Transcript EEE202_Lec10

Lecture 9. Op Amps I
• What is an Op Amp?
• Ideal Op Amps
• Applications
• Examples
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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.
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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.
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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.
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The Op Amp Symbol
High Supply
Non-inverting input
Inverting input
+
Output
Ground
Low Supply
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The Op Amp Model – Voltage Dependent
Source
Non-inverting
input
v+
+
Rin
Inverting input
v-
vo
+
-
-
A(v+ -v- )
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Typical Op Amp
• The input resistance Rin is very large (practically infinite).
• The voltage gain A is very large (practically infinite).
Non-inverting
input
v+
+
Rin
Inverting input
v-
vo
+
-
-
A(v+ -v- )
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“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
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The Basic Inverting Amplifier
R2
R1
Vin
+
-
+
+
Vout
-
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Solving the Amplifier Circuit
Nodal Analysis:
R2
i2
R1
i1
i-
i1 + i2 + i-=0
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Solving the Amplifier Circuit
i  0
vin  v vin
i1 

R1
R1
vout  v vout
i2 

R2
R2
i1 + i2 + i-=0
vin vout

0
R1 R2
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Solving the Amplifier Circuit
Solve for vout
vout
R1
  vin
R2
Amplifier gain:
vout
R2
G

vin
R1
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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-
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Where is the Feedback?
R2
R1
Vin
+
-
+
+
Vout
-
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The Non-Inverting Amplifier
+
+
vin
+
-
vout
R2
R1
-
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Nodal Analysis: Finding the nodes
+
+
vin
+
-
ii1
i2
vout
R2
R1
-
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Nodal Analysis: Apply KCL
i  0
 v  vin
i1 

R1
R1
vout  v vout  vin
i2 

R2
R2
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Nodal Analysis: Solve for Vout
 vin vout  vin

0
R1
R2
vout
 R2 

 vin 1 
R1 

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A Mixer Circuit
R1
v1
+
Rf
R2
-
v2
+
-
+
+
vout
-
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Nodal Analysis: Finding the nodes
R1 i1
v1
+
R2 i
2
v2
+
-
Rf
if
i-
+
+
vout
-
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Nodal Analysis: Apply KCL
v1  v v1
i1 

R1
R1
v2  v v2
i2 

R2
R2
i  0
vout  v  vout
if 

Rf
Rf
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Nodal Analysis: Solve for Vout
v1 v 2 vout


0
R1 R2 R f
vout  
Rf
R1
v1 
Rf
R2
v2
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Class Examples
• Seeing atoms with STM
1 nA
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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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