 8 100

0.1

0.2

0.3

0.4

Time (ns)

Voltage (

V)

0 2 4 6 8 100

0.1

0.2

0.3

0.4

Time (ns)

Voltage (

V)

R. B. Wu 22

Worst-Case Bits Pattern

t1 t2

t3

Time

0010000...+ 1101111...0010000...+ 1101111...

00010000...+ 11101111...00010000...+ 11101111...

Volt

age

0 100 200 300 4000

0.1

0.2

0.3

0.4

Time (ps)

Voltage (

V)

Worst-Case Eye Diagram

Eye shape

Still lack of jitter

information

Using only two anti-polarity one-bit

data patterns as the input signals can

simulate the worst-case eye diagram

for the transmission-line system with

a monotonic step response.

Single

Bit

R. B. Wu 23

System Transfer Function

where

,

, .

With assumption of low-loss line typically and 50S LR R fornearly matched termination,

Generally,

( ) ( )R j L G j Cg w w 2

2( ) 1

RC GL RGRG j RC GL j LC j LC

j LC j LCw w w

w w

1 12 2 2

RC GL RC GLj LC j LC

j LC j

R C G Lj LC

LLC Cw

w www

1 2 3( )g g g

Fourier transform1 2 3( ) ( ) ( ) ( )h t h t h t h t

0

2

0

( ) 1 ( )( )( ) ( ),

( ) 1 ( ) ( ) ( )

L

O S

S S L

HZV V

Z R H

w www w

w w w w

0( )

( )( )

R j LZ

G j C

w ww

w w

0

0

( )( )

( )

SS

S

R Z

R Z

ww

w0

0

( )( )

( )

LL

L

R Z

R Z

ww

w

0( ) / 50Z L Cw

( )( ) ( )

2.O S

HV V

ww w

( ) ( )( )

R j L G j C llH e e

w wgw

31 2( ) ll lH e e e gg gw

Low-loss assumption

R. B. Wu 24

Impulse Response

22

3

1[ ] ( )SR s C

lL

A

t

Au t

t

e

ep

(A). Time-delay term

1 11

1[ ] [) ]( l j LC lh t e eg w

1lim ( )

2j LC l j te e d

bw w

bbw

p0( )t td , 0t LC l time

δ(t) δ(t-t0)

t0

LC l

(B). Conductor-loss term

212

1 12 2[ ] [ ] ]( ) [S

l

R C R j Cl l

L Le eeh tw

g

21

lim ( )2

SR j Cl

j tLe e dwb

wbb

wp

21

lim ( )2

SR s Cl

stLe e dsj

b

bbp

7mil

FR44mil

( s)

4

SR lA

L

C

p

A=1.6*10-6

0.1600.9

S

WR

W T H(microstrip line)

[8]

R. B. Wu

Impulse Response

25

(C). Dielectric-loss term

3

| |1 1 12

32[ ] [ ] [( ) ]

d

l

G L G Ll l

C Ce eh t ew

g

| |

21

lim ( )2

dG Ll

j tCe e dwb

wbb

wp

2 2( )

B

B tpNon-Causal

(s)2

dG LB l

C

7mil

FR44mil

tanδ=0.02

(C-1). Kramer-Kronig Relation

In early days, K-K relation was proposed to solve the problem that the derived electric

susceptibility of dielectric material do not satisfy causality in time domain.

2 20

Re ( ')2Im ( ) '

'

GG P d

www w

p w w

2 20

' Im ( ')2Re ( ) '

'

GG P d

w ww w

p w w1

( ) ( )2

j tg t G e dww wp1

( ) ( )2

j tG g t e dtwwp

B=4.2*10-11

1tan , tan tan

1r re

d e ere r

G Ce e

d d de e [9]

R. B. Wu 26

Impulse Response

3( ) ( )B BgH e e e H

1 12

3 2

1( )

[1 / ]

1( ) ( )

[1 ]

g

g

H et B

B h t h zz

xxp

p

0 1 2 3 4 5 6 7 8 9 10-0.5

-0.25

0

0.25

0.5

0.75

1

Real part

Imaginary part

Hg(ξ

)

( B)x w

-5 -4 -3 -2 -1 0 1 2 3 4 5 -0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Impuls

e R

esponse

(V

/s) hg(z)

hg,K-K(z)

