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FYSE400 ANALOG ELECTRONICS

LECTURE 7

Operational Amplifier

1©Loberg University of Jyväskylä

OPERATIONAL AMPLIFIER

Introduction

RiVi

+

-

-

+

ivoVA−−−−

Ro

+ +

--

V1

V2

Vo

+

-

Circuit symbol of operational amplifier

+

-

Vi

V1

V2ivoo VAV −−−−====

0Avo >>>>

21i VVV −−−−====

2

Equivalent circuit of operational amplifier

Ideal Op-Amp

Input resistance ∞∞∞∞→→→→iR

Output resistance 0Ro ====Voltage gain 0VA ivo ====⇒⇒⇒⇒∞∞∞∞→→→→The bandwidth is infinite

When 0VVV o21 ====⇒⇒⇒⇒====

1.

2.

3.

4.

5.

Non-ideal Op-Amp

valuehighRi ====valuelow0Ro ≠≠≠≠

valuelow0VvaluehighA ivo ≠≠≠≠⇒⇒⇒⇒====

Limited bandwidth

0VandVV o21 ≠≠≠≠====

©Loberg University of Jyväskylä

Voltage gain


Inverting Op-Amp Stage

+

-

Vi

ivoo VAV −−−−====

0Avo >>>>+

-

V1

R1 R2

Vo

(a)

Assumption : Ii=0 ∞∞∞∞====iR

RiVi

+ +

Ro

Vo

+

+

R1 R2

V1

I

I

Ii

∞∞∞∞≠≠≠≠voA

3

0VAIRV ivooo ====++++−−−−0VIRV o2i ====−−−−−−−−

0VAIRIRIRV ivoo211 ====++++−−−−−−−−−−−−

⇒

(((( )))) o2vo1

2voo

1

oV

RRA1R

RAR

V

VA

++++++++++++−−−−======== Or βvo

1

2V

A

11

1

R

RA

++++−−−−====

21

1

RR

R

++++====βwhere

0Ro ====

RiVi

- - ivoVA−−−−

-

-V1

(b)


Input resistance

0VAV ivoo ====++++

0VRIV o22i ====−−−−−−−−

(((( )))) 0VARIIRIV ivo2i1111 ====++++−−−−−−−−−−−−

0VRIV i111 ====−−−−−−−−

0RIV iii ====−−−−

i12 III −−−−====


Inverting Op-Amp Stage

Ro=0Assumption : Ii=0 ∞∞∞∞≠≠≠≠iR ∞∞∞∞≠≠≠≠voA

RiVi

+ +

Ro

Vo

+

-

+

R1R2

V1

Ii

I2I1 I2

4

i12 III −−−−====

)(in1

1

i1

1

1'

i RRI

VR

I

VR −−−−++++====++++========

2i

i

vo

i2

)(inRR

Rwhere

A1

RRR

++++====

++++====−−−− β

β21i

1

vo

21

'

i

RjaRRwhen

RA1

RRR

>>>>>>>>

≈≈≈≈++++

++++≈≈≈≈

RiVi

- - ivoVA−−−−

-

-

V1

Ri'⇒


currentcircuitshort

voltageoutputunloadedRo ='


Inverting Op-Amp Stage Output resistance

RiVi

+

- -

+

ivoVA−−−−

Ro

Vo

+

-

+

R1 R2

V1

IIscIb

Ia

5

(((( ))))(((( )))) o2vo1

21o'

oRRA1R

RRRR

++++++++++++++++==== 21o

vo

o'

o RRRwhenA1

RR ++++<<<<<<<<

++++====

β

- - ivoVA−−−−

-

-


21

1

RR

R

++++====β


Noninverting Op-Amp Stage Voltage gain

+

-

Vi


0Avo >>>>+-

V1

R1 R2

Vo

Ri

Vi+-

-

+

ivoVA−−−−

Ro

Vo

+

-

+R1

R2

V1

II

6

(((( ))))1voo21

21voV

RARRR

RRAA

++++++++++++++++====

βvo

1

2V

A

11

1

R

R1A

++++

++++====

21

1

RR

R

++++====βwhere

-


OPERATIONAL AMPLIFIER Noninverting Op-Amp Stage

Input resistance

Ri

Vi+-

-

+

ivoVA−−−−

Ro

Vo

+

-

+R1

R2

V1 2rcm 2rcm

Ii

I2

I1

7

(((( )))) ∞∞∞∞========++++==== cmovoi

'

i rand0RwhenA1RR β

(((( )))) cmvoi

'

i rA1RR β++++==== Common mode input resistance 2rcm

-

Ri'


