Operational Amplifiers Basic Theory & Use in Analog Signal Processing By Muhammad Bilal PhD Candidate Department of Computer Engineering, LUMS.

Operational AmplifiersBasic Theory

& Use in Analog Signal Processing

By

Muhammad BilalPhD Candidate

Department of Computer Engineering, LUMS

Operational Amplifiers – Brief History

• Appeared around 1947 (vacuum tube age)

• Combination of High Gain & Negative Feedback

• Miniaturization after invention of BJT

• Integrated Circuit Operational Amplifier– Robert Widlar at Fairchild Semiconductor Corps

(1968)– Industry standard, the 741

Operational Amplifiers as Analog Computers

• Operational Amplifier– Addition– Subtraction– Multiplication by a constant (Gain)– Integration– Differentiation

• MONIAC

Operational Amplifiers

Op-Amps

Schematic

Block Diagram

Analysis Model (Ideal OpAmp)

• Differential Input– Input Resistance almost infinity– Output Resistance (Ro) almost zero– Gain (A) almost infinity

OpAmp Configurations

• Inverting Amplifier

OpAmp Configurations-- Inverting Amplifier

)()0(

)(

noutp

inout

npin

VAVV

AAVV

VVV

• No current can flow through Vp,Vn terminals

1

2

21

21

21

R

R

V

V

R

VA

V

RA

VV

R

VV

R

VV

ii

in

out

outoutout

in

outnnin

RR

OpAmp Configurations-- Inverting Amplifier

Lessons from Inverting Amp. configuration

• Gain is set via external components– Stable gain due to ratio of resistors

• Effects of extremely high gain

– Virtual short circuit (Vp = Vn)– Negative Feedback compensates for the

internal high gain of OpAmp

OpAmp Configurations– Non-Inverting Amplifier

Gain = 1 + R2 / R1

OpAmp Configurations– Voltage Follower

Due to negative feedback, virtual short will occur, forcing Vn to be equal to Vp which is in turn equal to Vs. Thus Vout = Vs and hence the name voltage follower.

OpAmp Configurations-- Inverting Amplifier

• Generic

• Gain = - Z2 / Z1

f

RZ

LjZ

CjZ

sistor

Inductor

Capacitor

2

1

Re

OpAmp Configurations-- Integrator

RC

j

jV

jV

in

out

)(

)(

0 10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

7

8

9

10Frequency Response of "Integrator"

Frequency

Mag

nitu

de

OpAmp Configurations-- Integrator

• Time Domain Analysis

OpAmp Configurations-- Differentiator

RCjjV

jV

in

out

)(

)(

0 10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

7

8

9

10Frequency Response of "Differentiator"

Frequency

Mag

nitu

de

OpAmp Configurations-- Differentiator

• Time Domain Analysis

OpAmp Configurations-- Filters

• Integrator– First Order Low Pass Filter– Extremely high gain at low frequencies

• Only used within a closed loop

• Differentiator– First Order High Pass Filter

OpAmp Circuits– Frequency Counter

• A ‘Differentiator’ followed by ‘Peak Detector’

OpAmp Circuits– Summer

Vout = -(Vs2 + Vs1) (R1=R2=R3)

OpAmp Circuits– Summer

OpAmp Circuits– Difference Amplifier

Vout = Vs2 – Vs1 (R1=R2=R3=R4)

OpAmp Circuits– Current Amplifiers

• V to V

• V to I

• I to V

• I to I

OpAmp Circuits– Filters

• First Order Filters

– Integrator (Low Pass)

– Differentiator (High Pass)

– Superposition (Band Pass)

OpAmp Circuits– Filters

•First Order Low Pass Filter

CRjR

R

jV

jV

in

out

21

2

1

1

)(

)(

OpAmp Circuits– Filters

•Second Order Low Pass Filter

OpAmp Non-linear Circuits

• Voltage Comparators

• Schmitt Trigger– Variable Threshold

OpAmp Non-linear Circuits

• Superdiode– Another manifestation of ‘virtual short’ due to

negative feedback

OpAmp Non-linear Circuits

• Signal Generators– Multivibrator

• Square wave to Triangular wave conversion– Integrator

OpAmp—Solution of Differential Equations

• Real time

• Precise

• Applicable to any order

• Constant Coefficient DE’s only

OpAmp—Solution of Differential Equations

• First Order Constant Coefficient DE

)(tfbxdt

dxa

OpAmp—Solution of Differential Equations

• First Order Constant Coefficient DE• R-C circuit simulation

ta

b

Aetx

tfbxdt

dxa

)(

)(

OpAmp—Solution of Differential Equations

• Second Order Constant Coefficient DE• R-L-C circuit simulation

))sin()cos(()(

)(2

2

tBtAetx

tfcxdt

dxb

dt

xda

at

OpAmp—Solution of Differential Equations

• Second Order DE simulation

– Hardware Simulation of R-L-C circuit without actual use of Inductor

– Implementation of precise mathematical relationships given by DE’s

Analog Signal Processing

• Pros– Inherently Analog World– Precision– Simplicity– Intuitive Designs vs ‘Programming’

• Cons– Non-linearity– Rigidity– Noise Floor– Temperature dependence

Practical OpAmps Limitations

• Gain-Bandwidth Product

• Common Mode Rejection

• Slew Rate

Open Loop OpAmp Characteristics

Device LM741C LF351 OP-07 LH0003 AD549K

Technology BJT BiFET BJTHybrid

BJTBiFET

AOL(typ) 200 k 100 k 400 k 40 k 100 k

Rin 2 M 1012 8 M 100 k 1013 || 1 pF

Ro 50 30 60 50 ~100

Slew Rate 0.5 V/s 13 V/s 0.3 V/s 70 V/s 3 V/s

CMRR 90 dB 100 dB 110 dB 90 dB 90 dB

References

• Design with Operational Amplifiers and Analog Integrated Circuits,Sergio Franco, 3rd Edition.

• Basic Engineering Circuit Analysis, David Irwin, 8th Edition.• Electronic Devices and Circuit Theory, Robert Boylsted, 9th Edition.

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