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  • 8/6/2019 Lecture28 Operational Amplifier

    1/17

    Operational Amplifiers

    Reading: Jaeger 11.1-11.5 and Notes

    ECE 3040 - Dr. Alan DoolittleGeorgia Tech

  • 8/6/2019 Lecture28 Operational Amplifier

    2/17

    Operational Amplifier

    Operational Amplifier or Op-Amp is a multistage amplifier that is used for

    .

    The numbers of applications possible with Op-amps are two numerous to list.

    Most everyone agrees: Op-Amp analysis is significantly easier than transistor

    analysis.

    Though they are often internally complex, their use in circuits most often

    simplifies the overall design.

    Model

    The circuit is modeled by an ideal voltage amplifier.

    Circuit Symbol

    +++

    +

    out

    -

    in

    -

    Vout

    -

    in

    -

    ECE 3040 - Dr. Alan DoolittleGeorgia Tech

  • 8/6/2019 Lecture28 Operational Amplifier

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    Ideal Operational Amplifier

    Rin = Infinity,

    Voltage Gain, Av=Infinity at all frequencies

    out=

    ++

    o e

    VoutVin

    --

    ECE 3040 - Dr. Alan DoolittleGeorgia Tech

  • 8/6/2019 Lecture28 Operational Amplifier

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    Ideal Operational Amplifier

    Infinite gain means that the device is useless without adding Feedback to

    control the overall gain to a finite value.

    i

    ioutv+

    Consider the circuit to the

    right with vin=0 vout

    n

    i-

    v-

    vvAv vout

    vini2

    0)v-(vforsatisfiedonlyisequationabovethe,AIf -v

    ECE 3040 - Dr. Alan DoolittleGeorgia Tech

    Feedback forces the two input voltages to be equal! This is known as a virtual ground.

    R1 and R2 form a Feedback Network

  • 8/6/2019 Lecture28 Operational Amplifier

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    Inverting Amplifier

    Finite voltage gain results from an infinite voltage gain amplifier with negative

    feedback (feedback that takes a fraction of the output voltage and mixes it back into the

    negative summation node).

    iin

    +

    ioutv+22

    221

    -

    resistanceinputinfinitetodue)20)1

    iiiivRiRiv

    in

    oinin

    vin

    vouti-

    -

    -

    1

    -nin

    v

    groundvirtualthetodue0but v

    Ri

    2

    1

    nin

    vv

    3,and21,Combining

    Ri)3

    2

    2

    1

    1

    1

    v

    0RR

    R

    Rv

    vRRv

    o

    oin

    Overall circuit gain is finite, negative (for

    this feedback configuration) and set by the

    ECE 3040 - Dr. Alan DoolittleGeorgia Tech

    feedback resistor network.

  • 8/6/2019 Lecture28 Operational Amplifier

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    Inverting Amplifier

    Input Resistance:

    iin

    +

    ioutv+1RivR inin

    vin

    vouti-

    -n

    2

    ECE 3040 - Dr. Alan DoolittleGeorgia Tech

  • 8/6/2019 Lecture28 Operational Amplifier

    7/17

    Inverting Amplifier

    itv+

    Output Resistance:

    v-

    i1

    0vsince0i

    but,

    1231t

    vt

    i2

    ii

    and

    -

    00v

    ,

    t

    thus

    0i

    v

    t

    t outR

    ECE 3040 - Dr. Alan DoolittleGeorgia Tech

  • 8/6/2019 Lecture28 Operational Amplifier

    8/17

    Non-Inverting AmplifierVirtual

    Ground

    iin

    v+

    or

    short

    vin

    i-

    v-

    ou

    1

    RR

    Rvv out

    i2-in

    -

    vv

    so,vthat vrequiresgroundvirtualThe

    so

    1

    21

    Rv

    R

    RR

    v

    v

    v

    v out

    in

    out

    0

    in

    in

    in

    in

    v

    i

    vR

    ECE 3040 - Dr. Alan DoolittleGeorgia Tech

    1Rvinv casenver ng-onorasc rcuameout

  • 8/6/2019 Lecture28 Operational Amplifier

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    Unity Gain Buffer or Voltage Follower

    0 12 RandRexceptamplifierinvertingNonasSame

    111

    2

    v

    out

    v AR

    R

    v

    vA

    inin vv 0inin i

    case)inverting-Nonforascircuit(Same0outR

    ECE 3040 - Dr. Alan DoolittleGeorgia Tech

    Can be used to isolate a high impedance circuit from a low impedance circuit

  • 8/6/2019 Lecture28 Operational Amplifier

    10/17

    Summing Amplifier

    v+

    iin,a v- iiii cinbinain ,,,2

    vin,avout

    i2

    RRR

    cRv

    bRv

    aRv

    Rv cinbinainout

    222

    1112,,,

    iin,b

    cR

    R

    vbR

    R

    vaR

    R

    vv

    cRv

    bRv

    aRvv

    cinbinainout

    cinbinainout

    1

    2

    1

    2

    1

    2

    111

    ,,,

    ,,,

    vin,b

    i ,Output is a scaled sum of inputs.