Noninverting Op-Amp Stage


Output resistance

Ri

Vi+-

+

VA−−−−

Ro

Vo

+

-

+R1

R2

V1

Isc

IbI1

I2

8

21o

vo

o'

o RRRkunA1

RR ++++<<<<<<<<

++++====

β

- ivoVA−−−−

-

-

Ro'


Input Offset Voltage VIO

Ideal Operational Amplifier 0VVwhen0V 21o ============

Nonideal Operational Amplifier 0Vo ≠≠≠≠

Nonideal Op-Amp Stage


9

o

A real OpAmp exhibits an imbalance caused by

a mismatch of the input transistors.

Unequal input currents

Unequal base-emitter voltages



Nonideal Op-Amp Stage Input Offset Voltage VIO

+

Vi 0Avo >>>>-

R1 R2

Eo

+

Vio

_

RiVi

+

-

+

VA−−−−

Ro

Eo

+

-

+

R1 R2

Vio

I1 I2

10

The direction of the

input offset voltage VIO

+

-VIO

+

-OR

Assumption : Ro=0 and Ri=∞

-ivoo VAV −−−−====

+

- - ivoVA−−−−

-


Output Error Voltage EO or -EO


Nonideal Op-Amp Stage Input Offset Voltage VIO

++++

++++−−−−====

βvo

1

21IOo

A

11

1

R

RRVE

1RiVi

+

-

+

VA−−−−

Ro

Eo

+

-

+

R1 R2

Vio

I1 I2

11

β1

IOo VE −≈ When loopgain

∞∞∞∞→→→→βvoA

β1=

∆∆

IO

O

V

EHigh voltage gain high

IOO VE ∆∆

- - ivoVA−−−−

-



++++−−−− bb IandI (fA - µA)

++++++++==== −−−−

1vo21

21vobo

RARR

RRAIE

Input Bias Currents

Inverting amplifier stage

Vi+ -

-

+

ivoVA−−−−

Ro

Eo

+

R1 R2

Ib+

I1

I2

Ib-

12

(((( ))))

++++==== −−−−

ββ

vo

21b

A

11

11RRI

( )β1

21 RRIE bo −= When loopgain ∞∞∞∞→→→→βvoA

- ivoVA−−−−

-


Nonideal Op-Amp Stage ++++−−−− bb IandI

Compensation of error

Input Bias Currents

Inverting amplifier stage

Vi+ -+

VA−−−−

Ro

Eo

+

R1 R2

IIb-

Req


13

(((( ))))[[[[ ]]]]β1

IRIRRE beqb21o ++++−−−− −−−−====

- ivoVA−−−−

-

Ib+Ib-


Nonideal Op-Amp Stage Input Bias Currents ++++−−−− bb IandI

Noninverting Amplifier

+

-

Vi

ivoo VAV −−−−====0Avo >>>>

R1 R2

Eo

Ib-

_

Ib+

R


14

(((( )))) 0V,0Rwhen1

RRIE 1S21bo ============ −−−− β

(((( ))))[[[[ ]]]] 0R,0Vwhen1

IRIRRE S1bSb21o ≠≠≠≠====−−−−==== ++++−−−− β

ivoo

++

- V1 = 0

Rs



Compensation of error

Input Bias Currents

+

-

Vi


0Avo >>>>

R1 R2

Eo

Ib-

_

Ib+

Rs

Rq

++++−−−− bb IandI


15

(((( ))))[[[[ ]]]] 0Vwhen1

IRIRRRE 1bSb21qo ====−−−−++++==== ++++−−−− β21qS RRRR ++++====

( )β1

+− −= bbSo IIRE

Noninverting

Amplifier

ivoo VAV −−−−====++

- V1=0

Rs



++++−−−− −−−−==== BBIO III

(((( )))) 21eq21IOo RRRwhen1

RRIE ========β

Inverting Amplifier

Input Offset Current IIO


16

(((( )))) 21eq21IOo β

(((( )))) 0R,RRRwhen1

RRIE q21S21IOo ============β

(((( )))) 21qSSIO21qIOo RRRRwhen1

RI1

RRRIE ++++========++++====ββ

Noninverting Amplifier


The effect of the voltage variation

of the power supply.

