E E 2315 Lecture 08 - Introduction to Operational Amplifiers.

E E 2315

Lecture 08 - Introduction to Operational Amplifiers

Operational Amplifiers

• Ideal operational amplifiers are easily analyzed

• Assumptions for ideal operation are realistic

• Inexpensive commercial Op-Amps available as integrated circuits

• Practical applications for instrumentation, signal processing and control circuits

A741 Pinout

1

2

3

4

8

7

6

5

A741Offset Null

Inverting Input

Non-inverting Input

Vcc-

Vcc+

Output

Offset Null

NC

Op Amp Terminals

+Vcc

-Vcc

Positive supplyvoltage

Output

InvertingInput

NoninvertingInput

Negative supplyvoltage

Op Amp Terminal Currents

+Vcc

-Vcc

Vcc Vcc

io

in

ip

ic+

ic-

Common Node

Op Amp Terminal Voltages

+Vcc

-Vcc

Vcc Vcc

+vp

-

+

vo

-

+

vn

-

Common Node

Equivalent Circuit

A(Vp-Vn)Ro

Ri+vo-

ip

in

io

Assumptions for Ideal Op Amp

• Open loop Gain, A vp - vn 0

• Then vp - vn 0 Ri

• Ri ip 0 and in 0

• Gain is linear up to the saturation voltage

• Saturation voltage equals power supply voltage

Open-Loop Characteristics

+Vcc

-Vcc

vp-vn

vo

A(vp-vn)

+Sat

-Sat

Linear

Inverting Amplifier

and

Vn = 0 and in = 0. Then KCL at node n yields:

+Vcc

-Vcc

RfRg

vg

+vn-

in

0

+vo-

0 00 0g o

g f

v v

R R

Saturated Mode

• Inverting Amplifier with +Vcc = 5 V and Vcc = -5V.

• Rf = 10 k and Rg = 1 k

t

1 V

-1 V

vgvo

t5 V

-5 V

Non-Inverting Amplifier

KCL at node n:

vn = vp = vg

+Vcc

-Vcc

vg

Rg

Rs

Rf0

0n

p+

vo

-

+vp-

+vn

-

0g g o

s f

v v v

R R

Summing Amplifier (1/2)

+Vcc

-Vcc

va

Ra

vb

Rb

vc

Rc

Rf

+

vo

-

Summing Amplifier (2/2)

0a b c o

a b c f

v v v v

R R R R

f f fo a b c

a b c

R R Rv v v v

R R R

Difference Amplifier (1/3)

KCL @ n:

+Vcc

-Vcc

RbRa

Rc

Rdvb

va +vo-

+vp-

n

p

0n a n o

a b

v v v v

R R

Difference Amplifier (2/3)

Voltage Divider @ p:

+Vcc

-Vcc

RbRa

Rc

Rdvb

va +vo-

+vp-

n

p

dn p b

c d

Rv v v

R R

Difference Amplifier (3/3)

Substitute:

into:

and simplify:

If: Then:

dn p b

c d

Rv v v

R R

d a b bo b a

a c d a

R R R Rv v v

R R R R

a c

b d

R R

R R b

o b aa

Rv v v

R

Analyzing an OpAmp Circuit

+Vcc

-Vcc

Rf

Ry

RL

Rx

Rg

vg