March 12, 2022 March 12, 2022 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation
April 18, 2023April 18, 2023
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
• Impulse response Frequency response• Convolution• Superposition
FFT
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LTI property: Equivalence of Time and Frequency Domain
Insertion loss S parameters(complex)
Insertion loss S parameters(Magnitude and phase)
FFT
Impulse response
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LTI property: Convolution
Tx symbol (mirror)
Impulse response
Pulse response
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LTI property: Superposition
Tx symbol
…000010000000…
In Out
Pulse response
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LTI property: Superposition of symbols
Tx symbol
…000010011100…
In Out
Response to pattern 100111
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LTI property: Superposition of coupled symbols
Tx symbol
…000010000000…
In
Out
FEXT Pulse response
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LTI property: Superposition of coupled symbols
Tx symbol
…000011111100…
In
Out
FEXT response
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LTI property: Superposition of coupled symbols
Out
Tx symbol…000011111100…
FEXT response
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LTI property: Superposition of coupled symbols
Out
Tx symbol…000010011100…
Insertion loss response
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LTI property: Superposition of coupled symbols
Out
Tx symbol…000010011100…
Tx symbol…000011111100…
FEXT response
Insertion loss response
Composite response
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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 noise*PSRR– Common mode noise*CMRR– Thermal noise– Comparator sensitivity– Comparator offset
• Determine worst-case eye
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Ideal sampling position Timing skew Jitter
Ideal reference point
Voltage offset
Voltage Noise and required comparatorinput
Margin Calculation
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Ideal sampling position Timing skew Jitter
Ideal sampling position
Voltage offset
Voltage Noise and required comparatorinputVoltage margin
Time margin
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
10” μstrip
• Differential, edge-coupled microstrip (10” @ 55Ω)
socket socket
• 2 Sockets
pkg pkg
• 2 Packages (2” @ 45Ω)
• 1pF pad capacitance
• 50Ω single-ended termination
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Differential S Parameters
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Eye diagram (100 bits @5Gb/s)
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Eye diagram (1000 bits @5Gb/s)
Random data eye (100 bits) --- Random data eye (1000 bits) ---
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Sample pulse response
cursorprecursor postcursor
ISI+ ISI-
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Step response
0 0 0 0 1 1 1 1 1 1 1 1 1 1 1
ISIcursorV
0V
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Worst-case 0
0 1 1 0 1 0 0 1 0 0 0 0 0
ISIV 0WC
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Worst-case 1
0 1 0 1 1 0 0 0 0 0
ISIcursorV 1WC
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How to find worst-case patterns
1 1 0 1 0 0 1
0 0 1 0 1 1 0
Worst-case 0
Worst-case 1
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Ideal reference placement
0 1 0 1 1 0 0 0 0 0 ISIcursorV 1WC
0 1 1 0 1 0 0 1 0 0 0 0 0 ISIV 0WC
2
VVV
1WC0WCreference
2
ISIcursorISI
2
ISIcursor
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Worst-case Received Voltage Difference (RVD) for WC1
reference1WCWC1 VVRVD
Worst-case 1
ISIcursorV 1WC
Reference
2
ISIcursorISIcursor
2
ISI
2
cursor
2
ISI
2
ISI
2
cursor
2
ISI
2
ISI
2
cursor
2
ISI
2
ISIISI
2
cursor
2
ISI
2
ISIISI
2
cursor
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Worst-case Received Voltage Difference (RVD) for WC0
0WCreferenceWC0 VVRVD
ISIV 0WC
Reference
Worst-case 0
ISI
2
ISIcursor
2
ISI
2
cursor
2
ISI
2
ISI
2
cursor
2
ISI
2
ISI
2
cursor ISI
2
ISI
2
ISI
2
cursor
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Worst-case Received Voltage Difference (RVD)
16 -3 42 -1 2 2
2
ISI
2
cursorRVD case-Worst
22
21-43-2
2
16
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5Gb/s Pulse Response
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5Gb/s Response due to worst-case data pattern
Worst-case 0
Worst-case 1
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Worst-case data response
Worst-case 1Lone 1
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Worst-case data eye
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WC response vs Random response
WC eye for cursor point only
1000 symbols random data eye
100 symbols random data eye
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5Gb/s WC eye shape
2
ISI
2
cursorRVDWC
Precursor Cursor Postcursor
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WC eye vs random data eye
WC eye shape
1000 symbols random data eye
100 symbols random data eye
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Co-channel Interference
