Difference Amplifier or Op Amp Subtractor

A difference amplifier or op amp subtractor is a specially designed op amp based amplifier circuit, which amplifies the difference between two input signals and rejects any signals common to both inputs.

Difference Amplifier or Op Amp Subtractor
Let us consider the above op amp circuit. Now, by applying Kirchhoff Current Law at node 1, we get,

We have written this equation by assuming that there is no current entering in the inverting terminal of the op amp.
Now, by simplifying the above equation, we get,

Now, by applying Kirchhoff Current Law, at node 2, we get,

We know that, in ideal op amp, voltage at inverting input is same as the voltage at non inverting input. Hence,

So, now from equation (i) and (ii), we get,

The difference amplifier must reject any signal common to both inputs. That means, if polarity and magnitude of both input signals are same, the output must be zero.

This condition must be satisfied only when,

In that case, equation (iii) becomes,

Again, if we make, R1 = R2, then equation (iv) becomes,

So, if R1 = R2 and also R3 = R4 then the difference amplifier becomes a perfect subtractor, which subtracts directly the input signals.
Finally, the circuit of op amp substractor becomes,
op amp substractor

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