Peak Distortion ISI Analysis

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Peak Distortion ISI Analysis

• Bryan CasperCircuits Research Lab
• Intel Corporation

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Agenda

• Properties of a Linear Time-invariant System
  (LTI)
• Margin calculation method (voltage and timing)
• Worst-case eye opening calculation methods
• Worst-case eye with crosstalk
• Complete Peak Distortion equations
• Compare worst-case eye w/ random data eye, lone 1
  or 0 eye, sine wave eye

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Properties of a Linear Time-invariant System
FFT

• Impulse response Frequency response
• Convolution
• Superposition

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LTI property Equivalence of Time and Frequency
Domain
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LTI property Convolution
Tx symbol (mirror)
Impulse response
Pulse response
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LTI property Superposition
Out
In
Tx symbol 000010000000
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LTI property Superposition of symbols
Out
In
Tx symbol 000010011100
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LTI property Superposition of coupled symbols
In
Out
Tx symbol 000010000000
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LTI property Superposition of coupled symbols
In
Out
Tx symbol 000011111100
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LTI property Superposition of coupled symbols
Out
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LTI property Superposition of coupled symbols
Out
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LTI property Superposition of coupled symbols
Out
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Max data rate calculation method

• Determine maximum value of all sample timing
  uncertainty (not including ISI)
• Transmitter and receiver sampling jitter
• Clock vs. Data skew
• Determine maximum value of all voltage
  uncertainty (not including ISI)
• Power supply noisePSRR
• Common mode noiseCMRR
• Thermal noise
• Comparator sensitivity
• Comparator offset
• Determine worst-case eye

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Margin Calculation
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Margin Calculation (zoomed)
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Worst-case eye calculation

• Eye diagrams are generally calculated empirically
• Convolve random data with pulse response of
  channel
• Pulse response is derived by convolving the
  impulse reponse with the transmitted symbol
• For eye diagrams to represent the worst-case, a
  large set of random data must be used
• Low probability of hitting worst case data
  transitions
• Computationally inefficient
• An analytical method of producing the worst-case
  eye diagram exists
• Computationally efficient algorithm

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Peak Distortion Analysis Reference

• Peak distortion analysis of ISI has been used for
  many years
• J. G. Proakis, Digital Communications, 3rd ed.,
  Singapore McGraw-Hill, 1995, pp. 602-603 (not
  much detailed info here)

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Interconnect Model

• Point to point differential desktop topology

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Differential S Parameters
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Eye diagram (100 bits _at_5Gb/s)
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Eye diagram (1000 bits _at_5Gb/s)
Random data eye (100 bits) --- Random data eye
(1000 bits) ---
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Sample pulse response
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Step response
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Worst-case 0
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Worst-case 1
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How to find worst-case patterns
Worst-case 0 ?
1 1 0 1 0 0 1
Worst-case 1 ?
0 0 1 0 1 1 0
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Ideal reference placement
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Worst-case Received Voltage Difference (RVD) for
WC1
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Worst-case Received Voltage Difference (RVD) for
WC0
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Worst-case Received Voltage Difference (RVD)
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5Gb/s Pulse Response
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5Gb/s Response due to worst-case data pattern
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Worst-case data response
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Worst-case data eye
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WC response vs Random response
WC eye for cursor point only
100 symbols random data eye
1000 symbols random data eye
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5Gb/s WC eye shape
Precursor Cursor Postcursor
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WC eye vs random data eye
WC eye shape
100 symbols random data eye
1000 symbols random data eye
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Co-channel Interference
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Pulse responses (differential)
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WC RVD w/ Co-channel Interference
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Random data eye w/ FEXT
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Random data eye w/ w/o FEXT
Random data eye w/ FEXT --- Random data eye
w/o FEXT ---
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WC eye w/ w/o FEXT
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Complete Peak Distortion Equations
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Worst-case 1 eye edge due to ISI

• Definitions
• y(t) is the pulse response of the interconnect
• T is the symbol period
• s1 is the eye edge due to a worst case 1

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Worst-case 1 eye edge due to ISI
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Worst-case 1 eye edge due to ISI
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Worst-case 1 eye edge due to ISI
y(0)
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Worst-case 1 eye edge due to ISI
y(1)
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Worst-case 1 eye edge due to ISI
y(2)
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Worst-case 1 eye edge due to ISI
y(12)
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Worst-case 1 eye edge due to ISI
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Worst-case 1 eye edge due to ISI
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Worst-case 1 eye edge due to ISI
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Worst-case 1 eye edge due to ISI
0
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Worst-case 1 eye edge due to ISI
0
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Worst-case 1 eye edge due to ISI
0
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Worst-case 1 eye edge due to ISI
0
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Worst-case 0 eye edge due to ISI
Remove y(t)
0
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Worst-case 0 eye edge due to ISI
0
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Worst-case 0 eye edge due to ISI
0
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Worst-case 0 eye edge due to ISI
0
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Worst-case 0 eye edge due to ISI
0
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Worst-case eye opening
0
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Worst-case eye opening
0
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Worst-case eye opening
0
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Worst-case eye opening
0
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Worst-case eye edges with ISI and CCI
Worst-case 1 eye edge where ti is the relative
sampling point of each cochannel pulse response.
Worst-case 0 eye edge
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How do different methods of SI analysis compare
with peak distortion analysis?

• Random data eye
• Lone pulse method
• Frequency domain method
• Measure the output amplitude due to a sine wave
  input (sine wave freq data rate/2)

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SI analysis comparison w/ 10 ustrip (previous
example)
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SI analysis comparison w/ 10 ustrip (previous
example)
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SI analysis comparison w/ multi-drop channel
2.5 Gb/s
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SI analysis comparison w/ multi-drop channel
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Conclusion

• Given S Parameters and the corresponding pulse
  response, the worst case eye shape can be
  determined analytically
• Worst-case co-channel interference can also be
  determined analytically
• Advantages Objective, Exact, Computationally
  Efficient

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Backup
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Complete equations for peak distortion analysis
To determine the worst-case voltage or timing
margin, the worst-case received eye shape is
extracted along with the peak sampling boundary.
Since sources such as intersymbol and cochannel
interference have truncated distributions, the
associated worst-case magnitudes can be directly
calculated from the unit pulse responses of the
system. The unit pulse response y(t) of a system
is given by Equation 1 Unit pulse response
of a communication system where c(t) is the
transmitter symbol response, p(t) is the impulse
response of the channel and receiver and denotes
convolution. The eye edge due to the worst-case 1
is given by Equation 2 Worst-case 1 eye edge
due to ISI where T is the symbol period.
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Complete equations for peak distortion analysis
If n cochannel interference sources exist and yi
is the cochannel pulse response, the worst-case 1
eye edge becomes Equation 3 Worst-case 1
eye edge due to ISI and cochannel
interference where ti is the relative sampling
point of each cochannel pulse response.
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Complete equations for peak distortion analysis
The eye edge due to the worst-case 0 is given
by Equation 4 Worst-case 0 eye
edge Therefore, the worst-case eye opening,
e(t), is defined as