ECEN474/704: (Analog) VLSI Circuit Design Spring 2016 Folded Cascode OTA Unity Gain Feedback Voltage

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Text of ECEN474/704: (Analog) VLSI Circuit Design Spring 2016 Folded Cascode OTA Unity Gain Feedback Voltage

  • Sam Palermo Analog & Mixed-Signal Center

    Texas A&M University

    Lecture 13: Folded Cascode OTA

    ECEN474/704: (Analog) VLSI Circuit Design Spring 2016

  • Announcements & Agenda

    • HW5 (Preliminary Project Report) Due Apr. 18

    • Single-Stage Cascode OTA • Folded Cascode OTA

    2

  • Simple OTA

    3

    M1 M2Vi+ Vi-

    VDD

    VSS

    Rbias

    Itail

    M5 M6

    M3 M4

    CL

    Vo

    ( )621 || oomoutmv rrgRGA == Gain DC

    • Gain is limited by single-transistor output resistance

  • Single-Stage Cascode OTA

    • Gain is larger by a gmro factor • Output swing range is limited

    due to large compliance voltage of cascode current source load

    4

    ( )6864241 || oomoommoutmv rrgrrggRGA ≈= Gain DC [Razavi]

  • Single-Stage Cascode OTA Unity Gain Feedback Voltage Range

    5

    ( ) !!! a than Less

    Range Input) (&Output conditionsat M2 into plugging and As

    saturation M4 byset V Minimum

    saturation M2 byset V Maximum

    out

    out

    TH

    THGSTH

    xGSxb

    THbout

    THxout

    V VVV

    VVVV VVV

    VVV

    244

    4

    4

    2

    −−= +=

    −≥

    +≤

    • Cascode configuration constrains output & unity-gain swing

    [Razavi]

  • Folded Cascode Circuits

    6

    • “Folding” about the cascode node will increase input and output swing range

    PMOS Input & NMOS Cascode

    NMOS Input & PMOS Cascode

    [Razavi]

  • Folded Cascode OTA

    7

    [Razavi]

  • Folded Cascode OTA Unity Gain Feedback Voltage Range

    8

    • With proper (high-value) choice of Vb2, a decent output and input swing range can be achieved

    1

    2 ||

    GSDSATIoutDSATNDSATNCout

    THPbout

    VVVVVV

    VVV MP

    Tail +≥+≥

    +≤

    OR saturation sourcecurrent tailor cascode NMOSoutput byset V Minimum

    saturation byset V Maximum

    out

    out

    MP

    MNC

  • TAMU-ELEN-474 2009 Jose Silva-Martinez

    - 9 -

    Folded-Cascode OTA: gm, rout and poles?

    VB1 and VB2 must keep M1

    - M5 in saturation region

    VB2 > Vsat,4 + VGS3

    VB1 < VDD - Vsat,5 – VSG2

    Notice that ID5 biases both M2 and M1

    ( )( ) ( )43351221 ; dsmdsdsdsmdsoutmm rgrrrgrrgG ≅=

    (for M4 sat)

    (for M5 sat)

  • TAMU-ELEN-474 2009 Jose Silva-Martinez

    - 10 -

    Example: Folded-Cascode OPAMP

    Find the gain and the phase from input to output and from input to node 2.

    The low frequency gain is 77 dB and the unity gain frequency is around 80 MHz. The behavior of the gain from the input to node 2 is interesting: above the dominant pole.

    51

    1

    oo

    m

    gg g +

    ≈ 2

    1

    m

    m

    g g

     

      

      

      

     +

    ≈ Loutoo

    m z Crgg

    g 1

    51

    2 2ω

  • TAMU-Elen-474 Jose Silva-Martinez-08

    - 11 -

     There is a limitation due the non- dominant pole

     IBIAS ↑ ⇒ ADC ↓

     Wcasc ↓ ⇒ VDSAT ↑

     

      

     +

      

     +

    −=

    o

    L

    mc

    po

    md

    in

    o

    g Cs1

    g C

    s1

    1 g

    g v v

    TYPICAL FOLDED CASCODE (One of the most popular circuit in ADCs)

  • TAMU-Elen-474 Jose Silva-Martinez-08

    - 12 -

    FOLDED-CASCODE OTA Frequency response:

    Righ hand side

    Righ hand side: 2 poles (at VW and Vout)

