1WAVECREST

Statistical and System Transfer Statistical and System Transfer Function Based Method For Function Based Method For

Jitter and Noise Estimation In Jitter and Noise Estimation In Communication Design and TestCommunication Design and Test

Mike Li and Jan WilstrupWavecrest

2WAVECREST

Purposes• Illustrate the shortfalls of simple parametric

based jitter/noise determination methods (Peak-to-Peak or RMS only)

• Introduce the PDF and CDF based statistical jitter/noise determination methods

• Introduce the jitter/noise transfer function and its role in serial data link

• Apply both statistical analysis and transfer function for jitter, noise, and BER in designing and testing > 1 Gb/s systems

3WAVECREST

Outline• Overview of jitter and noise basic

• Shortfalls for parametric peak-to-peak• PDF and CDF for jitter, noise, and BER

• Overview of serial communication systems

• Methods for estimating and testing jitter, noise, and BER

• Conclusion

• Jitter/noise transfer functions

4WAVECREST

Jitter And Noise Basics

∇v: amplitude noise

∇t: time jitter

Reference Amplitude v0

Reference Timing t0

• Timing Jitter : Any deviationfrom ideal timing

• Amplitude Noise: Any deviation from ideal amplitude

• Timing jitter occurs whenthere is an edge transition

• Amplitude noise is a constant activity

5WAVECREST

Jitter And Noise Viewed From Signal Theory

• Jitter/noise is a statistical process• Jitter/noise has a distribution• Jitter/noise has many different components• Jitter/noise can only be completely

quantified by its PDF !!!

6WAVECREST

Jitter/Noise Classification Scheme(Statistical Based)

Jitter/Noise

Deterministic Random

Static

PeriodicMulti-Gaussian Gaussian

BU

BU: Bounded uncorrelated

7WAVECREST

Relationship Between Total PDF And Component PDFs: Convolution

∫∞

∞−−=

=

τττ dtRJpDJp

tDJptRJptTJp

)()(

)(*)()(

• An example for timing jitter PDF

8WAVECREST

Why Deterministic Parametric (i.e, Peak-To-Peak or RMS) No Longer Sufficient?

• Peak-to-peak or RMS alone cannot determine a general PDF

• Peak-to-peak will be an unstable and size sample size dependent estimation in the presence of random component

• RMS will be an inaccurate estimation for a Gaussian random in the presence of deterministic component

9WAVECREST

Peak-To-Peak Shortfalls

0 1 2 3 4 5 6 7 8 9 10

x 10 4

0.18

0.185

0.19

0.195

0.2

0.205

0.21

0.215

0.22

0.225

0.23

Total Number of Hits

Peak

-To-

Peak

in U

I

a.) Sample Size Dependency

10WAVECREST

Peak-To-Peak Shortfallsb.) Probability distribution is un-symmetrical

0.6 0.65 0.7 0.75 0.8 0.850

50

100

150

200

250

300

350

Peak-to-Peak

Hits

11WAVECREST

Peak-To-Peak Shortfallsc.) Peak-to-peak cannot define a unique PDF

∆t

Probability

Peak-to-Peak

PDFs

Which one ?

12WAVECREST

A RMS Shortfall Case Study

RMS ≠ RJ sigma

σl σr

µl µr Jitter

Events

N_lmax, N_rmax

N_min

σ>

∆−∆−

= ∑=

2

1

)(1

1i

N

n

ttN

RMS

13WAVECREST

A Deterministic And Random PDF Estimation Method: TailFit

• Total jitter PDF = DJ PDF * RJ PDF

222)(

21)( σ

µ

π

−∆−=∆

tetp

• Tail parts of distribution preserve information on RJ process.

DJ pdf

RJ pdf *

Total pdf

• RJ PDF is a Gaussian

14WAVECREST

∆ t

prob

den

sity

J itter pdf

G aussian Tailfits

What Does The “TailFit” Offer ?

