EE290C – Spring 2011

Lecture 6: Link Performance Analysis

Elad AlonDept. of EECS

EE290C Lecture 5 2

Motivation

• Does eqn. above predict everything?

,12 2

in ampl off

noise

V VBER erfc

σ⎛ ⎞−

= ⎜ ⎟⎜ ⎟⎝ ⎠

EE290C Lecture 5 3

• Borrowed from computer systems• Built to be “error free” Worst-case analysis

• Voltage/Time (VT) Budget• Also called link budget (especially in wireless)• Key: separate random vs. deterministic error

sources

Traditional Approach

EE290C Lecture 5 4

Voltage Budget Example

EE290C Lecture 5 5

Voltage Budget Example

EE290C Lecture 5 6

Timing Budget: Jitter Definitions• Like voltage – need to separate deterministic

(bounded) from random (unbounded)

• Total jitter (TJ) = Deterministic (DJ) + random (RJ)

• DJ is measured as peak-to-peak, added linearly• RJ is measured as rms

• For BER = 10-12, “peak-to-peak” RJ is 14*RMS value

• Don’t forget that jitter gets filtered too• E.g., source synchronous, CDR

EE290C Lecture 5 7

Jitter Tolerance Mask

• Specifies amplitude of sinusoidal jitter (SJ) vs. frequency for which link must maintain BER spec• Mask drives CDR loop filter characteristics

CDR Tolerance & XAUI Sinusoidal Jitter Tolerance Mask

0.000.501.001.502.002.503.003.504.004.505.005.506.006.507.007.508.008.509.00

0.010 0.100 1.000 10.000 100.000

Jitter Frequency (MHz)

Jitt

er A

mpl

itude

(UI)

XAUI MaskLV at Vtt-Rx=1V & 3.125Gbps

XAUI Sinusoidal Jitter Mask

1.875MHz 20 MHz

0.1UI0.1UI

22KHz

EE290C Lecture 5 8

Jitter in Source Synchronous Systems

EE290C Lecture 5 9

Jitter in Source Synchronous Systems

EE290C Lecture 5 10

• Is worst-case realistic?• What if you had 100 taps of residual ISI?

• Can you really treat timing and voltage noise completely separately?

Issues with Traditional Approach

EE290C Lecture 5 11

• Model small deterministic errors as Gaussian• Find σ, multiply it to get “peak-to-peak” value at

given BER

• Works well at low BER (1e-3), but…

Communications Approach

EE290C Lecture 5 12

• Gaussian model breaks at lower probabilities

Issues with Communications Approach

0 25 50 75 100

-10

-8

-6

-4

-2

0

re sidual ISI [m V ]80 100 120 140 160 180

-10

-8

-6

-4

-2

0

40mV error @ 10-10

25% of eye height

4% Tsym bol

error @ 10-10

9% Tsym bol

log 10

pro

babi

lity

[cdf

]

log 10

Ste

ady-

Stat

e Ph

ase

Prob

abili

ty

phase count

Cumulative ISI distribution CDR phase distribution

EE290C Lecture 5 13

A More Modern Approach• Use direct noise and ISI statistics

• Don’t treat timing noise separately• Integrate with voltage noise sources• I.e., need to map from time to voltage

• Ref: V. Stojanovic, Ph.D. thesis

EE290C Lecture 5 14

Residual ISI• Generally can’t correct for all ISI

• Equalizers are finite length• Even with infinite equalizers, the coefficients are

quantized• And you may not be able to estimate coefficient

values perfectly

• Need to find distribution of this residual ISI

EE290C Lecture 5 15

Generating ISI Distributions

-3 -2 -1 0 1 2 -10

15

200

-10 10 0

0.25

0.5

0.75

1

-15 15 0

0.25

0.5

0.75

1

-25 -5 5 25 0

0.25

0.5

0.75

1

volta

ge [m

V]

sample #

[mV]

prob

abili

ty [p

mf]

prob

abili

ty [p

mf]

prob

abili

ty [p

mf]

[mV]

voltage [mV]

Convolution

Equalizedpulse response ISI distribution

EE290C Lecture 5 16

Real ISI Dist.: 5-tap TX FIR

-60 -40 -20 0 20 40 60 0

0.01

0.02

0.03

0.04

voltage [mV]

prob

abili

ty d

istri

butio

n of

resi

dual

ISI

-150 -100 -50 0 50 100 150 0

0.004

0.008

0.012

0.016

voltage [mV]

prob

abili

ty d

istr

ibut

ion

of re

sidu

al IS

I

Data sample distribution Edge sample distribution

EE290C Lecture 5 17

Effect of Timing Noise• Need to map from time to voltage

Ideal sampling

Jittered sampling

Voltage noiseVoltage noise when receiver clock is off

• Effect depends on jitter magnitude, input sequence, and channel

EE290C Lecture 5 18

Effect of TX Jitter: Decomposition

• Decompose output into ideal + noise• “Jitter” is pulse at front and end of symbol

