May 18, 2015May 18, 2015May 18, 2015 Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab...

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Peak Distortion ISI Analysis

Bryan CasperCircuits 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

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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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Tx symbol

…000011111100…

In

Out

FEXT response

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Out

Tx symbol…000011111100…

FEXT response

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Out

Tx symbol…000010011100…

Insertion loss response

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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


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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



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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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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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0

0)(1 )()()(

kk

kTtykTtytyts

Example pulse response

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0

0)(1 )()()(

kk

kTtykTtytyts

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0

0)(1 )()()(

kk

kTtykTtytyts

y(0)

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0

0)(1 )()()(

kk

kTtykTtytyts

y(1)

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0

0)(1 )()()(

kk

kTtykTtytyts

y(2)

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0

0)(1 )()()(

kk

kTtykTtytyts

y(12)

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0

0)(1 )()()(

kk

kTtykTtytyts

T=8

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0

0)(1 )()()(

kk

kTtykTtytyts

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0

0)(1 )()()(

kk

kTtykTtytyts

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0

0)(1 )()()(

kk

kTtykTtytyts

0

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0

0)(1 )()()(

kk

kTtykTtytyts

0

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0

0)(1 )()()(

kk

kTtykTtytyts

0

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0

0)(1 )()()(

kk

kTtykTtytyts

0

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0

0)(0 )()(

kk

kTtykTtyts

Remove y(t)

0

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0

0)(0 )()(

kk

kTtykTtyts

0

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0

0)(0 )()(

kk

kTtykTtyts

0

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0

0)(0 )()(

kk

kTtykTtyts

0

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0

0)(0 )()(

kk

kTtykTtyts

0

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Worst-case eye opening

).()()( 01 tstets

0

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).()()( 01 tstets

0

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).()()( 01 tstets

0

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).()()( 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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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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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

Date post:	17-Dec-2015
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