Lecture9 Ee720 Noise Sources

7/29/2019 Lecture9 Ee720 Noise Sources

http://slidepdf.com/reader/full/lecture9-ee720-noise-sources 1/47

Sam Palermo

Analog & Mixed-Signal Center

Texas A&M University

ECEN720: High-Speed Links

Circuits and SystemsSpring 2013

Lecture 9: Noise Sources



Agenda

• Noise source overview

• Common noise sources

• Noise budgeting• References

•Dally Ch 6

•Stateye paper posted on website

2



Noise in High-Speed Link Systems

• Multiple noise sources can degrade link timing and amplitude margin

3

[Dally]



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


• Signal dispersion causessignal to interfere with itself

• Random noise

• Thermal & shot noise

• Clock jitter components



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



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



Common Noise Sources


• Receiver offset

• Crosstalk • Inter-symbol interference

• Random noise

7



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]



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]



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]



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

==





• Receiver offset


• Random noise

12



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 == ∆ /,



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





• Receiver offset


• Random noise

15



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

16



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

17

OC

C

c

AcB

CC

Ck

VkV

+=

∆=∆

[Dally]



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]



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]



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

20



Transmission Line Crosstalk

21

• 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]



Transmission Line Crosstalk

22

• 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



Near- and Far-End Crosstalk

23

[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



Near- and Far-End Crosstalk

24

[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



25

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



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]





• Receiver offset


• Random noise

27



Inter-Symbol Interference (ISI)

28

( )

( )( )

( ) ( )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)



Peak Distortion Analysis Example

29

( )

( )

( ) ( )

( )( )( )

( ) ( ) 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



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



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

31



Convolving Individual ISI PDFs Together

32

* =

* =

• Keep going until all individual PDFs convolved together



Complete ISI PDF

33



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!



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



Combining Cursor CDFs

36



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




• Power supply noise• Receiver offset

• Crosstalk


• Random noise

38



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 , ,



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−

−

=



Signal with Added Gaussian Noise

• Finite probability of noise pushing signalpast threshold to yield an error

41



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]



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



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



Noise Source Classifications

• Determining whether noise source is• Proportional vs Independent

• Bounded vs Statistical

• is important in noise budgeting

45



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



Next Time

• Timing Noise• BER Analysis Techniques

Documents

Lecture9 Ee720 Noise Sources