( / B)z t

Causal1

4 3[( ]) ( )h Ht w2 2

2( )

( )

Bu t

B tp

through K-K relation

Gibbs phenomenon

4(0) 1h Bp

,

where

R. B. Wu 27

Normalized Impulse Response

0 50 100 150 200 250 300Time (ps)

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

A2 *

h2(

t)

A = 5*10-7

A = 10*10-7

A = 15*10-7

A = 20*10-7

( sec)unit

0 5 10 15 20 25 30

0

0.02

0.04

0.06

0.08

(sec)unit

0 50 100 150 200 250 300Time (ps)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

B *

h3(t

)B = 10*10-12

B = 30*10-12

B = 50*10-12

B = 70*10-12

223 /

( ) ( )A t

Ah t u t

t e

Conductor Impulse Response Dielectric Impulse Response

3 2 2

2( ) ( )

Bh t u t

B tp

2max. 0.67t Ap

R. B. Wu 28

Characteristic Charts

Eye-Diagram Characteristics vs. An, Bn

0

0

, 24

nd

nS B

A R l B G Z l

UI UIUI IA

Z Up

20 2 2

3

2( ) ( ) ( ) ( )

( )A

t

A Bh t t t u t u t

t Bt e

pd

p

UI : Unit Interval,

0 0

VO

Metal : Copper

εr = 4.4tan δ = 0.02

H

W2mil

Microstrip line( Z0 ≈ 50Ω, Length : l )

+ VS

RS=50Ω

RL=

50Ω

tr = 0.25UI

( ) ( ) ( ),o inV t V t h t where( ) 0.5 ( )in SV t V t

R. B. Wu 29

Effects of Risetime

Effects of Rising Edge and Bit Period

0 20 40 60 80 100

Signal rise time tr (ps)

30

40

50

60

70

80

Eye

Hei

gh

t / V

in (

%) W=76mil, l = 20"

W=8mil, l = 20"

W=18mil, l = 40"

UI = 200ps

50

0 20 40 60 80 100

Signal rise time tr (ps)

70

75

80

85

90

95

100

Eye

Wid

th / B

it P

erio

d (

%)

W=76mil, l = 20"

W=8mil, l = 20"

W=18mil, l = 40"

0%Error

50

3%Error

εr = 4.4tan δ = 0.02

H

W2mil

Length : l

UI

tr

Freq.

Freq.

S2

1 (

dB

)

0

(πUI)-1

(πtr)-1

-20dB/decade

-40dB/decade

V( f )

(UI)-1

R. B. Wu 30

Numerical Verification

0 80 160 240 320 400

Time (ps)

0

0.1

0.2

0.3

0.4

Volt

age

(V)

217 mV 177 ps

215 mV 172 ps

HSPI

CE

Proposed

Algorithm

Metal : Copper

εr = 4.4tan δ = 0.02

5mil

8mil2mil

l = 20”

00

0.1

0.2

0.3

0.4

Volt

age

(V)

80 160 240 320 400

Time (ps)

170 mV 154 ps

152 ps166 mV

Metal : Copper

εr = 4.4tan δ = 0.02

10mil

18mil2mil

l = 30”

PRBS :5Gbps, and

tr = 50ps.

R. B. Wu 31

Numerical Results (5/6)

Table I. Dimension settings and An-Bn parameters of microstrip lines (T=2mil).

Case # Length (inch) Height (H) Width (W) An Bn

1 5 mil 8 mil 0.064 0.135

2 10 mil 18 mil 0.029 0.138

3

20

40 mil 76 mil 0.007 0.140

4 5 mil 8 mil 0.127 0.270

5 10 mil 18 mil 0.058 0.275

6

40

40 mil 76 mil 0.014 0.279

Table II. Eye-diagram analysis by HSPICE’s and the proposed algorithm’s result.

