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Willy Sansen KULeuven, ESAT-MICAS Leuven, Belgiumocw.snu.ac.kr/sites/default/files/NOTE/7044.pdf ·...

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59
Willy Sansen 10-05 041 Noise performance of elementary transistor stages Willy Sansen KULeuven, ESAT-MICAS Leuven, Belgium [email protected]
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  • Will

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    Noi

    se p

    erfo

    rman

    ce

    of e

    lem

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    Will

    y Sa

    nsen

    KU

    Leuv

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    SAT-

    MIC

    AS

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    elgi

    umw

    illy.

    sans

    en@

    esat

    .kul

    euve

    n.be

  • Will

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    nsen

    10-0

    5 0

    42

    SNR

    and

    SN

    DR

    v OU

    T

    v IN

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    % d

    isto

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    n

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    dis

    tort

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    SN

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  • Will

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    nsen

    10-0

    5 0

    43

    Tab

    le o

    f con

    tent

    s

    �D

    efin

    ition

    s of

    noi

    se�

    Noi

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    �N

    oise

    of a

    follo

    wer

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    of a

    cas

    code

    �N

    oise

    of a

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    rent

    mirr

    or�

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    entia

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    r�

    Cap

    aciti

    ve n

    oise

    mat

    chin

    g

  • Will

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    nsen

    10-0

    5 0

    44

    Noi

    se v

    ersu

    s tim

    e

    t t

    v N v N2

    v N2

    is th

    e av

    erag

    e no

    ise

    pow

    er

    Ref

    . Van

    der

    Ziel

    (Pre

    ntic

    e H

    all 1

    954,

    Wile

    y 19

    86),

    Ott

    (Wile

    y 19

    88)

  • Will

    y Sa

    nsen

    10-0

    5 0

    45

    Noi

    se v

    ersu

    s fre

    quen

    cy

    v N2

    f

    dvN

    2Noi

    se d

    ensi

    ty V

    2 /H

    z

    whi

    te n

    oise

    1/f n

    oise

    f 1df

    f 2

    v 12

    =

    v N2

    =

    �dv N

    2df

    =

    (f2-

    f 1) d

    v N2

    f 1

    f 2V R

    MS

    Inte

    grat

    ed n

    oise

    V RM

    S/�H

    z

  • Will

    y Sa

    nsen

    10-0

    5 0

    46

    Noi

    se o

    f a r

    esis

    tor

    is th

    erm

    al n

    oise

    Rdv R

    2

    Rdi

    R2

    dvR

    2 =

    4kT

    R d

    f

    is

    whi

    te

    for R

    = 1

    k����

    dvR

    2=

    4 nV

    RM

    S/

    Hz

    depe

    nds

    on T

    , not

    on

    I R

    at T

    = 3

    00 K

    or 2

    7oC

    diR

    2 =

    =

    d

    f i

    s w

    hite

    dvR

    2

    R2

    4kT R

  • Will

    y Sa

    nsen

    10-0

    5 0

    47

    Inte

    grat

    ed N

    oise

    of R

    esis

    tor

    -1

    v out

    dvR

    s2

    v in

    RS

    CL

    BW

    f

    A

    dvR

    s2=

    4kT

    RS

    dfB

    W =

    1��

    RSC

    L

    �v R

    s2=

    dvR

    s2

    1 +

    (f/ B

    W) 2

    0

  • Will

    y Sa

    nsen

    10-0

    5 0

    48

    Inte

    grat

    ed N

    oise

    of R

    esis

    tor

    -2

    BW

    � 2B

    Wn

    f

    A

    �v R

    s2=

    dvR

    s2

    1 +

    (f/ B

    W) 2

    0

    BW

    �dx

    1 +

    x 2

    0

    �� 2

    ==

    v Rs2

    =kT C

    LC

    L =

    1pF

    vR

    s= 6

    5 �V

    RM

    S

    v Rs2

    =4k

    T R

    SBW

    � 2df

  • Will

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    nsen

    10-0

    5 0

    49

    Noi

    se d

    ensi

    ty v

    s int

    egra

    ted

    nois

    e

    BW

    BW

    n

    f

    A

    �v R

    s2=

    dvR

    s2

    1 +

    (f/ B

    W) 2

    0

    �=

    kT CL

    dvR

    s2=

    4kT

    RS

    df

    Noi

    se d

    ensi

    ty (

    V2/H

    z) ~

    RS

    (or 1

    /gm

    )

    Inte

    grat

    ed n

    oise

    (VR

    MS)

    ~ 1

    /CL

  • Will

    y Sa

    nsen

    10-0

    5 0

    410

    A r

    esis

    tor

    also

    has

    1/f

    nois

    e

    Rdv R

    f2dv

    Rf2

    = V

    R2

    for R

    = 1

    k���w

    ith 2

    0 �

    ‘s o

    f 50 ����

    and

    1 �m

    wid

    e an

    d V R

    = 0.

