This document discusses operational amplifiers and basic op amp circuits. It begins by introducing op amps and their ideal behavior, including that they have no voltage difference between inputs and infinite gain. Comparator and buffer circuits are presented as examples. The document then discusses inverting and non-inverting amplifiers, difference amplifiers, and summing amplifiers. Integrating and differentiating circuits using op amps are also introduced. Finally, the document discusses active filters and derivations for low-pass and high-pass filter circuits.

1. Dr. Bonnie H. Ferri
Professor and Associate Chair
School of Electrical and
Computer Engineering
School of Electrical and Computer Engineering
Module 2: Op Amps
Introduction and Ideal
Behavior
Introduce Op Amps and examine ideal behavior

2.  Introduce Operational Amplifiers
 Describe Ideal Op Amp Behavior
 Introduce Comparator and Buffer Circuits
Lesson Objectives
2

3. Operational Amplifiers (Op Amps)
Uses:
 Amplifiers
 Active Filters
 Analog Computers
Specialized circuit made up of transistors,
resistors, and capacitors fabricated on an
integrated chip
+Vs
-Vs
vo
v+
+
-v-
3

4. Vs = 10V, 15V
Op Amps in Circuits
 Active Element: has its own power supply
 Symbol ignores the +/- Vs in the symbol since it
does not affect circuit behavior
Symbol:
+Vs
-Vs
vo
v+
+
-v-
+
-
+Vs
-Vs
vo
v+
v-
4

5. Open Loop Behavior
+Vs
-Vs
vo
v+
+
-v-
vo= A(v+ - v-)
v+ - v-
vo
Vs
-Vs
5

6. V
Comparator Circuit
+Vs
-Vs
vo
v+
+
-v-
vin
vo
Vs
-Vs



<−
>
−=
0
0
ins
ins
o
vifV
vifV
V
vin
6

7. Csin(ωt)
Example
+Vs
-Vs
vo
v+
+
-v- v+ - v-
vo
Vs
-Vs
7

8. i+ = i- = 0
v+ - v- = 0
Ideal Op Amp Behavior
v+
v-
vo
+
-
i+
i-
+Vs
-Vs
vo
v+
v- Ri
Ro
vin
Avin
8

9. Buffer Circuit
vin = vo
vo
+
-
vin
vo
+
-
vin
9

10. Summary
 Op amps are active devices that can be used to filter or
amplify signals linearly
 Ideal op amps:
 Circuits: comparator and buffer
i+ = i- = 0
v+ - v- = 0
v+
v-
vo
+
-
i+
i-
10

11.  Buffer Circuit
 Basic Amplifier Configurations
 Differentiators and Integrators
 Active Filters
Remainder of Module 2: Op Amps
11

12. Dr. Bonnie H. Ferri
Professor and Associate Chair
School of Electrical and
Computer Engineering
School of Electrical and Computer Engineering
Buffer Circuits
Demonstrate buffer circuit behavior

13.  Introduce physical op amps in circuits
 Examine Buffer Circuit behavior
Lesson Objectives
13

14.  Use to boost power without changing voltage waveform
Buffer Circuit
vin = vo
vo
+
-
vin
vin
vo
VS
-VS
14

15. Example: Without Buffer
vin R
+
vo
+
15

16. Vs = 15V
Physical Op Amps
Signal PIN
v- 2
v+ 3
-Vs 4
vo 6
+Vs 7
+Vs
-Vs
vo
v+
+
-v-
16

17. Example: With Buffer
+
-vin
+
vo
+
R
vin R
+
vo
+
17

18. Example: With Buffer
+
-vin
+
vo
+
R
18

19. Summary
 Buffers boost the power without changing the voltage
waveform
 Demonstrated physical op amp circuits
19

20. Dr. Bonnie H. Ferri
Professor and Associate Chair
School of Electrical and
Computer Engineering
School of Electrical and Computer Engineering
Basic Op Amp
Amplifier
Configurations
Introduce Inverting and Non-Inverting Amplifiers, Difference and
Summing Amplifiers

21.  Introduce
 Inverting and Non-Inverting Configurations
 Difference and Summing Configurations
 Introduce the Gain of a circuit
Lesson Objectives
21

22. Non-Inverting Amplifiers
in
3
32
o V
R
RR
V
+
=
R
RR
G:Gain
3
32 +
=ino GVV =
+
-vin
vo
R2
R3
R1
22

23. If R2 = R3 = 200Ω,
 Since,G > 1, the input is
amplified
 If G < 1, the input is attenuated
Non-Inverting Amplifier Example
+
-vin
vo
R2
R3
R1
23