sply

IO

V

VPSR

∆∆====

Power Supply Rejection PSRNonideal Op-Amp Stage

+

-

Vi

ivoo VAV −−−−====0Avo >>>>

+

-

R1 R2

Eo

+

_

PSRVsply∆


17

splyV∆Different for the positive

and negative supply.

β1

VPSRE splyo ∆∆ ====

Reduced error voltage generator

+


Dual and Single Power OpAmp

PSR When V- = 0V

Noise

R1

R2

voAEt

Req

Eot


0Avo >>>>

R1ideal R2ideal

_

In+

Req id

Rs ideal

ET1 ET2

ETeq

In-Een

Eot


18

Total noise generator is reduced

to the input of the OpAmp.

Voltage noise : (((( )))) 12

f

f

2

nen ffanddffeE2

1

>>>>==== ∫∫∫∫

Current noise : (((( )))) 12

f

f

2

nin ffanddffiI2

1

>>>>==== ∫∫∫∫

+

Req id

ETs

Noise densities :

nn ei

Thermal noise voltage over resistance R (Johnson noise)


The units of the current and voltage densities can be as following :

Hzi,HzeorHzi,Hze nn

2

n

2

n

Noise densities :

[ ] HznVen = [ ] HzpAin =Voltage Current

Nonideal Op-Amp Stage Noise


19

Hzi,HzeorHzi,Hze nnnn

∫∫∫∫====2

1

ndeE 2

ne

ω

ω

ω ∫∫∫∫====2

1

ndiI 2

ni

ω

ω

ω

Where the ωωωω2 -ωωωω1 is the band width of the circuit.

RMS values


The Current and Voltage noise density in OpAmps

10

5

HznV10

HzpA



20

1 10 100 1000

Frequency

Vo

lta

ge n

ois

e

1

3

2

2.7Hz

10 100 1000 10000

Frequency

Cu

rren

t n

ois

e

1

3

140Hz

OP27


For example the voltage noise of

operational amplifier OP27 in the

band width 0.1Hz to 10Hz. 10

5

HznV

nV80V pp ≈≈≈≈−−−−


The Voltage noise density in OpAmp


21

1 10 100 1000Frequency

Vol

tage

noi

se1

3

22.7Hz

The probability that voltage noise

is over Vp-p is 0.1% when :

rmspp V6.6V ∗∗∗∗====−−−−


If noise densities are constant :

(((( ))))BWeE 2

nen ====

(((( ))))



22

(((( ))))BWiI 2

nin ====

2

n

2

3

2

2

2

1tot EEEEE L++++++++++++====


∞∞∞∞→→→→==== ββ votot Awhen1

EE

++++

====

ββcl

A

11

11A

Thrue noise

gain

R2

R1

voAEt

Req

Eot



23

(((( )))) (((( ))))[[[[ ]]]] (((( )))) BWRRkT4kTR4RRiRie1

E 21eq

2

21n

2

eqn

2

not ++++++++++++++++==== −−−−++++β

++++βvoA

1

(((( )))) (((( ))))[[[[ ]]]] (((( )))) BWRRkT4kTR4RRiRieE 21eq

2

21n

2

eqn

2

nt ++++++++++++++++==== −−−−++++

(((( ))))(((( ))))noiseJohnsonrms

BWkTR4


Architecture of two-stage Op-Amp

InputDifferential

AmplifierGain

Stage

Level

Shifter

Output

Stage

Output

CMRR Active Load VBE multiplier Complementary

1A 2A 1A3 ≈≈≈≈ 1A3 ≈≈≈≈

Inside The Op-Amp Stage


24

CMRR Active Load VBE multiplier Complementary

emitter follower

DC-coupled stages


Inside The Op-Amp Stage The two-stage architecture


25

The schematic diagram of the 741-type Op-Amp

Millman-Grabel



The simplified figure of the input stage.