Case Microstrip (T=2mil) Eye-Opening Height Eye-Opening Width

# Len. Height Width HSPICE’s Algorithm’s Error HSPICE’s Algorithm’s Error

1 5 mil 8 mil 219.3 mV 215.4 mV -1.8% 176 ps 172 ps -2.3%

2 10 mil 18 mil 275.2 mV 271.5 mV -1.4% 190 ps 187 ps -1.6%

3

20”

40 mil 76 mil 310.8 mV 308.3 mV -0.8% 194 ps 192 ps -1%

4 5 mil 8 mil 68.1 mV 66.4 mV -2.6% 97 ps 95 ps -2.1%

5 10 mil 18 mil 159.3 mV 156.3 mV -1.9% 152 ps 149 ps -2.0%

6

40”

40 mil 76 mil 228.6 mV 223.8 mV -2.1% 176 ps 172 ps -2.3%

εr = 4.4tan δ = 0.02

H

W2mil

Length : l

|Error| < 3%

R. B. Wu 32

Maximally Usable Length

0 0

04

Sn

R lA l

Z UIa

p

0

2d

nG Z l

B lUI

bMetal : Copper

εr = 4.4tan δ = 0.02

5mil

8mil2mil

UI = 200ps;

tr = 0.25UI = 50ps

Eye-diagram

specification

EH : 40%

EW : 60%0.13; 0.27a b

l1

l2

Find usable

length

1 2min( , )l l l

1 2Here, 27", 36" 27"l l l

R. B. Wu 33

Experimental Verification (1/4)

Metal : Copper

εr = 4.4tan δ = 0.02

0.4mm

0.72mm2mil

Metal : Copper

εr = 4.4tan δ = 0.02

1mm

1.9mm2mil

Case 1

Case 2

0

0

, 24

nd

nS B

A R l B G Z l

UI UIUI IA

Z Up

20 inch 30 inch 40 inch

Comp. Meas. Comp. Meas. Comp. Meas.

An 0.01 0.014 0.016 0.022 0.021 0.029 H=0.4mm,

W=0.72mm Bn 0.14 0.17 0.21 0.27 0.28 0.35

An 0.004 0.0061 0.006 0.0092 0.008 0.0122 H=1mm,

W=1.9mm Bn 0.14 0.16 0.21 0.25 0.28 0.33

lline

0 2 4 6 8 10-40

-30

-20

-10

0H=0.4 (mm) S21

Freq. (GHz)

(dB

)

20 (in)

30 (in)

40 (in)

(a)

S2

1 (dB

)

Frequency (GHz)

20 inch

30 inch

40 inch

Measured

Case 1

0 2 4 6 8 10-40

-30

-20

-10

0H=1.0 (mm) S21

Freq. (GHz)

(dB

)

20 (in)

30 (in)

40 (in)

(b)

S2

1 (dB

)

Frequency (GHz)

20 inch

30 inch

40 inch

Measured

Case 2

Agilent E8364B

PNA

Curve Fitting

50 line

R. B. Wu 34

Experimental Verification (2/4)

DUT

Agilent infiniium 54855A DSOAnritsu Pulse Pattern Generator MP1763C

Agilent 11500E

Environment for eye-diagram Measurement

Without DUT

325 mV30 ps

Time [50 ps/div]

Vo

lta

ge

[10

0 m

V/d

iv]

100 ps

R. B. Wu 35

Experimental Verification (3/4)

Metal : Copper

εr = 4.4tan δ = 0.02

0.4mm

0.72mm2mil

Case 1

Metal : Copper

εr = 4.4tan δ = 0.02

1mm

1.9mm2mil

Case 2

EH = 220mV, EW = 155ps EH = 150mV, EW = 147ps

EH = 240mV, EW = 165ps EH = 186mV, EW = 155ps

Length = 20” Length = 30”

R. B. Wu 36

Experimental Verification (4/4)

H=0.4mm,W=0.72mm

H=1mm,W=1.9mml

20"

30"

40"

1

2

3

4

5

6

1

2

3

4

5

6

1

2

3

4

5

6

1

2

3

4

5

6

Eye-Diagram Height (mV) Eye-Diagram Width (ps)

Predicted Measured Error (%) Predicted Measured Error (%)

217.8 220.0 -1.36 % 156.4 155.0 +0.09 %

156.0 150.0 +4.0 % 144.5 147.0 -1.70 %

113.8 118.5 -3.97 % 128.4 133.0 -3.46 %

227.5 239.8 -5.13 % 160.0 165.0 -3.03 %

182.0 185.7 -1.99 % 150.5 155.1 -2.97 %

143.0 149.5 -4.35 % 139.4 144.6 -3.60 %

εr = 4.4tan δ = 0.02

H

W2mil

Length : l

|Error| < 5%

R. B. Wu 37

Summary

• Propose a much faster methodology that only uses two anti-polarity one-

bit patterns as input signal to simulate the worst-case eye diagram at the

receiving end of transmission-line system with a monotonic step response.

