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E E 2315
Lecture 08 - Introduction to Operational Amplifiers
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Operational Amplifiers
• Ideal operational amplifiers are easily analyzed
• Assumptions for ideal operation are realistic
• Inexpensive commercial Op-Amps available as integrated circuits
• Practical applications for instrumentation, signal processing and control circuits
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A741 Pinout
1
2
3
4
8
7
6
5
A741Offset Null
Inverting Input
Non-inverting Input
Vcc-
Vcc+
Output
Offset Null
NC
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Op Amp Terminals
+Vcc
-Vcc
Positive supplyvoltage
Output
InvertingInput
NoninvertingInput
Negative supplyvoltage
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Op Amp Terminal Currents
+Vcc
-Vcc
Vcc Vcc
io
in
ip
ic+
ic-
Common Node
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Op Amp Terminal Voltages
+Vcc
-Vcc
Vcc Vcc
+vp
-
+
vo
-
+
vn
-
Common Node
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Equivalent Circuit
A(Vp-Vn)Ro
Ri+vo-
ip
in
io
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Assumptions for Ideal Op Amp
• Open loop Gain, A vp - vn 0
• Then vp - vn 0 Ri
• Ri ip 0 and in 0
• Gain is linear up to the saturation voltage
• Saturation voltage equals power supply voltage
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Open-Loop Characteristics
+Vcc
-Vcc
vp-vn
vo
A(vp-vn)
+Sat
-Sat
Linear
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Inverting Amplifier
and
Vn = 0 and in = 0. Then KCL at node n yields:
+Vcc
-Vcc
RfRg
vg
+vn-
in
0
+vo-
0 00 0g o
g f
v v
R R
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Saturated Mode
• Inverting Amplifier with +Vcc = 5 V and Vcc = -5V.
• Rf = 10 k and Rg = 1 k
t
1 V
-1 V
vgvo
t5 V
-5 V
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Non-Inverting Amplifier
KCL at node n:
vn = vp = vg
+Vcc
-Vcc
vg
Rg
Rs
Rf0
0n
p+
vo
-
+vp-
+vn
-
0g g o
s f
v v v
R R
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Summing Amplifier (1/2)
+Vcc
-Vcc
va
Ra
vb
Rb
vc
Rc
Rf
+
vo
-
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Summing Amplifier (2/2)
0a b c o
a b c f
v v v v
R R R R
f f fo a b c
a b c
R R Rv v v v
R R R
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Difference Amplifier (1/3)
KCL @ n:
+Vcc
-Vcc
RbRa
Rc
Rdvb
va +vo-
+vp-
n
p
0n a n o
a b
v v v v
R R
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Difference Amplifier (2/3)
Voltage Divider @ p:
+Vcc
-Vcc
RbRa
Rc
Rdvb
va +vo-
+vp-
n
p
dn p b
c d
Rv v v
R R
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Difference Amplifier (3/3)
Substitute:
into:
and simplify:
If: Then:
dn p b
c d
Rv v v
R R
d a b bo b a
a c d a
R R R Rv v v
R R R R
a c
b d
R R
R R b
o b aa
Rv v v
R
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Analyzing an OpAmp Circuit
+Vcc
-Vcc
Rf
Ry
RL
Rx
Rg
vg