    1 V

    dvR

    f2=

    16

    nVR

    MS/

    Hz

    at 1

    Hz

    df fis

    1/f

    KF R

    R�

    AR

    KF R

    Si�

    2 1

    0 -2

    1Sc

    m2

    KF R

    poly

    � 10

    KF R

    Si

    V R+ -

    Ref

    . Van

    dam

    me,

    ESS

    DER

    C ‘0

    4

  • Will

    y Sa

    nsen

    10-0

    5 0

    411

    Noi

    se o

    f a d

    iode

    is sh

    ot n

    oise

    I D

    diD

    2

    diD

    2 =

    2q I D

    df

    is

    whi

    te

    depe

    nds

    on I D

    , not

    on

    T

    for I

    D=

    50 �

    Adi

    D2

    = 4

    pAR

    MS/

    Hz

    q =

    1.6

    10-1

    9C

  • Will

    y Sa

    nsen

    10-0

    5 0

    412

    A d

    iode

    als

    o ha

    s 1/f

    nois

    e

    diD

    f2 =

    I D

    For a

    dio

    de o

    f AD

    = 5

    x 2

    �m

    = 1

    0 �m

    2an

    d I D

    = 0.

    1 m

    A

    diD

    f2=

    1 nA

    RM

    S/

    Hz

    at 1

    Hz

    df fis

    1/f

    KF D A

    D

    KF D

    � 10

    -21

    Acm

    2

    I D

    diD

    f2

  • Will

    y Sa

    nsen

    10-0

    5 0

    413

    Noi

    se o

    f a M

    OST

    r DS

    g mv G

    S

    v GS

    + -

    v out

    + -

    v in+ -

    diD

    S2

    dvG

    2 =

    4kT

    RG

    df

    dvG

    2R

    G

    diD

    S2 =

    d

    f = 4

    kT

    gm

    dfR

    CH

    4kT

    2 3R

    ef. V

    an d

    erZi

    el, P

    rent

    ice

    Hal

    l 195

    4, W

    iley

    1986

    .

  • Will

    y Sa

    nsen

    10-0

    5 0

    414

    MO

    ST: e

    quiv

    alen

    t inp

    ut n

    oise

    : w

    hite

    dvie

    q2 =

    4kT

    (Ref

    f) d

    f

    R

    eff=

    + R

    G

    r DS

    g mv G

    S

    v GS

    + -

    v in+ -dvie

    q2R

    G

    v out

    + -

    Hi F

    req.

    : di

    ieq2

    = (

    CG

    S

    )2dv

    ieq2

    is

    corr

    elat

    ed

    g m2/3

  • Will

    y Sa

    nsen

    10-0

    5 0

    415

    Poly

    Gat

    e re

    sist

    ance

    rG

    in a

    MO

    ST

  • Will

    y Sa

    nsen

    10-0

    5 0

    416

    Subs

    trat

    e re

    sist

    ance

    s rB

    in a

    MO

    ST Ref

    . Cha

    ng, K

    luw

    er19

    91

  • Will

    y Sa

    nsen

    10-0

    5 0

    417

    Noi

    se b

    y th

    e B

    ulk

    resi

    stan

    ce

    r DS

    g mv G

    S

    v GS+ -

    g mbv

    BS

    v BS

    + -

    v inG+ -dvrG

    2R

    G

    v inB

    =0

    + -

    dvrB

    2R

    B

    r DS

    g mv G

    S

    v GS+ -

    v in+ -dvie

    q2R

    Gdv

    ieq2

    = 4

    kT (R

    eff)

    df

    Ref

    f=

    + R

    G+

    RB

    (n-1

    )2g m2/

    3

    (n-1

    ) = C

    D/C

    ox=

    g mb/

    g m

  • Will

    y Sa

    nsen

    10-0

    5 0

    418

    Noi

    se b

    y th

    e So

    urce

    res

    ista

    nce

    r DS

    g mv G

    S

    v GS+ -

    v in

    + -dvie

    q2R

    G

    dvie

    q2 =

    4kT

    (Ref

    f) df

    Ref

    f=

    + R

    G+

    RS

    + R

    B(n

    -1)2

    g m2/3

    RS

    Noi

    se o

    f RS

    = no

    ise

    RG

  • Will

    y Sa

    nsen

    10-0

    5 0

    419

    Noi

    se b

    y So

    urce

    res

    isto

    r R

    i out

    diM

    2

    diou

    t2

    Rdi

    R2

    v in g

    m R

    >>

    1

    i out

    =v i

    n R

    diM

    2 =

    4kT

    2/3

    g m d

    fdi

    outM

    2 = (

    g mR

    )2di

    M2

    diR

    2 =

    df

    4kT R

    diou

    tR2

    = di

    R2

    diou

    t2 =

    4kT R

    (

    +

    1 )