• Introduce Kramer-Kronig relations to resolve the non-causality of the dielectric

loss related impulse response.

• Construct two design graphs for eye-diagram characteristics vs. An and Bn of

lossy transmission line.

• The variation of signal rising/falling edge will cause the eye-opening difference of

at most 3%, and the maximally usable length of transmission line under a

certain signal specification can be evaluated.

0 100 200 300 4000

0.1

0.2

0.3

0.4

Time (ps)

Voltage (

V)

-5 -4 -3 -2 -1 0 1 2 3 4 5 -0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Imp

uls

e R

esp

on

se (

V/s

) hg(z)

hg,K-K(z)

( / B)z t

R. B. Wu -20 -10 0 10 200

0.1

0.2

0.3

0.4

Normalized h3

B*

h3

t/B

D=0

D=2.31

Convergence Problem and Modified

K-K Relation• Modified mag-phase K-K relation:

exp ln lnH R j H R j

0

0 0

2 2ln ln

B BB B D

BR e

B

, t

B tB

R. K. AHRENKIE "Modified Kramers-Kronig Analysis of Optical Spectra," JOSA, Vol. 61, Issue 12, pp. 1651-1655 (1971)

D: unknown const

2

ln

2 2

j jj t t Dd dh t H e e e

2.31

The unknown constant D can

be determined numerically.

R. B. Wu

Comparison with Previous Solution

• Proposed modified method keeps same magnitude in frequency domain.

2

3 2 2

2BB u

tBh t

2

l 2

3

n .31

2

B j B B t Bj d BB h t e e

-10 -5 0 5 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Normalized h3

B*

h3

t/B

Modified h

3

Previous causal h3

Previous noncausal h3

1.885maxt B

0maxt

or

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

H3 Comparison

Mag

nit

ud

e

B*f

modified

previous

2 fBe

0 0.5 1 1.5 2 2.5-1

-0.5

0

0.5

1

H3 Comparison

H3

B*f

Re(H3) modified

Re(H3) previous

Im(H3) modified

Im(H3) previous

R. B. Wu

Verification w/ Circuit Simulator

5.5 6 6.5 70

0.1

0.2

0.3

0.4

Pulse Response

Vo

ltag

e (V

)

time (ns)

Modified

Previous

ADS

No conductor loss, A=0No dielectric loss, B=0

5.5 6 6.5 70

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Pulse Response

Volt

age

(V)

time (ns)

Modified

Previous

ADS

8mil

2mil

5milεr=4.4

length=40inch

0 5 10 15 20-60

-50

-40

-30

-20

-10

0

H verification, Zc = 50.4

Mag

nit

ude

(dB

)

Frequency (GHz)

H fitted

H ADS

H fitted, previous

0 5 10 15 20-15

-10

-5

0

H verification, Zc = 51.1

Mag

nit

ude

(dB

)

Frequency (GHz)

H fitted

H ADS

H fitted, previous

R. B. Wu

Eye Height/width Contour

8mil

2mil

5milεr=4.4, tanD=0.02

length=40inch

σ=5.78e7 S/m

0

0

10

10

20

20

30

30

40

40

50

50

50

60

60

60

70

70

70

7080

80

80

80

90

90

90

Eye width /UI (%), tr /UI = 0.25

Bn

An

0 0.05 0.1 0.15 0.2 0.25 0.30

0.05

0.1

0.15

0

0

10

10

20

20

20

30

30

30

3040

40

40

40

50

50

50

60

60

60

70

70

80

80

90

Veye

/Vh (%), t

r /UI = 0.25

Bn

An

0 0.05 0.1 0.15 0.2 0.25 0.30

0.05

0.1

0.15

4%

24

%

5.5 6 6.5 70

0.05

0.1

0.15

0.2

0.25

Pulse Response

Vo

ltag

e (V

)

time (ns)

