OPERATIONAL AMPLIFIERS

Ho Kyung Kim, Ph.D.

hokyung@pusan.ac.kr

School of Mechanical Engineering

Pusan National University

Basic Experiment and Design of Electronics

Outline

• Ideal Op-amp

• Inverter

• Non-inverter

• Difference

• Integrators

• Differentiators

• Active rectifiers

2

• Let us consider, CD player (source) + Amplifier + Speakers (load)

Ideal Op-Amp

Equivalent source circuit that

the amplifier sees from its input port

Equivalent load resistance

seen from the output port of the amplifier

)()( tAvtv SL

• Amplification factor depends upon

– the source and load impedances

– the input and output resistance of the amplifier

• The given amplifier would perform differently with different loads or sources

• What are the desirable characteristics of the amplifier?

– (large input impedance) Rin >> 1

– (small output impedance) Rout << 1 (or Rout = 0)

)(tvRR

Rv S

inS

inin

Lout

LinL

RR

RAvv

S

Lout

L

inS

inL v

RR

R

RR

RAv

amplification factor

Sin vv 1lim

inS

in

R RR

R

in

inL Avv

• Operational amplifier (simply, op-amp)

– is an integrated circuit (IC)

– has a great number of operations such as addition, filtering, and integration

– is found in most measurement and instrumentation applications

• Open-loop model

– an ideal differential amplifier that amplifies the difference between two input voltages

– near-infinite input resistance and very small output resistance

• Rin =

• : AV(OL) = open-loop voltage gain (105 ~ 107)

0ini

)()(

vvAv OLVout

Inverter

inFS iii

S

S

SR

vvi

F

out

FR

vvi

0v

vAvvAv OLVOLVout )()( )(

)(OLV

out

A

vv

F

Sout

OLVSFOLVSF

outSR

Rv

ARRARRvv

)()(

1

/

1

/

1

0ini

KCL;

Ohm's law;

Ground;

Open-loop model;

or

FS ii

FOLV

out

F

out

SOLV

out

S

S

RA

v

R

v

RA

v

R

v

)()(

SOLV

out

FOLV

out

F

out

S

S

RA

v

RA

v

R

v

R

v

)()(

or

inverting amplifier closed-loop gain

• Let us consider the inverting terminal voltage;

• The effect of the feedback connection from output to inverting (noninverting) input is to force the voltage at the inverting (noninverging) input to be equal that at the noninverting (inverting) input ( virtual grounds)

• Useful assumptions for analysis of ideal op-amp with negative feedback

①

②

0)(

OLV

out

A

vv vvor

vv

0ini

Summing amplifier

FN iiii 21

S

S

nR

vi n

F

out

FR

vi

F

outN

n S

S

R

v

R

v

n

n 1

n

n

S

N

n S

Fout v

R

Rv

1

KCL;

Ohm's law;

Non-Inverter

SinSF iiii

S

SR

vi

F

outF

R

vvi

vvv S

S

S

F

Sout

R

v

R

vv

S

F

S

out

R

R

v

v1

Voltage Follower

vv

Svv

outvv

outS vv

Differential Amplifier

2

21

2 vRR

Rv

1

11

R

vvi

2

2R

vvi out

)(

)(

12

1

2

2

211

2

21

2

1

12

vvR

R

vRRR

R

RR

v

R

vRvout

Instrumentation Amplifier

v2

noninverting amp differential amp

1

2

1

2 21

2/1

R

R

R

RA

)(2

1)( 21

1

221 vv

R

R

R

RAvAv

R

Rv FF

out

1

2

21

21

R

R

R

R

vv

vA Fout

V

Integrator

)()( titi FS

S

SS

R

tvi

)(

dt

tdvCti out

FF

)()(

dt

tdvtv

CR

out

S

FS

)()(

1

t

S

FS

out dttvCR

tv ')'(1

)(

KCL;

Ohm's law;

From the definition of a capacitor;

Differentiator

)()( titi FS

dt

tdvCi S

SS

)(

F

out

FR

vti )(

dt

tdvCRtv S

SFout

)()(

KCL;

Ohm's law;

Active low-pass filter

S

FLPF

Z

ZjwA )(

FF

F

F

FFCjwR

R

jwCRZ

1

1| |

SS RZ

FF

SF

S

FLPF

CjwR

RR

Z

ZjwA

1

/)(

FF CR

10

dB 3log202log20log20)( 0 S

F

S

F

dBLPFR

R

R

RjA

cutoff freq. or – 3dB freq.

Active high-pass filter

S

SSjwC

RZ1

FF RZ

SS

SF

S

FHPF

CjwR

CjwR

Z

ZjwA

1)(

S

FHPF

w R

RjwA

)(lim

Active band-pass filter

Analog computer