Lecture9 Ee720 Noise Sources
Transcript of Lecture9 Ee720 Noise Sources
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Sam Palermo
Analog & Mixed-Signal Center
Texas A&M University
ECEN720: High-Speed Links
Circuits and SystemsSpring 2013
Lecture 9: Noise Sources
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Agenda
• Noise source overview
• Common noise sources
• Noise budgeting• References
•Dally Ch 6
•Stateye paper posted on website
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Noise in High-Speed Link Systems
• Multiple noise sources can degrade link timing and amplitude margin
3
[Dally]
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Noise Source Overview
• Common “noise” sources• Power supply noise
• Receiver offset
• Crosstalk
• Inter-symbol interference
• Random noise
• Power supply noise
• Switching current throughfinite supply impedance
causes supply voltage dropsthat vary with time andphysical location
• Receiver offset
• Caused by random device
mismatches4
• Crosstalk • One signal (aggressor)
interfering with anothersignal (victim)
• On-chip coupling (capacitive)
• Off-chip coupling (t-line)• Near-end
• Far-end
• Inter-symbol interference
• Signal dispersion causessignal to interfere with itself
• Random noise
• Thermal & shot noise
• Clock jitter components
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Bounded and Statistical Noise Sources
• Bounded or deterministic noise sources
• Have theoreticallypredictable values withdefined worst-case bounds
• Allows for simple (butpessimistic) worst-caseanalysis
• Examples
• Crosstalk to small channel
count• ISI
• Receiver offset
5
• Statistical or random noisesources
• Treat noise as a random process
• Source may be psuedo-random
• Often characterized w/ Gaussian stats
• RMS value
• Probability density function (PDF)
• Examples
• Thermal noise
• Clock jitter components
• Crosstalk to large channel count
• Understanding whether noise source is bounded or
random is critical to accurate link performance estimation
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Proportional and Independent Noise Sources
• Some noise is proportional to signal swing
• Crosstalk
• Simultaneous switchingpower supply noise
• ISI
• Can’t overpower this noise
• Larger signal = more noise
6
• Some noise is independent to signal swing
• RX offset
• Non-IO power supply noise
• Can overpower this noise
NISNN
VVK V
+=Total noise
Proportional noiseconstant
Signal swing
Independent noise
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Common Noise Sources
• Power supply noise
• Receiver offset
• Crosstalk • Inter-symbol interference
• Random noise
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Power Supply Noise
• Circuits draw current from the VDD supply nets andreturn current to the GND nets
• Supply networks have finite impedance• Time-varying (switching) currents induce variations on
the supply voltage
• Supply noise a circuit sees depends on its location in
supply distribution network 8
[Hodges]
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Power Routing
9
Bad – Block B will
experience excessivesupply noise
Better – Block B will experience 1/2
supply noise, but at the cost of doublethe power routing through blocks
Even Better – Block A & B will experience similarsupply noise
Best – Block A & Bare more isolated
[Hodges]
[Hodges]
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Supply Induced Delay Variation
• Supply noise can induce variations in circuit delay• Results in deterministic jitter on clocks & data signals
10
( ) ( )
( ) ( )
VDDVVDD
VDD
VVDDCvW
VDDC
LEVVDD
VVDDCvW
VDDC
I
VDDCt
TN
TNoxsatN
L
NCN TN
TNoxsatN
L
DSATN
L
PHL
≈∝−
∝
−≈
+−−
==
Delay
2
222
• CMOS delay is approximately directly proportional to VDD
• More delay results in more deterministic jitter
[Hodges]
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Simultaneous Switching Noise
• Finite supply impedancecauses significantSimultaneous SwitchingOutput (SSO) noise
(xtalk)• SSO noise is proportional
to number of outputsswitching, n, andinversely proportional tosignal transition time, tr
11r
s
r
NtZ
LVn
t
iLV
0
==
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Common Noise Sources
• Power supply noise
• Receiver offset
• Crosstalk • Inter-symbol interference
• Random noise
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Receiver Input Referred Offset
• The input referred offset is primarily a function of Vth mismatch and a weaker function of β (mobility) mismatch
13WL
A
WL
At
t
V
V
β
β β σ σ == ∆ /,
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Receiver Input Referred Offset
14
WLA
WLA t
t
VV
β
β β σ σ == ∆ /,
• To reduce input offset 2x, we need to increase area 4x
• Not practical due to excessive area and power consumption
• Offset correction necessary to efficiently achieve good sensitivity
• Ideally the offset “A” coefficients are given by the designkit and Monte Carlo is performed to extract offset sigma
• If not, here are some common values:
• A Vt = 1mVµm per nm of tox
• For our default 90nm technology, tox=2.8nm → A Vt ~2.8mVµm
• A β is generally near 2%µm
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Common Noise Sources
• Power supply noise
• Receiver offset
• Crosstalk • Inter-symbol interference
• Random noise
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Crosstalk
• Crosstalk is noise induced by one signal (aggressor) thatinterferes with another signal (victim)
• Main crosstalk sources
•
Coupling between on-chip (capacitive) wires• Coupling between off-chip (t-line/channel) wires