Modified

Previous

ADS

6%

31%

Enhanced Eye Height Estimation with

Mismatched Lossy Transmission Lines

Shih-Ya Huang , Yung-Shou Cheng , Bob Liu , and Ruey-Beei Wu

Department of Electrical Engineering and Graduate Institute of Communication

Engineering, National Taiwan Univ., Taipei, Taiwan.

e-mail: f00942001@ntu.edu.tw and rbwu@ew.ee.ntu.edu.tw

Oct 21-24, 2012 / Tempe, Arizona

IEEE Electrical Performance of

Electronic Packing and Systems

R. B. Wu

Peak Distortion Analysis (PDA)

43

0worst _V ISI

1worst _ HV V | ISI |

1 0H ,wc worst _ worst _

H

E V V

V ISI ISI

o

0-2 V Transmission line

s

Transmission line system ( TD > UI ) :

[3] B. K. Casper, M. Haycock, and R. Mooney, “An accurate and efficient analysis

method for multi-Gb/s chip-to-chip signaling schemes,” in IEEE VLSI Circuits Symp.,

June 2002, pp. 54–57.

TD

Vo

t

UI UI UI UI UI UI UI

ISI -

ISI+

Sampled value at

main signal

HV

ISI ,ISI

Cursor

Post- Cursor

Single pulse response :

R. B. Wu

Ideal Tx-Line , TD> UI, TD N UI

44

Only with ISI

With andISI ISI

11

S O

H ,wc H H

S O

E V ISI ISI V

It’s a good approximation for general , even when TD UI TD N UI

and : same polarityS

O

and :opposite polarityS

O

V0

o

0-2 V

s

Ideal Transmission Line

=VH

V0 (1+Γ)o

V0Γo

ΓoΓsV0

VHΓΓs o

osV0 ΓΓ2

ΓΓo s2 2

V0

VHΓΓs o2 2

0V oΓ3Γs

2

......

TD=N UI, TD >UI

R. B. Wu

2

1

0 0

M

H ,wc S O

m

m

H pL,m pR,mA AE V V V V V

Lossy Tx-Line, TD＞UI

The reference values of the post-cursors

can be found at the main pulse. 2

m

pcL,m pL,m S OV V 2m

pcR,m pR,m S OV V ,

Only main

pulse and α

are needed!There would be a time shift 2 %UIm m TD

m : number of reflected pulses.

45

R. B. Wu

Matched Tx. Line :

Loss constant α

46

2

1

H

H

V

V

Time (nsec)

1 2 3 4 5 6 7 80

0

0.2

0.4

0.6

0.8

1.0

Vol

tage

(V

)

TD TD

0-2 V 50 ohm Lossy

Transmission Line

s= 0 o= 0

0-2 V 50 ohm Lossy Transmission Line

s= 0 o= 0

2

R. B. Wu

Eye-Height Determination General Mismatched Tx Line

47

M=10 would be adequate

2

1

0 01 1M

H ,wc S O S O

m

mmatch match match match match

H pL,m pR,mA AE V V V V V

Step 1 : Matched Pulse response

1

1

2

2

3

3

4

4

TD

0-2 VΓs Γo

50 Ohm Microstrip line

Mismatched

Pulse Response

Mismatched tx-line system

Step 2 : Proposed formula

:

R. B. Wu

o

-1 0.8 -0.6 0.4 -0.2 0 0.2 0.4 0.6 0.8 1--

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

s

0.2

0.4

0.6

0.8

1

1.2

1.8

1.6

1.6 1.8

1.21

0.60.2

0.40.8

1.4

1.4

Eye Height v.s. Γs and Γo

Contour Map for Best Eye Height

• For arbitrary Tx-line system, a

general solution space is given

to facilitate termination design.

• Two trend-lines :

Source-end matching

Load-end matching

• Best eye height region is marked

as hatched region. (RS<Z0<RO)

• Drop-off rapidly when Γs<-0.6,

Γo>0.4

0-2 V50 strip lineOhm Micro

0.75 (W)

0.4 (H)

0.01 (T)

，Metal: Copper Unit=mm，

os

30 cm

48

Drop

rapidly

R. B. Wu

Testing Environment

49

Tektronix

CSA8000B

Communication

Signal Analyzer

80A03 Probe

Interface + P7313

Differential Probe

Anritsu Pulse

Pattern Generator

MP1763C

3

017

5

Differential

Probe

R. B. Wu

Measurement Results

50

0.238 V

Predicted EH=

0.245V

Predicted EH= 0.590

V

Measure EH=0.584

VMeasure EH=0.238

VError = 1.03 %Error = 2.94 %

0.584

V

Peak Distortion Analysis and

FIR Filter for Arbitrary Lines

Y.-S. Cheng and R.-B. Wu, “Direct eye diagram

optimization for arbitrary transmission lines using

FIR filter,” IEEE Trans. Compon., Packag.,

Manuf. Technol., vol. 1, pp. 1250-1258, Aug.

