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Fast Eye-Diagram Analysis
吳瑞北, Ruey-Beei Wu
Rm. 340, Department of Electrical Engineering
E-mail: [email protected]
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
R. B. Wu
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: [email protected] and [email protected]
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, ...