1. Peak Distortion ISI Analysis
Bryan Casper Circuits Research Lab
Intel® Corporation
April 15, 2017

2. Peak Distortion Analysis
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
Peak Distortion Analysis
April 15, 2017

3. Properties of a Linear Time-invariant System
FFT
Impulse response Frequency response
Convolution
Superposition
Peak Distortion Analysis
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4. LTI property: Equivalence of Time and Frequency Domain
Insertion loss S parameters
(complex)
FFT
Impulse response
Insertion loss S parameters
(Magnitude and phase)
Peak Distortion Analysis
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5. LTI property: Convolution
Tx symbol (mirror)
Impulse response
Pulse response
Peak Distortion Analysis
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6. LTI property: SuperpositionIn
Out
Pulse response
Tx symbol
… …
Peak Distortion Analysis
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7. LTI property: Superposition of symbolsIn
Out
Tx symbol
… …
Response to pattern
Peak Distortion Analysis
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8. LTI property: Superposition of coupled symbolsIn
Out
FEXT Pulse response
Tx symbol
… …
Peak Distortion Analysis
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9. LTI property: Superposition of coupled symbolsIn
Out
Tx symbol
… …
FEXT response
Peak Distortion Analysis
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10. LTI property: Superposition of coupled symbols
Tx symbol
… …
Out
FEXT response
Peak Distortion Analysis
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11. LTI property: Superposition of coupled symbols
Out
Tx symbol
… …
Insertion loss response
Peak Distortion Analysis
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12. LTI property: Superposition of coupled symbols
Tx symbol
… …
Out
Tx symbol
… …
FEXT response
Insertion loss response
Composite response
Peak Distortion Analysis
April 15, 2017

13. 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 noise*PSRR
Common mode noise*CMRR
Thermal noise
Comparator sensitivity
Comparator offset
Determine worst-case eye
1. Most noise sources can be characterized as being bounded. However, thermal noise is gaussian and has an infinite peak amplitude. However, gaussian noise peak amplitude can be considered as bounded within a certain probability. For example, a gaussian source with 1mV of rms noise will exceed 10mV with a probability of 10E-21 (practically speaking, this is an infinitely small chance)
Peak Distortion Analysis
April 15, 2017

14. Peak Distortion Analysis
Margin Calculation
Ideal sampling position
Timing skew
Jitter
Voltage Noise and
required comparator
input
Voltage offset
Ideal reference point
Peak Distortion Analysis
April 15, 2017

15. Margin Calculation (zoomed)
Ideal sampling position
Timing skew
Jitter
Voltage offset
Voltage Noise and
required comparator
input
Voltage margin
Time margin
1. To determine the maximum data rate, increase the symbol rate until the margins approach 0.
Peak Distortion Analysis
April 15, 2017

16. 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
Peak Distortion Analysis
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17. 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 (not much detailed info here)
Peak Distortion Analysis
April 15, 2017

18. Peak Distortion Analysis
Interconnect Model
Point to point differential desktop topology
10” μstrip
Differential, edge-coupled microstrip 55Ω)
socket
2 Sockets
pkg
2 Packages 45Ω)
1pF pad capacitance
50Ω single-ended termination
Peak Distortion Analysis
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19. Differential S Parameters
Peak Distortion Analysis
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20. Eye diagram (100 bits @5Gb/s)
This eye is a single-ended representation of a differential eye.
Explain the process of constructing eye (S->IFFT>H(t)>random data
Peak Distortion Analysis
April 15, 2017