2011.

51

R. B. Wu

Peak Distortion Analysis for Arbitrary Lines

S

Time (UI)

10 2 3 4 5 6

Volt

age

S

Time (UI)

10 2 3 4 5 6 7 8

Volt

age

Y.-S Cheng, and R.-B. Wu, “Direct eye diagram optimization for arbitrary transmission lines

using FIR filter,” IEEE Trans. Comp., Packag., Manuf. Technol., 2011. (accepted)

• Downward Response: Step response drops to steady at late time.

– sM1: 1st max. before it drops to steady

sm2: min. before it grows.

sM2: max. before it drops again, …

– Treat 1st min. at steady, and sm1 = s∞.

• Upward Response: Step response rises to steady at late time.

– sm1: 1st min. before it grows to steady

sM1: max. before it drops.

sm2: min. before it grows again, …

R. B. Wu

Fast Eye Diagram Analysis

Time (UI)0 1

S

0

lb

HV

ub

HV

0.2 0.5 0.8

thVTiming

JitterEye Width

Voltage

Variation

1Jt 2Jt

wc

HE

0

ubV

0

lbV

1

1 1 0

0

2

k klb

H mi Mi wc lb ub lbi i H H H

lb ub

H

V s sE V V V s

V s V

1

1 1

k kub

H Mi mi

i i

V s s

0

ub lb

HV s V

No

n-tap FIR filter

System Step

response

nà n+1

Optimal b[n] for

different tap num.

Yes

n=1

b[n]=[b0 b1…bn]Direct Search

Worst-case eye

diagram simulation

Objective

function

Define obj. function

Fast eye diagram

analysis

Tap Coefficient Optimization

0

( ) ( - )N

k

k

y t b x t kT

• The output of FIR filter

0 1, ,k Nb b b b

• Tap coefficients of FIR filter

( ) lb ub

k H Hobj b V V

• Obj. function for the optimized

FIR filter design by

0

( ) ( )N

r k

k

s t b s t kT

( )s t

( )rs t

R. B. Wu

Optimal FIR Filter Design

RXVO

inR

Channel

0 50 , Length:Z TX

7 mil1 mil

4 mil

Metal: Copper

εr = 4.4, tanδ = 0.02

VS

Vin

SZ

LZ

Pre-emphasis

w/ FIR filter

w/o FIR filter

w / o FIR filter

w / FIR filter

Step Reponse

Sampled Voltages

Local maximum

Local minimum

166.9 mV

157.5 ps

399.5 mV

172.0 ps

0 1 2 3 4 5 6 7 8 9 10

Vo

lta

ge

(V

)Time (UI)

0

0.4

0.8

1.2

1.6

2

w / o FIR filter

w / FIR filter

Step Reponse

Sampled Voltages

Local maximum

Local minimum

w/ FIR filter

w/o FIR filter

281.4 mV

147.4 ps

1046.8 mV

192.1 ps

FIR filter as pre-emphasis

b[n]=[1, -0.091, -0.158, -0.0325] b[n]=[1, 0.34, 0.453]

ZS = 120 Ω

CL = 0.2pF

ZS = 18 Ω

CL = 0.2pF

R. B. Wu

Experimental Verification

0 1 2 3 4 5 6 7 8 9 10

Time (UI)

Vo

lta

ge

(V

)

0

0.2

0.4

0.6

0.8

1

w / o FIR filter

w / FIR filter

Step Reponse

Sampled Voltages

Local maximum

Local minimum

w/ FIR filter

w/o FIR filter

Eye diagram closure

Worst Case Eye Contour

0.4

0.2

0

-0.4

-0.2Volt

age

(V)

0.20 0.6-0.2 0.4Time (ns)

Eye diagram closure

Time [125ps/div]

