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• What is an Op Amp?
• Ideal Op Amps
• Applications
• Examples
Lecture 9. Op Amps I
1
2
What is an Op Amp?
• 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.• It has usually differential inputs and a single output.
3
Use of Op Amps
• Op amps can be configured in many different ways using resistors and other components.
• 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.
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.
5
The Op Amp Symbol
+
-
Non-inverting input
Inverting input
Ground
High Supply
Low Supply
Output
6
The Op Amp Model – Voltage Dependent Source
+
-Inverting input
Non-inverting input
Rin
v+
v-
+
-A(v+ -v- )
vo
7
Typical Op Amp
• The input resistance Rin is very large (practically infinite).
• The voltage gain A is very large (practically infinite).
+
-Inverting input
Non-inverting input
Rin
v+
v-
+
-A(v+ -v- )
vo
8
“Ideal” Op Amp
• The input resistance is infinite.• The gain is infinite.• The op amp is in a negative feedback configuration. • 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
9
The Basic Inverting Amplifier
-
+Vin
+
-
+
-Vout
R1
R2
10
Solving the Amplifier Circuit
Nodal Analysis:
i1 + i2 + i-=0
-R1
R2
i1 i-
i2
11
0i
111 R
v
R
vvi inin
222 R
v
R
vvi outout
Solving the Amplifier Circuit
021
R
v
R
v outini1 + i2 + i-=0
12
Amplifier gain:
inout vR
Rv
2
1
1
2
R
R
v
vG
in
out
Solve for vout
Solving the Amplifier Circuit
13
How to solve Op Amp Circuit?
• Nodal analysis or other methods to solve for the output voltage in terms of the input(s).
• Keep in mind that the ideal op amp model leads to the following conditions:
i- = 0
v+ = v-
14
Where is the Feedback?
-
+Vin
+
-
+
-Vout
R1
R2
15
The Non-Inverting Amplifier
+
-
vin
+
-
+
-
vout
R1
R2
16
Nodal Analysis: Finding the nodes
+
-
vin
+
-
+
-
vout
R1
R2
i-
i1 i2
17
0i
111 R
v
R
vi in
222 R
vv
R
vvi inoutout
Nodal Analysis: Apply KCL
18
Nodal Analysis: Solve for Vout
021
R
vv
R
v inoutin
1
21R
Rvv inout
19
A Mixer Circuit
-
+v2
+
-
+
-vout
R2
RfR1
v1
+
-
20
Nodal Analysis: Finding the nodes
-
+v2
+
-
+
-vout
R2
RfR1
v1
+
-
i1
i2
if
i-
21
Nodal Analysis: Apply KCL
1
1
1
11 R
v
R
vvi
2
2
2
22 R
v
R
vvi
0i
f
out
f
outf R
v
R
vvi
22
Nodal Analysis: Solve for Vout
02
2
1
1 f
out
R
v
R
v
R
v
22
11
vR
Rv
R
Rv ff
out
23
Class Examples
• Seeing atoms with STM
1 nA
24
Class Examples
• Solar cell
1 nA
A circuit constructed for measuring current from the solar cell. The first Op Amp is the current-to-voltage converter and the second op Amp inverts the voltage.
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