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ECE 340ELECTRONICS I
OPERATIONAL AMPLIFIERS
OPERATIONAL AMPLIFIER
• THEORY OF OPERATION
• CHARACTERISTICS
• CONFIGURATIONS
THEORY OF OPERATION
• AMPLIFIES DIFFERENCE OF TWO INPUT SIGNALS
• PRODUCES SINGLE OUTPUT
• OPERATES OVER WIDE FREQUENCY RANGE
CHARACTERISTICS
• LARGE OPEN LOOP GAIN
• LARGE INPUT IMPEDANCE
• SMALL OUTPUT IMPEDANCE
• LARGE BANDWIDTH
OPAMP DEFINITIONS
• OPEN LOOP GAIN – AO
• INPUT RESISTANCE – RIN
• OUTPUT RESISTANCE – ROUT
• NON-INVERTING INPUT CURRENT – i+
• INVERTING INPUT CURRENT – i-
SYMBOL
+
-
vout
v-
+VPOS
-VNEG
v+
IDEAL OPERATIONAL AMPLIFER
• INFINITE OPEN LOOP GAIN
• INFINITE INPUT RESISTANCE
• ZERO OUTPUT RESISTANCE
• ZERO INPUT CURRENT
IDEAL CHARACTERISTICS
00
0
ii
RR
A
OUTIN
O
IDEAL RELATIONSHIPS
vvvvAv
vvv
Oout
in
CIRCUIT MODEL
vo
+
v+
-
v-
-
vin
Rout
+ AO*vin+
vo-Rin
CONFIGURATIONS
• INVERTING GAIN AMPLIFIER
• NON- INVERTING GAIN AMPLIFIER
• UNITY GAIN AMPLIFIER
• SUMMING AMPLIFIER
• DIFFERENCE AMPLIFIER
CONFIGURATIONS
• VOLTAGE INTEGRATOR
• VOLTAGE DIFFERENTIATOR
INVERTING GAIN AMPLIFIER
RF
vo
+
-
vi
RI
VIRTUAL GROUND
io
ii
CURRENT PROPERTIES
oi
f
oo
i
ii
ii
R
vi
R
vi
VOLTAGE RELATIONSHIPS
i
f
i
o
f
o
i
i
R
R
v
v
R
v
R
v
NON-IDEAL ANALYSIS
oIF
Ii
IF
F
F
o
I
i
IF
IF
F
o
I
i
FIF
o
I
i
vRR
Rv
RR
Rv
R
v
R
v
RR
RRv
R
v
R
vv
RRR
vv
R
vv
11
0
SUBSTITUTION INTO OPAMP EQUATION
iIF
FO
IF
IOo
oIF
Ii
IF
FOo
oIF
Ii
IF
F
Oo
vRR
RA
RR
RAv
vRR
Rv
RR
RAv
vRR
Rv
RR
Rvv
vvAv
1
0
0
VOLTAGE GAIN EQUATION
OI
FI
F
i
o
OI
F
O
I
F
i
o
IOIF
FO
i
o
IF
IO
IF
FO
i
o
AR
RR
R
v
v
ARRA
R
R
v
v
RARR
RA
v
v
RR
RA
RR
RA
v
v
111
1
1
1
GAIN ERROR
%1001
1%
111
111
1
11
1
OI
F
OI
F
I
F
i
o
OI
FI
F
i
o
AR
Rerrorgain
AR
R
R
R
v
v
ARRR
R
v
v
small
HIGH GAIN INVERTING AMPLIFIER
R2 R4
R3
R5
+
-
vO
R1
vI
vx
VOLTAGE AND CURRENT RELATIONSHIPS
21
43232
32
432
32
32
32
R
vi
R
vi
ii
vRRRRR
RRvv
RRR
RR
RRRR
v
XO
II
OI
OXOX
VOLTAGE GAIN CALCULATION
324
1
2
32
43232
1
2
43232
32
21
111
1
RRR
R
R
v
v
RR
RRRRR
R
R
v
v
vRRRRR
RR
Ri
R
vi
I
O
I
O
OOI
I
DESIGN CONSIDERATIONS
3
2
1
2
42
324
1
2
2
111
R
R
R
R
v
v
RRIf
RRR
R
R
v
v
I
O
I
O
NON-INVERTING GAIN AMPLIFIER
io
vi
RI
+
-
vo
RF
IDEAL NON-INVERTING GAIN AMPLIFIER EQUATIONS
i
IF
oo
vv
RR
vi
GAIN CALCULATION
I
F
i
o
oIF
Ii
oIF
IoI
R
R
v
v
vRR
Rvvv
vRR
RviRv
1
NON-IDEAL EQUATIONS
FI
I
O
i
o
FI
IO
O
i
o
iOFI
IOoo
FI
IiOo
oFI
Ii
RRR
Av
v
RRRA
A
v
v
vARR
RAvv
RR
RvAv
vRR
Rvvv
11
1
1
NON-IDEAL EQUATIONS
OI
FII
FI
i
o
IO
FI
FI
i
o
IO
FI
FI
i
o
FI
I
O
i
o
ARRRR
RR
v
v
RARRRR
v
v
RARRRR
v
v
RRR
Av
v
11
1
11
