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ECEN474/704: (Analog) VLSI Circuit Design Fall spalermo/ecen474/lecture10_ee474_simple... · PDF file 2018. 3. 6. · Announcements & Agenda • Simple OTA Parameters • OTA w/ Cascode

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  • Sam Palermo Analog & Mixed-Signal Center

    Texas A&M University

    Lecture 10: Simple OTA

    ECEN474/704: (Analog) VLSI Circuit Design Fall 2018

  • Announcements

    • HW2 is due today

    • No class on Thursday Mar 8

    2

  • Announcements & Agenda

    • Simple OTA Parameters • OTA w/ Cascode Load & Tail Current

    Source

    • References • Razavi Chapters 4, 6, 9.8-9.11 • Sedra/Smith Section 9.5.5

    3

  • OpAmps and OTAs

    • High voltage gain • High input impedance • Voltage source output

    (low impedance) 4

    OpAmp OTA

    • High “voltage” gain • High input impedance • Current source output

    (high impedance)

  • Operational Transconductance Amplifier

    • Important Parameters • Differential Gain • Gain-Bandwidth Product • Common-Mode Input Range • Common-Mode Gain • Common-Mode Rejection

    Ratio (CMRR) • Power-Supply Rejection Ratio

    (PSRR) • Slew Rate

    5

    M1 M2Vi+ Vi-

    VDD

    VSS

    Rbias

    Itail

    M5 M6

    M3 M4

    CL

    Vo

  • OTA Differential Gain

    6

    M1 M2Vi+ Vi-

    VDD

    VSS

    Rbias

    Itail

    M5 M6

    M3 M4

    CL

    Vo

     

    idoutmo

    mmmm

    id outm

    m

    mid outmo

    id i

    id i

    vrgv gggg

    vrg g gvrgv

    vVvV

    1

    6521

    6 5

    1 2

    and design By 22

    2 and

    2 Let

     

      

      

     

      

     

    26

    1 1

    oo

    m outm

    id

    o DM gg

    grg v vA

     

  • TAMU-ELEN-474 2009 Jose Silva-Martinez

    - 7 -

    Frequency Response

    id1

    IB

    M1 M1

    v1

    id2

    iout id1

    0.5gmvd RXCX

    Vx

        gdndbndgpdbpgspX

    mpmpPX

    d XX

    Xm X

    CCCfactormillerCCC

    ggrrR

    V CSR RgV

    

     

    

    12

    /1/1|||| 1

    5.0

    001

    Magnitude

    gmRX

    1/RXCX

    VX

    Consider node VX

    v2

    2 dv

    2 dv

  • TAMU-ELEN-474 2009 Jose Silva-Martinez

    - 8 -

    Low Frequency Response

    0.5gmvd 1/gmp’CX

    Vx

    gmR0

    gmpvx

    CO

    Vo

    -0.5gmvd

    Ro

    Vout

    OPONO RRR 

    id1

    MP

    id1

    IB

    M1 M1

    v1

    id2

    iout VX

    MP’

     

    odmo

    mp x

    ompx d

    mo d

    mo

    Rvgv

    g R

    RgRvgRvgv

      

      

     

      

    1 222

    dv 2 dv

  • TAMU-ELEN-474 2009 Jose Silva-Martinez

    - 9 -

    Frequency Response

    0.5gmvd 1/gmp’CX

    Vx

    gmR0

    1/R0C0

    gmpvx

    CO

    Vo

    -0.5gmvd

    Ro

    Vout

    AV1

    AV2

    OPONO RRR 

    id1

    MP

    id1

    IB

    M1 M1

    v1

    id2

    iout VX

    MP’

       

       

       

      

       

       

     

       

      

     

      

     

        

       

       

      

       

      

    mp

    x

    mp

    x

    oo

    d omo

    mp

    xoo

    d omo

    oo

    omp

    mp

    x

    mpd m

    oo

    od mo

    g Cs

    g Cs

    CsR vRgv

    g CsCsR

    vRgv

    CsR Rg

    g Cs

    gvg CsR

    Rvgv

    1

    2

    1 1

    2

    1

    11 1

    1 2

    11

    1

    212 2 dv

    2 dv

  • OTA Gain-Bandwidth Product (GBW)