• Width of pulse set by jitter magnitude

ideal

noise

kb

kT

TXkε

Tk )1( +

TXk 1+ε

kT

TXkε

Tk )1( +

TXk 1+ε

+

kb−

kb

kb

1

2

EE290C Lecture 5 19

Converting to Voltage

• Variable width pulses annoying to deal with

• Approximate noise pulses with deltas of same area• Channel is low-pass and will filter them anyways

TXkε

TXk 1+ε

kb−

kb

≈TXkkb ε−

TXkkb 1+ε

EE290C Lecture 5 20

Jitter Propagation Model

• Channel bandwidth matters• If h(T/2) is small, jitter voltage noise is small

TXw )( jTp

)(sHjit

PLL

ka kb

TXkk 1, +ε

inn⎟⎠⎞

⎜⎝⎛ +

2TjTh

+ kxISIk

x

jitTXk

x RXkε

kaprecoder

impulseresponse

pulseresponse

vddn

RX

ideal

noise

∑−=

− +=++sbE

sbSjijk

RXki

ISI jTpbkTx )()( φεφ

( ) ( )∑−=

−+−− ⎥⎦⎤

⎢⎣⎡ −+−−−++=++

sbE

sbSj

TXjk

RXki

TXjk

RXkijk

RXki

jitter TjThTjThbkTx 1)2

()2

()( εεφεεφεφ

EE290C Lecture 5 21

Implications• TX Jitter

• High frequency (period) jitter is bad• Changes the energy (area) of the symbol)• Uncorrelated noise sources add up

• Low frequency jitter isn’t as bad• Just shifts waveform• Correlated noise sources partially cancel

• RX jitter• Shifts TX sequence – same as low f TX jitter

εkRx

≡εk

Rx

EE290C Lecture 5 22

Implications• For same source jitter

(white)• Noise from TX jitter larger

than RX jitter• TX jitter “enhanced” by

channel

• Bandwidth of jitter sets final magnitude• Like any other white noise

source

0 0.5 1 1.5 2 2.5 3

-60

-50

-40

-30

Pow

er s

pect

ral d

ensi

ty [d

BV]

frequency [GHz]

Source – white jitter

Noise from Tx jitter

Noise from Rx jitter

EE290C Lecture 5 23

Including the CDR

• Need jitter on actual sampling clock• Not just jitter from source, PLL

Slicer

PD

deserializer

PLL

dataOut

ref Clk

Phasecontrol

Phasemixeredge Clk

data Clk

RX

dn-1

dn

en (late)

dn

en

EE290C Lecture 5 24

CDR Model• Model as a state

machine• Current phase position

is the state• Transitions caused by

early/late signals

• On average move to right position• But probability of incorrect transition not small

0 50 100 150 200 2500

0.2

0.4

0.6

0.8

1

Accumulate-resetfilter, length 4Pr

obab

ility

Phase count

p-early

p-hold

p-late

p-no-validtransitions

p-up p-dn

EE290C Lecture 5 25

What You Really Care About• Final steady-state probability of being in

each phase position (state)

• Can find using “Markov model”• Fancy way of saying that you iteratively apply

the transition probabilities

iφ1−iφ 1+iφ0φ Lφ

iholdp ,

iupp ,

idnp ,

0 50 100 150 200 2500

0.2

0.4

0.6

0.8

1

Accumulate-resetfilter, length 4Pr

obab

ility

Phase count

p-early

p-hold

p-late

p-no-validtransitions

p-up p-dn

EE290C Lecture 5 26

Result: CDR Phase PDF

• This is the “jitter” distribution• (With nominal phase subtracted out)

0 50 100 150 200 250

-15

-10

-5

0

Phase Count

log 10

Ste

ady-

Stat

e Pr

obab

ility

EE290C Lecture 5 27

ISI and CDR Distributions

• Vertical slice: ISI distribution @ given time• Horizontal weight: CDR phase distribution

50 60 70 80 90 100 110-300

-200

-100

0

100

200

300

time [ps]

volta

ge [m

V]

-30

-25

-20

-15

-10

-52PAM - lin. eq

EE290C Lecture 5 28

Putting It All Together: BER Contours

• Voltage margin @ given BER:• Distance from probability contour to threshold (0)

0 20 40 60 80 100 120 140 160-150

-100

-50

0

50

100

150

time [ps]

mar

gin

[mV]

-30

-25

-20

-15

-10

-5

0 20 40 60 80 100 120 140 160-150

-100

-50

0

50

100

150

time [ps]

mar

gin

[mV]

-30

-25

-20

-15

-10

-5

5 tap Tx Eq 5 tap Tx Eq + 1 tap DFE

EE290C Lecture 5 29

Model and Measurements

-80-60-40-200 20 40 60 80

-14

-12

-10

-8

-6

-4

-2

0

log1

0(B

ER)

Voltage Margin [mV]