Class2!10!11 12 Differential Signaling

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    Differential Signaling

    Introduction

    Reading Chapter 6

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    Agenda Differential Signaling Definition

    Voltage ParametersCommon mode parametersDifferential mode parameters

    Current mode logic (CML) bufferRelate to parametersModeling & simulation

    Timing parametersClock recoveryEmbedded clock

    AC couplingCommon mode responseIssues with simulation

    8B10B encodingDC balanced codes

    Duty Cycle distortionCycle

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    Single Ended Signaling All electrical signal circuits require a loop or return

    path. Single ended signal subject several means ofdistortions and noise.

    Ground or reference may move due to switching currents(SSO noise). We touched on this in the ground conundrumclass.

    A single ended receiver only cares about a voltage that isreferenced to its own ground.Electromagnetic interference can impose voltage on a singleended signal.Signal passing from one board to another are subject to thelocal ground disturbance.

    We can counteract many of these effect by addingmore ground.

    As frequencies increase beyond 1GHz, 80% of thesignal will be lost.

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    Review of threshold sensitivity

    The wave is referenced to either Vcc or Vss.Consequently the effective DC value of the wave willbe tied to one of these rails.

    The wave is attenuated around the effective DCcomponent of the waveform, but the reference doesnot change accordingly. Hence the clock trigger pointbetween various clock load points is very sensitive todistortion and attenuation.

    TxVss

    Vss Rx2

    Long lineVss Rx1

    Short line

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    Differential Signaling Any signal can be considered a loop is completed by two wires. One of the wires in single ended signaling is the ground plane Differential signaling uses two conductors

    The transmitter translates the single input signal into a pairof outputs that are driven 180 out of phase.The receiver, a differential amplifier, recovers the signal as the differencein the voltages on the two lines.

    Advantages of differential signaling can be summed up as follows

    Differential Signaling is not sensitive to SSO noise.A differential receiver is tolerant of its ground moving around.If each wire of pair is on close proximity of one and other. electromagneticinterference imposes the same voltage on both signals. The differencecancels out the effect.Since the AC currents in the wires are equal but opposite and proximal,radiated EMI is reduced.

    Signals passing from one board to another are not subject to the local grounddisturbances.As frequencies increase beyond 1GHz, up to 80% of the signal may be lost,but difference still crosses 0 volts.

    There are still loss issues for differential signaling but only come into play in high losssystem. Most single ended systems assume approximately 15% channel loss.

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    Differential Signaling - Cons

    The cost is doubling the signal wires, butthis may not be so bad as compared toadding grounds to improve single endedsignaling.

    Routing constraint: Pair signals need tobe routed together.Differential signal have certain

    symmetry requirements that may poserouting challenges.

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    Differential Signal Parameters

    Voltage on line 1 = a

    Voltage on line 2 = b Differential voltage d = a-b Common mode voltage c= (a+b)/2 Odd mode signal, o = (a-b)/2

    Even mode signal, e = (a+b)/2 Signal on line 1 a = e+o Signal on line 2 b = e-o Useful relations; o = d/2; e = c

    Line 1 Line 2

    Reference

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    Propagation Terms to Consider

    Differential mode propagationCommon mode propagationSingle ended mode (uncoupled)

    propagationThis is when the other line is not drivenbut terminated to absorbed reflections.

    Transmission line matrixes will reflectthese modes.

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    Differential Microstrip Example

    Z0 Zse:=

    Sse .0000ns

    ft=Sse L00C00:=Zse .00000=Zse

    L00

    C00:=

    Sc .1111ns

    ft=Sc L00 L00

    +( ) C00C00

    ( )

    :=Zco mm .00000

    =Zcomm

    L00 L00+

    C00C00:=

    Sd .0000ns

    ft=Sd L00L00( ) C00C00+( ):=

    Zdiff .11111=Zdiff 0L00L00

    C00C00+:=

    inductance and

    capacitance matrixes

    C00

    C00

    C00

    C00

    L00

    L00

    L00

    L00

    Transmission

    line

    C00 C00:=C00 C00:=C00 .000000000-00

    farad

    in:=C00 .000000000

    -11farad

    in:=

    L00 L00:=L00 L00:=L00 .000000000-0

    henry

    in:=L00 .000000000-0

    henry

    in:=

    SE: single ended = uncoupled

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    Differential Impedance

    Coupling between lines in a pair alwaysdecreases differential impedanceDifferential impedance is always less

    that 2 times the uncoupled impedanceDifferential impedance of uncoupled

    lines is 2 times the uncoupled impedance.

