CR · Operational amplifier

The Difference Amplifier and Common-Mode Rejection

Sometimes you want to amplify only the difference between two signals and throw away the noise they picked up together. Feed one signal into the non-inverting input and the other into the inverting input, and the op-amp amplifies their difference while erasing what they share. Learn this principle of difference amplification.

The output responds only to the difference

V1 = 1 V is fixed on the inverting side, and V2 goes into the non-inverting side. The differential gain set by the resistor ratio is 2. Slide V2. The output Vout = 2(V2 − V1) responds only to the difference of the two inputs. When V2 equals V1 the output is zero. Set V2 so the output reaches the target of 6 V.

Non-inverting input V2V2 = 1.5 V

Output voltage Vout = G(V2−V1)

Vout = 2(V2 − V1) = 1.0 V

Far from 6 V

One signal to +, the other to −

The inverting amplifier took only one input, and through the inverting terminal at that. The difference amplifier splits two signals across both inputs: V2 enters the non-inverting (+) side, V1 the inverting (−) side. While the virtual short keeps the two input potentials equal, the + side pulls the potential toward V2 and the − side holds against V1. The result of that tug-of-war appears at the output, and remarkably it responds only to the difference of the two signals.

Whatever comes in common disappears

When the same signal rides on both inputs — say the noise two wires running side by side picked up together — that is the common mode. Since the difference V2 − V1 is zero, the common mode appears nowhere in the output. When the resistors are matched exactly, that is when the ratio of R1 to Rf on the inverting side equals the ratio of R3 to R2 on the non-inverting side, the common part cancels perfectly. So when a weak signal is brought in from afar over two wires, the difference amplifier erases the noise smeared equally on both and amplifies only the difference. This common-mode rejection is the heart of the instrumentation amplifier.

Differential gain and pure subtraction

The output of a matched difference amplifier is Vout = (Rf/R1)(V2 − V1). The leading Rf/R1 is the differential gain, setting how much the difference is amplified. Make all four resistors equal and the gain becomes 1, so Vout = V2 − V1, a subtractor that takes one voltage straight from the other. Where the inverting amplifier flipped the sign and the non-inverting kept it, the difference amplifier merges their two paths — subtracting one input and adding the other — to become the noise-tolerant building block of measurement.

ObserveVout = G(V2 − V1)

The output is the difference of the inputs.

ChooseV1 = V2 → Vout = ?

The common part disappears.

Fill inG = ?

The differential gain is the resistor ratio.

On your ownR1 = Rf → Vout = ?

Equal resistors give pure subtraction.

Back to the first screen

As you slid V2, the output grew as 2(V2 − V1) and reached the target of 6 V at V2 = 4 V (V1 = 1). Where V2 equaled V1 the output was zero, so you saw with your own eyes that the output responds only to the difference. This structure, one signal to + and the other to −, erases the noise smeared equally on two wires and amplifies only the difference. This difference amplification, merging the paths of the inverting and non-inverting amplifiers, is the building block of measurement that draws a weak signal in cleanly from afar.

A difference amplifier feeds one signal into the non-inverting (+) input and the other into the inverting (−) input to amplify only their difference. With matched resistors the output is Vout = (Rf/R1)(V2 − V1), so a component common to both inputs (the common mode) cancels and vanishes, its difference being zero. Make all four resistors equal and it is a unity-gain subtractor. It erases the noise smeared equally on two wires and lifts a weak signal — the heart of the instrumentation amplifier.