24. Inverting Amplifier
ino GVV =
in
1
f
o V
R
R
V −=
+
-
vin
vo
Rf
R1
24

25. R1 = 1000Ω, Rf = 2000Ω
 If,G > 1, the input is amplified
 If G < 1, the input is attenuated
Inverting Amplifier Example
+
-
vin
vo
Rf
R1
25

26. Difference Circuit
+
-
v1
vo
Rf
R1
v2
R1
R2
)( 12
1
F
o VV
R
R
V −=
26

27. Difference Circuit
+
-
v1
vo
Rf
R1
v2
R1
R2
)( 12
1
F
o VV
R
R
V −=
27

28. Summing Amplifier
+
-
v1
vo
Rf
R2
v2
R1
2
F
2
1
F
1
2211o
R
R
G
R
R
G
VGVGV
−=−=
+=
28

29. Summary
 Gain:
 Amplifier Circuit Configurations
 Non-Inverting Amplifier
 Inverting Amplifier
 Difference Amplifier
 Summing Amplifier
ino GVV =
29

30. Dr. Bonnie H. Ferri
Professor and Associate Chair
School of Electrical and
Computer Engineering
School of Electrical and Computer Engineering
Introduce Integrating and Differentiating Op Amp Circuits
Differentiators and
Integrators

31.  Introduce Differentiators and Integrators
 Demonstrate the performance of both circuits on an
oscilloscope
Lesson Objectives
31

32. Differentiator Circuit
dt
dV
RCV in
o −=
+
-
vin
vo
R
C
v-
v+
c
c
V
dt
dV
Ci =
32

33. Differentiator Circuit
Derivation:
1. KVL: Vin = Vc + Ri + Vo
2. Vin = Vc
3. Vo = -Ri = -RC(dVin / dt)
dt
dV
RCV in
o −=
+
-
vin
vo
R
C
v-
v+
33

34. Differentiator Example
+
-
vin
vo
1000Ω
1µF
v-
v+
vin v+
vo
+VS= 15v
-VS = -15v
-VS
v-
+VS
34

35. Results
dt
dV
RCV in
o −=
35

36. Integrator Circuit
dtV
RC
V
t
ino ∫
−
=
0
1
c
c
V
dt
dV
Ci = ∫=
t
c idt
C
V
0
1
+
-
vin
vo
R
v-
v+
C
36

37. Integrator Circuit
Derivation:
For t<0: Vin = iR and Vo = 0
For t>0: Vin = iR i = Vin/R
Vin = iR + Vc + Vo
Vo = -Vc = -1/C ∫t
Vin/R dt0
dtV
RC
V
t
ino ∫
−
=
0
1
c
c
V
dt
dV
Ci = ∫=
t
c idt
C
V
0
1
+
-
vin
vo
R
v-
v+
C
37

38. Integrator Example
vin v+
vo
+VS= 15v
-VS = -15v
-VS
v-
+VS
+
-
vin
vo
1000Ω
v-
v+
1µF
38

39. Results
dtV
RC
V
t
ino ∫
−
=
0
1
39

40. Summary
 Differentiator and Integrator Op Amp circuits examined
40

41. Dr. Bonnie H. Ferri
Professor and Associate Chair
School of Electrical and
Computer Engineering
School of Electrical and Computer Engineering
Active Filters
Introduce active filters and show different types of filters

42.  Introduce active filter circuits
Lesson Objectives
42

43. Analog Filters
Analog Filter
Vin Vout
0 0.05 0.1 0.15 0.2 0.25
-2
-1
0
1
2
Time (sec)
v(t)
0 0.05 0.1 0.15 0.2 0.25
-1.5
-1
-0.5
0
0.5
1
1.5
Time (sec)
v(t)
0 200 400 600 800 1000
0
0.2
0.4
0.6
0.8
1
ω
Magnitude
H(ω)
|H(ω)|
ω (rad/sec)
43

44. Quiz
Vin = 1 + cos(10(2πt)) + cos(100(2πt)) Vout = 0.45cos(10(2πt)+θ1) + 0.97cos(100(2πt) +θ2)
44

45. Summary of RC and RLC (Passive) Filters
vin
R +
-
vo
C
vin
R +
-
vo
C
L
vin R
+
-
vo
C
ω
Magnitude(dB)
Bode Plots
ω
Magnitude(dB)
ω
Magnitude(dB)
45

46.  Depletes power
 No isolation
Limitations of RLC Passive Filters
Analog
FilterVin Vo
vin
R +
-
vo
C
46

47. – has its own power supply
 Most common active filters are made from op amps
 Provide isolation
Active Filters
Op Amp
CircuitVin Vout
47

