Essential Principles of Jitter Part 3 Dr. Alan Blankman Product Manager, High Speed Serial Data Products, Teledyne LeCroy and Dr. Eric Bogatin, Dean, Teledyne LeCroy Signal Integrity Academy, Teledyne LeCroy

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Essential Principles of Jitter, or Jitter 101

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1 Introduction to Jitter: The Time Interval Error: TIE

2 Jitter Synthesis: The Jitter Components

3 Jitter Analysis Extrapolation and Decomposition

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Check out Alan’s new app note: “Understanding Jitter Calculations, why Dj

can be less than DDj” TeledyneLeCroy.com

Where to get a copy of the slides: www.beTheSignal.com

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Jitter part 1: The Time Interval Error (TIE)

The actual edge arrival times – the expected edge arrival times, for each edge

Expected arrival times from CDR circuitry

Plotted over time: the TIE track

Apply the power of statistics to analyze the TIE track

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Jitter part 2: The Jitter Components

The power of statistical analysis

The five fundamental types of jitter: ISI, DCD, Periodic, Random, Other

Synthesized examples based on their root cause

Gaussian statistics in 3 minutes

The jitter “tree”

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Data stream

TIE Track

Statistical Analysis

Tools

Intersymbol interference

“ISI”

Duty Cycle Distortion

“DCD”

Periodic “Pj”

Unbounded, Random

“Rj”

Other, bounded, uncorrelated with

the data, jitter “OBUJ”

Classification of Jitter Types: The Jitter Tree from the “Bottom Up”

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Total Jitter – “Tj”

Intersymbol interference

“ISI”

Duty Cycle Distortion

“DCD”

Bounded Deterministic (not random)

“Dj”

Correlated Jitter Data Dependent Jitter

“DDj”

Periodic “Pj”

Unbounded, Random

“Rj”

Bounded, uncorrelated Jitter

“BUJ”

Other, bounded, uncorrelated with the data,

jitter “OBUJ”

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Section 3: Two Important Goals

1. Extrapolate: We measure 107 bits, we want to know how 1012 to 1015 bits behave Given the Tj (total jitter) spec (~ 60% UI), what is the BER of

the link? Does it meet the spec? Is there sufficient margin?

2. Decompose: if we want to reduce the Tj… Need to find the root cause of the Tj: what are the major

contributors? Extract from a Tj measurement, where most of the jitter is

coming Rj Pj DCD ISI OBUj

Fix the root cause of the major contributors

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“Are you sure about this Stan? It seems odd that a pointy head and a long beak is what makes them fly”

Fastest way to fix a problem is to find the root cause:

Hope and luck should play no

role in the design process

How to Extrapolate? Model the total jitter we can measure and use the model to predict the total jitter in extreme cases

The Dual Dirac Model The industry standard model describes “total jitter” as:

Two Dirac Delta functions, convolved with a Gaussian

Dj(δδ) is the “deterministic” jitter term, extracted based on the model,

not to be confused with the “deterministic” jitter term in the bottoms up jitter tree.

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( ) ( ) ( ) ( )Tj BER BER x Rj Dj= α δδ + δδ

The contribution to total jitter that includes the

extrapolated random jitter

{ The offset of the centers

of the Gaussians

{

“Total jitter” is the confidence interval (psec) of where all the TIE values

will lay, except for the outliers, a fraction, BER

{ (σ)

For BER = 10-12, α = 14.069

The Dual Dirac Model isn’t a very good fit to an actual jitter distribution

The fit in the middle of the jitter histogram is terrible!

And we don’t care!

The center part of the histogram does not contribute to outliers that create bit errors- it’s the tails that matter

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( ) ( ) ( ) ( )Tj BER BER x Rj Dj= α δδ + δδ

Jitte

r PD

F

Time from edge, t

Measured jitter

Dj(δδ)

Tj (BER) = α(BER) *Rj(δδ) + Dj(δδ)

Modeled jitter

Jitte

r PD

F

Time from edge, t

bit errors will be created here

The Dual Dirac Model is a Good fit to the Tails of the Jitter Distribution

The fit in the middle of the jitter histogram is terrible!

And we don’t care! The center part of the histogram does not

contribute to outliers that create bit errors

But it’s a good fit to the tails! And that’s where the bit errors will arise

In practice, we fit the model to the tails

With two parameters: Rj(δδ) and Dj(δδ)

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( ) ( ) ( ) ( )Tj BER BER x Rj Dj= α δδ + δδ

Dj(δδ)

Tj (BER) = α(BER) *Rj(δδ) + Dj(δδ)

Jitte

r PD

F

Time from edge, t

Measured jitter

Modeled jitter

The Secret Sauce: How do we fit the Dual Dirac Jitter Model to a Measured Jitter Distribution?

