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Nonlinear Analog Circuits

Apr 06, 2018

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Bharavi K S
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  • 8/3/2019 Nonlinear Analog Circuits

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    Rectifier transfer characteristic and response for sinusoidal input waveform. (a) Half-

    wave rectifier. (b) Full-wave rectifier.

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    Simple diode half-wave rectifier. (a) Rectifier circuit. (b) Equivalent circuit for Vin > -0.6 V.

    (c) Equivalent circuit for Vin < -0.6 V. (d) dc transfer characteristic. (e) Response tosinusoidal input.

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    -

    ! 1exp T

    io

    S

    V

    VV

    II

    io aVV !

    out

    S

    T

    iV

    IIIn

    aVV !

    ! 1

    1

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    Active precision half-wave rectifier. (a) Rectifier circuit. (b) dc transfer

    characteristic.

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    Active precision half-wave rectifier. (c) Input and output waveforms for the

    precision half-wave rectifier.

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    Improved precision rectifier. (a) Rectifier circuit. (b) Equivalent circuit for

    Vin < 0. (c) Equivalent circuit for Vin > 0.

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    The Emitter-Coupled Pair as a Simple Multiplier

    !

    T

    id

    EE

    c

    V

    V

    II

    exp1

    1

    !

    T

    id

    EE

    c

    VV

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    exp1

    2

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    !!(

    T

    id

    EEccc

    V

    VIIII

    2

    tanh21

    1222tanh }T

    id

    T

    id

    T

    id

    V

    V

    V

    V

    V

    V

    !(

    T

    id

    EEc

    VVII2

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    Emitter-coupled pair.

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    The dc transfer characteristic of emitter-coupled pair.

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    onBEioEE VVKI $ 2

    T

    onBEiido

    c

    V

    VVVKI

    2

    2

    !(

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    Two-quadrant analog multiplier.

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    Gilbert multiplier circuit.

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    The dcAnalysis of the Gilbert Multiplier Cell

    !

    T

    c

    c

    V

    VII

    1

    1

    3

    exp1

    !

    T

    c

    c

    VV

    II

    1

    1

    4

    exp1

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    !

    T

    c

    c

    VV

    II

    1

    2

    5

    exp1

    !

    T

    c

    c

    VV

    II

    1

    2

    6

    exp1

    !

    T

    EE

    c

    V

    V

    II

    2

    1

    exp1

    !

    T

    EE

    c

    V

    V

    II

    2

    2

    exp1

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    -

    -

    !

    TT

    EE

    c

    V

    V

    V

    V

    II

    21

    3

    exp1exp1

    -

    -

    !

    TT

    EE

    c

    V

    V

    V

    V

    II

    12

    4

    exp1exp1

    -

    -

    !

    TT

    EE

    c

    V

    V

    V

    V

    II

    21

    5

    exp1exp1

    -

    -

    !

    TT

    EE

    c

    V

    V

    V

    V

    II

    12

    6

    exp1exp1

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    46536453 cccccc

    IIIIIII !!(

    5463 cccc

    IIII !

    -

    -

    !

    TT

    EE

    V

    V

    V

    VI

    2tanh

    2tanh 21

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    The Gilbert Cell as anAnalog Multiplier

    3tanh

    3

    xxx ! .

    xx }tanh

    }(

    TT

    EE

    VV

    VVII

    2221 V1, V2,

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    Gilbert multiplier with emitter degeneration applied to improve input

    voltage range on V2 input.

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    1111 VKII o !

    1112VKII

    o!

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    Gilbert multiplier with predistortion circuits.

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    Inverse hyperbolic tangent circuit.

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    !(

    S

    o

    T

    S

    o

    T

    IVKIInV

    IVKIInVV 111111

    !

    111

    111

    VKI

    VKIInV

    o

    o

    T

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    !

    x

    x

    Inx

    1

    1

    2

    1

    tanh

    1

    !(

    1

    111tanh2o

    T

    IVKVV

    !(2

    22

    1

    11

    oo

    EE

    I

    VK

    I

    VKII

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    1

    11

    1

    1

    K

    I

    VK

    Ioo

    2

    2

    2

    2

    2

    K

    IV

    K

    Ioo

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    Complete four-quadrant multiplier.

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    Input and output waveforms for phase detector with large input signals.

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    tVtVmmm

    [cos!

    4

    2sin

    ,cos1 T

    T

    [n

    n

    AtnAtVnc

    nnc

    !g

    !

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    Input and output spectra for a balanced modulator.

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    Typical input and output waveforms for a phase detector.

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    Phase-locked-loop system

    Phase-Locked Loop Concepts

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    Typical phase detector output during capture transient.

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    The Phase-Locked Loop in the Locked Condition

    dt

    tdt oscosc

    J[ !

    dtttt

    osctoscosc ! ! 00 [JJ

    oOoosc VK! [[

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    Block diagram of PLL system.

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    (a)

    Root locus and frequency response of a first-order, phase-locked loop.

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    Response of loop output voltage to step changes in input frequency, example

    first-order loop.

    (b)

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    Integrated-Circuit Phase-Locked Loops

    !

    T

    J21

    CEEaverage RIV

    -

    !

    J T

    J[[[[

    T 0sinsin

    1tdttdtVRgV iCmaverage

    T

    Jcos2iCm

    VRg!

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    Sinusoid multiplied bya synchronous square wave.

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    Voltage-controlled, emitter-coupled multivibrator.

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    Equivalent circuit during one half-cycle.

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    Waveforms within the emitter-coupled multivibrator.

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    Phase comparator of the 560B phase-locked loop

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    Nonlinear Function Synthesis

    (a)

    (b)

    Bipolar nonlinear function circuits. (a) Square root. (b) Square law.

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    Folded-cascode OTA

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    Fully differential folded-cascode op-amp