• Signal return coupling
• Crosstalk is a proportional noise source
• Cannot be reduced by scaling signal levels
• Addressed by using proper signal conventions, improving channeland supply network, and using good circuit design and layouttechniques
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Crosstalk to Capacitive Lines
• On-chip wires have significant capacitance to adjacentwires both on same metal layer and adjacent vertical layers
• Floating victim
• Examples: Sample-nodes, domino logic
• When aggressor switches• Signal gets coupled to victim via a capacitive voltage divider
• Signal is not restored
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OC
C
c
AcB
CC
Ck
VkV
+=
∆=∆
[Dally]
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Crosstalk to Driven Capacitive Lines
• Crosstalk to a drivenline will decay awaywith a time-constant
18
( )OCOxc CCR +=τ
• Peak crosstalk isinversely proportional
to aggressor transitiontimes, tr, and driverstrength (1/R O)
( )
( )
≥
−−
−−
<
−−
=∆
−=∆
r
xcxc
r
r
xcc
r
xcr
xcc
B
r
xc
cB
ttttt
tk
ttt
tk
tV
t
tktV
if
if
: Time,RiseFinitewithStep
:StepUnitIdeal
τ τ
τ
τ
τ
τ
expexp
exp1
exp
[Dally]
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Capacitive Crosstalk Delay Impact
• Aggressor transitioning near victim transition can modulatethe victim’s effective load capacitance
• This modulates the victim signal’s delay, resulting indeterministic jitter
19CgndL
gndL
CgndL
CCC
CC
CCC
2+=
=
+=
:WayOppositeSwitchingAggressor
:WaySameSwitchingAggressor
:StaticAggressor
[Hodges]
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Mitigating Capacitive (On-Chip) Crosstalk
• Adjacent vertical metal layers should be routedperpendicular (Manhattan routing)
• Limit maximum parallel routing distance
• Avoid floating signals and use keeper transistors with
dynamic logic• Maximize signal transition time
• Trade-off with jitter sensitivity
• For differential signals, periodically “twist” routing to make
cross-talk common-mode• Separate sensitive signals
• Use shield wires
• Couple DC signals to appropriate supply
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Transmission Line Crosstalk
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• 2 coupled lines:
( ) ( )dt
txdVk
dt
txdV Acx
B ,,=
• Transient voltage signal on A is coupled to B capacitively
whereCS
Ccx
CC
Ck
+=
• Capacitive coupling sends half the coupled energy in each direction withequal polarity
I A
IB [Dally]
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Transmission Line Crosstalk
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• 2 coupled lines:
• Transient current signal on A is coupled to B through mutual inductance
( ) ( )
( ) ( ) ( ) ( )dx
txdV
kdx
txdV
L
M
dt
txdI
Mdx
txdV
xL
txV
t
txI
Alx
AAB
AA
,,,,
,,
=
=−=
∂
∂−=
∂
∂
where L
M
klx =
I A
IB [Dally]
• Inductive coupling sends half the coupled energy in each directionwith a negative forward traveling wave and a positive reversetraveling wave
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Near- and Far-End Crosstalk
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[Hall]
• Near-end crosstalk (NEXT) is immediatelyobserved starting at the aggressor transitiontime and continuing for a round-trip delay
• Due to the capacitive and inductive couplingterms having the same polarity, the NEXT signalwill have the same polarity as the aggressor
• Far-end crosstalk (FEXT) propagates along thevictim channel with the incident signal and isonly observed once
• Due to the capacitive and inductive couplingterms having the opposite polarity, the FEXTsignal can have the either polarity, and in a
homogeneous medium (stripline) cancel out
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Near- and Far-End Crosstalk
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[Dally] ( )
( )
2
4
lxcxfx
lxcxrx
kkk
kkk
−=
+=
For derivation of k rx and k fx, seeDally 6.3.2.3
Reverse Coupling Coefficient
k rx (NEXT)
Forward Coupling Coefficient
k fx (FEXT)tx
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Off-Chip Crosstalk
Occurs mostly inpackage and board-to-board connectors
FEXT is attenuatedby channel responseand has band-passcharacteristic
NEXT directly couplesinto victim and hashigh-pass
characteristic
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Signal Return Crosstalk
• Shared return path with finite impedance• Return currents induce crosstalk occurs among signals
26
VkZ
ZVV xr
Rxr ∆=∆=
0
:VoltageCrosstalkReturn
∆ V
-Vxr
[Dally]
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Common Noise Sources
• Power supply noise
• Receiver offset
• Crosstalk • Inter-symbol interference
• Random noise
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Inter-Symbol Interference (ISI)
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( )
( )( )
( ) ( )thtctykk dd
∗=
y(1)(t) sampled relative to pulse peak:
[… 0.003 0.036 0.540 0.165 0.065 0.033 0.020 0.012 0.009 …]
k =[ … -2 1 0 1 2 3 4 5 6 …]
By Linearity: y(0)(t) =-1*y(1)(t)
cursor
post-cursor ISI
pre-cursorISI
…
• Previous bits residual state candistort the current bit, resulting ininter-symbol interference (ISI)
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Peak Distortion Analysis Example
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( )
( )
( ) ( )
( )( )( )
( ) ( ) 288.0389.0007.0540.02
389.0
007.0
540.0
0
0
1
0
0
1
)1(0
=−−=
=−
−=−
=
∑
∑∞
≠
−∞=>−
∞
≠
−∞=<−
ts
kTty
kTty
ty
k
kkTty
k
kkTty
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Worst-Case Eye vs Random Data Eye
• Worst-case data pattern can occur at very low probability!