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    Propagation Velocities

    For TEM structures, (striplines)Differential mode, Common Mode, andsingle ended velocities are the same

    For Non TEM and Quasi-TEM structures

    (microstrip)Differential mode, Common Mode, andsingle ended velocities and impedances arenot the same.

    Common mode can be converted todifferential mode at a receiver and result ina differential signal disturbance.

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    Example of Common Mode

    Line 1 and line 2 have the same DC offset.

    This is DC common mode.It can be defined as an average DC for timeduration of many UI cycles value as well.

    Line1 and line 2 have the same AC offset

    This is AC common mode AC common mode also result from time

    differences (skew) between signal on line 1and line 2. This can result in AC common modeand differential signal loss. The following slide will be used to clarify the

    above

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    Differential Signaling Basics

    For long channels, at GHz frequencies, signaltend look like sine waves.

    The artificial offset common to line 1 and 2has an average of 1 and varies around thataverage by +/-0.1 in a period manor.

    Voltages a and b are respective of signals on lines and0 0

    We will use a GHz sine wave for the signal and offset defined below0

    offseti .0 modti

    ns

    0

    f ns,

    .0+:= ramp wave centered around 0

    ai sin 0 f ti( ) offseti+:= bi sin 0 f ti( ) offseti+:=

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    Individual signalsPlot individual line voltages and offset voltage

    0 .111 .000 .00 .000 .000 00

    .000

    .000

    0

    .000

    .0000

    ai

    bi

    offset i

    ti

    ns

    Devices need to have enough common mode dynamic voltage rangeto receive or transmit the waveforms. In this case the signalsswing between -0.1 and 2.1.

    The sine wave amplitude is 1 and peak to peak is 2. Signal a and b is what would be observed with 2 oscilloscope probes

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    Differential Mode Signal

    0 .111 .000 .00 .000 .000 00

    0

    0

    0

    0

    a b

    t

    ns

    Plot Differential voltage

    The differential amplitude is 2 and peak to peak is 4which is 2 times the individual signal peak to peakamplitude.

    Notice the distortions are gone.

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    Common Mode Signal

    The DC common mode signal is 1 The AC common mode signal is .2 v peak to peakSome may specifications may call this 0.1 v peak from the DCaverage

    We will add this common mode to the signals a and b

    Plot common mode voltage

    0 0 0 0 0 0.11

    .11

    0

    .00

    ai bi+

    0

    ti

    ns

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    Add 150 ps skew to signal b

    Plot individual line voltages and offset voltage

    0 .111 .000 .00 .000 .000 00

    .000

    .000

    0

    .000

    .000

    0

    ai

    bi

    offseti

    ti

    ns

    Waveforms do not look so good. We even have what appears to be non-monotonic

    behavior.

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    Differential signal looks OK

    0 .111 .000 .00 .000 .000 00

    0

    0

    0

    0

    a b

    t

    ns

    Plot Differential voltage

    max a b( ) min a b( ) .0000=

    However we lost differential signal amplitude. It used to be 4 peak to peak and now is

    3.562.

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    Common mode measurements are different

    0 0 0 0 0 0

    .00

    0

    .00

    0

    ai bi+

    0

    ti

    ns

    Plot common mode voltage

    meana b+

    0

    0= maxa b+

    0

    mina b+

    0

    .1111=

    max meana b+

    0

    max

    a b+

    0

    mean

    a b+

    0

    min

    a b+

    0

    ,

    .0000=

    Average is still 1. Peak to peak is 0.944 but peak is 0.504 AC common mode signals can be converted to differential

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    PWB structures that introduce Skew

    An escape froma BGA orconnector pinsintroduces

    skew

    This is anexample of

    skewcompensation

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    Bends introduce skew

    Back to backbendscompensate for

    skew fromfrequenciesbelow 2 GHz.

    Back to backbendscompensate for

    skew fromfrequenciesbelow 2 GHz.

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    More Terms: Balanced and Unbalanced

    Good Agilent Technologies article on balance

    and unbalanced signalinghttp://we.home.agilent.com/upload/cmc_upload/tmo/d

    Unbalanced signaling in reference to ground

    Balanced signaling is referenced only to theother port terminal.

