Operational Amplifiers
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Transcript Operational Amplifiers
The Ideal Op-amp
(Operational amplifier)
v+
+
v–
–
+
–
+15V
15
+
VOUT
–
–15V
VOUT=A(v+–v–)
A~105
VOUT [V]
VIN
VOUT
saturation
10
5
0
-400
-200
0
-5
-10
-15
200
400
VIN [μV]
Op-amp Feedback
VIN
v+
v–
R2
v+
+
v–
–
VOUT
VOUT
+
VO U T A v
–
R1
Non-Inverting
Amplifier Circuit
VO U T
v
R2
A V I N V O U T
R1 R2
R2
V O U T 1 A
R1 R2
VO U T
VI N
A
1
AR2
R1 R2
AV I N
R1 R2
R2
Op-amp Feedback
v+
+
v–
–
Assumptions:
Gain is very large (A)
Inputs draw no current (ZIN=)
Output attempts to make input voltage
difference zero (v+=v–)
VIN
v+
v–
R2
VOUT
+
–
R1
Non-Inverting
Amplifier Circuit
Inverting Amplifier Circuit
R2
i
VIN
R1
v–
i
V1
V2
V3
R1
R1
i
–
v+
VOUT
+
v–
v+
v
R2
i
V1
R1
VO U T
–
+
VOUT
V2
R1
R2
R1
0
R1
VO U T
VI N
VI N
i
R1
v
V3
R1
V1
VO U T
R2
R2
R1
VO U T
R2
V2 V3
Summing amplifier
RF
i
V1
V2
V3
R1
v–
R2
v+
–
+
VOUT
R3
VO U T
V1
V3
V2
R F
R
R
R
2
3
1
Difference amplifier
R1
V1
v–
v+
R1
V2
R2
–
VOUT
+
VO U T v
R2
v
v
V2
v
v
iR 2
V1 v
R1
R 2
R
R
v 1 2 V1 2
R1
R1
R2
R1 R2
V O U T V2
R2
R1 R2
V2 V1
R2
R1
R1 R2
R1
R
V1 2
R1
Integrator
dt
VIN
VOUT
Capacitor as integrator
R
Vi
C
Vin t VC
Vint
VC
1
RC
1
C
t
0
1
C
t
0
Id t '
t
Vi V C
0
R
Vi d t '
dt '
If RC>>t
VC<<Vi
Op-amp Integrator
C
i
VIN
R
v–
i
v+
–
+
VOUT
v
v
0
VO U T VC
VO U T
VO U T
1
C
1
C
t
0
idt
t
VI N
0
R
dt
Differentiation
Vi
V diff VR
C
R
Vdiff
dV R
dV i
RI RC
dt
dt
Small RC
dV i
dt
V diff RC
dV R
dV i
dt
dt
Op-amp Differentiator
d
VIN
VIN
R
i
C
v–
i
v+
dt
–
VOUT
+
v
v
0
V O U T iR
V O U T RC
dV I N
dt
VOUT
Complex analysis
C
V0
R2
i
R1
v–
i
ejωt
V O U T iR 2
High pass filter
v+
V0 e
R1
j CR 2 e
1 j CR
–
VOUT
+
j t
j
R2
C
j t
V0
1
0
VO U T 0
VO U T
R2
R1
V0 e
j t
Exploiting op-amp saturation
v+
+
v–
–
VOUT =
A
VOUT
A(v+–v–)
Saturation voltage
VOUT = +VSat
v+>v–
VOUT = –VSat
v+<v–
Bridge circuits
Z1
V0
VA
Z3
VB
+
–
Z2
Z4
Bridge balanced when VAVB=0
Z 2Z 3 Z 4Z 1
VOUT
Analogue – digital conversion (ADC)
V0
+
R
–
+
R
VIN
–
+
R
–
+
R
–
Oscillator
R
VOUT
+
C
R1
R1
Op-amp applications
Building block of analogue electronics
Signal amplifiers
Audio amplifiers
Integrators / differentiators
Voltage / current sources
Active filters
Oscillators
Digital-analogue and analogue-digital convertors