Instrumentation amplifier

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 Definition

An instrumentation amplifier is an electronic device for processing weak electrical signals. The typical application is the processing of signals from measurement sensors. Its operation is based on the principle of differential amplification.

The instrumentation amplifier is generally made from one or more operational amplifiers, in such a way that it improves their intrinsic characteristics: offset, drift, amplification noise, open loop gain, common mode  rejection ratio (CMRR), input impedance.


fig 1 :instrumentation amplifier

The first stage:

we will use the fact that the inputs v + and v- of the amplifiers are equal, and that the input impedances are infinite.



the current flowing in Rg and in the two resistors R is the same, so We can write:

V1 − V2 = Rg× i

Vod = (2R+Rg) x i

Vod = (V1-V2) x ((2R+Rg) /Rg)

The common mode voltage at the input of the assembly is:

(Vcm)input = (V1+V2) / 2

the common output mode is equal to:

(Vcm)output= (Vo1+Vo2) / 2

We can calculate the values of Vo1 and Vo2 :

Vo1 = V1+Ri

Vo2 = V2-Ri

 so we can deduce that:

(Vcm)input = (Vcm)output

Op amp in linear regime:

v + = v-

Millman's theorem :

(V1)=((Vo1/R)+(V2/Rg))/(1/R+1/Rg)=(RgVo1+RV2 )/(Rg+R)

(V2)=((Vo2/R)+(V1/Rg))/(1/R + 1/Rg)=(RgVo2+RV1 )/(Rg+R)

Vo2 – Vo1 = (1+(2R/Rg))(V2 – V1)

To make this circuit usable, we will have to get rid of the common mode, and reference the output signal Vod to ground. We will do this by adding a classic differential amplifier circuit at the output of the first stage.

the second stage :

differential amplifier :



Millman's theorem:

(V-)=((Vi1/R1)+(Vo/R2))/(1/R1 + 1/R2)=(R2Vi1 + R1vo )/(R3+R4)

(V+)=  R2/(R1+R2)×Vi2

Vo = (R2/(R1+R2))×((R2+R1)/R2))×Vi2-R2/R1×Vi1 

If R2 = R1 then:

Vo = Vi2 – Vi1

The Output stage of the instrumentation op amp is a differential amplifier.

If R2 = R1 then:

Vo = Vi2-Vi1 = Vo2- Vo1 = 1 + (2R/Rg).(V2 – V1)

Ad= 1 + (2R/Rg) 

The gain of the circuit is regulated by the resistance RG. We immediately see that the input impedance is very large since the inputs are connected directly and only to the non-inverting inputs which do not absorb current.


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