    Left hand side: 4 poles !!! (at VX, VY, VZ and

    Vout)

    The poles at Vy and Vz are associated to

    N-type transistors  higher frequencies

    ( )

    mp

    PC

    out

    out out1mV

    g sC1

    1

    g sC1

    1RgsA +

    ∗ +

    ∗≅

    vin-

    2ID1

    M1

    MP

    vout

    VB2

    VB1 vin+

    2ID1

    VB2 iOUT1

    2ID1

    VDD

    -VSSMN

    VB3

    MN

    VB1

    VWVX

    VY

    VZ

  • TAMU-Elen-474 Jose Silva-Martinez-08

    - 13 -

    Output referred noise

    M1 produces an output current given by

    Each transistor M2 generates a differential output current

    Similarly, for each transistor M5

    At low and medium frequencies, noise contribution of the cascode transistors can be neglected (M3 and M4)

    Vn4

    ro5

    i04

    M4 05

    4n 4n

    054m

    4m 04 r

    v v

    rg1 g

    i ≅ +

    =

    For cascode transistors

    1n1m01 vgi =

    2n2m02 vgi =

    5n5m05 vgi =

    vin-

    2ID1

    M1

    M2

    vout

    VB2

    VB1 vin+

    2ID1

    VB2 iOUT1

    2ID1

    VDD

    -VSSMN

    VB3

    MN

    VB1

    VW VX

    VY

    VZ M4

    M5

    M3

    iout2 = 2(ieq12 + ieq22 + ieqn2 )meq kTgi 3 82 =Remember

  • TAMU-Elen-474 Jose Silva-Martinez-08

    - 14 -

    Noise density and noise level

    The output referred current spectral density is

    And the input referred noise density becomes

    The noise level is

    ( )25n25m22n22m21n21m2T0 vgvgvg2i ++=

    2 1m

    2 5n

    2 5m

    2 2n

    2 2m

    2 1n

    2 1m2

    in,eq g

    vgvgvg 2v

    ++ =

    ∫∫   

       

     ++==

    BW 2

    1m

    2 5n

    2 5m

    2 1m

    2 2n

    2 2m2

    1n BW

    2 in,eqnoise df

    g

    vg

    g

    vg v2dfvv

    FOLDED-CASCODE OTA

    vin-

    2ID 1

    M1

    M2

    vout

    VB2

    VB1vin+

    2ID 1

    VB2 iOUT1

    2ID

    VDD

    -VSSM5

    VB3

    M5

    VB1

    VWVX

    VY

    VZ

  • TAMU-Elen-474 Jose Silva-Martinez-08

    - 15 -

    Noise level for the folded-cascode OTA

    Lets consider thermal noise (vn2 =(8/3)KT/(gm))

    Low-noise is associated with large gm1 and relatively small gm2 and gm5

    ∫   

       

     ++=

    BW 2

    1m

    2 5n

    2 5m

    2 1m

    2 2n

    2 2m2

    1nnoise df g

    vg

    g

    vg v2v

    ∫  

      

     ++=

    BW m

    m

    m

    m

    m noise dfg

    g g g

    g kTv 2

    1

    5 2

    1

    2

    1

    1 3

    16

    ( )  

       

     ++

     

       

     ≈

    1

    5

    1

    2

    1

    18

    m

    m

    m

    m

    m noise g

    g g gBW

    g kTv

    Or for a dominant (single) pole system with NBW = (π/2)BW

    vin-

    2ID1

    M1

    M2

    vout

    VB2

    VB1 vin+

    2ID1

    VB2 iOUT1

    2ID1

    VDD

    -VSSM5

    VB3

    M5

    VB1

    VW VX

    VY

    VZ

    Noise of diff pair Noise Factor (due to other transistors)

  • Next Time

    • Two Stage Miller OTA

    16

    ECEN474/704: (Analog) VLSI Circuit Design Spring 2016 Announcements & Agenda Simple OTA Single-Stage Cascode OTA Single-Stage Cascode OTA �Unity Gain Feedback Voltage Range Folded Cascode Circuits Folded Cascode OTA Folded Cascode OTA �Unity Gain Feedback Voltage Range Slide Number 9 Slide Number 10 Slide Number 11 FOLDED-CASCODE OTA Slide Number 13 Slide Number 14 Slide Number 15 Next Time