lecture28 operational amplifier
TRANSCRIPT
8/6/2019 Lecture28 Operational Amplifier
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Operational Amplifiers
Reading: Jaeger 11.1-11.5 and Notes
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
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Operational Amplifier
•Operational Amplifier or “Op-Amp” is a multistage amplifier that is used for
.
•The numbers of applications possible with Op-amps are two numerous to list.
•Most everyone agrees: “Op-Amp analysis is significantly easier than transistor
analysis.”
•Though they are often internally complex, their use in circuits most often
simplifies the overall design.
Model
•The circuit is modeled by an ideal voltage amplifier.
Circuit Symbol
+++
+
out
-
in
-
V out
-
in
-
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
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Ideal Operational Amplifier
•R in = Infinity,
•Voltage Gain, Av=Infinity at all frequencies
• out=
++
o e
V outV in
--
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Ideal Operational Amplifier
•Infinite gain means that the device is useless without adding “Feedback” to
control the overall gain to a finite value.
i
i outv+
•Consider the circuit to the
right with vin=0 v out
n
i-
v-
vv Av vout
vini 2
0)v-(vfor satisfiedonlyisequationabovethe,AIf -v
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
•Feedback forces the two input voltages to be equal! This is known as a “virtual ground”.
•R1 and R2 form a “Feedback Network”
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Inverting Amplifier
•Finite voltage gain results from an infinite voltage gain amplifier with “negative
feedback” (feedback that takes a fraction of the output voltage and mixes it back into the
negative summation node).
iin
+
i outv+22
221
-
resistanceinputinfinitetodue)20)1
iiiiv Ri Riv
in
oinin
vin
v outi-
-
-
1
-nin
v
groundvirtualthetodue0 but v
R i
2
1
nin
vv
3,and21,Combining
R i)3
2
2
1
1
1
v
0R R
R
Rv
v R Rv
o
oin
Overall circuit gain is finite, negative (for
this feedback configuration) and set by the
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
feedback resistor network.
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Inverting Amplifier
•Input Resistance:
iin
+
i outv+1 R
iv R in
in
vin
v outi-
-n
2
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Inverting Amplifier
i tv+
•Output Resistance:
v-
i1
0vsince0i
but,
1231t
v t
i 2
ii
and
-
00v
,
t
thus
0i
v
t
t out R
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Non-Inverting Amplifier Virtual
Ground
iin
v+
or
“short”
vin
i-
v-
ou
1
R R
Rvv out
i 2-in
-
vv
so,vthat vrequiresgroundvirtualThe
so
1
21
Rv
R
R R
v
v
v
v out
in
out
0
in
in
in
in
v
i
v R
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
1 Rvin
v casenver ng-onor asc rcuame out
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Unity Gain Buffer or “Voltage Follower”
0 12 Rand Rexcept amplifier inverting NonasSame
111
2
v
out
v A R
R
v
v A
inin vv
0inin i
case)inverting- Nonfor ascircuit(Same 0out R
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
•Can be used to isolate a high impedance circuit from a low impedance circuit
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Summing Amplifier
v+
iin,a v- iiii cinbinain ,,,2
vin,av out
i 2
R R R
c Rv
b Rv
a Rv
Rv cinbinainout
222
1112,,,
iin,b
c R
R
vb R
R
va R
R
vv
c Rv
b Rv
a Rvv
cinbinainout
cinbinainout
1
2
1
2
1
2
111
,,,
,,,
vin,b
i ,
•Output is a scaled sum of inputs.
•Scaling can be controlled by
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
n,c
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Difference Amplifier
vin,a v-
v+
v-
v+
v th
v outv out
vin,b vin,b
2 R21
21
, R R
thainth
Using Superposition we can combine the results of the Inverting and Non-inverting solutions:
vin,a=0vin,b=0
22
1
2
1
1
R Rvv
R
Rvv thout
1
2 bin,v
R Rvout
2 bin,ain,
1
2 bin,
1
2ain,
vv
vv
Rv
R R
R Rv
out
out
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
1
2
,
121
,
R
R
vv ainout
1
This circuit amplifies the
difference of two signals
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Non-Ideal (Real World) Operational AmplifiersFinite Open-Loop Gain
• ea op-amps o not ave n n te open oop w t out ee ac ga n.
•Voltage gains are typically large but finite: ~104-106 V/V
βvR
vv out1
out
v v-
+
factor feedback theasknownis
R R
R
21
1
21
where
out
A,Av
A
,vvsinceso
openloop
openloopoutloopclosedv,
in
outopenloopopenloopout
gainlooptheiswhere
resultaininfinitethea roachesR
11
A
1Av
2
openloop
openloop
If in
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
R 1 ,
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Non-Ideal (Real World) Operational AmplifiersFinite Open-Loop Gain
•Finite open-loop gain means the Virtual Ground is not perfect!
openloopA inv Small but finite
openloopopenloop A1A1 ininout in
and - terminals
v v-
+
out
•The Gain Error (GE) that results from the Non-infinite open-loop gain can be quantified as:
openloopA1
inv
vGE
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
openloopopenloop
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Non-Ideal (Real World) Operational AmplifiersFinite Output Impedance
•Real Op-Amps have a small but finite output impedance, Ro .
•We want to find the Output impedance of the various circuits we have examined .
•All the configurations have a common circuit for calculating the output impedance .
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Non-Ideal (Real World) Operational AmplifiersFinite Output Impedance
2iii
i
v R
o x
x
x
out
,
v
R
vv Av
i
x
o
openloopv x
o
21
1
21
2212
vv R R
R
v
R R
x x
x
21
,1 11
R R R
A
v
i R
o
openloopv
x
x
out
21
,1 R R A Ropenloopv
oout
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
Ro is very small so this term is EXTREMELY small!
FEEDBACK REDUCES OUTPUT IMPEDANCE!
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Non-Ideal (Real World) Operational AmplifiersFinite Input Impedance: Non-Inverting Case
•Real Op-Amps have a large but finite
input resistance, R ID
ID
x
x R
vvi
xopenloopvout out vv Avv Rv
Ri Riv
,1
1211
21ID21x or toueantocomparecurrentt eeg ect ng
x
openloopv
openloopvv
A
Av
,
,
21
1
IDopenloopv
x
ID
x
openloopv
openloopv x
x R A
v
R
v A
v
i
,
,
,
1
1
FEEDBACK
INCREASES INPUT
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
IDopenloopvin ,
RID is very large so Rin is EXTREMELY large!
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Non-Ideal (Real World) Operational AmplifiersFinite Input Impedance: Inverting Case
• ea p- mps ave a arge ut n te
input resistance, R ID
•Rin=R 1 +R’in
in in
•Find R’in by forming a new test circuit
openloopvout
R
v Av
R
v
R
vv
R
viii
1,111121
openloopv
ID
in
R
R
A
Rv
i R
2
2
,
1
11
'
11'
R’in
openloopv
IDin
R
Thus
A ,
,
1
openloopv
IDin A ,1 1
Since RID>>R2 /(1+Av,openloop) and
Av,openloop is very large,
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
1
,
21
,
21
11 R
A
R R R
A
R R R R
openloopv
in
openloopv
IDin