    If each channel is identical, then this suggests avirtual AC ground between the two terminals. It

    is often useful to allow this AC ground to be a DCvoltage to biasing devices.

    http://we.home.agilent.com/upload/cmc_upload/tmo/downloads/EPSG084733.pdfhttp://we.home.agilent.com/upload/cmc_upload/tmo/downloads/EPSG084733.pdf
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    Ethernet 10/100BASE-T example

    TN0

    TP050

    50

    50

    50

    TransformerFilter

    Common-mode choke

    Unbalanced Balanced

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    Low Voltage Differential Signaling: LVDS 200MHz 500 MHz Range

    Published by IEEE in 1995 Lacks robustness for GHz Signaling Well suite distributing system clocks Good noise margin Common mode impedance has wide range provide

    buffer design flexibility Differential impedance is optimize around 100 Differential receiver switching thresholds are

    tighter than for single ended logic.

    Most device require external termination and biasresistors Does not have capacitance or package spec. This

    severely limits GHz operation

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    Current Mode Logic Emerging technology

    No real spec yet but can infer operation fromspecs like PCI Express , Infiniband, USB,SATA, etc. Tx and Rx lines are separate

    The Tx driver steers current between thedifferential terminals AC coupling between Tx and Rx with a series

    capacitor provides common mode designflexibility Termination is in buffers. This may require

    compensation or a band gap reference toinsure a tight resistance range.

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    Example of Simple CML Differential Behavioral Circuit

    Vcc

    Vss

    I_source

    r_termn,C_term

    r_termp,C_term

    0 00 00 000

    0

    Data Pulses

    0 00 00 000

    .11

    0

    Data Waves

    wave t( ) 0 epulse t( )

    0

    per

    ns:=

    Wavep t( )

    Wavep t( ) 0r_termn balancep

    Waven t td( ) 0

    Waven t td( )r_termn balancen

    PositiveTerminal

    NegativeTerminal

    This exponentdetermines wave

    shape

    This switchtime offset

    Balance betweenfor FET switch

    2

    nd lectur

    e

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    Example of Sensitivities: I, balance, C

    Vcc

    I_source

    More prominentfor faster edges

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    Example of Sensitivities: Slew, Skew, R

    Vcc

    I_source

    +/skew

    R/F slew

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    Serial Differential

    GHz transmission will have many UIs ofdata in transit on the interconnect atany points in time.Hence it becomes useful to think of this

    as serial data transmission.Often multiple single channels are

    ganged in parallel to achieve even higher

    data throughput.

    30

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    AC coupling issues

    Series capacitors can build up charge

    difference between differentialterminals for the following reasons.

    Unequal numbers of zero and ones

    Duty cycle (UI) distortion.The solution is to use a data code that isDC balanced.

    8B10B (8 bit 10 bit) with disparity is onesuch code

    Tight UI control is a basic requirementfor keeping the signal eye open

    31

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    Eye Diagram The eye diagram is a convenient way to represent

    what a receiver will see as well as specifyingcharacteristics of a transmitter. The eye diagram maps all UI intervals on top of one

    and other. The opening in eye diagram is measure of signal

    quality. This is the simplest type of eye diagram. The are

    other form which we will discuss later

    Eye Diagram

    32

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    Creating eye diagram

    Plot periodic voltage time ramps (sawtooth waves) on x verses the voltagewave on Y. Can be done with Avanwaves expression

    calculator and can be saved in aconfiguration file.

    33

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    Create ramp with expression builder

    Start ofrelative eyeposition

    Time of eyestartUnit Interval

    34

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    Copy Ramp to X Axis

    Use middle button to drag ramp toCurrent X-Axis

    35

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    Voltage and period volt-time ramp

    36

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    Clocking The one thing omitted in the suggests in the

    previous slides on eye diagrams was the chopfrequency.We assumed it was UI. This is simple for

    simulation. Time marches along and all signalsstart out synchronized in time. This is nottrue for real measurement since edges willsignificantly jitter and make it difficult todeterminate where the exact UI is positioned. Presently, there are basically two forms of

    GHz+ clockingEmbedded clockingForwarded clocking

    37

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    Embedded clocking

    This what is used in Fiber Channel, Gigabit

    Ethernet, PCI Express, Infiniband, SATA,USB, etc. The clock is extracted from the data

    There is requirement that data transitions are ata minimum rate. 8B/10B guarantees this. Wediscuss this in more detail later.

