Essentials of jitter part 3 webinar slides

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
Teledyne LeCroy Signal Integrity Academy 1
Check out the Teledyne LeCroy Signal Integrity Academy at
www.beTheSignal.com

Essential Principles of Jitter, or Jitter 101
2
1
Introduction to Jitter: The Time Interval Error: TIE
2
Jitter Synthesis: The Jitter Components
3
Jitter Analysis Extrapolation and Decomposition
Teledyne LeCroy Signal Integrity Academy

For More Information
www.beTheSignal.com The Signal Integrity Academy Online video training
Published by Prentice Hall, 2009
3
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 Teledyne LeCroy Signal Integrity Academy 4

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

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”
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”
7
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”

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
“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.
()()()()TjBERBERxRjDj=αδδ+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
Jitter PDF
Time from edge, t
Measured jitter
Dj(δδ)
Tj (BER) = α(BER) *Rj(δδ) + Dj(δδ)
Modeled jitter
Jitter PDF
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)
Dj(δδ)
Tj (BER) = α(BER) *Rj(δδ) + Dj(δδ)
Jitter PDF
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
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
13
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
e.g. Signal is late
Ref
data
Interpolate
early late
TIE value

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

20us Acquisition: Simulated Waveform and TIETrack

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

Overlaid Iterations of the TIETrack: TIETrack is repetitive as well

Overlaid Iterations of the TIETrack

Including the Averaged Iteration, or “DDJPlot”

DDJ Plot: Average TIETrack for an iteration of the pattern

Determining DDj from DDJPlot

Use the averaged TIE Track, which is the “DDj Plot”
23
: Negative edges
: Positive edges

Next Step: Remove the DDj from the TIETrack

RjBUj Track: Random and Bounded-Uncorrelated Jitter

With 5ps Pj Contributor

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

Pj Contributors are Recognized in the FFT of the RjBUjTrack

Pj is the Inverse FFT

Determination of σ

Need this to extrapolate the tails of the Gaussian

Key to predicting Tj for BER beyond what’s measured
31

RjBUj Histogram is Extrapolated

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) 33

Integrate from the Outside in to form the CDF

CDF is an “Inside-Out” Bathtub Curve
log10BER
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

Tj @ BER = 10^-13

Last Step: Perform Fit

Fit to Tj= α(BER) *Rj(δδ) + Dj(δδ) letting both Rj(δδ) and Dj(δδ) vary
39
Use Tj values in vicinity
of the BER that the user selects
Tj1 = α(BER1) * Rj + Dj
α(BER):

Contrasting the Dual-Dirac Fit to the Observed Data
•
White cursors show position of delta functions
•
1 sigma = 0.925 divs

Contrasting the Dual-Dirac Fit to the Observed Data
•
White cursors show the interval for Tj(BER=10-12). Note the extrapolation.

Example With Signal with Much Less DDJ
•
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.
43

Thank You! For More Information:
www.beTheSignal.com The Signal Integrity Academy Online video training teledynelecroy.com
Published by Prentice Hall, 2009
@beTheSignal

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