    df �

    2/3

    g mR

    4kT R

    df

    dvin

    2 =

    4kT

    R d

    f

  • Will

    y Sa

    nsen

    10-0

    5 0

    420

    MO

    ST: e

    quiv

    alen

    t inp

    ut n

    oise

    : E

    xerc

    ise

    dvie

    q2 �

    4kT

    (

    ) d

    f

    r DS

    g mv G

    S

    v GS

    + -

    v in+ -dvie

    q2

    v out

    + -

    g m2/3

    dvie

    q2

    � ?

    for I

    DS

    = 65

    �A

  • Will

    y Sa

    nsen

    10-0

    5 0

    421

    dvie

    qf2

    =

    r DS

    g mv G

    S

    v GS

    + -

    v in+ -dvie

    qf2

    RG

    WL

    Cox

    2

    KF F

    v out

    + -

    df fpM

    OST

    KF F

    � 1

    0-32

    C2 /

    cm2

    nMO

    STK

    F F �

    4 1

    0-31

    C2 /

    cm2

    pJFE

    TK

    F F �

    10-

    33C

    2 /cm

    2

    W &

    L in

    cm

    ; Cox

    inF/

    cm2

    MO

    ST: e

    quiv

    alen

    t inp

    ut n

    oise

    : 1/

    f noi

    se

  • Will

    y Sa

    nsen

    10-0

    5 0

    422

    Noi

    se v

    s cur

    rent

    : co

    rner

    freq

    uenc

    y

    dvie

    q2

    ff c

    hif c

    lo

    I DSl

    ow

    hite

    noi

    se ~

    ~

    I DSh

    i

    Cor

    ner f

    requ

    ency

    ~ g

    m

    1/f n

    oise

    ~

    g m1WL

    WL1

  • Will

    y Sa

    nsen

    10-0

    5 0

    423

    Noi

    se v

    s cur

    rent

    : ex

    erci

    se f c

    dvie

    q2

    ff c

    hif c

    lo

    I DSl

    ow

    hite

    noi

    se ~

    I DSh

    i

    1/f n

    oise

    g m1

    Ex. :

    fc?

    For I

    DS

    = 65

    �A

    ; K

    ’ n=

    60 �

    A/V

    2an

    d L

    = 1 �m

    (0.3

    5 �m

    pro

    cess

    )f c

    � 37

    0 kH

    z

  • Will

    y Sa

    nsen

    10-0

    5 0

    424

    Noi

    se se

    en a

    t the

    Bul

    k

    dvie

    q2dv

    ieqb

    2

    dvie

    q2 =

    4kT

    (

    ) d

    f

    dvie

    qf2

    =

    WL

    Cox

    2

    KF F

    df f

    g m2/3

    n-1

    = g mg m

    b

    dvie

    qb2

    = 4

    kT (

    )

    df

    dvie

    qfb2

    =

    WL

    Cox

    2

    KF F

    df f

    2/3

    g m g mb2

    g m2

    g mb2

  • Will

    y Sa

    nsen

    10-0

    5 0

    425

    Noi

    se o

    f a B

    ipol

    ar tr

    ansi

    stor

    r og m

    v BE

    +vB

    E

    -

    v out

    + -

    v in+ -

    diC

    2

    dvB

    2 =

    4kT

    r Bdf

    dvB

    2r B

    diB

    2 =

    2q

    I Bdf

    diC

    2 =

    2q

    I Cdf

    diB

    f2 =

    A

    EB

    KF B

    I Bdf f

    KF B

    � 1

    0-21

    Acm

    2

    r �di

    B2

    C E

    Ref

    . Van

    der

    Ziel

    (Pre

    ntic

    e H

    all 1

    954)