    A phase interpolator is normally used to extractthe clock from the data. We discussed the phaseinterpolator in the clocking class. The phaseinterpolator is tied to the PCI Express-like jitterspec: Median and Jitter outlier.

    38

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    Jitter Median and Outlier Spec

    Eye opening is defined from a stable UI.

    Jitter median used to determine a stable UIIt is used as a reference to determine eye opening Jitter Outlier is used to guarantee limits of

    operation

    Jitter Median

    Jitter outlier

    Eye diagram

    UI

    39

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    Forwarded Clocking The Tx clock is sourced and received down

    stream. The clock is a Tx data buffersynchronized with the Tx data bits. A synchronization or training sequence on a

    data line is used to adjust the receiver clockso that it is in phase synchronization with thedata. The caveat is that the actual data clock lags

    the real data by a few cycles. The whole idea is that the jitter introduced

    over these cycles would be smaller than thejitter associated with two the PLLs used toprovide base clocks for an embedded clockdesign.

    40

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    Aspects of AC coupling

    We will explore issues with AC coupling with a

    simulation example. First we will create a simple CML differential

    model Next we will tie it to a differential

    transmission line and a terminator. Assignment 7 is to reproduce these effects

    with a HSPICE program. The outputAvanwaves with a power point story summary

    what you will hand in. The basis for our work will be last semesters

    testckt.sp deck

    41

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    Behavioral Data Model Example

    12 bit of repeating data

    010101 001001 v(t) data

    UI = 500 psTr=Tf=100ps

    .).)*(( tve

    Rterm=50Cterm=0.25pf

    Vswing = 800 mV

    I=Vswing/(50||50)/2

    Wave shape*

    * Refer to first course

    3rdle

    ctur

    e

    42

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    AC coupled Differential Circuit

    nH0

    nH0

    nH0

    nH0

    . pf00

    . pf00

    . pf00 . pf00

    ma11

    n11

    n00

    .00gHz

    / mV1111

    Vcc

    +

    -

    VCR+

    -

    VCR

    00

    00

    0000

    AC coupling caps arenormally larger, butare scaled down to

    illustrate commonmode effects

    0 to 1V

    43

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    Top Level HSPICE CODE

    Modified

    Convenience

    44

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    No initial conditions on DC blocking caps 300 ns of simulation time! Cblkn pkg2_nb pkg2_n 1nf $ic=400mv

    Cblkp pkg2_pb pkg2_p 1nf $ic=400mv 101010 101010 repeating 12 bit pattern

    Differential

    Single ended

    Reproduce this at

    package 2 (receiver)

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    N l l fi d

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    Not completely fixed

    Initial voltage for D+ and D+ is not 0 so

    there is a step response when the wavereaches the receiver.We can fix this by multiplying both n

    and p control waves for the VCR(voltage controlled resistor) by 0 forthe first cycle.

    This forces the DC solution at the otherend of the line to 0 volts differential.

    47

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    Insure both legs start at same voltage

    Qualifying voltage

    Qualifying voltagep control voltage

    Qualifying voltagen control voltage

    48

    R lt P tt d

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    Results Pretty good

    Differential

    Single ended

    Reproduce this at

    package 2 (receiver)

    May have to ignore

    first 1-2 cycles

    49

    l h b

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    Now lets change bit pattern 100000001010

    The pattern creates a DC charge to be built up in thecap The solution is to create a code that has equal

    amount of 1s and zeros. This is the rational for 8bit10 bit (8b10b) coding

    Differential

    Single ended

    Reproduce this atpackage 2 (receiver)

    50

    C Off

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    Crossing Offset

    The crossing offset is the horizontal

    line that is in the vertical center of theeye and it should be at 0 volts for adifferential signal.