Volt

age

[100m

V/d

iv]

182.7 mV

448.1 ps

Worst Case Eye Contour

0.20 0.6-0.2 0.4Time (ns)

0.4

0.2

0

-0.4

-0.2Volt

age

(V)

193 mV472 ps

Vo

lta

ge [

10

0m

V/d

iv]

Time [125ps/div]

b[n]=[1, 0.34, 0.453]

Y.-S. Cheng & R.-B. Wu, “Direct eye diagram optimization for arbitrary transmission lines

using FIR filter,” IEEE T-CPMT, 2011. (accepted)

R. B. Wu

FIR: y(n) = b0 * x(n) + b1 *x (n-UI)

Data

x(n)Output

y(n)Main

Driver (b0)

1 bit

Delayde-emphasis

Driver

b1

Cursor

Post-Cursor

|b0| + |b1| = 1

1 1 0 11 1b b

2-Tap FIR Filter

0 1UI 2UI

0b

0 1( )b bsatV

Early Settle

t0

Step response

FIRV

0 1UI 2UI

0b

1b

t0

Pulse response

FIRV 0 1 satb b V

Desired tap coefficients

R. B. Wu

Passive FIR Realization

7 mil1 mil

4 mil

Metal: Copper

εr = 4.4, tanδ = 0.02

0.5UIZh

Vo

RL

RT

Zo = 50 Ω

VS

RS=Z0

～

X

A

1UI

Z1

1UI

Z1

VFIR

Vin

Realization of 2-tap FIR

by single-stub tx-line

Equivalent circuit representation

1; ; h TZ Z R

Design parameters:

Y.-S. Cheng and R.-B. Wu, “Passive FIR filter design using reflections from

stubs for high speed links,” EDAPS, Hangzhou, China, Dec. 2011.

R. B. Wu

Equalizer Design

415mV

113psV

olt

ag

e (V

)

Time (ps)Time (ps)

Vo

lta

ge

(V)

204mV

69ps

Equalizer

100%

64%

7 mil1 mil

4 mil

Metal: Copper

εr = 4.4, tanδ = 0.02

0.5UIZh

Vo

RT

Zo = 50 Ω, l = 20 in.

VS

RS= Z0

～

X

A

1UI

Z1

1UI

Z1

RL= Z0

VFIR VS : PRBS,

tr/tf=30ps, 2V,

8Gbps

RS=RL=Z0=50

1 69 ,

165 ,

31

h

T

Z

Z

R

R. B. Wu

Equalizer Design 2 – Unmatched

Source

Time (ps)

Vo

lta

ge

(V)

309mV

72ps

Time (ps)

Vo

lta

ge

(V)

565mV

111ps

Simulated

by ADS

0

: 2 ,

8 Gbps

50

s p p

L

V V V

R Z

7 mil1 mil

4 mil

Metal: Copper

εr = 4.4, tanδ = 0.02

0.5UIZh

Vo

RT

Zo = 50 Ω, l = 20 in.

VS

RS

～

X

A

1UI

Z0

1UI

Z0

RL= Z0

VFIR

Mismatched RS Topology 23 ,

115 ,

21

S

h

T

R

Z

R

Design parameters: ; ; s h TR Z R

Application Examples

R. B. Wu

High-Pass Response

Lossy Response

(Low-Pass)Equalized Response

(Low-Pass)

|H(ω)|

f(GHz)0

0dB

fopt

Application to Via-Stubs in IPC

• QPI (CPU to CPU) :

Length: 26~29cm

trise: 53.5ps(10~90%)

32.8ps(20~80%)

Data rate: 6.4Gbit/s

71

LL

2Rt

ViaPort 1

+

-

0.7 mm

Top

Via Stub

Via

Port 2+

-

0.7 mm

Top

Via Stub25 cm

Gnd

In-1

eq. ckt

Hchannel

Heq

Y.-S. Cheng, et al., “SI-aware layout and equalizer design to enhance performance of

high-speed links in blade servers,” EPEPS, San Jose, CA, pp. 199-202, Oct. 2011

R. B. Wu

Eye Diagram ComparisonData Rate=10 Gbit/s, tr= 33 ps

72

75 ps

279 mV

Time (ps)

Vo

lta

ge

(V)

SimulationMeasurement

w/o equalization

90 ps343 mV

Time (ps)

Vo

lta

ge

(V)

Time [20 ps/div]

Vo

lta

ge

[12

0 m

V/d

iv]

82 ps

321 mV

w/ equalization

R. B. Wu

Next Generation Wide I/O Memory on

3D IC 3D IC is a 3-dimensional integration of the hetero or homogeneous

chips by connecting them vertically in one package.

