Investment Managers: Jionghan Dai Tyler Haida Joseph Kim Layla Liang Meiling Liu
Microelectric Circuit by Meiling CHEN 1 Lecture 11 Operational Amplifiers.
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Transcript of Microelectric Circuit by Meiling CHEN 1 Lecture 11 Operational Amplifiers.
Microelectric Circuit by Meiling CHEN
1
Lecture 11Lecture 11Operational AmplifiersOperational Amplifiers
Microelectric Circuit by Meiling CHEN
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Topics Topics • Ideal op Amplifiers• Ideal OPA circuits analysis• Non-ideal op amplifiers• Non-ideal OPA circuit analysis
Microelectric Circuit by Meiling CHEN
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Ideal operational amplifier
1. Infinite input impedance2. Zero output impedance3. Infinite bandwidth4. Infinite open-loop gain5. Zero common-mode gain (infinite CMRR)
Ideal OPA characters
Microelectric Circuit by Meiling CHEN
4
)( VVRuGV mo
Microelectric Circuit by Meiling CHEN
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Microelectric Circuit by Meiling CHEN
6
VCC
VEE
2
1
X1UA741
VCC
VEE4
3
X2UA741
R1
R2
stableVVV
VVAVVV
VVAV
VIRV
oo
oo
o
o
)(
)(
Negative feedback
Positive feedback
unstableVVVV
VVVV
VVAV
VIRV
satoo
satoo
o
o
)(
Microelectric Circuit by Meiling CHEN
7
CMRR
BW
A
R
R
o
in
0
Non-ideal cases
CMRR
BW
VVA
R
iiR
o
in
)(
0
)0(
Ideal OPA characters
Microelectric Circuit by Meiling CHEN
8
Consider finite open-loop gain
A
)2()(
)1(0
0
21
21
AvvvAv
R
vv
R
vv
vv
A
oi
1
2
12
12
/)/1(1
/
R
R
v
v
Aif
ARR
RR
v
v
i
o
i
o
A
Microelectric Circuit by Meiling CHEN
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Input and output resistance
I
Oain v
vG
1
2
21
000
R
R
v
vG
R
v
R
v
I
Oain
OI
Example 2.11Ri
vR
i
iin
MR
MRif
100
1
2
1
An impractically large valueSo we may have the problem of input resistance.
Microelectric Circuit by Meiling CHEN
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0I
VRout
V
I
)( VVAV
Viv
0oR
2R
1R
0
Output resistance
Microelectric Circuit by Meiling CHEN
11
Example 2.2
)1(
)2(000
)1(00
3
4
2
4
1
2
21
432
R
R
R
R
R
R
v
v
R
v
R
v
R
vv
R
v
R
v
i
o
XI
oXXX
Comparing with Example 2.1Design a amplifier with a gain –100 and an input resistance of 1M.
MRkR
MRMR
R
R
R
R
R
R
v
v
i
o
1,2.10
1,1
)1(
43
21
3
4
2
4
1
2
Example 2.2:
MR
MR
100
1
2
1
Example 2.1:
Microelectric Circuit by Meiling CHEN
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Exercise 2.6
Vk
kv
k
v
k
vk
vv
k
v
oo
o
101
100
101
1
)2(0
)1(0101
1
mAii
mAi
mAk
i
mAk
i
Find
L
1
11
110
)10(0
101
10
21
0
2
Microelectric Circuit by Meiling CHEN
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Weighted summer
nn
fffo
f
o
n
n
f
o
n
n
vR
Rv
R
Rv
R
Rv
R
v
R
v
R
v
R
v
R
v
R
v
R
v
R
v
22
11
2
2
1
1
2
2
1
1 )1(00000
Microelectric Circuit by Meiling CHEN
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Exercise D2.8
xv
)()(
)(
)(
22
11
44
33
44
33
22
11
vR
Rv
R
R
R
Rv
R
Rv
R
Rv
vR
Rv
R
Rv
R
Rv
vR
Rv
R
Rv
aa
b
ccco
xb
ccco
aax
Microelectric Circuit by Meiling CHEN
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Non-inverting amplifier
Io
oII
vR
Rv
R
vv
R
v
)1(
00
1
2
21
Ideal case:
Non-ideal case: A
)()1(
)2.().........(
)1....(00
21
21
2
21
RR
RR
R
vv
vvAv
R
vv
R
v
o
io
oii
A
v
v
RR
RR
i
o
1
2
1
2
11
1
Microelectric Circuit by Meiling CHEN
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Voltage follower
Microelectric Circuit by Meiling CHEN
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Exercise D2.9 Exercise D2.13
)32
)(32
32)(
9
1
1
1(9
)9
1
1
1(9)1(
)32
()3
1
2
1()2(
)2(032
)1(091
0
21
21
21
k
v
k
v
kk
kk
kkk
vkk
kv
k
v
k
v
kkv
k
vv
k
vvk
vv
k
v
vv
o
o
Vkkk
v
k
v
k
Vvv
o
o
109)9
1
1
1(
)1(09
1
1
01
1
Microelectric Circuit by Meiling CHEN
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CMRR ( Common-Mode Rejection ratio )
cm
d
A
ACMRR log20
icmcmiddo vAvAv
Common-mode inputDifferent-mode input
Why use difference amplifier ?
