OPERATIONAL AMPLIFIERSWhy do we study them at this point???

1. OpAmps are very useful electronic components

2. We have already the tools to analyze practical circuits using OpAmps

3. The linear models for OpAmps include dependent sources

TYPICAL DEVICE USING OP-AMPS

OP-AMP ASSEMBLED ON PRINTED CIRCUIT BOARD APEX PA03

PIN OUT FOR LM324

DIMENSIONAL DIAGRAM LM 324

LM324 DIP

LMC6294

MAX4240

CIRCUIT SYMBOL FOR AN OP-AMP SHOWING POWER SUPPLIES

LINEAR MODEL OUTPUT RESISTANCEINPUT RESISTANCE

GAIN75

125

1010:

501:

1010:

A

R

R

O

i

TYPICAL VALUES

CIRCUIT WITH OPERATIONAL AMPLIFIER

DRIVING CIRCUIT

LOAD

OP-AMP

TRANSFER PLOTS FOR SOME COMERCIAL OP-AMPS

SATURATIONREGIONLINEAR

REGION

IDENTIFY SATURATION REGIONSOP-AMP IN SATURATION

CIRCUIT AND MODEL FOR UNITY GAINBUFFER

0 inOOis VAIRIRV :KVL

0 inOO VAIRoutV- :KVL

IRV iin : VARIABLEGCONTROLLIN

iOO

is

out

RARRV

V

1

1

SOLVING

1S

outO V

VA

WHY UNIT GAIN BUFFER?

BUFFERGAIN

PERFORMANCE OF REAL OP-AMPSOp-Amp BUFFER GAINLM324 0.99999LMC6492 0.9998MAX4240 0.99995

A

)(0 vvAvR OO

THE IDEAL OP-AMP

iR

ARR iO ,,0IDEAL

i

i

THE UNITY GAIN BUFFER – IDEAL OP-AMP ASSUMPTION

svv

vv

OUTv v

OUT Sv v

OUTv

1OUT

S

v

v

USING LINEAR (NON-IDEAL) OP-AMP MODEL WE OBTAINED

1

1

out

is

O O i

VRV

R A R

PERFORMANCE OF REAL OP-AMPS

Op-Amp BUFFER GAINLM324 0.99999LMC6492 0.9998MAX4240 0.99995

IDEAL OP-AMP ASSUMPTION YIELDS EXCELLENT APPROXIMATION!

WHY USE THE VOLTAGE FOLLOWER OR UNITY GAIN BUFFER?

svv

vv

vvO

SO vv

SO vv

THE VOLTAGE FOLLOWER ACTS AS BUFFER AMPLIFIER

THE SOURCE SUPPLIES POWERTHE SOURCE SUPPLIES NO POWER

THE VOLTAGE FOLLOWER ISOLATES ONECIRCUIT FROM ANOTHERESPECIALLY USEFUL IF THE SOURCE HASVERY LITTLE POWER

CONNECTION WITHOUT BUFFER CONNECTION WITH BUFFER

LEARNING EXAMPLE

s

out

V

VG GAIN THE DETERMINE

0v

0 vvvAo

0v

0 iiRi

000

21

R

V

R

V outs

- v@KCL APPLY

0i

1

2

R

R

V

VG

s

out

LEARNING EXAMPLE: DIFFERENTIAL AMPLIFIER

THE OP-AMP IS DEFINED BY ITS 3 NODES. HENCE IT NEEDS 3 EQUATIONS

THINK NODES!

KCL AT V_ AND V+ YIELD TWO EQUATIONS(INFINITE INPUT RESISTANCE IMPLIES THAT i-, i+ ARE KNOWN)

OUTPUT CURRENT IS NOT KNOWN

DON’T USE KCL AT OUTPUT NODE. GET THIRD EQUATION FROM INFINITEGAIN ASSUMPTION (v+ = v-)

LEARNING EXAMPLE: DIFFERENTIAL AMPLIFIER

NODES @ INVERTING TERMINAL

NODES @ NON INVERTING TERMINAL

IDEAL OP-AMP CONDITIONS

243

42

43

40 vRR

Rvv

RR

Rvi

1

2

1

1

21

1

2

1

2 11 vvR

R

R

Rv

R

Rv

R

RvO

)(, 121

21324 vv

R

RvRRRR O

LEARNING EXAMPLE: USE IDEAL OP-AMP

Ov FIND1v

1v

2v

2v

1ov

2ov

1mv

2mv

6 NODE EQUATIONS + 2 IDEAL OP-AMP

22

11

vv

vv

22

11

m

m

vv

vv

FINISH WITH INPUT NODE EQUATIONS…USE INFINTE GAIN ASSUMPTION

2211vvvv

2211vvvv

mm

USE REMAINING NODE EQUATIONS

00:@1

2121

2

011

1

R

vv

R

vv

R

vvv o

G

m

00:@2

212

1

22

2

R

v

R

vv

R

vvv

G

o

m

ONLY UNKWONS ARE OUTPUT NODE VOLTAGES

1 VARIABLE REQUIREDFOR SOLVE

oovv

LEARNING EXTENSION AMP-OPIDEAL ASSUMEI FIND O.

Vv 12

VvAO 12

0 iRi

Vv 12

02

12

12

12:

kk

Vv o KCL@ VVo 84

mAk

VI oO 4.810

“inverse voltage divider”

ii vR

RRvv

RR

Rv

1

2100

21

1

0i

INFINITE INPUT RESISTANCE

NONINVERTING AMPLIFIER - IDEAL OP-AMP

LEARNING EXTENSION

v

_vov

SET VOLTAGE iv v

INFINITE GAIN ASSUMPTION

i iv v v v

R 2

R 1

ivv

0v

LEARNING EXAMPLE UNDER IDEAL CONDITIONS BOTH CIRCUITS SATISFY

1 28 4

OV V V

1 2If 1 2 , 2 3

dc supplis are 10

V V V V V V

V

DETERMINE IF BOTH IMPLEMENTATIONS PRODUCE THEFULL RANGE FOR THE OUTPUT

1 22

XV V V

1 21 2 , 2 3 1 2

XV V V V V V V V V OK!

XV

4O XV V

1 2 4 8X O

V V V V V V !OV OK

18

YV V

11 2 16 8

YV V V V V V

EXCEEDS SUPPLY VALUE.THIS OP-AMP SATURATES!

POOR IMPLEMENTATION