73

On-chip DeCAP :

(tens of pF)

Silicon Interposer

Package/PCB

RF

BumpTSV

Micro-Bump

On-chip

DeCAP

MemoryDigital IC

On-chip

DeCAP

• Reduced RC Delay

• Reduced Power Consumption

• Reduced Area Consumption

System Performance

&Packaging Density

R. B. Wu

Signal/Power Integrity Design

74

Signal integrity issue:

Signal will be distorted when propagating through TSVs.

Case 1:

• TSVs, micro bumps and ideal RDL are included in the simulation.

• Transmitted signal: Pseudo-Random Binary Sequence (PRBS) at 20 Gb/s with rise/fall time 5ps.

Rx:

Eye diagram:

Tx:

Eye Height: 0.164V

Jitter: 0.7ps

diameter 10 μm

pitch 40 μm

height 100 μm

TSV: diameter 20 μm

pitch 40 μm

height 20 μm

bump:

R. B. Wu

Eye Diagram Analysis

75

4 stacked TSV2 stacked TSV1 stacked TSV

Vin: 0.5V

Frequency:10Gbps

210-1 PRBS

Rise/Fall time:20ps

±

8 stacked TSV

R. B. Wu

TSV Parameters

• Electrical modeling

76

Structural parameters

• TSV diameter: 2a

• TSV height: h

• TSV-to-TSV pitch: 2d

• Insulator thickness : b-a

R. B. Wu

Simplified Circuit Model

77

0.1 1 10

Frequency (GHz)

-8

-6

-4

-2

0

|S21|

(dB

)

Full eq. ckt.

Simplified eq. ckt.

1-stacked TSV

10-stacked TSV

Oxide

thickne

ss

(Tox)

TSV

PITCH

(P)

TSV

DIAMET

ER

(D)

TSV

length

(LTSV)

SiO2 Si Si

0.2 m 100 m 50 m 100 m 3.9 11.920

S/m

2SiOSi

Si

R. B. Wu

RC Equalizer

78

2

0

_

eq

Si t

ZR

R

0

2

0

_ _

_

( )Si t Si t

eq ox t

Z R RC C

Z

0.1 1 10

Frequency (GHz)

-8

-6

-4

-2

0

|S21|

(dB

)

Compensated result

RC equalizer

TSV

0.1 1 10

Frequency (GHz)

-8

-6

-4

-2

0

|S21| (d

B)

Compensated result

RC equalizer

TSV

Single TSV 10-stacked TSV

R.-B. Sun, C.-Y. Wen, and R.-B. Wu, “Passive equalizer design for through silicon vias

with perfect compensation,” T-CPMT, pp. 1815-1822, Nov. 2011

R. B. Wu

Equalized Simulation Results

0.1 1 10Frequency(GHz)

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

|S21|(

dB

) Before equalizer

After equalizer

Equalizer response

0.1 1 10Frequency(GHz)

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

|S2

1|(

dB

)

Before equalizer

After equalizer

Equalizer response

0.1 1 10Frequency(GHz)

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

|S21|(

dB

)

Before equalizer

After equalizer

Equalizer response

0.1 1 10Frequency(GHz)

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

|S21|(

dB

)

Before equalizer

After equalizer

Equalizer response

1 stacked TSV

4 stackedTSV

2 stacked TSV

8 stackedTSV

Improved eye height, & nearly ZERO jitter!

R. B. Wu 80

Conclusions

• Freq.-dependence in loss incurs “long tail” response,

thus ISI and eye diagram deterioration.

• Peak distortion analysis and analytic derivation gives

universal design curves for eye height/width.

• RL/RC equalizers are proposed for conductor/

dielectric loss dominant tx-lines.

• Generalization to tx-lines with unmatched load,

crosstalk, or faster edge is done by PDA & FIR filter.

• Topologies for next generation interconnects need

further study, e.g., RF, AC-coupled, optical,

nanowire, ...