1 2
3 4
5 6
12 Port
7 8
9 10
11 12
FEXT Attacking differential
pairs
Victim differential
pair
NEXTECHO
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Pulse responses (differential)
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WC RVD w/ Co-channel Interference
4
ECHONEXTFEXTISI-cursorRVD SBD
2
FEXTISI-cursorRVD dinterleave-non UD
2
NEXTISI-cursorRVD dinterleave UD
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Random data eye w/ FEXT
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Random data eye w/ & w/o FEXTRandom data eye w/ FEXT ---Random data eye w/o FEXT ---
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Random data eye ---WC eye w FEXT …Random data eye ---WC eye w/o FEXT …WC eye w FEXT …
WC eye w/ & w/o FEXT
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Complete Peak Distortion Equations
n
i ktkTtyi
i
kk
kTtyi
itkTtykTtytyts1
0)(
0
0)(1 )( )()()(
n
i ktkTtyi
i
kk
kTtyi
itkTtykTtyts1
.0)(
0
0)(0 )( )()(
).()()( 01 tstets
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April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis
Worst-case 1 eye edge due to ISI
0
0)(1 )()()(
kk
kTtykTtytyts
• 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
0
0)(1 )()()(
kk
kTtykTtytyts
Example pulse response
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Worst-case 1 eye edge due to ISI
0
0)(1 )()()(
kk
kTtykTtytyts
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April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis
Worst-case 1 eye edge due to ISI
0
0)(1 )()()(
kk
kTtykTtytyts
y(0)
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Worst-case 1 eye edge due to ISI
0
0)(1 )()()(
kk
kTtykTtytyts
y(1)
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Worst-case 1 eye edge due to ISI
0
0)(1 )()()(
kk
kTtykTtytyts
y(2)
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Worst-case 1 eye edge due to ISI
0
0)(1 )()()(
kk
kTtykTtytyts
y(12)
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Worst-case 1 eye edge due to ISI
0
0)(1 )()()(
kk
kTtykTtytyts
T=8
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Worst-case 1 eye edge due to ISI
0
0)(1 )()()(
kk
kTtykTtytyts
Bryan Casper - CRL
April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis
Worst-case 1 eye edge due to ISI
0
0)(1 )()()(
kk
kTtykTtytyts
Bryan Casper - CRL
April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis
Worst-case 1 eye edge due to ISI
0
0)(1 )()()(
kk
kTtykTtytyts
0
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April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis
Worst-case 1 eye edge due to ISI
0
0)(1 )()()(
kk
kTtykTtytyts
0
Bryan Casper - CRL
April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis
Worst-case 1 eye edge due to ISI
0
0)(1 )()()(
kk
kTtykTtytyts
0
Bryan Casper - CRL
April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis
Worst-case 1 eye edge due to ISI
0
0)(1 )()()(
kk
kTtykTtytyts
0
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Worst-case 0 eye edge due to ISI
0
0)(0 )()(
kk
kTtykTtyts
Remove y(t)
0
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Worst-case 0 eye edge due to ISI
0
0)(0 )()(
kk
kTtykTtyts
0
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Worst-case 0 eye edge due to ISI
0
0)(0 )()(
kk
kTtykTtyts
0
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Worst-case 0 eye edge due to ISI
0
0)(0 )()(
kk
kTtykTtyts
0
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Worst-case 0 eye edge due to ISI
0
0)(0 )()(
kk
kTtykTtyts
0
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Worst-case eye opening
).()()( 01 tstets
0
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Worst-case eye opening
).()()( 01 tstets
0
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Worst-case eye opening
).()()( 01 tstets
0
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Worst-case eye opening
).()()( 01 tstets
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.
n
i ktkTtyi
i
kk
kTtyi
itkTtykTtytyts1
0)(
0
0)(1 )( )()()(
n
i ktkTtyi
i
kk
kTtyi
itkTtykTtyts1
.0)(
0
0)(0 )( )()(
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)
0
50
100
150
200
250
300
350
400
Eye Opening (mV)
Eye Opening (mV) 190 310 275 235 400
worst-case100 bits random
data1000 bits
random datalone pulse
frequencydomain
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SI analysis comparison w/ multi-drop channel2.5 Gb/s
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SI analysis comparison w/ multi-drop channel
0
50
100
150
200
250
300
Eye Opening (mV)
Eye Opening (mV) 52 150 90 252 300
worst-case100 bits
random data1000 bits
random datalone pulse
frequencydomain
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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 ISIwhere T is the symbol period.
)()()( tptcty
0
0)(1 )()()(
kk
kTtykTtytyts
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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.
n
i ktkTtyi
i
kk
kTtyi
itkTtykTtytyts1
0)(
0
0)(1 )( )()()(
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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
n
i ktkTtyi
i
kk
kTtyi
itkTtykTtyts1
.0)(
0
0)(0 )( )()(
).()()( 01 tstets