• RJ PDFS• DJ PDF (via deconvolution)• Subspace statistical parameters

15WAVECREST

DJ PDF Via Deconvolution

-0.3 -0.2 -0.1 0 0.1 0.2 0.30

2

4

6

t (UI)

TJ P

DF

-0.3 -0.2 -0.1 0 0.1 0.2 0.3-0.1

0

0.1

0.2

Rem

aind

er

-0.3 -0.2 -0.1 0 0.1 0.2 0.30

5

10

t (UI)

DJ

PDF

TJ PDF and DJ PDF

-0.3 -0.2 -0.1 0 0.1 0.2 0.3-2

-1

0

1

2

Erro

r

16WAVECREST

A Jitter/Noise Spectrum Estimation Method: Autocorrelation (Patented)

)))((*2()( ntRxxcFFTfPSD ∆−=

Ideal Clock

0 1N UI

Data

∆t0 ∆tn∆t1

17WAVECREST

What Does The “Autocorrelation” Offer ?

• RJ PSD • PJ PSD• DDJ (DJ without PJ and BUJ) PSD

f

psd(

f)

P J R J

18WAVECREST

Jitter And Noise In One View: Eye-Diagram

Timing jitter pdf Amplitude noise pdf

19WAVECREST

Jitter, Noise, And BER

pdf

ts

BER (cdf)

zero level

eye-diagram

0 1 ts

0.5 0.5

UI

opening

∆ t

20WAVECREST

• BER: metric for overall system performance• BER: CDF from jitter and noise PDFS

Jitter, Noise, And BER Cont…

)]()()()([21)()( tdt

st

trPtdt

sttlPtCDFtBER ss ∆∆∫

∞−+∆∆∫

∞==

21WAVECREST

A Serial Data Communication System

Transmitter Receiver

PLL

Data

Clock/ PLL

D

C

Q

Medium

CR/ PLL

Data

22WAVECREST

A PLL Frequency Response Function

Frequency (f)

Mag

nitu

de (d

B)

HL(f)

fc

23WAVECREST

Receiver Jitter Transfer Function

CR/ PLL

Jitter in +

-

Jitter out

Receiver “sees” a difference function for jitter

• A “difference” function

θi θe

24WAVECREST

What Does A Difference Function Mean?

• Jitter is referenced to a recovered bit clock• Receiver has a jitter transfer function• “Intrinsic” jitter referenced to an ideal bit clock

is not the jitter “seen” by the receiver• BER of the system should be estimated

based on jitter “seen” by the receiver

25WAVECREST

Jitter Transfer/Tolerance Functions For Data Recovery

Frequency (f) fc

Mag

nitu

de

(dB)

HH(f): Jitter Transfer

HT (f) Jitter Tolerance

26WAVECREST

What Constitutes A Valid Jitter Estimating/Testing Method?

• Estimate the jitter as the receiver “sees” !!!• CR/PLL and difference functions or their

equivalents are required

CR/ PLL

Data in +

-

Measurement System

27WAVECREST

Compliance Estimating/Testing:Total Jitter And BER Function

• Total jitter = UI – eye opening @ 10-12

28WAVECREST

A Valid Jitter Estimating/Testing Method For Serial Links

Estimating/testing total jitter PDF via an appropriate bit clock reference

Estimating/Testing BER/CDF function to < 10-12

Estimating/Testing total jitter @ BER = 10-12 or smaller

Pass/Fail

29WAVECREST

Jitter Transfer Function For PCI Express

Ref Clock (100 MHz) Tx

PLL 25X

PLL 25X

Rx

D

C

Q

D

C PI

• System block diagram for common clock mode

30WAVECREST

Jitter Transfer Function For PCI Express Cont..

X(s): Ref Clock Jitter

Tx PLLH1(s) PI

H3(s)

Rx PLLH2(s)

+

-

Y(s): Jitter At The Rx

• System Transfer Function Block Diagram

31WAVECREST

Jitter Transfer Function For PCI Express Cont..• Math Relationships

)(3))(2)(1()( sHsHsHstH •−=

)()()( sXstHsY •=

32WAVECREST

Summary And Conclusion• Deterministic parametric methods for jitter and

noise no longer sufficient (e.g., Peak-to-Peak)• Statistical functional (PDF/CDF) methods are

required for jitter, noise, and BER estimation/test• “Tailfit” offers deterministic and random PDF/CDF

estimation/test• “Autocorrelation” offers PSD for periodic and

random components• Transfer function is required in estimating

relevant jitter, noise, and BER for the system• Statistical PDF/CDF + transfer function gives a

complete and accurate system performance estimation/testing