• Considering worst-case is too pessimistic
Worst-Case Eye
100 Random Bits1000 Random Bits1e4 Random Bits
30
Constructing ISI Probability Density
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Constructing ISI Probability DensityFunction (PDF)
• Using ISI probability densityfunction will yield a more accurateBER performance estimate
• In order to construct the total ISIPDF, need to convolve all of the
individual ISI term PDFs together• 50% probability of “1” symbol ISI and
“-1” symbol ISI
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Convolving Individual ISI PDFs Together
32
* =
* =
• Keep going until all individual PDFs convolved together
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Complete ISI PDF
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Cursor PDF – Data 1
34
* =
• Data 1 PDF is centered about the cursor value
and varies from a maximum positive value tothe worst-case value predicted by PDA
• This worst-case value occurs at a low probability!
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Cursor Cumulative Distribution Function (CDF)
• For a given offset, whatis the probability of aData 1 error?
•
Data 1 error probabilityfor a given offset is equalto the Data 1 CDF
35
( ) ( )∫∞−
=
X
dxPDFXBER
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Combining Cursor CDFs
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Bit-Error-Rate (BER) Distribution Eye
37
• Statistical BER analysistools use this techniqueto account for ISIdistribution and also
other noise sources• Example from Stateye
• Note: Different channel & data rate from previousslides
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Common Noise Sources
• Power supply noise• Receiver offset
• Crosstalk
• Inter-symbol interference
• Random noise
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Random Noise
• Random noise is unbounded and modeledstatistically
•Example: Circuit thermal and shot noise
• Modeled as a continuous random variabledescribed by
•Probability density function (PDF)
•
Mean, µ•Standard deviation, σ
39
( ) ( ) ( ) ( )dxxPxdxxxPxPPDF nnnnnn ∫∫∞
∞−
∞
∞−
−===22 µ σ µ , ,
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Gaussian Distribution
• Gaussian distribution is normally assumed for random noise• Larger sigma value results in increased distribution spread
40
( )( )
2
2
2
2
1σ
µ
σ π
nx
n exP−
−
=
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Signal with Added Gaussian Noise
• Finite probability of noise pushing signalpast threshold to yield an error
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Cumulative Distribution Function (CDF)
• The CDF tells whatis the probabilitythat the noisesignal is less thanor equal to acertain value
42
( ) ( )( )
dueduuPxx
u
ux
u
nn
n
∫∫−∞=
−−
−∞=
==Φ2
2
2
2
1σ
µ
σ π
[Dally]
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Error and Complimentary Error Functions
• Error Function:
• Relationship between normalCDF and Error Function:
• The complementary errorfunction gives the probability
that the noise will exceed agiven value
43
( ) ( )∫= −=
x
uduuxerf
0
2
exp
2
π
( )
+=Φ
21
2
1 xerf x
( ) ( )
=
−=Φ−=
221
21
2
11
xerfc
xerf xxQ
( )
−==
22
1
σ
µ µσ
xerfcxQ
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Bit Error Rate (BER)
44
• Using erfc to predict BER:
• Need a symbol of about 7σ for BER=10-12
• Peak-to-peak value will be 2x this
[Dally]
Normal (0,1) PDF
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Noise Source Classifications
• Determining whether noise source is• Proportional vs Independent
• Bounded vs Statistical
• is important in noise budgeting
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Noise Budget Example
46
Parameter K n RMS Value
(BER=10-12)
Peak DifferentialSwing
0.4V
RX Offset +Sensitivity
5mV
Power SupplyNoise
5mV
Residual ISI 0.05 20mV
Crosstalk 0.05 20mV
Random Noise 1mV 14mV
Attenuation 10dB = 0.684 0.274V
Total Noise 0.338V
Differential EyeHeight Margin 62mV
• Peak TX differential swing of 400mVppd equalized down 10dB
• ±200mV → ±63mV
+63mV
-63mV 31mV
31mV
• Conservative analysis • Assumes all distributionscombine at worst-case
• Better technique is to usestatistical BER link simulators
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Next Time
• Timing Noise• BER Analysis Techniques