And, along the way, decompose the jitter into its components? Tj, Rj(δδ), Dj(δδ), Pj, ISI, DDj, DCD

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Dr. Alan Blankman Product Manager, High Speed Serial

Data Products, Teledyne LeCroy

Jitter Calculation Flow

1. Make TIE measurements 2. Form TIE Track 3. Quantify data-dependent jitter 4. Remove DDJ from TIE Track to get Track of Rj & BUj 5. Quantify Pj from spectrum of Rj & BUj Track 6. Remove Pj from spectrum of Rj & BUj Track 7. Quantify sigma of Gaussian shape 8. Extrapolate tails 9. Bring DDJ back in to get extrapolated jitter PDF, CDF 10. Perform dual-Dirac fit to get Tj, Rj and Dj

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Understanding SDAIII Jitter Calculation Methods: http://teledynelecroy.com/doc/docview.aspx?id=7499

Everything About Jitter Starts with TIE

Measured Arrival Time of an edge – Expected Arrival Time for the edge = Time Interval Error for the edge

TIE describes how early or late an edge arrives vs. its expected arrival Multi-step process to make the measurement

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e.g. Signal is late Ref

data

Interpolate

early

la

te

TIE

valu

e

Let’s Perform the Jitter Analysis on this Link: PRBS7, 10.3125GB/s

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20us Acquisition: Simulated Waveform and TIETrack

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Zoomed in, Viewing 100ns Window. See the repetitive pattern.

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Overlaid Iterations of the TIETrack: TIETrack is repetitive as well

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Overlaid Iterations of the TIETrack

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Including the Averaged Iteration, or “DDJPlot”

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DDJ Plot: Average TIETrack for an iteration of the pattern

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Determining DDj from DDJPlot

Use the averaged TIE Track, which is the “DDj Plot”

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: Negative edges : Positive edges

Next Step: Remove the DDj from the TIETrack

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RjBUj Track: Random and Bounded-Uncorrelated Jitter

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With 5ps Pj Contributor

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1ps Pj Contributor… Not too easy to see the Pj in the time domain

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Pj Contributors are Recognized in the FFT of the RjBUjTrack

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Pj is the Inverse FFT

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Determination of σ

Need this to extrapolate the tails of the Gaussian Key to predicting Tj for BER beyond what’s measured

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RjBUj Histogram is Extrapolated

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Determining the Extrapolated PDF/CDF

Convolve extrapolated RjBUj with DDj histogram

Yields overall extrapolated jitter histogram When appropriately normalized, this is the

jitter probability density function (PDF)

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Integrate from the Outside in to form the CDF

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CDF is an “Inside-Out” Bathtub Curve

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log1

0BE

R

0

-2

-4

-6

-12

-8

-10

-14

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Width of CDF: Tj @ BER Width of Bathtub: Eye Opening @ BER sum = 1 UI time

Tj @ BER = 10^-12

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Tj @ BER = 10^-13

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Last Step: Perform Fit

Fit to Tj= α(BER) *Rj(δδ) + Dj(δδ) letting both Rj(δδ) and Dj(δδ) vary

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Use Tj values in vicinity of the BER that the user selects

Tj1 = α(BER1) * Rj + Dj

Tj3 = α(BER3) * Rj + Dj Tj2 = α(BER2) * Rj + Dj

Tj4 = α(BER4) * Rj + Dj

α(BER):

Contrasting the Dual-Dirac Fit to the Observed Data

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• White cursors show position of delta functions

• 1 sigma = 0.925 divs

Contrasting the Dual-Dirac Fit to the Observed Data

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• White cursors show the interval for Tj(BER=10-12). Note the extrapolation.

Example With Signal with Much Less DDJ

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• Extrapolation is more apparent – but useful when looking to predict jitter!

Essentials of Jitter Part 3 – Summary

TIE is the fundamental nugget of jitter

Determination of DDj, ISI, DCD, Pj: can be measured with acquired TIE measurements DDJ and ISI are best measured with sufficient statistics with a suitable

length pattern

In serial data analysis, Tj is defined as Tj(@BER) rather than Tj(pk-pk) Tj(δδ) avoids using faulty pk-pk measurements to characterize jitter

Dj(δδ), Rj(δδ) are the result of a fit to the dual-Dirac jitter model.

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Thank You! For More Information:

www.beTheSignal.com The Signal Integrity Academy

Online video training

teledynelecroy.com

Published by Prentice Hall, 2009 @beTheSignal