Analysis and Design of Analog Integrated Circuits Lecture 8 Cascode · PDF file...

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  • M.H. Perrott

    Analysis and Design of Analog Integrated Circuits Lecture 8

    Cascode Techniques

    Michael H. Perrott February 15, 2012

    Copyright © 2012 by Michael H. Perrott All rights reserved.

  • M.H. Perrott

    Review of Large Signal Analysis of Current Mirrors

    M2M1

    I1

    Vdd

    Vss=0

    I2

    VTH+ΔV1 VTH+ΔV2

    Vds2 > Vdsat2

    I2 μnCox

    W2 L2

    1 2 (VGS2-VTH)

    2(1+λ2Vds2)

    ΔV2

    I1 μnCox W1 L1

    1 2 (VGS1-VTH)

    2(1+λ1Vds1)

    ΔV1

    =

    ΔV1 = ΔV2But, VTH+ΔV1=VTH+ΔV2

    I2 W2 L2

    (1+λ2Vds2) I1 W1

    L1 (1+λ1Vds1)

    =

    Mismatch due to Vds difference

    Current setting

    based on geometry

    Note: for accurate ratio, set L1 = L2 Vds2

    I2

    Triode

    Saturation

    Vdsat2

    M2 in

    M2 in

    2

  • M.H. Perrott

    The Issue of Vds Mismatch in Current Mirrors

     Issue: Current I2 can vary significantly as a function of the drain voltage of M2- We often want a tightly controlled current set only by I1

    and transistor sizes  How do we improve the current mirror matching

    performance?

    M2M1

    I1

    Vdd

    I2

    Vds2

    I2 W2 (1+λ2Vds2)

    I1 W1 (1+λ1Vds1) =

    Mismatch

    due to Vds difference

    Current

    setting

    based on

    geometry

    Note: we are assuming L1 = L2 Vds1

    3

  • M.H. Perrott

    Cascoded Current Source

     Offers increased output resistance - Reduces small signal dependence of output current on

    the output voltage of the current source - From Lecture 6, we derived:

     Output resistance boosted by intrinsic gain of M3, gm3ro3  But how do we reduce the influence of large signal Vds

    mismatch between M1 and M2?

    M1M2

    Ibias

    Iref

    ro1

    M3 Vbias

    Rthd3

    M3 Vbias

    Rthd3

    4

  • M.H. Perrott

    Match Vds of Current Mirror Devices With Proper Bias

     Key transistor for determining I2 is M1- Why is M2 less important?  Above biasing approach provides a much closer

    match between Vds1 and Vds4

    I2 W1 L1

    (1+λ1Vds1) I1 W4

    L4 (1+λ4Vds4)

    =

    Mismatch due to Vds difference

    Current setting

    based on geometryM1

    I1

    Vdd

    Vss=0

    I2

    VTH+ΔV

    W/L

    W/L

    M2

    VTH+ΔV VTH+ΔV

    VTH+ΔV

    W/L

    W/L M4

    M3 Vds2 > ΔV

    Vds1 = VTH+ΔV

    Vo Recall:

    I2 = W1 W4

    1 + λVds1 1 + λVds4

    I1 ≈ W1 W4

    I1 5

  • M.H. Perrott

    The Drawback of Basic Cascode Bias Approach

     Output voltage range is reduced - Now Vo must be > VTH + 2V- What will happen to the output impedance of the current

    source if the output voltage is too low? - Can we improve the voltage range?

    I2

    V1

    M1 and M2 in saturation

    M1 and M2 in triode

    M1

    I1

    Vdd

    Vss=0

    I2

    VTH+ΔV

    W/L

    W/L

    M2

    VTH+ΔV VTH+ΔV

    VTH+ΔV

    W/L

    W/L M4

    M3 Vds2 > ΔV

    Vds1 = VTH+ΔV VTH+2ΔV

    M1 in saturation M2 in triode

    Vo

    Vo

    calculation of V1 is nontrivial

    6

  • M.H. Perrott

    Improved Swing Cascode

     Key idea: set size of M3 such that Vds1 = V- Assuming strong inversion for M1 and M3:

    M1 and M2 in saturation

    Vo

    no wasted voltage region

    I2

    Vdsat1+Vdsat2

    M1 and M2 in triode

    M6

    I1

    Vdd

    Vss=0 VTH+ΔV

    αW/L

    W/L

    M5

    VTH+2ΔV VTH+ΔV

    VTH+ΔV

    W/L

    W/L

    M4

    M3

    M1

    I2

    M2

    VTH+ΔV

    VTH+ΔV

    W/L

    W/L

    Vds2 > ΔV

    Vds1 = ΔV

    Vo

    2VTH+3ΔV

    VTH+2ΔV

    7

  • M.H. Perrott

    Alternative Implementation of Improved Swing Cascode

     Set  as on previous slide  Note: both implementations share a common problem

    M1

    I1

    Vdd

    Vss=0

    I2

    VTH+ΔV

    αW/L

    W/L

    M2

    VTH+2ΔV VTH+ΔV

    VTH+ΔV

    W/L

    W/L M4

    M3 Vds2 > ΔV

    Vds1 = ΔV

    Vo

    M5 M6 M7 Wp/LpWp/LpWp/Lp

    I1I1

    M1 and M2 in saturation

    Vo

    no wasted voltage region

    I2

    M1 and M2 in triode

    2ΔV

    8

  • M.H. Perrott

    The Issue of Current Mismatch

     The improved swing approach causes a systematic mismatch between I2 and I1- Key issue: Vds1  Vds4

     Can we fix this problem?