    The amount of offset is the average DCvalue. A simple approximation is oneminus the ratio of ones to zeros times

    the received vswing/2.This does not included edge shape effects

    51

    R f 5 d 6

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    Repeat patterns of 5 ones and 6 zeros

    000

    0 00

    0 .1111=

    Approx. offset

    Reproduce this atpackage 2 (receiver)

    Hint:start eyediagramat 200 ns

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    8b/10b encoding and background

    Courtesy ofScott Gardiner, Intel

    53

    8b/10b Si l S h

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    8b/10b - Simple Scheme

    The encoding is comprehended in a set oftables which conform to a set ofpredetermined rules

    Helpful Hint: Complete tables that give all

    the literal 10b encodings do exist- and theycomprehend all of the encoding rules

    8 bits are encoded into 10 bits

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    8b/10b Ch t C ti s

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    8b/10b Character Conventions Both Data Characters and Special Control

    Characters exist; (nomenclature: D.a.b &K.a.b)D/K = Signifies Data or Controla = 5 bit block to be encoded

    b = 3 bit block to be encoded Set of Available Data and ControlCharacters

    Data (D.a.b)

    D0.0-D31.0, D0.1-D031.1, .... D0.7 D31.7All 256 Possible 8-bit Data characters (00 through FFHEX)

    Control (K.a.b)K28.0 K28.7, K23.7, K27.7, K29.7, K30.7

    56

    8b/10b DC b l i & Di it

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    8b/10b - DC balancing & Disparity

    Never more than 5 consecutive 1s or 0sallowed in a row (consecutively)..i.e. themaximum run rate is 5 to maintain a DCbalanced transmission.

    This guarantees the lowest frequency tobe 1/10 of the max frequency. i.e. only 1decade data bandwidth required.

    With 8b/10b, either positive (RD+) ornegative (RD-) disparity encoding ispossible

    57

    8b/10b Disparity

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    8b/10b - Disparity

    Disparity is the difference between the

    number of ones and zeros...positive andnegative disparity refer to an excess of onesor zeros respectively.

    Note: neutral disparity is said to occur whenRD+ and RD- encoding are identical-meaningthey will eachhave the same number of onesand zeros (there are some exceptions)

    A given sub-block or symbol can have an actualdisparity number of either a zero (neutral), +2or 2, though the Running Disparity is said onlyto be Positive, Negative or Neutral.

    58

    8b/10b Running Disparity

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    8b/10b Running Disparity

    The Running or Current Disparity (a

    binary value of + or -) is tracked by theTX/RX and is computed at every sub-block boundary and at each symbol

    boundary. The value from one sub-block or symbol

    is used with that of the next sub-block

    or symbol to give a running orcurrent status.

    59

    8b/10b Running Disparity Algorithm

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    8b/10b Running Disparity Algorithm For a given encoding of a byte, the starting disparity

    is what existed at the end of the previous symbol

    The running disparity is then calculated first for the6 bit sub-block, comprehending the startingdisparity value;

    The 6 bit sub block disparity valueis then used asthe starting disparity when the running disparitycalculated for the 4 bit sub-block

    The running disparity for the entire 10 bit symbol isnow the sameas the running disparity found at theend of the 4 bit sub-block (and the runningdisparity at the beginning of the next symbol /6 bitsub-block is the sameas that found at the end ofthe this symbol)

    Again, a given sub-block or symbol can have an actualdisparity number of either a zero (neutral), +2 or 2,though the Running Disparity is only said to bePositive, Negative or Neutral.

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    b/ b l l l h

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    8b/10b - Running Disparity Calculation Algorithm:

    Assumptions: The 8b to 10b encoding has

    already been done; A current disparity value isalready assumed Process: Calculate the disparity for the

    leftmost 6 bits first, keeping in mind the

    current disparity value before entering thealgorithm. Then calculate the disparity for therightmost 4 bits keeping in mind the disparityvalue determined after analyzing the previous 6bits. The disparity for both the 6-bit and the4-bit blocks should be calculated as follows:

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    8b/10b R i Di it C l l ti M th d

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    8b/10b - Running Disparity Calculation Method Method:

    If # of 1s > 0s

    Disparity = Positive (1)Else if # of 0s > 1s

    Disparity = Negative (0)Else if 6-bit = 000111

    Then Disparity = Positive (1)

    Else if 6-bit = 111000Then Disparity = Negative (0)

    Else if 4-bit = 0011Then Disparity = Positive (1)

    Else if 4-bit = 1100Then Disparity = Negative (0)Else Disparity = Disparity (if none of the above, then the disparity

    value doesnt change)

    Note: Assuming a encoding, more1s across the entire 10b code

    yields positive

    disparity, more 0s yields negative

    disparity, and even #s of 1s and

    0s yields neutral disparity

    (i.e. disparity is the same as it wasbefore).

