Transcript
Dr. Bonnie H. FerriProfessor and Associate ChairSchool of Electrical and Computer Engineering
School of Electrical and Computer Engineering
Module 2: Op AmpsIntroduction and Ideal Behavior
Introduce Op Amps and examine ideal behavior
Introduce Operational Amplifiers Describe Ideal Op Amp Behavior Introduce Comparator and Buffer Circuits
Lesson Objectives
2
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
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
vov+
v-
4
Open Loop Behavior
+Vs
-Vs
vo
v+ +
-v-
vo= A(v+ - v-)
v+ - v-
voVs
-Vs
5
V
Comparator Circuit+Vs
-Vs
vo
v+ +
-v-
vin
voVs
-Vs
<−>
−=00
ins
inso vifV
vifVV
vin
6
Csin(ωt)
Example
+Vs
-Vs
vo
v++
-v- v+ - v-
voVs
-Vs
7
i+ = i- = 0v+ - v- = 0
Ideal Op Amp Behaviorv+
v-
vo+
-
i+
i-
+Vs
-Vs
vo
v+
v- Ri
RovinAvin
8
Buffer Circuit
vin = vo
vo+-
vin vo+-
vin
9
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- = 0v+ - v- = 0
v+
v-
vo+
-
i+
i-
10
Buffer Circuit Basic Amplifier Configurations Differentiators and Integrators Active Filters
Remainder of Module 2: Op Amps
11
Dr. Bonnie H. FerriProfessor and Associate ChairSchool of Electrical and Computer Engineering
School of Electrical and Computer Engineering
Buffer Circuits
Demonstrate buffer circuit behavior
Introduce physical op amps in circuits Examine Buffer Circuit behavior
Lesson Objectives
13
Use to boost power without changing voltage waveform
Buffer Circuit
vin = vo
vo+-
vin
vin
voVS
-VS
14
Example: Without Buffer
vin R+vo+
15
Vs = 15V
Physical Op Amps
Signal PIN
v- 2
v+ 3
-Vs 4
vo 6
+Vs 7
+Vs
-Vs
vo
v+ +
-v-
16
Example: With Buffer
+-vin
+vo+
R
vin R+vo+
17
Example: With Buffer
+-vin
+vo+
R
18
Summary
Buffers boost the power without changing the voltage waveform
Demonstrated physical op amp circuits
19
Dr. Bonnie H. FerriProfessor and Associate ChairSchool of Electrical and Computer Engineering
School of Electrical and Computer Engineering
Basic Op Amp AmplifierConfigurations
Introduce Inverting and Non-Inverting Amplifiers, Difference and Summing Amplifiers
Introduce Inverting and Non-Inverting Configurations Difference and Summing Configurations
Introduce the Gain of a circuit
Lesson Objectives
21
Non-Inverting Amplifiers
in3
32o V
RRR
V+
=
R
RRG :Gain
3
32 +=ino GVV =
+-vin
vo
R2
R3
R1
22
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
Inverting Amplifier
ino GVV =
in1
fo V
RRV −=
+
-
vin
vo
Rf
R1
24
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
Difference Circuit
+
-
v1
vo
Rf
R1
v2
R1
R2
)( 121
Fo VVRRV −=
26
Difference Circuit
+
-
v1
vo
Rf
R1
v2
R1
R2
)( 121
Fo VVRRV −=
27
Summing Amplifier
+
-v1
vo
Rf
R2
v2
R1
2
F2
1
F1
2211o
RRG
RRG
VGVGV
−=−=
+=
28
Summary
Gain: Amplifier Circuit Configurations
Non-Inverting Amplifier Inverting Amplifier Difference Amplifier Summing Amplifier
ino GVV =
29
Dr. Bonnie H. FerriProfessor and Associate ChairSchool of Electrical and Computer Engineering
School of Electrical and Computer Engineering
Introduce Integrating and Differentiating Op Amp Circuits
Differentiators and Integrators
Introduce Differentiators and Integrators Demonstrate the performance of both circuits on an
oscilloscope
Lesson Objectives
31
Differentiator Circuit
dtdVRCV in
o −=
+
-
vin
vo
R
Cv-
v+
cc V
dtdV
Ci=
32
Differentiator Circuit
Derivation:1. KVL: Vin = Vc + Ri + Vo
2. Vin = Vc
3. Vo = -Ri = -RC(dVin / dt)
dtdVRCV in
o −=
+
-
vin
vo
R
Cv-
v+
33
Differentiator Example
+
-
vin
vo
1000Ω
1µFv-
v+
vin v+
vo+VS= 15v
-VS = -15v
-VS
v-
+VS
34
Results
dtdVRCV in
o −=
35
Integrator Circuit
dtVRC
Vt
ino ∫−
=0
1
cc V
dtdV
Ci= ∫=t
c idtC
V0
1
+
-
vin
voR
v-
v+
C
36
Integrator Circuit
Derivation:For t<0: Vin = iR and Vo = 0For t>0: Vin = iR i = Vin/RVin = iR + Vc + Vo
