1. Operational amplifiers are widely used electronic components that can perform mathematical operations such as amplification, integration, differentiation, and summation. 2. An ideal op-amp has infinite input impedance, infinite gain, zero output impedance, and can operate at infinite bandwidth. 3. Op-amps are used in various circuit configurations including inverting amplifiers, non-inverting amplifiers, summing amplifiers, voltage followers, and filters.

1. 1
Slides taken from:
A.R. Hambley, Electronics, © Prentice Hall, 2/e, 2000
A. Sedra and K.C. Smith, Microelectronic Circuits,
© Oxford University Press, 4/e, 1999
Operational
Amplifiers

2. 2Figure 2.1 Circuit symbol for the op amp.
Operational Amplifier Symbol

3. 3Figure 2.3 Op-amp symbol showing power supplies.
Operational Amplifier Symbol

4. 4
Internal Structure of Op Amps
+
-
vid
vo
+
-
Transcoductance
Differential
Amplifier
High Gain
Voltage
Amplifier
Unity
Gain
Buffer
C

5. 5Figure 2.2 Equivalent circuit for the ideal op amp. AOL is very large
(approaching infinity).
The ideal OA

6. 6
The ideal OA
 Infinite input impedance
 Infinite open-loop gain for the differential input
 Zero gain for the common mode signal
 Zero output impedance
 Infinite Bandwidth

7. 7
The OA Transfer Curve
vO
vid

8. 8
Feedback
 Negative Feedback
Part of the output signal is returned to the input
in opposition to the source signal
 Positive Feedback
The signal returned from the output to the input
aids the original source signal

9. 9
Figure 2.5 Inverting amplifier.
The Inverting Amplifier

10. 10Fig. 2.5 Analysis of the inverting configuration
Analysis of the Inverting Amplifier

11. 11
Figure 2.6 An inverting amplifier that achieves high gain with a smaller
range of resistor values than required for the basic inverter.
Another Inverting Amplifier

12. 12
Figure 2.11 Non-inverting amplifier.
The Non-inverting Amplifier

13. 13Figure 2.12 Voltage Follower.
The Voltage Follower

14. 14
Figure 2.14 Difference amplifier.
Difference Amplifier (1)

15. 15
Fig. 2.22 Application of superposition to the analysis of the difference
amplifier
Difference Amplifier (2)

16. 16
Fig. 2.23 Finding the input resistance of the difference amplifier.
Difference Amplifier (3)

17. 17
Figure 2.7 Summing amplifier.
Summing Amplifier

18. 18
Figure 2.13 Inverting or non-inverting amplifier.
Inverting/Non-Inverting Amplifier (1)

19. 19
Inverting/Non Inverting Amplifier (2)

20. 20
Inverting/Non inverting Amplifier (3)

21. 21Figure 2.10a Schmitt trigger circuit.
A positive feedback’s example:
Schmitt Trigger

22. 22
Figure 2.10b Schmitt trigger circuit and waveforms.
A positive feedback’s example:
Schmitt Trigger

23. 23Figure 2.20 If low-value resistors are used, an impractically large
current is required.
Practical Design Considerations:
Non-inverting Amplifier

24. 24Figure 2.21 If very high value resistors are used, stray capacitance can couple
unwanted signals into the circuit.
Practical Design Considerations:
Non-inverting Amplifier

25. 25
Figure 2.22 To attain large input resistance with moderate resistances for an inverting
amplifier we cascade a voltage follower with an inverter.
Practical Design Considerations:
Inverting Amplifier

26. 26
OP-AMP Imperfections
 Non-linearity in the range of operation
 Finite input impedance and non-zero output
impedance
 Limited bandwidth and gain
 Saturation
 Output Current Limit
 Slew Rate non linearity
 DC offset

27. 27
Figure 2.25 Bode plot of open-loop gain for a typical op amp.
Gain and Bandwidth Limitations

28. 28Figure 2.26 Non-inverting amplifier.
Effect of the gain and bandwidth limitations.

29. 29
Figure 2.27 Bode plots for the non-inverting amplifier.
Effect of the gain and bandwidth limitations.

