Chapter 30

Operational Amplifiers

2

Introduction

• Characteristics– High input impedance– Low output impedance– High open-loop gain– Two inputs– One output– Usually + and – dc power supplies

3

Introduction

• Ideal Characteristics– zin (inverting) ≈ ∞

– zin (non-inverting) ≈ ∞

– zout ≈ 0

– Av ≈ ∞

-

+

V-

V+

Output

InvertingInput

Non-InvertingInput

4

Introduction

• Uses– Comparators– Voltage amplifiers– Oscillators– Active filters– Instrumentation

amplifiers

-

+

V-

V+

Output

InvertingInput

Non-InvertingInput

5

Introduction• Single-ended amplifier

– One input grounded– Signal at other input

• Double-ended amplifier/Differential amplifier– Signals at both inputs

-

+

V-

V+

Output

InvertingInput

Non-InvertingInput

6

Differential Amplifier and Common-Mode Signals

• Basic differential amplifier– Q1 identical to Q2 – RC1 = RC2

– IC1 = IC2 and emitter currents equal– Also, IC ≈ IE for high β– and VBE ≈ 0.7 V

• Similar calculation of Bias

∴

7

Differential Amplifier and Common-Mode Signals

RE

–VEE

IE

___-

___-

RC2RC1IC1

IC2

VCC

Q1 Q2

8

RE

–VEE

IE

RC2RC1IC1

IC2

VCC

Q1 Q2

___-

___-

Differential Amplifier and Common-Mode Signals

• Apply same signal to both BasesVout = Vout1 – Vout2 ≈ 0– Eliminates common-

mode signals– 60 Hz– Noise

9

Differential Amplifier and Common-Mode Signals

• Apply sinusoids to both bases:– Same amplitude,

180° difference in phase,

if Vin1 = –Vin2

Vout = 2Vin

∴RE

–VEE

IE

Q1 Q2

___-

RC2RC1IC1

IC2

VCC

___-

10

Differential Amplifier and Common-Mode Signals

• Common-mode signals– Differential voltage gain

also called open-loop voltage gain

20,000 ≤ Av ≤ 200,000

outvd

d

vA

v=

11

Differential Amplifier and Common-Mode Signals

• Common-mode signals– Common-mode voltage gain

outvc

c

vA

v=

12

Differential Amplifier and Common-Mode Signals

• Common-mode rejection ratio (CMRR)– Equations

– Values

10[ ] 20log ( )

70 90

vd

vc

db

ACMRR

A

CMRR CMRR

db CMRR db

=

=

≤ ≤

13

Differential Amplifier and Common-Mode Signals

• Noise– Static in audio signal– Increases as signal is

amplified– Common mode signal– Significantly reduced

by differential amplifier

___- ___

-

-+

vnoise

vin

14

Negative Feedback• Op-amp

– Large differential, open-loop voltage gain

• Avol ≈ 100,000

– Small input yields saturated output (VCC or VEE)

15

Negative Feedback• Negative feedback

– Returns a portion of output signal to the input– Open-loop voltage gain decreased

16

Negative Feedback• Input impedance still

high

• Output impedance low

• Circuit voltage gain, Av

– Adjustable– Stable

-+

NegativeFeedback

___-

vin

vout

outv

in

vA

v=

17

Inverting Amplifier• Basic circuit

18

Inverting Amplifier• Output 180° out of phase with input

• Significant decrease in gain– Gain now called closed-loop voltage gain

• Output impedance ≈ 0

• vd ≈ 0

19

Inverting Amplifier• Inverting input at virtual

ground, vin(-) ≈ 0

• iin to op-amp ≈ 0

• Input current only dependent on vin and R1

• Avcl only dependent on input resistor and feedback resistor

1

1

1

inin

out in Fvcl

in in

Fvcl

vi

R

v i RA

v i R

RA

R

=

= =−

=−

20

Inverting Amplifier

-

+

___-

vout(OC)

vd+

-

Rin

RF

-+___

-

vin

R1

+

-

• Modelvd ≈ 0Rin ≈ ∞iin = if zin ≈ R1

i = 0

iin

if

Rout

Avolvdinternal

21

Inverting Amplifier

-

+

___-

iout(sc)

vd Rin

RF

-+___

-

vin

R1

+

-

i = 0

iin

if

Rout

i1

___-

Avolvdinternal

( )