)(21
vvv
vvv
icm
id
DC
DC
DC
DC
DCV
V
V V
V Vicmv
2idv
2idv
Microelectric Circuit by Meiling CHEN
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Difference Amplifier
2343
11
2
212
21
12
43
2
21
1
1)
11()2(
)11
()()1(
)2(0
)1(0
i
ii
o
i
oi
vRRR
v
vR
Rv
RRR
R
v
R
vvRv
R
v
R
vv
R
vv
R
vv
vv
Method I:
Microelectric Circuit by Meiling CHEN
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)()(
),()1(
12121
221
241321
22
1
2
43
42
11
21
iidiiooo
iio
io
vvAvvR
Rvvv
RRRRletvR
Rv
R
R
RR
Rv
vR
Rv
Different-mode inputMethod I: superposition
Microelectric Circuit by Meiling CHEN
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Common-mode input
0,
]1[
][
1][
1
2413
1
2
4
3
43
4
1
2
43
3
43
421
2243
4
143
3
43
4
11
cm
cm
icmo
icmo
icmicmicm
ARRRR
R
R
R
R
RR
RA
vR
R
RR
R
RR
Rvii
RivRR
Rv
vRRR
Rv
RR
Rv
Ri
CMRR=infinite
0, 2413 cmARRRRif
CMRR=infinite
Microelectric Circuit by Meiling CHEN
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1)(
111111
2
2
RR
iRRiRiv
diffin
id
Consider the problem of input resistance
Differential mode input resistance
ido vR
Rv
1
2 oin vRRif 1
Microelectric Circuit by Meiling CHEN
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Instrumentation Amplifier
Not is differential mode, common mode input can be pass.
idv
idv
))(1(
))(1(
121
2
3
4
121
2
3
4
iio
iiid
ido
vvR
R
R
Rv
vvR
Rv
vR
Rv
)1(.2
.1
1
2
3
4
R
R
R
RA
R
d
in
Big differential gain
Defects:1. Common mode gain=differential mo
de gain.2. Resistance have to match.
sato vv
))(1( 121
2iiid vv
R
Rv
21 RandR
Advantages:
Microelectric Circuit by Meiling CHEN
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Remove the point x
Microelectric Circuit by Meiling CHEN
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DC non-ideal characters
1. Finite open loop gain ( finite CMRR)2. Finite BW3. Offset voltage4. Input bias and offset current
Microelectric Circuit by Meiling CHEN
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Frequency response (open-loop)
bot
ob
t
b
o
A
AdBsA
sA
:01
)(
Microelectric Circuit by Meiling CHEN
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Frequency response (closed loop)
ARRR
R
v
v
i
o
/)1(11
2
1
2
b
o
sA
sA
1)(
)1/(1
)1/()1(
11
1
2
1
2
1
21
2
0
1
2
RRsR
R
RRs
RR
A
RR
v
v
tt
i
o
1
23
1 RRt
dB
Microelectric Circuit by Meiling CHEN
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Output voltage saturation
mAi
Vv
o
o
20
13
max
max
Microelectric Circuit by Meiling CHEN
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Slew rate
)/(max sVdt
dvSR o
)1()()(
)(
),0(1
1
/1
11
1
12
1
2
1
2
to
tt
to
i
t
i
o
b
o
i
o
teVtvs
V
s
V
s
V
ssV
stepunitVvlet
RRsv
v
s
AA
AR
RR
R
v
v
bot A
Microelectric Circuit by Meiling CHEN
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Offset voltage
Output = + saturation or - saturation
mVvos 5~1
From the component mismatches in the input differential stage
May be positive or negative
Microelectric Circuit by Meiling CHEN
31
1. Reduce the allowable signal swing2. When input is dc we would not know th
e output is due to vos or signals
Microelectric Circuit by Meiling CHEN
32
Solution 1: Offset-nulling terminals
Solution 2: Capacitive coupling (only ac signal be amplified)
)1(1
2
R
Rvv oso
Microelectric Circuit by Meiling CHEN
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Offset current
Input bias currents21
21
2
BBos
BBB
III
III
Input offset currentnAInAI osB 10,100
221 RRIV Bo
