lecture 91 loop analysis (3.2) circuits with op-amps (3.3) prof. phillips february 19, 2003
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![Page 1: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/1.jpg)
lecture 9 1
Loop Analysis (3.2)Circuits with Op-Amps (3.3)
Prof. Phillips
February 19, 2003
![Page 2: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/2.jpg)
lecture 9 2
Op Amps
• Op Amp is short for operational amplifier.
• An operational amplifier is modeled as a voltage controlled voltage source.
• An operational amplifier has a very high input impedance and a very high gain.
![Page 3: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/3.jpg)
lecture 9 3
Use of Op Amps
• Op amps can be configured in many different ways using resistors and other components.
• Most configurations use feedback.
![Page 4: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/4.jpg)
lecture 9 4
Applications of Op Amps
• Amplifiers provide gains in voltage or current.
• Op amps can convert current to voltage.
• Op amps can provide a buffer between two circuits.
• Op amps can be used to implement integrators and differentiators.
• Lowpass and bandpass filters.
![Page 5: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/5.jpg)
lecture 9 5
The Op Amp Symbol
+
-
Non-inverting input
Inverting input
Ground
High Supply
Low Supply
Output
![Page 6: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/6.jpg)
lecture 9 6
The Op Amp Model
+
–Inverting input
Non-inverting input
Rin
v+
v-
+–
A(v+ -v- )
vo
![Page 7: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/7.jpg)
lecture 9 7
Typical Op Amp
• The input resistance Rin is very large (practically infinite).
• The voltage gain A is very large (practically infinite).
![Page 8: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/8.jpg)
lecture 9 8
“Ideal” Op Amp
• The input resistance is infinite.
• The gain is infinite.
• The op amp is in a negative feedback configuration.
![Page 9: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/9.jpg)
lecture 9 9
The Basic Inverting Amplifier
–
+Vin+
–Vout
R1
R2
+–
![Page 10: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/10.jpg)
lecture 9 10
Consequences of the Ideal
• Infinite input resistance means the current into the inverting input is zero:
i- = 0
• Infinite gain means the difference between v+ and v- is zero:
v+ - v- = 0
![Page 11: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/11.jpg)
lecture 9 11
Solving the Amplifier Circuit
Apply KCL at the inverting input:
i1 + i2 + i-=0
–R1
R2
i1 i-
i2
![Page 12: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/12.jpg)
lecture 9 12
KCL
0i
111 R
v
R
vvi inin
222 R
v
R
vvi outout
![Page 13: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/13.jpg)
lecture 9 13
Solve for vout
Amplifier gain:
21 R
v
R
v outin
1
2
R
R
v
v
in
out
![Page 14: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/14.jpg)
lecture 9 14
Recap
• The ideal op-amp model leads to the following conditions:
i- = 0 = i+
v+ = v-
• These conditions are used, along with KCL and other analysis techniques, to solve for the output voltage in terms of the input(s).
![Page 15: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/15.jpg)
lecture 9 15
Where is the Feedback?
–
+Vin+
–Vout
R1
R2
+–
![Page 16: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/16.jpg)
lecture 9 16
Review
• To solve an op-amp circuit, we usually apply KCL at one or both of the inputs.
• We then invoke the consequences of the ideal model.
– The op amp will provide whatever output voltage is necessary to make both input voltages equal.
• We solve for the op-amp output voltage.
![Page 17: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/17.jpg)
lecture 9 17
The Non-Inverting Amplifier
+
–
vin
+
–
vout
R1
R2
+–
![Page 18: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/18.jpg)
lecture 9 18
KCL at the Inverting Input
+
–
vin
+
–
vout
R1
R2
i-
i1 i2
+–
![Page 19: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/19.jpg)
lecture 9 19
KCL
0i
111 R
v
R
vi in
222 R
vv
R
vvi inoutout
![Page 20: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/20.jpg)
lecture 9 20
Solve for Vout
021
R
vv
R
v inoutin
1
21R
Rvv inout
![Page 21: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/21.jpg)
lecture 9 21
A Mixer Circuit
–
+v2+
–vout
R2
RfR1
v1
+–
+–
![Page 22: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/22.jpg)
lecture 9 22
KCL at the Inverting Input
–
+v2+
–vout
R2
RfR1
v1
i1
i2
if
i-
+–
+–
![Page 23: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/23.jpg)
lecture 9 23
KCL
1
1
1
11 R
v
R
vvi
2
2
2
22 R
v
R
vvi
![Page 24: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/24.jpg)
lecture 9 24
KCL
0i
f
out
f
outf R
v
R
vvi
![Page 25: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/25.jpg)
lecture 9 25
Solve for Vout
02
2
1
1 f
out
R
v
R
v
R
v
22
11
vR
Rv
R
Rv ff
out
![Page 26: Lecture 91 Loop Analysis (3.2) Circuits with Op-Amps (3.3) Prof. Phillips February 19, 2003](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d485503460f94a24321/html5/thumbnails/26.jpg)
lecture 9 26
Class Example