( )

(1 )

out OCout

out SC

outout vcl

vol

vz

i

Rz A

A

=

⎛ ⎞= − ⎜ ⎟

⎝ ⎠

• Low output impedance

22

Non-Inverting Amplifier• Circuit

23

The Non-Inverting Amplifier

• Very high input impedance• Voltage gain related to the two resistors• Very low output impedance• Excellent buffer

24

Non-Inverting Amplifier

• Differential voltage– vd ≈ 0

• Input current to op-amp– i = 0

• Closed-loop voltage gain (Avcl) is a resistor ratio

25

Non-Inverting Amplifier

1

1

1

1

outv

in

F F Fv

F

Fvcl

vA

v

R i R iA

R i

RA

R

=

+=

= +

26

Non-Inverting Amplifier• Model

• Input impedance

-

+

___-

vout

vd Rin

RF

-

+___-

vin

R1

iin

if

Rout

Avolvdinternal

+

-- +

1

din

in

volin in

vcl

vi

R

Az R

A

=

⎛ ⎞= +⎜ ⎟⎝ ⎠

zin

27

Non-Inverting Amplifier• Model

• Output impedance

-

+

___-

vd Rin

RF

-

+___-

R1

iin

if

Rout

Avolvdinternal

+

-- +

___-iout(sc)

i2( ) 2out sc f

vclout out

vol

i i i

Az R

A

= +

⎛ ⎞=⎜ ⎟⎝ ⎠

28

Non-Inverting Amplifier• Very high zin

• Very low zout

• Good buffer circuit

• Also called voltage follower (gain = 1)

• Or adjustable gain > 1

29

Non-Inverting Amplifier• Voltage Follower Buffer Circuit

– Gain = 1– High impedance source drives low impedance

load

30

Op-Amp Specifications• LM 741 series

– Inexpensive– Widely used– Good general specifications– Characteristic of all op-amp specifications

• Provide Minimum, Typical, and Maximum ratings

31

Op-Amp Specifications• Input Offset Voltage, Vio

– LM741C, Vio typical is 2 millivolts

– Model is voltage source with value, Vio in series with + input

32

Op-Amp Specifications• Input Offset Voltage, Vio

– Without feedback this would saturate output with no input

– With negative feedback, output due to Vio is closed-loop gain times Vio

33

Op-Amp Specifications• Input Offset Current, Ios

• Ios = Difference between bias currents at + and – inputs of op-amp

• 741C typical Ios is 20 nanoamps

• Multiplying resistor used to measure Ios

34

Op-Amp Specifications• Input Resistance

– 741C: minimum = .3 MΩ, typical = 2 MΩ

• Open-Loop Voltage gain (Avol)

– 741C: Avol = Large Signal Voltage Gain• minimum = 20,000, typical = 200,000

– Closely related to Bandwidth, BW

35

Op-Amp Specifications• Gain-bandwidth product

– 741C = 1,000,000 = 106 MHz

36

Op-Amp Specifications

• Gain versus frequency curve for op-amp

37

Op-Amp Specifications• Slew rate

– Maximum rate of change of output voltage

• 741C maximum slew rate = 0.5 V/μsec

VSlew Rate

t

Δ=

Δ

38

Op-Amp Specifications

• Fastest time for output to go from 0 to 10 volts is 20 μsec

• Can distort waveforms that have too fast a rise time

39

Op-Amp Specifications• Slew rate required for

Sinusoid with frequency f and amplitude A

• Maximum amplitude of a sine wave with frequency f for a given slew rate

40

Op-Amp Specifications• Bias

Compensation: use RC = R1||RF

41

Troubleshooting an Op-Amp Circuit

• Problems occur when circuit is first built• Most important

– Correct connection of dual power supply

• Connecting a – supply to a + input (or vice versa) can burn out an op-amp

• Single earth ground• Short connecting wires