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Page 1: May 18, 2015May 18, 2015May 18, 2015 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

Page 2: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak 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

Page 3: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Properties of a Linear Time-invariant System

• Impulse response Frequency response• Convolution• Superposition

FFT

Page 4: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

LTI property: Equivalence of Time and Frequency Domain

Insertion loss S parameters(complex)

Insertion loss S parameters(Magnitude and phase)

FFT

Impulse response

Page 5: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

LTI property: Convolution

Tx symbol (mirror)

Impulse response

Pulse response

Page 6: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

LTI property: Superposition

Tx symbol

…000010000000…

In Out

Pulse response

Page 7: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

LTI property: Superposition of symbols

Tx symbol

…000010011100…

In Out

Response to pattern 100111

Page 8: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

LTI property: Superposition of coupled symbols

Tx symbol

…000010000000…

In

Out

FEXT Pulse response

Page 9: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

LTI property: Superposition of coupled symbols

Tx symbol

…000011111100…

In

Out

FEXT response

Page 10: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

LTI property: Superposition of coupled symbols

Out

Tx symbol…000011111100…

FEXT response

Page 11: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

LTI property: Superposition of coupled symbols

Out

Tx symbol…000010011100…

Insertion loss response

Page 12: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

LTI property: Superposition of coupled symbols

Out

Tx symbol…000010011100…

Tx symbol…000011111100…

FEXT response

Insertion loss response

Composite response

Page 13: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

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

Page 14: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Ideal sampling position Timing skew Jitter

Ideal reference point

Voltage offset

Voltage Noise and required comparatorinput

Margin Calculation

Page 15: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Ideal sampling position Timing skew Jitter

Ideal sampling position

Voltage offset

Voltage Noise and required comparatorinputVoltage margin

Time margin

Margin Calculation (zoomed)

Page 16: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

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

Page 17: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

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)

Page 18: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

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

Page 19: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Differential S Parameters

Page 20: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Eye diagram (100 bits @5Gb/s)

Page 21: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Eye diagram (1000 bits @5Gb/s)

Random data eye (100 bits) --- Random data eye (1000 bits) ---

Page 22: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Sample pulse response

cursorprecursor postcursor

ISI+ ISI-

Page 23: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Step response

0 0 0 0 1 1 1 1 1 1 1 1 1 1 1

ISIcursorV

0V

Page 24: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Worst-case 0

0 1 1 0 1 0 0 1 0 0 0 0 0

ISIV 0WC

Page 25: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Worst-case 1

0 1 0 1 1 0 0 0 0 0

ISIcursorV 1WC

Page 26: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

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

Page 27: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

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

Page 28: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

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

Page 29: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

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

Page 30: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Worst-case Received Voltage Difference (RVD)

16 -3 42 -1 2 2

2

ISI

2

cursorRVD case-Worst

22

21-43-2

2

16

Page 31: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

5Gb/s Pulse Response

Page 32: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

5Gb/s Response due to worst-case data pattern

Worst-case 0

Worst-case 1

Page 33: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Worst-case data response

Worst-case 1Lone 1

Page 34: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Worst-case data eye

Page 35: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

WC response vs Random response

WC eye for cursor point only

1000 symbols random data eye

100 symbols random data eye

Page 36: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

5Gb/s WC eye shape

2

ISI

2

cursorRVDWC

Precursor Cursor Postcursor

Page 37: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

WC eye vs random data eye

WC eye shape

1000 symbols random data eye

100 symbols random data eye

Page 38: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

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

Page 39: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Pulse responses (differential)

Page 40: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

WC RVD w/ Co-channel Interference

4

ECHONEXTFEXTISI-cursorRVD SBD

2

FEXTISI-cursorRVD dinterleave-non UD

2

NEXTISI-cursorRVD dinterleave UD

Page 41: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Random data eye w/ FEXT

Page 42: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Random data eye w/ & w/o FEXTRandom data eye w/ FEXT ---Random data eye w/o FEXT ---

Page 43: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

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

Page 44: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

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

Page 45: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

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

• 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

Page 46: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

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

Example pulse response

Page 47: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

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

Page 48: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

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

y(0)

Page 49: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

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

y(1)

Page 50: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

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

y(2)

Page 51: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

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

y(12)

Page 52: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

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

T=8

Page 53: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

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

Page 54: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

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

Page 55: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

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

Page 56: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

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

Page 57: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

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

Page 58: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

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

Page 59: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Worst-case 0 eye edge due to ISI

0

0)(0 )()(

kk

kTtykTtyts

Remove y(t)

0

Page 60: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Worst-case 0 eye edge due to ISI

0

0)(0 )()(

kk

kTtykTtyts

0

Page 61: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Worst-case 0 eye edge due to ISI

0

0)(0 )()(

kk

kTtykTtyts

0

Page 62: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Worst-case 0 eye edge due to ISI

0

0)(0 )()(

kk

kTtykTtyts

0

Page 63: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Worst-case 0 eye edge due to ISI

0

0)(0 )()(

kk

kTtykTtyts

0

Page 64: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Worst-case eye opening

).()()( 01 tstets

0

Page 65: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Worst-case eye opening

).()()( 01 tstets

0

Page 66: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Worst-case eye opening

).()()( 01 tstets

0

Page 67: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

Worst-case eye opening

).()()( 01 tstets

0

Page 68: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

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

Page 69: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak 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)

Page 70: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

SI analysis comparison w/ 10” ustrip (previous example)

Page 71: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

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

Page 72: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

SI analysis comparison w/ multi-drop channel2.5 Gb/s

Page 73: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

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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Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak 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

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Backup

Page 76: May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel ® Corporation.

Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

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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Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

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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Bryan Casper - CRL

April 18, 2023April 18, 2023Peak Distortion AnalysisPeak Distortion Analysis

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