21. Eye diagram (1000 bits @5Gb/s)
Random data eye (100 bits) ---
Random data eye (1000 bits) ---
This eye is a single-ended representation of a differential eye.
The problem with generating an empirical eye diagram is that it doesn’t accurately represent the worst-case eye without running millions (or billions) of bits of random data. This is computationally difficult.
Peak Distortion Analysis
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22. Peak Distortion Analysis
Sample pulse response
ISI+
ISI-
Precursor is previous bit time
Postcursor is next bit time after cursor
precursor
cursor
postcursor
Peak Distortion Analysis
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23. Peak Distortion Analysis
Step response
Peak Distortion Analysis
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24. Peak Distortion Analysis
Worst-case 0
Peak Distortion Analysis
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25. Peak Distortion Analysis
Worst-case 1
Peak Distortion Analysis
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26. How to find worst-case patterns
Worst-case 1 
Peak Distortion Analysis
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27. Ideal reference placement
Peak Distortion Analysis
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28. Worst-case Received Voltage Difference (RVD) for WC1
Reference
Peak Distortion Analysis
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29. Worst-case Received Voltage Difference (RVD) for WC0
Reference
Worst-case 0
Peak Distortion Analysis
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30. Worst-case Received Voltage Difference (RVD)16 -3 4 2 -1
Peak Distortion Analysis
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31. Peak Distortion Analysis
5Gb/s Pulse Response
Differential output swing is 1V.
Peak Distortion Analysis
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32. 5Gb/s Response due to worst-case data pattern
Differential output swing is 1V.
Peak Distortion Analysis
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33. Worst-case data response
Lone 1
Worst-case 1
Differential output swing is 1V.
Peak Distortion Analysis
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34. Peak Distortion Analysis
Worst-case data eye
Differential output swing is 1V.
Peak Distortion Analysis
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35. WC response vs Random response
1. This is the worst-case eye only at the cursor point. To determine the worst-case eye shape, it is best to apply the worst case RVD equation across the entire eye.
WC eye for cursor point only
100 symbols random data eye
1000 symbols random data eye
Peak Distortion Analysis
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36. Peak Distortion Analysis
5Gb/s WC eye shape
Precursor Cursor Postcursor
Emphasize the difference in calculation
Peak Distortion Analysis
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37. WC eye vs random data eye
WC eye shape
100 symbols random data eye
1000 symbols random data eye
Peak Distortion Analysis
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38. Co-channel Interference1 2 3 4 5 6
12 Port 7 8 9 10 11 12
Attacking
differential
pairs
FEXT
NEXT
ECHO
Victim
differential
pair
Peak Distortion Analysis
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39. Pulse responses (differential)
Peak Distortion Analysis
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40. WC RVD w/ Co-channel Interference
Take out N
Peak Distortion Analysis
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41. Peak Distortion Analysis
Random data eye w/ FEXT
Peak Distortion Analysis
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42. Random data eye w/ & w/o FEXT
Random data eye w/ FEXT
Random data eye w/o FEXT
Peak Distortion Analysis
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43. Peak Distortion Analysis
WC eye w/ & w/o FEXT
Random data eye
WC eye w/o FEXT …
WC eye w FEXT …
Random data eye
WC eye w FEXT …
Peak Distortion Analysis
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44. Complete Peak Distortion Equations
Peak Distortion Analysis
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45. 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
Peak Distortion Analysis
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46. Worst-case 1 eye edge due to ISI
Example pulse response
Peak Distortion Analysis
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47. Worst-case 1 eye edge due to ISI
Peak Distortion Analysis
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48. Worst-case 1 eye edge due to ISI
Peak Distortion Analysis
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49. Worst-case 1 eye edge due to ISI
Peak Distortion Analysis
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50. Worst-case 1 eye edge due to ISI
Peak Distortion Analysis
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51. Worst-case 1 eye edge due to ISI
Peak Distortion Analysis
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52. Worst-case 1 eye edge due to ISI
Peak Distortion Analysis
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53. Worst-case 1 eye edge due to ISI
Peak Distortion Analysis
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54. Worst-case 1 eye edge due to ISI
Peak Distortion Analysis
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55. Worst-case 1 eye edge due to ISI
Peak Distortion Analysis
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56. Worst-case 1 eye edge due to ISI
Peak Distortion Analysis
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57. Worst-case 1 eye edge due to ISI
Peak Distortion Analysis
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58. Worst-case 1 eye edge due to ISI
Peak Distortion Analysis
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59. Worst-case 0 eye edge due to ISI
Remove y(t)
Peak Distortion Analysis
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60. Worst-case 0 eye edge due to ISI
Peak Distortion Analysis
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61. Worst-case 0 eye edge due to ISI
Peak Distortion Analysis
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62. Worst-case 0 eye edge due to ISI
Peak Distortion Analysis
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63. Worst-case 0 eye edge due to ISI
Peak Distortion Analysis
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64. Worst-case eye opening
Peak Distortion Analysis
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65. Worst-case eye opening
Peak Distortion Analysis
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66. Worst-case eye opening
Peak Distortion Analysis
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67. Worst-case eye opening
Peak Distortion Analysis
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68. Worst-case eye edges with ISI and CCI
where ti is the relative sampling point of each cochannel pulse response.
Worst-case 0 eye edge
Peak Distortion Analysis
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69. Peak Distortion Analysis
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)
Peak Distortion Analysis
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70. SI analysis comparison w/ 10” ustrip (previous example)
Peak Distortion Analysis
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71. SI analysis comparison w/ 10” ustrip (previous example)
Peak Distortion Analysis
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72. SI analysis comparison w/ multi-drop channel
2.5 Gb/s
Peak Distortion Analysis
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73. SI analysis comparison w/ multi-drop channel
Peak Distortion Analysis
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74. Peak Distortion Analysis
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
Peak Distortion Analysis
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75. Peak Distortion Analysis
Backup
Peak Distortion Analysis
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76. 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.
Peak Distortion Analysis
April 15, 2017

77. 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.
Peak Distortion Analysis
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78. 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
Peak Distortion Analysis
April 15, 2017