48.  An is a circuit that has a specific shaped frequency
response
 A is made of op amps and has its own power supply.
Advantages over RLC passive filters:
 Provides isolation (cascade filters)
 Boosts the power
 Can provide sharper roll-off
Summary
48

49. Derivation: Vin = iZ1
Vo = -iZf = -(Zf/Z1)Vin
Impedance Gain
in
in
F
o V
Z
Z
V
−
=
49

50. Dr. Bonnie H. Ferri
Professor and Associate Chair
School of Electrical and
Computer Engineering
School of Electrical and Computer Engineering
First-Order
Lowpass Filters
Introduce lowpass filters

51.  Introduce active lowpass filters
Lesson Objectives
51

52. Lowpass Filters
ω
Linear Plot
Magnitude
KDC
ωB
0.707KDC ω
Bode Plot
Magnitude(dB)
20log10(KDC)
3dB
 Lowpass filters pass low frequency components and attenuate high
frequency components
Transfer Function H(ω)
52

53. First-Order Filter
Bandwidth, ωB = 1/τ
DC Gain = H(0) = KDC
ω
Linear Plot
Magnitude
KDC
ωB
0.707KDC
0
1j
1
KH DC
+ωτ
=ω)(
53

54. From Passive to Active Lowpass Filters
CircuitVin Vo
Vin Vo
R
C
Vo
R
C
+
-vin
Vin
R
C
+
-
vo
54

55. First-Order Inverting Lowpass Filter
+
- vo
R1
C
Rf
vin
in
f1
f
o V
1CjR
1
R
R
V
+ω
−=
55

56. Frequency Characteristics of LP Filter
ω
|H(ω)|
Rf/R1
.707 Rf/R1
ωb
180°
90°
H(ω)
ω1
f
R
R
GainDC −=
)(
)(
1CjR
1
R
R
H
f1
f
+ω
−=ω
1)ωCR(
1
R
R
)|ω(H|
2
ff
f
1 +
=
)ωCRarctan(180)ω(H ff−=∠
f
b
CR
1
ω,Bandwidth
f
=
56

57. Derivation: Lowpass Filter
+
- voZ1
vin
Zf
+
- vo
R1
C
Rf
vin
57

58. Design an inverting lowpass filter to have a
DC gain of -2 and a bandwidth of 500
rad/s:
Example
+
- vo
R1
C
Rf
vin
1CjR
1
R
R
H
f1
f
+ω
−=ω)(
58

59.  A passes low frequency signals and attenuates high
frequency signals
 Three first-order lowpass configurations:
 Noninverting, isolation at the input
 Noninverting, isolation at the output
 Inverting, isolation at input and output
Summary
Vo
R
C
+
-vin
Vin
R
C
+
-
vo
+
- vo
R1
C
Rf
vin
59

60. Dr. Bonnie H. Ferri
Professor and Associate Chair
School of Electrical and
Computer Engineering
School of Electrical and Computer Engineering
First-Order
Highpass Filters
Introduce highpass filters

61.  Introduce active highpass filters
Lesson Objectives
61

62.  Passes high frequency components and attenuates low
frequency components
Highpass Filter
Linear Plot
ω
Magnitude
62

63. First-Order Filter
Corner Frequency, ωc = 1/τ
Passband Gain= KPB = K/τ
Linear Plot
1j
Kj
H
+ωτ
ω
=ω)(
ω
Magnitude
KPB
ωc
0.707KPB
0
63

64. Inverting Highpass Filter Configuration
in
1
f
o V
1CjR
CjR
V
)( +ω
ω−
=
+
- vo
R1C
Rf
vin
+
- voZ1
vin
Zf
64

65. Frequency Characteristics of HP Filter
CR
1
FreqCorner
1
c =ω.,
1
f
R
R
GainPassband −=∞→ω )(
)arctan()( ω−°−=ω∠ CR90H 1
)(
)(
1CjR
CjR
H
1
f
+ω
ω−
=ω
1CR
CR
H
2
1
f
+ω
ω
=ω
)(
|)(|
|H(ω)|
Rf/R1
ωc = 1/R1C ω
0.707KPB
0
-90°
H(ω)
ω
0°
65

66. Design a highpass filter to have a passband
gain of 2 and a corner frequency of 1k rad/s:
Example
+
- vo
R1C
Rf
vin
66

67.  A passes high frequency components in signals and
attenuates low frequency components
 First-order highpass filter
 Design based on
 Corner frequency of the passband, ωc
 Passband gain, KPB
Summary
+
- vo
R1C
Rf
vin
)(
)(
1CjR
CjR
H
1
f
+ω
ω−
=ω
67