Transcript
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Operational Amplifiers

Reading: Jaeger 11.1-11.5 and Notes

ECE 3040 - Dr. Alan DoolittleGeorgia Tech

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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

-

V  out

-

in

-

ECE 3040 - Dr. Alan DoolittleGeorgia Tech

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Ideal Operational Amplifier 

•R in = Infinity,

•Voltage Gain, Av=Infinity at all frequencies

• out=

++

o e

V  outV in

--

ECE 3040 - Dr. Alan DoolittleGeorgia Tech

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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

i outv+

•Consider the circuit to the

right with vin=0 v out

 n

i-

v-

vv Av vout 

vini 2

0)v-(vfor satisfiedonlyisequationabovethe,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”

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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

+

i outv+22

221

-

resistanceinputinfinitetodue)20)1

iiiiv Ri Riv

in

oinin

vin

v outi-

-

-

1

-nin

v

groundvirtualthetodue0 but v

R i

 2

1

nin

vv

3,and21,Combining

R i)3

2

2

1

1

1

v

0R R 

 R

 Rv

v R Rv

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.

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Inverting Amplifier 

•Input Resistance:

iin

+

i outv+1 R

iv R in

in

vin

v outi-

-n

 2

ECE 3040 - Dr. Alan DoolittleGeorgia Tech

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Inverting Amplifier 

i tv+

•Output Resistance:

v-

i1

0vsince0i

  but,

1231t

v t

i 2

ii

and

-

00v

,

t

thus

0i

v

t

t out  R

ECE 3040 - Dr. Alan DoolittleGeorgia Tech

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 Non-Inverting Amplifier Virtual

Ground

iin

v+

or

“short”

vin

i-

v-

 ou

1

 R R

 Rvv out 

i 2-in

-

vv

so,vthat vrequiresgroundvirtualThe

so

1

21

 Rv

 R

 R R

v

v

v

v out 

in

out 

0

in

in

in

in

v

i

v R

ECE 3040 - Dr. Alan DoolittleGeorgia Tech

1 Rvin

v casenver ng-onor asc rcuame out 

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Unity Gain Buffer or “Voltage Follower”

0 12 Rand  Rexcept amplifier inverting NonasSame

111

2

v

out 

v A R

 R

v

v A

inin vv

0inin i

case)inverting- Nonfor ascircuit(Same 0out  R

ECE 3040 - Dr. Alan DoolittleGeorgia Tech

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

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Summing Amplifier 

v+

iin,a v- iiii cinbinain ,,,2

vin,av out

i 2

 R R R

c Rv

b Rv

a Rv

 Rv cinbinainout 

222

1112,,,

iin,b

 

 

 

c R

 R

vb R

 R

va R

 R

vv

c Rv

b Rv

a Rvv

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 

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Difference Amplifier 

vin,a v-

v+

v-

v+

v th

v outv out

vin,b vin,b

2 R21

21

, R R

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

 R Rvv

 R

 Rvv thout 

 

 

  

  

1

2 bin,v

 R Rvout 

2 bin,ain,

1

2 bin,

1

2ain,

vv

vv

 Rv

 R R

 R Rv

out 

out 

ECE 3040 - Dr. Alan DoolittleGeorgia Tech

1

2

,

121

,

 R

 R

vv ainout 

   1

This circuit amplifies the

difference of two signals

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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

 

βvR 

vv out1

out

v v-

+

factor feedback theasknownis

R R 

R  

21

1

21

  where

 out

A,Av

A

,vvsinceso

openloop

openloopoutloopclosedv,

in

outopenloopopenloopout

   gainlooptheiswhere

resultaininfinitethea roachesR 

11

A

1Av

2

openloop

openloop

   If in

ECE 3040 - Dr. Alan DoolittleGeorgia Tech

R 1 ,

  

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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   inv Small but finite

openloopopenloop A1A1        ininout in  

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   

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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

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 Non-Ideal (Real World) Operational AmplifiersFinite Output Impedance

2iii

i

v R

o x

 x

 x

out 

,

v

 R

vv Av

i

 x

o

openloopv x

o

21

1

21

2212

vv R R

 R

v

 R R

 x x

 x

 

21

,1 11

 R R R

 A

v

i R

o

openloopv

 x

 x

out 

 

21

,1  R R A Ropenloopv

oout   

 

  

ECE 3040 - Dr. Alan DoolittleGeorgia Tech

Ro is very small so this term is  EXTREMELY small!

FEEDBACK REDUCES OUTPUT IMPEDANCE!

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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, R ID

 ID

 x

 x R

vvi

 xopenloopvout out  vv Avv Rv

 Ri Riv

     ,1

1211

21ID21x or toueantocomparecurrentt eeg ect ng

 x

openloopv

openloopvv

 A

 Av

  

  

,

,

21

1

IDopenloopv

 x

 ID

 x

openloopv

openloopv x

 x R A

v

 R

v A

v

i  

  

,

,

,

1

1

 

 

FEEDBACK

INCREASES INPUT

ECE 3040 - Dr. Alan DoolittleGeorgia Tech

 IDopenloopvin ,

RID is very large so Rin is  EXTREMELY  large!

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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, R ID

•Rin=R 1 +R’in

in in

•Find R’in by forming a new test circuit

openloopvout 

 R

v Av

 R

v

 R

vv

 R

viii

1,111121

  

openloopv

 ID

in

 R

 R

 A

 Rv

i R

2

2

,

1

11

'

11'

R’in

  

 

 

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

11 R

 A

 R R R

 A

 R R R R

openloopv

in

openloopv

 IDin

 

 

 

 

 

 

 

 


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