    10

    M

    m pm

    L

    oo po

    pmpo

    oo

    m DM

    C g

    C gg

    gg gA

    526

    26

    1

     

     

    

    

    ,

    node mirror"" theat and nodeoutput theat

    poles 2 have willcircuit The

    L

    m

    L

    oo

    oo

    m poDMdBDM C

    g C

    gg gg

    gAAGBW 126 26

    1 3 

      

       

      

     

     

    dominates and spaced widely are poles the Assuming po

  • OTA Common-Mode Input Range

    11

    • Common-mode input range set by transistor saturation conditions • Low-end set by tail current source

    saturation 1

    14

    14 2

    Tn

    oxn

    tail

    oxn

    tail SSGSDSATSSicm V

    L WC

    I

    L WC

    IVVVVV  

    • High-end set by differential pair saturation

    15

    5

    151 TnTp

    oxp

    tail DDTGSDDTocmicm VV

    L WC

    IVVVVVVV     

       

     

    15

    5

    1

    14

    2 TnTp

    oxp

    tail DDicmTn

    oxn

    tail

    oxn

    tail SS VV

    L WC

    IVVV

    L WC

    I

    L WC

    IV    

      

     

  • OTA Common-Mode Gain

    12

    • Ideally, common-mode perturbations are suppressed by the differential amplifier, i.e. Acm = 0

    • Finite common-mode gain exists due to amplifier asymmetries and finite tail current source impedance

    • Note transistor numbers are different from previous slides, as I borrow figures from Sedra/Smith text

    [Sedra]

  • OTA Common-Mode Gain

    13

    [Sedra]

    • Modeling the input transistors as a transconductance current source with a parallel output resistance

       

    icm

    m oSS

    oSS icms v

    g rR

    rR vv 

     

    1 1

    1

    12

    2

    SSicm

    o mcm

    SS

    icm o

    Rv iG

    R vi

    2 1

    2

    

  • OTA Common-Mode Gain

    14

    [Sedra]

     

      2222

    1111

    22

    22

    2 1

    oSSmoSSo

    oSSmoSSo

    SSicm

    o mcm

    rRgrRR

    rRgrRR

    Rv iG

    

    

    

     

      

     

     

      

     

    3 3144

    3 313

    1

    1

    m ooicmmcmm

    m ooicmmcmg

    g rRvGgi

    g rRvGv

  • OTA Common-Mode Gain

    15

    KCL at vo

    Since Ro2>>ro4 and Ro1>>ro3 and gm3=gm4

    [Sedra]  

      

     

    3 3144

    1

    m ooicmmcmm g

    rRvGgi

     

      

      

      

     

    

    3 314

    24

    22 4

    11 2

    0

    m oom

    SS

    oo icmo

    o

    o

    o

    o icmmcm

    g rRg

    R Rr

    vv

    r v

    R vivG

    SSm CM

    omSS

    o

    icm

    o CM

    Rg A

    rgR r

    v vA

    3

    33

    4

    2 1

    1 1

    2

    

     

  • OTA Common-Mode Gain & Rejection Ration (CMRR)

    16

    • To improve (lower) common-mode gain, we need a high tail current impedance

    cm

    dm

    A ACMRR 10log20

    462 1

    omCM

    o cm rgv

    vA 

    • An amplifier figure-of-merit is the common-mode rejection ratio (CMRR)

     46 26

    1 1010 2log20log20 om

    oo

    m

    cm

    dm rg gg

    g A ACMRR 

      

     

    

  • OTA Power-Supply Rejection Ration (PSRR)

    17

      

       

     

      

       

     

    SSo

    dm 10

    DDo

    dm 10

    vv Alog20PSRR

    vv A

    log20PSRR

    42

    1

    42

    1

    1

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