AERO
ASTRO
16.682 - Prototyping Avionics
Spring 2006
LECTURE 4
February 21, 2006
DEPARTMENT OF AERONAUTICS AND ASTRONAUTICS
Alvar Saenz-Otero
Outline
•
Amplifiers
– Ideal vs. Real
– Basic linear uses
• Voltage follower (current source)
• Voltage amplifier
• Voltage invert & subt ract
– Positive feedback
– Active filters
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16.682 - Prototyping Avionics
Operational Amplifiers
• Assume ideal during development:
– v+=v– i+=0, i-=0
– Saturation at input power voltage only
– Linear
vpwr+
i+=0 v+
• Keep in mind for implementation:
i-=0 v-
– Maximum amplification (e.g., 100, +
-
vout
1000, normally max < 106) vpwr-
– Saturation
• Op-Amps require external +/- supplies!
– Non-linear region
• Frequency region
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16.682 - Prototyping Avionics
OpAmp Examples
Buffer/follower
•
Amplifier
VCC
8
8
VCC
Vin
3 +
3 +
Vin
1
Vout
Vout
R1
4
2 -
1
2 -
4
•
R2
v+ = v−
v+ = v−
v + = Vin
v + = Vin
v − = Vout
i − = 0 → iR =
Vout = Vin
v − = R2
Vout
= v + = Vin
R1 + R2
Vout = Vin
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Vout
R1 + R2
R1 + R2
R2
16.682 - Prototyping Avionics
OpAmp Examples
Buffer/follower
•
Amplifier
VCC
8
8
VCC
Vin
3 +
3 +
Vin
1
Vout
Vout
R1
4
2 -
1
2 -
4
•
R2
v+ = v−
v+ = v−
v + = Vin
v + = Vin
v − = Vout
i − = 0 → iR =
Vout = Vin
v − = R2
Vout
= v + = Vin
R1 + R2
Vout = Vin
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Vout
R1 + R2
R1 + R2
R2
16.682 - Prototyping Avionics
OpAmp Examples
•
Inverting Amplifier
•
Amplifier/subtract
VCC
VCC
V2
8
8
R1
R1
1
3 +
Vout
2 -
R2
1
2 -
V1
Vout
R1
4
4
Vin
3 +
R2
-VCC
R2
v+ = v−
v+ = v− = 0
i − = 0 → iR =
v + = V2
Vin
R1
Vout = −iR ⋅ R2 = −Vin
R2
R1 + R
2
v − = Vout + R2
R2
R1
Vout =
V1 −Vout
R1 + R2
R2
(V2 −V1 )
R1
But these do NOT work when Vin>0. Why? ...
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16.682 - Prototyping Avionics
OpAmp Examples
•
Inverting Amplifier
•
Amplifier/subtract
VCC
R1
R1
3 +
1
Vout
2 -
3 +
V2
R2
1
2 -
V1
Vout
R1
4
4
Vin
8
8
VCC
-VCC
R2
-VCC
R2
v + = v
−
v+ = v− = 0
i − = 0 → iR =
v + = V2
Vin
R1
Vout = −iR ⋅ R2 = −Vin
R
2
R1 + R
2
v − = Vout + R2
R2
R1
Vout =
V1 −Vout
R1 + R2
R2
(V2 −V1 )
R1
Need a NEGATIVE power supply! (Since Vin is inverted.)
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16.682 - Prototyping Avionics
Saturation
• Positive feedback is unstable and usually leads
to saturation of the output voltage
– Positive Feedback is not very useful for linear
tasks, but it can be useful for other jobs...
Vin
– Create “digital” signals from analog sources
R2
Vref
v
+ = v
− =
Vref
VCC
i + = 0 → v + = Vout + R2
8
R1
Vref
2 -
1
4
Vin
3 +
Vout
Vout =
-VCC
Vin −Vout
R1 + R2
R1 + R2
R
Vref − 2 Vin
R1
R1
Vcc
Vout
• While the “ideal” math says that the system should
be linear, in reality positive feedback saturates the -V
cc
output to the input voltages (+/- Vcc)
– Can use R2= ∞ (open, no feedback)
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16.682 - Prototyping Avionics
Active Filters
OpAmps allow active filtering of signals
– The OpAmp provides power to follow the signals better
– Feedback increases the performance of the filters
– Enables to create both differentiators (high pass) and integrators (low
pass)
R
C
4
R
2
Vin
1
Vout
3
1
8
8
+
3
-
2
-VCC
-VCC
v+ = v− = 0
v+ = v− = 0
i − = 0 → iR =
i − = 0 → iR = C
Vout = −RC
Vout
+
C
Vin
VCC
4
VCC
-
•
dVin
dt
Vin
dt
RC
1
=−
Vin dt
RC ∫
VC = ∫
dVin
dt
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Vin
R
Vout
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16.682 - Prototyping Avionics
Real Operational Amplifiers
•
Remember the non-ideal conditions
•
Ideal
i+=0
vpwr
•
+
vpwr+
v+
i-=0 v-
Real
offset+
i+~0 v+
+
-
vout
i-~0 v-
vpwr
+
-
vout
offset-
–
–
–
–
–
–
Non-linear
Frequency dependent
Offsets
Saturation
Hysteresis
Temperature dependant
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vpwr-
16.682 - Prototyping Avionics