Essentials of jitter part 3 webinar slides
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Transcript of 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
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Check out the Teledyne LeCroy Signal Integrity Academy at www.beTheSignal.com
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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For More Information
www.beTheSignal.com
The Signal Integrity Academy
Online video training
Published by Prentice Hall, 2009
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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)
11 Teledyne LeCroy Signal Integrity Academy
( ) ( ) ( ) ( )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