AI_1
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Transcript of AI_1
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246
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2211
22s111
22122
out21111
s
RIRIRIVRIV
RIRIVVRIRIV
0V
+=
++=
+=
++=
=
21
out11
2111out1
out21111
RRVV
I
RIRIVVVRIRIV
+
=
+=
++=
( )
21
22
212
22122
RRVI
RRIRIRIV
+
=
+=
+=
(1)(2)
(3)
from (1)
from (2)
substituting into (3)
( )
( ) ( )
( )
( )211
2out
1out221
1out2221
221out112211
221out1211
221
21
21
out1
22111
VVRRV
RVRVVRVRVRV
RVRVRVRVRVRVRVVRRV
RRR
VRRR
VVRIRIV
=
=
=
+=+
+=+
+
+
+
=
+=
Now, the input resistance ofthe negative input isunbalanced with respect tothe positive input. If V1 isgrounded, then Rin of V2 isR1 + R2. If V2 is grounded,then Rin of V1 is R1 (sincewhen V2 is grounded, thenegative input is a virtualearth). This can causeproblems with unevenloading of the sources. Toovercome this, we can designan input stage using voltagefollowers.
Note: The negative input to the op-amp is not a virtual earth (0 V) in thiscircuit. The internal input resistanceof the op-amp is M but becausethe input bias currents are nA, Vs= 0and so the voltage at negative inputis equal to I2R2.
1
2
21
outd R
RVV
VA =
=
difference gain
3.3.1 Difference amplifier
V1
R2
R1Vout
R3 = R1V2
VS
R4 = R2
I1
I2
I1
I2
+
2473.3 Instrumentation amplifier
-
The common mode rejection ratio (CMRR) is the ratio of the differentialgain to the common mode gain. The common mode gain is that obtainedwhen V1 = V2
cm
d10
cm
dAA
log20AA
CMRR ==
The more general expression for difference gain is:
11
22
43
21
1
4out VR
RVRRRR
RRV
+
+=
With a common mode signal, V1 = V2, thus:
cm
1
2
43
21
1
4
in
out
A
RR
RRRR
RR
VV
=
+
+=
Small variations in resistor valuesin a circuit can lead to somecommon mode gain.
Now consider the following circuitwhere the source voltages and outputresistances are included:
( )
1S
1S11
111
1S11S
RRVR
V
RIVRRIV
+
=
=
+=
( )( )
( )
( )
21S
2S21
43S
2S432
4322
43S22S
RRRVRRRRR
VRRV
RRIVRRRIV
++
+
=
++
+
=
+=
++=
for matched resistors
Now, even if VS1 = VS2 and resistors arematched, V1V2 and thus some commonmode gain is the result. The difference inV1 and V2 gets smaller as RS is reduced.At RS = 0, V1 = V2 = VS and no commonmode gain. For the highest common moderejection ratio, the amplifier should bedriven by low impedance sources suchas a voltage follower.
3.3.2 CMRR
R2
VS1
VS2
RS
RS
V1 R1Vout
R3=R1V2
VS
R4=R2
I1
I2
I1
I2
-
+
Newnes Interfacing Companion248
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Unity gain ( = 1) voltage followers: high input impedance, low outputimpedance.
5oldin
ooldinnewin
10R
A1RR
+= = 1Ao = 105
Signal sources see only high impedances, therefore maximum transferof Vs and no uneven loading of the sources.
The amplifier itself is driven by low impedance sources (Rout of an op-amp is very small: 75 ). CMRR is improved. The effect on CMRR ofsource impedance is much greater than resistance mismatches.
3.3.3 Difference amplifier with voltage follower inputs
R2
R1Vout
R3 = R1
VS
R4 = R2
I1
I2
I1
I2
+
V1
V2
+
+
2493.3 Instrumentation amplifier
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Feedback resistors Ra and Rbtend to keep the negative andpositive inputs to the op-ampat equal potential hencevoltages at R are V1 and V2
( )
( ) ( )
( )R
RRRA
VVRRR
VVVV
RRR
VVVVVV
RR
VVVV
RR
VVVV
RVVI
IRVVIRVVIRVV
bai
21ba21
2o1o
ba21
2o211o
b21
2o2
a21
11o
21
b2o2
a11o
21
++
=
++
=
+
=+
=
=
=
=
=
=Now,
thus
Note: This input stage isnot a difference amplifier.The difference in the outputvoltages = the gain timesthe difference in the inputvoltages. Common modesignals are passed throughwithout being amplified. Aproper difference amplifierrejects the common modesignal altogether.
Gain increases as R decreases.If R is made very large, the gainapproaches 1
This is the gain of the input stage.The gain of the input stage canthus be altered by adjusting justone resistor R.
3.3.4 Difference amplifier with cross-coupled inputs
To amplifierinputs
V1
Ra
+
V2
+
Rb
R
VO1
VO2
Newnes Interfacing Companion250
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( )( )
1AVV
RR
VVVVRR
VVVV
RR
RR
VVV
IRVV
VRR
VVVIRV
IRVVVVVV
2VV2VV
A
cm
21
a21
21a21
2o1o
ba
b21
2
b22o
1a21
1a1o
21
21
2o1o
21
2o1ocm
=
+=
++
=+
=
+
=
=
+
=
+=
=
+
+
=
+
+
=
but
and
if
then
Now,
i
cm
cm
i
ACMRR1AAACMRR
=
=
=
butthus
But, Ai is the gain of the inputstage which is adjustable via R.This means that the CMRR isadjustable. For highest CMRRwe thus require a high value ofAi (and hence a low value of R).
therefore
2VV
V 21cm+
=
3.3.5 CMRR cross-coupled inputs
V1
Ra
+
V2
+
Rb
R
VO1
VO22VVV
VVVV
VV2
VV2
VVVV
2VVVV
21cm
cm21cm
cm221
21cm2
21cm1
+
=
+=
=
+=
=
If the input signal consists of acommon mode component,(e.g. V1 = 5 V, V2 = 3 V means thatVcm = 3V and V1 V2 = 2V) then:
Since common mode signalsare not amplified, then:
2VV
Vo 2o1ocm+
=
thus
2513.3 Instrumentation amplifier
-
An instrumentation amplifier is characterised by a high gain andhigh CMRR.
Both inputs have a high input impedance. The gain of the amplifier can be easily adjusted via R. The resistors R1 at the input to the final differential amplifier are trimmed
to eliminate amplification of any common mode signal.
( )RRRR
VVVV ba212o1o ++
=
The gain of the input stage is:
The gain of the amplifier stage is:
1
2d R
RA =
Thus the total gain is the product of the two:
( )
( )
( )211
2av
1
2aa
21
1
2ba
21v
VVRR1
RR2
A
RRRRR
RVV
RRRRR
RVVA
+=
++
=
++
=
letting Ra = Rb
It is usual to have the requiredgain of the overall circuitobtained from the input stageand the R2/R1 term drops out.The difference amplifier D isdesigned for a gain of 1 and itspurpose is to reject anycommon mode signal.
3.3.6 Instrumentation amplifier
A
B
D
R2
R1Vout
R1
VS
R2
I1
I2
I1
I2
+
V1
Ra
+
V2
+
Rb
R
VO1
VO2
Newnes Interfacing Companion252