The Difference Amplifier and Common-Mode Rejection
The output responds only to the difference
V1 = 1V is fixed on the upper, inverting-input side, and V2 enters on the lower, non-inverting-input side. The differential gain set by the resistor ratio is 2. Slide V2 and the arrow on the output side grows and shrinks to follow Vout = 2(V2 − V1), responding only to the difference between the two inputs. When V2 equals V1 the output is 0. Set V2 so the output reaches the target of 6V on the white dashed line.
One signal to +, the other to −
The inverting amplifier took one input, and only into the inverting input. The differential amplifier splits two signals between the two inputs: V2 goes through R3 into the non-inverting (+) input, and V1 goes through R1 into the inverting (−) input. The non-inverting input's potential is set by R3 and R2 dividing V2, and the virtual short brings the inverting input to that same potential. That fixes the current coming in from V1 through R1, and that current, passing through Rf, sets the output; with matched resistors, the result responds only to the difference between the two signals.
Whatever comes in common disappears
When the same signal rides on both inputs, such as noise picked up together by two wires running side by side, it is called common mode. Since the difference V2 − V1 is 0, the common mode does not appear at the output. For this cancellation to be perfect, though, the resistors must be matched exactly so that Rf/R1 = R2/R3; even a slight mismatch lets that much common mode leak to the output. That is how a differential amplifier, bringing a weak signal from far away over two wires, erases the noise that landed equally on both wires and amplifies only the difference. This common-mode rejection is the heart of the instrumentation amplifier.
Differential gain and pure subtraction
With matched resistors, the differential amplifier's output is Vout = (Rf/R1)(V2 − V1). The leading Rf/R1 is the differential gain, setting how much the difference is enlarged. Make all four resistors equal and the gain becomes 1, so Vout = V2 − V1: a subtractor that simply takes one voltage from the other. If the inverting amplifier flipped the sign and the non-inverting amplifier kept it, the differential amplifier joins the two paths, subtracting one input and adding the other, and becomes a basic building block for noise-resistant measurement circuits.
Back to the first screen
As you slid V2, the output arrow grew as 2(V2 − V1), reaching the target of 6V at V2 = 4V (V1 = 1). Where V2 equaled V1 the output was 0, so you saw with your own eyes that the output responds only to the difference. This arrangement, one signal into + and the other into −, erases the noise that landed equally on both wires and enlarges only the difference. Joining the inverting and non-inverting paths, differential amplification is the basic building block of measurement that brings a weak signal cleanly from far away.