30. 30Figure 2.28 For a real op amp, clipping occurs if the output voltage reaches
certain limits.
Saturation

31. 31
Output Current Limit
 The current that an op amp can supply to a
load is limited (typically +/-25 mA)
 If a small-value load draw a current outside the
limit, the output waveform becomes clipped

32. 32Figure 2.30 Output for R1=1Kohm R2= 3Kohm RL = 10kohm and Vs max = 5V.
Max Output Voltage Swing

33. 33
Slew Rate Limitation
 The output voltage of an op amp cannot
change in magnitude at a rate exceeding the
slew rate limit

34. 34Figure 2.31 Output for RL = 10kohm and vs(t) = 2.5 sin (105
π t).
Effect of Slew Rate Limitation

35. 35
Effect of Slew Rate Limitation
Fig. 2.29 (a) Unity-gain follower. (b) Input step waveform. (c) Linearly
rising output waveform obtained when the amplifier is slew-rate limited.

36. 36
Effect of Slew Rate Limitation
 Full-power bandwidth fFPB:
range of frequencies for which the op amp can
produce an undistorted sinusoidal output with peak
amplitude equal to the guaranteed maximum output
voltage.

37. 37
DC Imperfections
 Input Bias Current
 Input Offset Current
 Input Offset Voltage

38. 38Figure 2.33 Current sources and a voltage source model the dc imperfections
of an op amp.
Modeling DC Imperfections

39. 39
Modeling DC Imperfections

40. 40
Modeling DC Imperfections

41. 41
Modeling DC Imperfections

42. 42
Modeling DC Imperfections

43. 43Figure 2.35 Adding the resistor R to the inverting amplifier circuit causes the
effects of bias currents to cancel.
Canceling the Effects of Bias Currents

44. 44Figure 2.36 Non-inverting amplifier, including resistor R to balance the
effects of the bias currents.
Canceling the Effects of Bias Currents

45. 45
Figure 2.46 Unity-gain amplifiers.
Common OA Circuits: unity gain amplifiers

46. 46Figure 2.47 Inverting amplifier.
Common OA Circuits: Inverting Amplifier

47. 47Figure 2.48 Ac-coupled inverting amplifier.
Common OA Circuits:
AC coupled inverting amplifier

48. 48Figure 2.49 Summing amplifier.
Common OA Circuits:
Summing Amplifier

49. 49Figure 2.50 Non-inverting amplifier. This circuit approximates an
ideal voltage amplifier.
Common OA Circuits: Non-Inverting Ampl.

50. 50Figure 2.51 Ac-coupled non-inverting amplifier.
Common OA Circuits:
AC coupled non inverting amplifier

51. 51Figure 2.52 Ac-coupled voltage follower with bootstrapped bias resistors.
AC coupled follower (1)

52. 52
AC coupled follower (2)

53. 53
AC coupled follower (3)

54. 54
AC coupled follower (4)

55. 55
AC coupled follower (5)

56. 56Figure 2.53 Difference amplifier.
Common OA Circuits: Difference Amplifier

57. 57Figure 2.54 Instrumentation-quality differential amplifier.
Common OA Circuits:
Instrumentation Difference Amplifier

58. 58Figure 2.55 Voltage-to-current converter (transconductance amplifier).
Common OA Circuits:
Voltage/Current Converter

59. 59Figure 2.56 Voltage-to-current converter with grounded load.
Common OA Circuits:
Voltage/Current Converter (Inverting)

60. 60Figure 2.56 Voltage-to-current converter with grounded load.
Voltage/Current Converter (Non Inverting)
(step 1)

61. 61
Voltage/Current Converter (non Inverting)
(step 2)

62. 62
Voltage/Current converter (step 3)

63. 63
Figure 2.57 Current-to-voltage converter (transresistance amplifier).
Common OA Circuits:
Current/Voltage Converter

64. 64Figure 2.58 Current amplifier.
Common OA Circuits: Current Amplifier

65. 65Figure 2.59 Variable-gain amplifier.
Common OA Circuits: Variable Gain Ampl.

66. 66
Common OA Circuits: Filters
-
+
+
-
+
-
Z2
Z1

67. 67
Figure 2.60 Integrator Filter.
Common OA Circuits: Integrator

68. 68
Figure 2.63 Differentiator Filter.
Common OA Circuits: Derivator

69. 69Figure 2.64c Comparative Bode plots.
OA’s Bode Plot

70. 70Figure 2.64a Comparative Bode plots.
Integrator’s Bode Plot

71. 71Figure 2.64b Comparative Bode plots.
Differentiator’s Bode Plot