  • Will

    y Sa

    nsen

    10-0

    5 0

    426

    Bip

    olar

    tran

    s.: e

    quiv

    alen

    t inp

    ut n

    oise

    dvie

    q2 =

    4kT

    (Ref

    f) d

    f

    R

    eff=

    + R

    B +

    RE

    r og m

    v BE

    v out

    + -

    g m1/2

    diie

    q2 =

    di B

    2 =

    2q

    I Bdf

    + v B

    E

    -

    v in+ -dv i

    eq2

    RB

    r �di

    ieq2

  • Will

    y Sa

    nsen

    10-0

    5 0

    427

    Tab

    le o

    f con

    tent

    s

    �D

    efin

    ition

    s of

    noi

    se�

    Noi

    se o

    f an

    ampl

    ifier

    �N

    oise

    of a

    follo

    wer

    �N

    oise

    of a

    cas

    code

    �N

    oise

    of a

    cur

    rent

    mirr

    or

    �N

    oise

    of a

    diff

    eren

    tial p

    air

    �C

    apac

    itive

    noi

    se m

    atch

    ing

  • Will

    y Sa

    nsen

    10-0

    5 0

    428

    Noi

    se o

    f an

    ampl

    ifier

    with

    act

    ive

    load

    v out

    M1M2

    v in

    CL

    dv22

    dv12

    dvB

    2

    +

    If d

    v B2

    is

    negl

    igib

    le :

    diou

    t2 =

    gm

    12 d

    v 12

    + g m

    22 d

    v 22

    dvie

    q2 =

    dv 1

    2 +

    dv22

    ()2

    g m1

    g m2

    dvie

    q2 =

    dv 1

    2 (1

    +

    )g m

    1

    g m2

    Smal

    l gm

    2: s

    mal

    l (W

    /L) 2

    or l

    arge

    (V G

    S-V

    T ) 2

    dvie

    q2

    V B

  • Will

    y Sa

    nsen

    10-0

    5 0

    429

    1/f N

    oise

    of a

    mpl

    ifier

    with

    act

    ive

    load

    v out

    M1

    M2

    v in

    CL

    dv2f

    2

    dv1f

    2

    dvB

    2

    +

    If dv

    B2

    is

    negl

    igib

    le :

    dvif2

    = d

    v 1f2

    +dv

    2f2 (

    )2

    g m

    1

    g m2

    dvif2

    = d

    v 1f2

    [1 +

    (

    )2

    ()2

    ]

    dvif2

    has

    min

    imum

    at

    g m1

    g m2

    dv1f

    dv2f

    dvif2

    = d

    v 1f2

    [1 +

    (

    )2]

    KF 1

    KF 2

    L 2L1

    K’ 1

    K’ 2

    L 1op

    t= L

    2�

    10 L

    2th

    en d

    v if2

    = 2

    dv 1

    f2

    KF 2

    KF 1

    K’ 2

    K’ 1

    V B

  • Will

    y Sa

    nsen

    10-0

    5 0

    430

    Noi

    se fi

    gure

    of a

    n am

    plifi

    er

    v in+ -

    dvS2

    RS d

    i ieq2dv

    ieq2

    v out

    + -

    AR

    in=

    NF

    =

    =

    1 +

    NS

    + N

    A

    NS

    NA

    NS

    NF

    = 1

    + 4k

    T R

    S df

    dvie

    q2+

    RS2

    diie

    q2Vo

    ltage

    driv

    e N

    F ~

    Cur

    rent

    driv

    e N

    F ~

    RS1 RS

  • Will

    y Sa

    nsen

    10-0

    5 0

    431

    Res

    istiv

    e no

    ise

    mat

    chin

    g

    RS

    NF

    NS

    NA

    Rso

    pt

    =

    100

    r B=

    100 �

    Rso

    pt=

    dvie

    q2

    diie

    q2

    g m=

    3.8

    mS

  • Will

    y Sa

    nsen

    10-0

    5 0

    432

    Tab

    le o

    f con

    tent

    s

    �D

    efin

    ition

    s of

    noi

    se�

    Noi

    se o

    f an

    ampl

    ifier

    �N

    oise

    of a

    follo

    wer

    �N

    oise

    of a

    cas

    code

    �N

    oise

    of a

    cur

    rent

    mirr

    or�

    Noi

    se o

    f a d

    iffer

    entia

    l pai

    r�

    Cap

    aciti

    ve n

    oise

    mat

    chin

    g

  • Will

    y Sa

    nsen

    10-0

    5 0

    433

    Noi

    se o

    f an

    emitt

    er fo

    llow

    er

    i CE

    v INRS

    diie

    2dv

    ie2

    v OU

    T

    CL

    RT

    A

    dvA

    2

    diA

    2I T

    dvie

    q2

    dvie

    q2 =

    dv i

    e2 +

    dv A

    2 +

    (RS

    -)2

    diie

    2 +

    dvS2

    diT2

    1 g m

    diT2

    + di

    A2

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    deam

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  • Will

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