    Scaling can be controlled by

    ECE 3040 - Dr. Alan DoolittleGeorgia Tech

    n,c

  • 8/6/2019 Lecture28 Operational Amplifier

    11/17

    Difference Amplifier

    vin,a v-

    v+

    v-

    v+

    vth

    voutvout

    vin,b vin,b

    2R21

    21

    ,RR

    thainth

    Using Superposition we can combine the results of the Inverting and Non-inverting solutions:

    vin,a=0vin,b=0

    22

    1

    2

    1

    1

    RRvv

    R

    Rvv thout

    1

    2bin,v

    RRvout

    2bin,ain,

    1

    2bin,

    1

    2ain,

    vv

    vv

    Rv

    RR

    RRv

    out

    out

    ECE 3040 - Dr. Alan DoolittleGeorgia Tech

    1

    2

    ,

    121

    ,

    R

    R

    vv ainout

    1This circuit amplifies the

    difference of two signals

  • 8/6/2019 Lecture28 Operational Amplifier

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    Non-Ideal (Real World) Operational AmplifiersFinite Open-Loop Gain

    ea op-amps o not ave n n te open oop w t out ee ac ga n.

    Voltage gains are typically large but finite: ~104-106 V/V

    vR

    vv out1

    out

    v v-

    +

    factorfeedbacktheasknownis

    RR

    R

    21

    1

    21

    where

    out

    A,Av

    A

    ,vvsinceso

    openloop

    openloopoutloopclosedv,

    in

    outopenloopopenloopout

    gainlooptheiswhere

    resultaininfinitethea roachesR

    11

    A

    1Av

    2

    openloop

    openloop

    Ifin

    ECE 3040 - Dr. Alan DoolittleGeorgia Tech

    R1,

  • 8/6/2019 Lecture28 Operational Amplifier

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    Non-Ideal (Real World) Operational AmplifiersFinite Open-Loop Gain

    Finite open-loop gain means the Virtual Ground is not perfect!

    openloopA in

    v Small but finite

    openloopopenloop A1A1 ininoutin

    and - terminals

    v v-

    +

    out

    The Gain Error (GE) that results from the Non-infinite open-loop gain can be quantified as:

    openloopA1

    inv

    vGE

    ECE 3040 - Dr. Alan DoolittleGeorgia Tech

    openloopopenloop

  • 8/6/2019 Lecture28 Operational Amplifier

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    Non-Ideal (Real World) Operational AmplifiersFinite Output Impedance

    Real Op-Amps have a small but finite output impedance, Ro .

    We want to find the Output impedance of the various circuits we have examined .

    All the configurations have a common circuit for calculating the output impedance .

    ECE 3040 - Dr. Alan DoolittleGeorgia Tech

  • 8/6/2019 Lecture28 Operational Amplifier

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    Non-Ideal (Real World) Operational AmplifiersFinite Output Impedance

    2iii

    i

    vR

    ox

    x

    x

    out

    ,

    v

    R

    vvAv

    i

    x

    o

    openloopvx

    o

    211

    21

    2212

    vvRR

    R

    v

    RR

    xx

    x

    21

    ,1 11

    RRR

    A

    v

    iR

    o

    openloopv

    x

    x

    out

    21,1

    RRAR openloopvoout

    ECE 3040 - Dr. Alan DoolittleGeorgia Tech

    Ro is very small so this term is EXTREMELYsmall!

    FEEDBACK REDUCES OUTPUT IMPEDANCE!

  • 8/6/2019 Lecture28 Operational Amplifier

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    Non-Ideal (Real World) Operational AmplifiersFinite Input Impedance: Non-Inverting Case

    Real Op-Amps have a large but finite

    input resistance, RID

    ID

    x

    xR

    vvi

    xopenloopvoutout vvAvvRv

    RiRiv

    ,1

    1211

    21ID21x ortoueantocomparecurrentt eeg ect ng

    x

    openloopv

    openloopvv

    A

    Av

    ,

    ,

    21

    1

    IDopenloopv

    x

    ID

    x

    openloopv

    openloopvx

    xRA

    v

    R

    vA

    v

    i

    ,

    ,

    ,

    1

    1

    FEEDBACK

    INCREASES INPUT

    ECE 3040 - Dr. Alan DoolittleGeorgia Tech

    IDopenloopvin ,

    RID is very large so Rin is EXTREMELY large!

  • 8/6/2019 Lecture28 Operational Amplifier

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    Non-Ideal (Real World) Operational AmplifiersFinite Input Impedance: Inverting Case

    ea p- mps ave a arge ut n te

    input resistance, RID

    Rin=R1 +Rin

    in in

    Find Rinby forming a new test circuit

    openloopvout

    R

    vAv

    R

    v

    R

    vv

    R

    viii

    1,111121

    openloopv

    ID

    in

    R

    R

    A

    Rv

    iR

    2

    2

    ,

    1

    11

    '

    11'

    Rin

    openloopv

    IDin

    R

    Thus

    A ,

    ,

    1

    openloopv

    IDin A ,1 1

    Since RID>>R2/(1+Av,openloop) and

    Av,openloop is very large,

    ECE 3040 - Dr. Alan DoolittleGeorgia Tech

    1,

    21

    ,

    21

    11R

    A

    RRR

    A

    RRRR

    openloopv

    in

    openloopv

    IDin