differential pair

A differential pair is two carefully matched transistors that share one tail current source feeding their joined sources, and together they answer a single question: which of your two inputs is higher, and by how much? Picture a seesaw fed by a fixed flow of water at the pivot. The total water is constant, so when one input rises and tips the seesaw, current shifts from one transistor to the other — but the sum never changes. The output is read as the imbalance between the two sides, which means the pair amplifies the difference of the inputs and quietly ignores any voltage they share. Lift both inputs by the same amount and the seesaw stays level; nothing happens at the output. That is the whole point: it listens to the difference and is deaf to the common part.

This deafness has a name — common-mode rejection — and it is why the differential pair is the input front-end of nearly every op-amp. Real-world signals ride on top of shared garbage: power-supply hum, ground bounce, picked-up interference. Because that noise is common to both inputs, the pair rejects it while faithfully amplifying the small wanted difference. We grade this with CMRR, the ratio of differential gain to common-mode gain (bigger is better, often quoted in dB); it improves the more ideal the tail current source is, since a stiff tail holds the sum constant and refuses to let common-mode shifts leak through.

The gain itself comes from each transistor's transconductance gm — how strongly its gate voltage steers current — working into the resistance at the output, so the small-signal gain is roughly gm times that load resistance, in the same spirit as a common-source stage but now driven by the input difference. For a MOSFET in saturation, gm = 2*Id/Vov, so the tail current you choose and how hard you bias the devices set both the gain and the speed. Pair this front-end with a current-mirror load to turn the two-sided swing into one clean output, and you have the first stage of a classic two-stage op-amp.