AI_1

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

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

+

+


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


( )( )

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


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


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