Operational Amplifiers

Instructor: Chia-Ming TsaiElectronics Engineering

National Chiao Tung UniversityHsinchu, Taiwan, R.O.C.

Contents• Introduction

• Operational Amplifiers (OP AMPs)

• Ideal OP AMP

• Inverting AMP

• Noninverting AMP

• Summing AMP

• Difference AMP

• Cascaded OP AMP Circuits

• Applications

Introduction

• The op amp is a basic building block for performing mathematical operations such as summation, amplification, integration, and differentiation

• The concept of virtual short between the differential inputs of the op amp is extremely important for circuit analysis

OP AMPs

• Complex circuit networks consisting of transistors, resistors, capacitors, and diodes

Cont’d

12

12

210 (KCL)

vvAAvv

vvv

iiiii

do

d

Equivalent circuit of an op amp

+

_

Cont’dParameter Typical

rangeIdeal value

Open-loop gain, A

105 to 108

Input resistance, Ri

105 to 1013

Output resistance, Ro

10 to 100

0

Supply voltage, VCC

5 to 24 V

Slope = A

Example

? Find

50

102

1026

5

so

o

i

vv

R

R

A

short virtualare inputs alDifferenti

0 V 20

9999699.1

2, & 1 nodeat KCL Applying

1

v

v

v

s

o

Ideal OP AMP• Infinite open-loop voltage gain: A • Infinite input resistance: Ri

• Zero output resistance: Ro 0

• v1 = v2 (virtual short) assumed for analysis

Inverting AMP

The equivalent circuit

f

oi

R

vv

R

vvii

1

1

121

1, nodeat KCL Applying

if

o vR

Rv

vv

1

21

0

amp, op idealan For

(feedback resistor)

Example: I-to-V Converters

Riv so

i1 i2

i3

a

2

3

1

31 1

R

R

R

RRiv so

Noninverting AMP

f

o

R

vv

R

vii

v

1

1

121

1

0

, nodeat KCL Applying

if

o

i

vR

Rv

vvv

1

21

1

amp, op idealan For

Voltage Follower• Conditions: Rf = 0 or R1 = or both

• Unity gain: Av = 1

• Useful as a buffer amp due to its very high Ri and very low Ro

Summing AMP

3

3

2

2

1

1321

, nodeat KCL Applying

R

v

R

v

R

viiii

a

3

32

21

1

vR

Rv

R

Rv

R

Rv fff

o

Difference AMP

43

2

21

1

, nodeat KCL Applying

, nodeat KCL Applying

R

v

R

vv

b

R

vv

R

vv

a

bb

oaa

121

2

4321

11

22

43

21

1

2

, If

1

1

vvR

Rv

RRRR

vR

Rv

RR

RR

R

Rv

vv

o

o

ba

Cascaded OP AMP Circuits

321

and 0

amps, op idealFor

AAAA

RR oi

Applications: DAC[S1 S2 S3 S4] Decimal - Vo

0000 0 0

0001 1 0.125

0010 2 0.25

0011 3 0.375

0100 4 0.5

0101 5 0.625

0110 6 0.75

0111 7 0.875

1000 8 1.0

1001 9 1.125

1010 10 1.25

1011 11 1.375

1100 12 1.5

1101 13 1.625

1110 14 1.75

1111 15 1.875

Digital-to-Analog Converter (DAC)

4321ref 2488

SSSSVR

RV f

o

Applications:Instrumentation Amplifier (IA)

Gv

vo

R

RA

vvAv

21

12

Cont’d• Characteristics of IA

– Voltage gain adjustable by RG

– Very high Ri and very low Ro

– The differential voltage is amplified and the common-mode voltage is rejected