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

2. 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

3. Operational Amplifiers as Analog Computers
Addition
Subtraction
Multiplication by a constant (Gain)
Integration
Differentiation
MONIAC

4. Operational Amplifiers Op-Amps

5. Schematic

6. Block Diagram

7. Analysis Model (Ideal OpAmp)
Differential Input
Input Resistance almost infinity
Output Resistance (Ro) almost zero
Gain (A) almost infinity

8. OpAmp Configurations
Inverting Amplifier

9. OpAmp Configurations-- Inverting Amplifier
No current can flow through Vp,Vn terminals

10. OpAmp Configurations-- Inverting Amplifier

11. 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

12. OpAmp Configurations– Non-Inverting Amplifier
Gain = 1 + R2 / R1

13. 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.

14. OpAmp Configurations-- Inverting Amplifier
Generic
Gain = - Z2 / Z1

15. OpAmp Configurations-- Integrator

16. OpAmp Configurations-- Integrator
Time Domain Analysis

17. OpAmp Configurations-- Differentiator

18. OpAmp Configurations-- Differentiator
Time Domain Analysis

19. 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

20. OpAmp Circuits– Frequency Counter
A ‘Differentiator’ followed by ‘Peak Detector’

21. OpAmp Circuits– Summer
Vout = -(Vs2 + Vs1) (R1=R2=R3)

22. OpAmp Circuits– Summer

23. OpAmp Circuits– Difference Amplifier
Vout = Vs2 – Vs1 (R1=R2=R3=R4)

24. OpAmp Circuits– Current Amplifiers
V to V
V to I
I to V
I to I

25. OpAmp Circuits– Filters
First Order Filters
Integrator (Low Pass)
Differentiator (High Pass)
Superposition (Band Pass)

26. OpAmp Circuits– Filters
First Order Low Pass Filter

27. OpAmp Circuits– Filters
Second Order Low Pass Filter

28. OpAmp Non-linear Circuits
Voltage Comparators
Schmitt Trigger
Variable Threshold

29. OpAmp Non-linear Circuits
Superdiode
Another manifestation of ‘virtual short’ due to negative feedback

30. OpAmp Non-linear Circuits
Signal Generators
Multivibrator
Square wave to Triangular wave conversion
Integrator

31. OpAmp—Solution of Differential Equations
Real time
Precise
Applicable to any order
Constant Coefficient DE’s only

32. OpAmp—Solution of Differential Equations
First Order Constant Coefficient DE

33. OpAmp—Solution of Differential Equations
First Order Constant Coefficient DE
R-C circuit simulation

34. OpAmp—Solution of Differential Equations
Second Order Constant Coefficient DE
R-L-C circuit simulation

35. 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

36. Analog Signal Processing
Pros
Inherently Analog World
Precision
Simplicity
Intuitive Designs vs ‘Programming’
Cons
Non-linearity
Rigidity
Noise Floor
Temperature dependence

37. Practical OpAmps Limitations
Gain-Bandwidth Product
Common Mode Rejection
Slew Rate

38. Open Loop OpAmp Characteristics
Device
LM741C
LF351
OP-07
LH0003
AD549K
Technology
BJT
BiFET
Hybrid BJT
AOL(typ)
200 k
100 k
400 k
40 k
Rin
2 M
1012 
8 M
100 k
1013  || 1 pF Ro
50 
30 
60 
~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

39. 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.

40. ?