    M1

    I2

    W/L

    M2VTH+2ΔV

    VTH+ΔV

    M4 Vds1 = ΔV

    I1

    Vds4 = VTH+ΔV

    I2 W2 (1+λ2Vds2) I1 W1 (1+λ1Vds1)

    =

    Mismatch due to Vds difference

    W/L

    Recall:

    9

  • M.H. Perrott

    Techniques to Reduce Current Mismatch

     Systematic mismatch between I1 and I2 is greatly reduced by using the above circuit (now Vds1 ≈ Vds4)- Note that gate bias on M2 and M3 may be provided by

    previously discussed circuits  Additional techniques for accurately matching I1 and I2- Set L1 = L4 >> Lmin

     Note: set L2 = L3 ≈ Lmin for lower area and capacitance- Set W2/W3 = I2/I1 so that V2 = V3

    M1

    I2

    W/L

    M2VTH+2ΔV

    VTH+ΔV

    M4 Vds1 = ΔV

    I1

    Vds4 = ΔV W/L

    M3

    VTH+ΔV

    W/LW/L

    10

  • M.H. Perrott

    Another Common Cascode Bias Topology

     Key issue: needs two bias current branches

    M1

    I2

    W/L

    M2

    VTH+2ΔV

    VTH+ΔV

    M4 Vds1 = ΔVVds4 = ΔV

    W/L

    M3

    VTH+ΔV

    W/LW/LI1

    Vdd

    W/L M8

    M5 M6 M7 Wp/LpWp/LpWp/Lp

    I1I1

    W/L

    W/L

    W/L

    W/L

    W/L

    M9

    M10

    M11

    M12

    M13

    11

  • M.H. Perrott

    Utilizing a Simple Resistor to Achieve One Bias Branch

     Issue: poly resistor is large and won’t track NMOS devices across temperature and process variations

    M1

    I2

    W/L

    M2

    VTH+2ΔV

    VTH+ΔV

    M4 Vds1 = ΔVVds4 = ΔV

    W/L

    M3

    VTH+ΔV

    W/LW/LI1

    M5 M7 Wp/LpWp/Lp

    I1

    RBΔV

    12

  • M.H. Perrott

    Better Approach: Use PMOS Device In Triode Region

     Much smaller, better tracking with NMOS devices than resistor

    M1

    I2

    W/L

    M2

    VTH+2ΔV

    VTH+ΔV

    M4 Vds1 = ΔVVds4 = ΔV

    W/L

    M3

    VTH+ΔV

    W/LW/LI1

    M5 M7 Wp/LpWp/Lp

    I1

    ΔV M6

    Wp/Lp

    13

  • M.H. Perrott

    Wilson Current Mirror

     Relies on feedback in its operation  Using Hybrid- analysis

    - Output resistance comparable to cascode current source  This circuit is rarely used these days

    I1

    M1

    I2

    M2

    M3

    Rthd2

    14

  • M.H. Perrott

    Enhanced Cascode Current Source

     Offers output resistance comparable to double cascode current source

     As with Wilson mirror, analysis is tricky due to source/gate coupling - Using results shown in the following slide:

    M4

    M3

    M1M2

    Ibias IrefIbias2

    15

  • M.H. Perrott

    Thevenin Resistances for CMOS Transistor Feedback Pair

    RC

    RB

    -gmb4vs4vgs4

    vs4

    ro4gm4vgs4

    RC

    M4

    M3

    RA

    RB

    Rthd

    Rths

    Rthd

    -gmb3vs3 vgs3ro3 gm3vgs3

    RA

    vs3=0

    Rths

    M4

    M3

    S

    D

    S

    D

    16

  • M.H. Perrott

    Basic Cascode Amplifier

     Allows improved frequency response (discussed later)  Reduction to two-port will be done in several steps

    Vout

    RD

    RG

    Vin RS

    Rthg1

    RG

    vin Av1vg1vg1

    is1

    RS

    Rths1

    Rthd11 is1α

    g1

    s1

    d1

    M1

    M2

    M1

    is2Rths2

    Rthd2 vout2is2α

    s2

    d2

    M2

    RD

    Common Gate

    General Model

    17

  • M.H. Perrott

    Eliminate Middle Sections

     Calculation of Gm1 same as for common source amp  To reduce further, note that

    Vout

    RD

    RG

    Vin RS

    Rthg1

    RG

    vin vg1 Rthd1m1 vg1G

    g1 d1

    M1

    M2

    M1

    is2Rths2

    Rthd2 vout2is2α

    s2

    d2

    M2

    RD

    18

  • M.H. Perrott

    Resulting Two-Port Similar to Common Source Amp

     Key difference: drain impedance much larger

    Vout

    RD

    RG

    Vin RS

    Rthg1

    RG

    vin vg1

    m1vg1G

    g1

    M1

    M2

    M1

    Rthd2 vout

    d2

    M2

    RD

    19

  • M.H. Perrott

    Slight Twist to Cascode Amplifier

     What