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    8b/10b Di it & E di E l

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    8b/10b - Disparity & Encoding Example:

    Transmitter keeps running track of current

    disparity (it is either RD, RD+ or neutral)Neutral means the disparity tracker keeps theprevious RD- or RD+ value

    A Running Disparity of RD+ is always followedby an RD- encoding and vice versa

    If Running Disparity is RD+, the following isencoded for the data byte F1:

    HGF EDCBA abcdei fghj11110001 1000110111(RD- encoding)

    If Running Disparity is RD-, the following isencoded for the data byte F1:

    HGF EDCBA abcdei fghj111 10001 100011 0001(RD+ encoding)

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    8b/10b - Disparity & Encoding Example:

    Note that the number of ones and zeros in the

    currently chosen encoding works to balance out theoffset in the number of ones and zeroes (tracked bythe Running Disparity value) from the previousencoding

    I.E. : Dont confuse the definition of Positive Disparity with

    the RD+ encoding choice!Positive Disparity means there is a current running total ofmore onesthanzeros!Thus, an RD+ encoding generally has more zeros thanones!

    Also note that it is possible that the 4-bit sub-block

    of a RD- or RD+ symbol encoding can yield a negativeor positive disparity, respectively thus forcing morethan one RD- encoding to be used consecutively

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    Summary: Example conversion

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    Summary: Example conversion

    HEX Data Byte (8b) to be Encoded

    OR

    Binary Data Byte (8b) to be Encoded

    10b Encoded symbol (RD-) 10b Encoded symbol (RD+)

    F1

    100011 0111 100011 0001

    1111 0001

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    P ssibl P tt ns

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    Possible Patterns Repeating Comma [K28.5] Pattern (RD- followed by

    RD+):001111 1010 110000 0101 001111 1010 110000 0101(RD-) (RD+) (RD-) (RD+)

    6 bit encoding starts with an RD- and uses an positivedisparity encoding.6 bits encoding yields an RD+..4-bitencoding starts with a RD +4-bit encoding picks a negative

    (or neutral encoding) and thus yields a neutral and thuskeeps the RD+. Checks out.

    Low Frequency Pattern?? (D30.0 (RD- followed byRD-)

    011110 0100 011110 0100 011110 0100 011110 0100

    (RD-) (RD-) (RD-) (RD-)100001 1011 100001 1011 100001 1011 100001 1011

    (RD+) (RD+) (RD+) (RD+)

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    Possible Patterns

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    Possible Patterns High transition density/frequency pattern:

    D21.5 (RD- followed by RD+)

    101010 1010 101010 1010 101010 1010 101010 1010(RD-) (RD+) (RD-) (RD+)

    Low transition density pattern:K28.7 (RD-) & D24.3 (RD+) (although K28.7 is reserved....)

    001111 1000 001111 1000 001100 1100 001111 1000 001100 1100(RD-) (RD+) (RD-) (RD+)D24.6 (RD-) & D24.6 (RD+)1100110110 0011000110 1100110110 0011000110

    (RD-) (RD+) (RD-) (RD+)

    Composite pattern:D30.7 (RD-) & D13.7 (RD-)011110 0001 101100 1000 011110 0001 101100 1000

    (RD-) (RD-) (RD-) (RD-)

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    References

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    References

    Infiniband Architecture Release Specification 1.0

    October 24, 2000, Volume 2, Section 5.2x (beginning with page 66) Franaszek & Widmer (IBM) Patent # 4,486,739

    December 4, 1984, Byte Oriented DC Balanced 8B/10B PartitionedBlock Transmission Code

    3GIO Architecture Specification- Key Developer Draft

    August 21, 2001, Appendix C, pg148-154 ANSI X3.230-1994, clause 11 (and also IEEE 802.3z, 36.2.4).

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    Other sources of common mode

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    Other sources of common mode

    A DC voltage will build up across the blockingcapacitor if the charge and discharge is not equal.

    We have see this can happen if the number of bits isunbalance.

    Another source of imbalance is possible if the dutycycle of the one and zeros is not 50%.

    This can happen in two waysThe time for a one differs from that of a zero. This can becaused by edge jitter.The rising time and falling time are miss matchedOn the next slide we will take our example with101010101010 pattern and change the rise time to 50 ps andfall time to 150 ps for the single ended signals

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    CM offset from tr/tf mismatch

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    CM offset from tr/tf mismatch

    Reproduce this atpackage 2 (receiver)