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
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
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
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
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
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
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
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
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
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