Upper limit R2
Microelectric Circuit by Meiling CHEN
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Solution : introducing R3
0
//)1(
)]1([
)(
21
1
2
23
1
232
21
1
321232
o
Bo
BBB
BBBo
V
RR
RR
RRchoose
R
RRRIV
IIIif
R
RIIRRIV
Microelectric Circuit by Meiling CHEN
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Inverse amplifier
Non-inverse amplifier
Reduce the effect of Vos
Reduce the effect of Ios
Reduce the effect of Vos
Reduce the effect of Ios
Microelectric Circuit by Meiling CHEN
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1
2
21
000
Z
Z
v
vG
Z
v
Z
v
I
O
OI
Integrator & Differentiator
Microelectric Circuit by Meiling CHEN
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1202
122
221
)()()(
0)](0[)(0)(0
R
v
R
vvsC
R
tv
R
tv
dt
tdvC
dt
tvdC
R
tv
R
tv
io
ioo
ooi
220
22
1
2
122
11
2
1
1
1
RC
RsC
RR
v
v
RsCRRZ
Z
v
v
I
O
I
O
Microelectric Circuit by Meiling CHEN
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Miller Integrator
Microelectric Circuit by Meiling CHEN
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Consider Vos offset voltage
Consider Ios offset current
satV
satV
Microelectric Circuit by Meiling CHEN
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Solution :
osV
tos
oso
osCR
RCosos
R
Ro
R
R
R
RR
os
o
f
oosoosos
CfR
ff
ff
f
eRC
VVtv
Vs
VVsC
v
sCsC
sC
V
v
R
vV
sC
vV
R
V
1
)(
]1[
]1[
01
1
1
1
1
1
1
1
11
tRC
VVtv os
oso )(
osCR
RC
osf
f
ossCf
o
Vs
VCsRR
R
VR
Rsv
f
)1(
)1
11(
)//
1()(
1
1
1
Microelectric Circuit by Meiling CHEN
41
fR
tCR
BBo
f
BB
f
BB
f
fB
o
fBo
f
f
oBoBB
feCIRItv
CRs
CIRI
RsC
IRI
RsC
RsC
RRI
v
RsC
RRIv
RsC
R
vRI
sC
vRI
R
RI
1
22
22
22
2
2
222
)()(
)1
()1
()1
(
]11
[
]11
[)1
(
0/1
tC
IRIv os
Bo 2
Microelectric Circuit by Meiling CHEN
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Example 2.7 sketch output response
VV
MRR
nFC
kR
sat
FF
13
1,
10
10
Case I: FR
Case II: MRF 1
dttvRC
tvt
io )(1
)(0
F
F
I
O
RsC
RR
v
v
2
1
1
Microelectric Circuit by Meiling CHEN
43
Differentiator
Microelectric Circuit by Meiling CHEN
44
Problem *2.31
Microelectric Circuit by Meiling CHEN
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Problem *2.43
]1248[16
]1248[80
5
]80402010
[5
00
80
50
40
50
20
50
10
50
080402010
0123
01230
01230
00123
00123
SSSSk
R
SSSSk
RV
k
S
k
S
k
S
k
SRV
R
V
k
S
k
S
k
S
k
S
R
VV
k
SV
k
SV
k
SV
k
SV
f
f
f
f
f
Microelectric Circuit by Meiling CHEN
46
Problem **2.69
Microelectric Circuit by Meiling CHEN
47
Problem *2.77
Microelectric Circuit by Meiling CHEN
48
Problem *2.78
Microelectric Circuit by Meiling CHEN
49
Problem C*2.126
))((
)(
0
21
1
2
12
21
12
11
2
112
122
11
1
0
2
0
1
0
2
0
11
sCsCi
o
sC
io
sC
sC
i
sC
sCsC
i
RR
R
v
v
R
vv
R
RR
R
vv
R
v
v
R
v
R
v
Microelectric Circuit by Meiling CHEN
50
Non-ideal OP amplifiers1. Type A: Finite open-loop gain (unknown)2. Type B: Finite open-loop gain = K3. Type C:
1. Infinite input impedance2. Zero output impedance3. Zero common-mode gain4. Infinite open-loop gain5. Infinite bandwidth
Ideal OPA characters
iovo RRA ,0,
Microelectric Circuit by Meiling CHEN
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Type A: Finite open-loop gain (unknown)
vv
Microelectric Circuit by Meiling CHEN
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Type B: Finite open-loop gain =K
)( vvKvo
Microelectric Circuit by Meiling CHEN
53
Type C: iov RRA ,0,
oRiR
ovivvA
v
v
v
i
oRiR
ovivvA
2R
1R
v
vIv
0)(
0
2
21
o
voo
o
i
I
R
vvAv
R
vv
R
vv
R
vv
R
vv