The active element in the differential

pair is formed by the CC-CB connected

transistors Q1-Q3 and Q2-Q4.

Differential stage

The two-stage architecture


26

Millman-Grabel



CB-stage

CC-stage

- input+ input


Differential stage


27

Input resistance RiCB is emitter

resistance of the CC-stage

6o

4o6o

0

44)CB(i

R

rR1

rR

β

π

++++====

We have to calculate high-resistance active load Ro6 for input resistance of CB-stage.

Millman-Grabel

Millman-Grabel



ΩΩΩ

ΩΩ M5.14k1k658

k12501M5.10

Rr

R1rR

E6

E06o6o ====

++++⋅⋅⋅⋅++++====

++++++++====

π

β


Differential stage


28

Ro6 is output resistance of the

CE-stage with RE

Millman-Grabel



Ω

ΩΩΩ

Ωk10

M5.14

M26.5M5.142501

k658

R

rR1

rRR

6o

4o6o

0

4)CC(E4i ≈≈≈≈

++++====

++++========

β

πInput resistance of the

CB-stage :

Loaded voltage gain of the CC-stage :


Differential stage


29

(((( ))))(((( ))))

(((( ))))8.0

M5.10k10251k658

M5.10k102501

rR1r

rR1A

2oE02

2oE0

)4Ri,CC(V ≈≈≈≈⋅⋅⋅⋅++++

⋅⋅⋅⋅++++====

⋅⋅⋅⋅++++++++⋅⋅⋅⋅++++

≈≈≈≈ΩΩΩ

ΩΩβ

β

π

Output resistance of

the CC-stage is : Ωk63.2g

1

1

r

1

rrRrR

2m0

2

0

22bs2oTh ====≈≈≈≈

++++≈≈≈≈

++++++++++++====

ββππ

1A )CC(V ≈≈≈≈Unloaded voltage gain of the CC-stage : ∞∞∞∞→→→→ER



C

L0

0

is

L)CB(V

R

R1

RR

RA

β

β

++++++++−−−−====

6

46

o

oo

C

L

R

rR

R

R =

C

Li

R

Rr

R

0

4

1 βπ

+≈

where :

And Rs is output resistance

of the CC-stage 2.63kΩ

Voltage gain of the CB-stage


Differential stage

sR

4iR

CB-stageCC-stage

vCCAvCBA

CC-stage

CB-stageQ2

Q4


30

1170

R

Rr1

R

Rr1

r

1

r

RrA

6o

6o4o

0

0

6o

6o4o

0

4

0

2

6o04

)CB(V −−−−≈≈≈≈++++

++++++++

++++

−−−−====

β

β

ββππ

ΩM26.5r 4o ====ΩM5.14R 6o ====

2500 ====βΩk658rr 24 ======== ππ

where :

Voltage gain of the diff. Amp

(inverting input) :1170AAA cCBvCCvdif −−−−≈≈≈≈====


CB-stageCC-stage


Output resistance of the

differential amplifier : 6o)CB(o)diff(o RRR ====

Ω=

+++= M

rrR

RrR

bs

soCBo 5.101 0

)(π

β

2500 ====βΩM26.5rr 4oo ========

Ωk63.2g

1R

2m

s ====≈≈≈≈

0rb ====


Differential stage


31

0rb ====Ωk658rr 4 ======== ππΩ=ΩΩ= MMMR diffo 1.65.145.10)(

( ) ( ) 420

40202)( 1

11 πππ

ππ βββ rr

rrRrR ECCi +=

+++≈++≈Input resistance of

the CC-stage is:

( ) ( ) Ω=Ω+Ω=+= MkkrrRid 6.265865822 42 ππInput resistance of the

differential amplifier



Equivalent circuit of differential amplifier:

1170AV −−−−====ΩM1.6Ro ====

ΩM6.2Rid ====

(calculated from inverting input)


Differential stage


32

id

High output resistance needs high load resistance.