GAIN ERROR CALCULATION
%1001
1%
111
11
11
11
1
OI
F
OI
F
I
FI
i
o
OI
FI
I
FI
i
o
OI
FI
I
FI
i
o
OI
FII
FI
i
o
AR
Rerrorgain
AR
R
R
RR
v
v
AR
RR
R
RR
v
v
AR
RR
R
RR
v
v
ARRRR
RR
v
v
UNITY GAIN AMPLIFIER
vi
+
-
vo
UNITY GAIN AMPLIFIER EQUATIONS
oi
oi
vvvv
vvvv
ii
00
PRACTICAL UNITY AMPLIFIER EQUATIONS
O
O
i
o
O
iOo
oiOoOo
oi
A
A
v
v
A
vAv
vvAvvvAv
vvvv
11
INVERTING SUMMING AMPLIFIER
R2
v3
v1
R1
v2
+
-
RF
voR3 0 V
GAIN CALCULATIONS
33
22
11
3
3
2
2
1
1
321
vR
Rv
R
Rv
R
Rv
R
v
R
v
R
v
R
v
iiii
FFFo
F
o
o
NON-INVERTING SUMMING AMPLIFIER
vO
v2
R3
RF
R2
v3
RA
R1
v1 +
-
VOLTAGE RELATIONSHIPS USING SUPERPOSITION
o
AF
A
oAF
A
vRR
Rv
RRR
RRv
RRR
RRv
RRR
RR
vvvRR
Rv
vRRR
RRv
RRR
RRv
RRR
RRv
3321
212
213
131
132
32
3321
212
213
131
132
32
INPUT VOLTAGE ONE EQUIVALENT
1
32132
321
132
32
1
132
32
32
32
1132
32
vRRRRR
RRv
RRR
RR
v
RRRRR
RRRR
vRRR
RR
INPUT VOLTAGE TWO EQUIVALENT
2
13213
132
213
13
2
213
13
13
13
2213
13
vRRRRR
RRv
RRR
RR
v
RRR
RR
RR
RR
vRRR
RR
INPUT VOLTAGE THREE EQUIVALENT
3
21321
213
321
21
3
321
21
21
21
3321
21
vRRRRR
RRv
RRR
RR
v
RRRRR
RRRR
vRRR
RR
OUTPUT VOLTAGE RELATIONSHIP
oAF
A
oAF
A
vRR
R
vRRRRR
RRv
RRRRR
RRv
RRRRR
RR
vRR
Rv
RRR
RRv
RRR
RRv
RRR
RR
321321
212
13213
131
32132
32
3321
212
213
131
132
32
FINAL OUTPUT VOLTAGE EQUATION
321213132133221
21321
321
13213
213
32132
1321
vRRvRRvRRRRRRRRR
RRv
RRRRR
vRR
RRRRR
vRR
RRRRR
vRR
R
Rv
A
AFo
A
Fo
DIFFERENCE AMPLIFIER
R3
v1
v2
R1
+
-
R2
vo
R4
VOLTAGE EQUATIONS
121
2
21
1
243
4
vRR
Rv
RR
Rv
vRR
Rv
o
EQUATING INPUT VOLTAGES
121
22
43
4
1
21
121
2
21
12
43
4
vRR
Rv
RR
R
R
RRv
vRR
Rv
RR
Rv
RR
R
vv
o
o
DESIGN CONSIDERATIONS
121
2
4231
121
22
43
4
1
21
vvR
Rv
RRandRRIf
vRR
Rv
RR
R
R
RRv
o
o
VOLTAGE INTEGRATOR
+
-vi
R1
R2
vO
C
INTEGRATOR EQUATIONS
io
oi
oi
ooI
i
vCsR
v
sCvR
vii
sCviR
vi
1
1
1
1
PRACTICAL VOLTAGE INTEGRATOR
+
-vI
R1
R2
vO
R3
C
PRACTICAL INTEGRATOR EQUATIONS
io
oi
oi
PP
oo
ii
vCsRR
Rv
vR
CsR
R
vii
CsR
RZ
Z
vi
R
vi
31
3
3
3
1
3
3
1
1
1
1
1
VOLTAGE DIFFERENTIATOR
+
-vI
C
R2
vO
R1
DIFFERENTIATIOR EQUATIONS
io
oioi
ooii
vCsRv
R
vsCvii
R
visCvi
1
1
1
PRACTICAL VOLTAGE DIFFERENTIATOR
+
-vi
CR1
R2
vO
R3
PRACTICAL DIFFERENTIATOR EQUATIONS
io
oioi
ooS
S
ii
vCsR
CsRv
R
v
CsR
sCvii
R
vi
sCRZ
Z
vi
1
3
31
31
1
1
1
INSTRUMENTATION AMPLIFIER
R2
+
-
vo
+
-
R4
R4
i1
R3
+
-
R1
vo2R3R2
vo1
vi2
vi1
VOLTAGE AND CURENT RELATIONSHIPS
12202
12101
1
211
iRvv
iRvv
R
vvi
i
i
ii
VOLTAGE SUBSTITUTIONS
11
22
1
202
1
212202
21
21
1
201
1
212101
1
1
iiii
i
iiii
i
vR
Rv
R
Rv
R
vvRvv
vR
Rv
R
Rv
R
vvRvv
OUTPUT VOLTAGE CALCULATION
121
2
3
40
01023
40
21 ii vv
R
R
R
Rv
vvR
Rv