Vo = -Vc = -1/C ∫t Vin/R dt0
dtVRC
Vt
ino ∫−
=0
1
cc V
dtdV
Ci= ∫=t
c idtC
V0
1
+
-
vin
voR
v-
v+
C
37
Integrator Examplevin v+
vo
+VS= 15v
-VS = -15v
-VSv-
+VS
+
-
vin
vo1000Ω
v-
v+
1µF
38
Results
dtVRC
Vt
ino ∫−
=0
1
39
Summary
Differentiator and Integrator Op Amp circuits examined
40
Dr. Bonnie H. FerriProfessor and Associate ChairSchool of Electrical and Computer Engineering
School of Electrical and Computer Engineering
Active Filters
Introduce active filters and show different types of filters
Introduce active filter circuits
Lesson Objectives
42
Analog Filters
Analog FilterVin 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 10000
0.2
0.4
0.6
0.8
1
ω
Mag
nitu
de
H(ω)
|H(ω)|
ω (rad/sec)43
Quiz
Vin = 1 + cos(10(2πt)) + cos(100(2πt)) Vout = 0.45cos(10(2πt)+θ1) + 0.97cos(100(2πt) +θ2)
44
Summary of RC and RLC (Passive) Filters
vinR +
-voC
vin
R +
-vo
CL
vin R+
-vo
C
ω
Mag
nitu
de (d
B)
Bode Plots
ω
Mag
nitu
de (d
B)
ω
Mag
nitu
de (d
B)
45
Depletes power
No isolation
Limitations of RLC Passive Filters
Analog FilterVin Vo
vinR +
-voC
46
– has its own power supply Most common active filters are made from op amps Provide isolation
Active Filters
Op Amp CircuitVin Vout
47
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
Derivation: Vin = iZ1
Vo = -iZf = -(Zf/Z1)Vin
Impedance Gain
inin
Fo V
ZZV −
=
49
Dr. Bonnie H. FerriProfessor and Associate ChairSchool of Electrical and Computer Engineering
School of Electrical and Computer Engineering
First-OrderLowpass Filters
Introduce lowpass filters
Introduce active lowpass filters
Lesson Objectives
51
Lowpass Filters
ω
Linear Plot
Mag
nitu
de
KDC
ωB
0.707KDC ω
Bode Plot
Mag
nitu
de (d
B)
20log10(KDC)3dB
Lowpass filters pass low frequency components and attenuate high frequency components
Transfer Function H(ω)
52
First-Order Filter
Bandwidth, ωB = 1/τDC Gain = H(0) = KDC
ω
Linear Plot
Mag
nitu
de
KDC
ωB
0.707KDC
0
1j1KH DC +ωτ
=ω)(
53
From Passive to Active Lowpass Filters
CircuitVin VoVin Vo
RC
Vo
RC
+-vin
Vin
RC
+-
vo
54
First-Order Inverting Lowpass Filter
+
- voR1
C
Rf
vin
inf1
fo V
1CjR1
RRV
+ω−=
55
Frequency Characteristics of LP Filter
ω
|H(ω)|Rf/R1
.707 Rf/R1
ωb
180°90°
H(ω)
ω1
f
RRGainDC −=
)()(
1CjR1
RRH
f1
f
+ω−=ω
1)ωCR(
1RR)|ω(H|
2ff
f
1 +=
)ωCRarctan(180)ω(H ff−=∠
fb CR
1ω,Bandwidthf
=
56
Derivation: Lowpass Filter
+
- voZ1vin
Zf
+
- voR1
C
Rf
vin
57
Design an inverting lowpass filter to have a DC gain of -2 and a bandwidth of 500 rad/s:
Example
+
- voR1
C
Rf
vin
1CjR1
RRH
f1
f
+ω−=ω)(
58
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
RC
+-vin
Vin
RC
+-
vo
+
- voR1
C
Rf
vin
59
Dr. Bonnie H. FerriProfessor and Associate ChairSchool of Electrical and Computer Engineering
School of Electrical and Computer Engineering
First-OrderHighpass Filters
Introduce highpass filters
Introduce active highpass filters
Lesson Objectives
61
Passes high frequency components and attenuates low frequency components
Highpass Filter
Linear Plot
ω
Mag
nitu
de
62
First-Order Filter
Corner Frequency, ωc = 1/τPassband Gain= KPB = K/τ
Linear Plot
1jKjH+ωτω
=ω)(
ω
Mag
nitu
de
KPB
ωc
0.707KPB
0
63
Inverting Highpass Filter Configuration
in1
fo V
1CjRCjRV
)( +ωω−
=
+
- vo
R1C
Rf
vin
+
- voZ1vin
Zf
64
Frequency Characteristics of HP Filter
CR1FreqCorner1
c =ω.,1
f
RRGainPassband −=∞→ω )(
)arctan()( ω−°−=ω∠ CR90H 1
)()(
1CjRCjRH
1
f
+ωω−
=ω
1CR
CRH2
1
f
+ω
ω=ω
)(|)(|
|H(ω)|Rf/R1
ωc = 1/R1C ω
0.707KPB
0
-90°
H(ω)ω0°
65
Design a highpass filter to have a passbandgain of 2 and a corner frequency of 1k rad/s:
Example
+
- vo
R1C
Rf
vin
66
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
)()(
1CjRCjRH
1
f
+ωω−
=ω
67
top related