Gain stage should have high input resistance

⇒⇒⇒⇒



Gain stage



33

CC-stage CE-stage with

active load

Differential

stage

Millman-Grabel



16or

The small-signal

equivalent circuit

of the gain stage.


Gain stage


34

2500 ====β0r 16b ====

Ωk391A16

mV25250

I

V

gr

16CQ

T0

16m

016 ====⋅⋅⋅⋅============

µββ

π

ΩM1.6Rs ====Ωk50RE ====

ΩM25.6A16

V100

I

Vr

16C

A16o ============

µ

(((( ))))(((( )))) 66.0

rR1rrR

rR1A

16oE01616bs

16oE0

)CC(V ≈≈≈≈++++++++++++++++

++++====

ββ

π

ΩΩΩ k17k86.25k50

1

rrRrRR

0

1616bs16oE)CC(o

========

++++++++++++====

βπ

Output resistance of CC-stage

Voltage gain of CC-stage

Millman-Grabel



Voltage gain of CE-stage 334

R

R1RrrR

RA

C

L0E1717bs

L0)CE(V −−−−====

++++++++++++++++

−−−−====β

β

π

2500 =β0=br

where

Voltage gain of CC-CE-cascade :


Gain stage


35

0=br

Ω== kA

Vro 8.181

550

10017 µ

Ω=== kA

VrR BoC 9.90

55050

13 µΩ== krrR BooL 6.601317

Ω== kRR CCos 17)(

Ω== kI

Vr

CQ

T 4.1117

017 βπ

22033466.0)()( −=⋅−=⋅= CEVCCVV AAA


Ωk8.71RrrR

R1rRR

Ebs

E0oC

'

o ====

++++++++++++++++====

π

β

The output resistance of the CC-CE cascade is :2500 =β

0=br

Ω= kro 1.18117

Ω= kr 4.1117π

Ω== kRR CCos 17)(

Ω= 100R

where


The two-stage architecture Gain stage


36

Ω= 100ER

(((( ))))(((( ))))(((( )))) ΩΩ

Ω

M2.5rk19251r

rRk501rrR

16o16

16oiCE0biCC

≈≈≈≈++++≈≈≈≈

++++++++++++====

π

π β

The input resistance of the CC-CE cascade is :

(((( ))))[[[[ ]]]]Ωk30

RRr

R1rRrrR

EC17o

C017oE17b17iCE ≈≈≈≈

++++++++++++++++++++++++====

βπ


5

OL 106.2A ××××≈≈≈≈Ωk72Ro ≈≈≈≈

Diff Gain


Gain stage


37

1170Adm −−−−≈≈≈≈ 220A CECC −−−−≈≈≈≈−−−−

Ωk72Ro ≈≈≈≈



Level Shift

V7.0VVVV −−−−≈≈≈≈−−−−====



38

V7.0VVVV IBEIO −−−−≈≈≈≈−−−−====

21

2

RR

R

++++VO is attenuated by

)RIV(VV 1OBEIO ++++−−−−====

)VV(VV ZBEIO ++++−−−−====

Millman-Grabel


Millman-Grabel


Voltage Multiplier


Level Shift


39

(((( )))) )914(R

R1VRR

R

VV

4

3BE43

4

BE −−−−

++++====++++====

Variable


)1114(1

Rg1

RRgRg1

RgA

41m

432m22m

22mV −−−−≈≈≈≈

++++++++++++++++

≈≈≈≈


Level Shift


40

Millman-Grabel

)1014(R

R2VVV

4

3BEIO −−−−

++++−−−−====

1Rg1 22m0 >>>>>>>>>>>>>>>>β

41m

432

Rg1

RRRsekä

++++++++>>>>>>>>

when


The basic Complementary Emitter-follower

Output Stage



41

Crossover

distortion

Millman-Grabel



Elimination of Crossover distortion


Output Stage


42

Millman-Grabel



Current

limitersVBE-multiplier Current

limiters

Elimination of Crossover distortion


Output Stage


43

Darlington pair

instead of diodes

Millman-Grabel Millman-Grabel


The End of Part 7


44

The End of Part 7


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