E1 · op-amp

The Differential Pair: Amplify the Difference, Drop the Common

The mouth of an op-amp amplifies only the difference of its two inputs and presses the common part down. Spread the two inputs apart yourself and see the shared tail current steer to one side, making a differential output.

Spread the inputs and steer the current

The pair below shares a single tail current. Spread the input difference vdiff = v+ − v−. When the difference is zero the current splits equally left and right, but as one input rises the current steers to that branch and a differential output appears.

Differential input vdiffvdiff = 0 mV

Current steering and differential output

I1 : I2 = 50 : 50

vod = Ad vdiff   (Ad = gm Rd)

The two inputs are equal. The tail current splits evenly, so the two branch currents match. The difference of the outputs is zero.

Balanced · no diff output

A pair sharing a tail current

A differential pair ties together the sources (or emitters) of two identical transistors and hangs a single constant tail current source below them. The sum of the current the two branches can use is always fixed at this tail current. So if one branch takes more, the other takes exactly that much less. The two inputs only decide how this fixed sum is split left and right.

It amplifies the difference: current steers

When one input v+ rises above the other v−, that transistor turns on harder and draws more of the tail current. The opposite branch loses exactly that much. With equal load resistors on the two branches, the branch with more current drops more voltage and the other drops less, so the difference of the two outputs widens in proportion to the input difference. This differential gain is Ad = gm Rd, the same form as the common-source amplifier’s.

It rejects the common: CMRR

Now suppose both inputs rise together by the same amount. The difference between them is still zero, so there is no reason to steer the current either way. Moreover, the tail current source below holds the sum constant, so the two branch currents are still an equal half each. The differential output therefore does not budge. Common signals that ride equally on both inputs, like noise, temperature drift, and supply wobble, are rejected this way. The ratio of differential gain to common-mode gain is the common-mode rejection ratio, CMRR, and the larger it is the better. This property of cleanly amplifying only the difference is why a differential pair is the input stage of every op-amp.

ObserveI1 + I2 = Itail

The sum of the two branch currents is always fixed at the tail current.

Choosevod = Ad ?

The differential output amplifies the difference of the two inputs.

Fill inAd = gm ?

The differential gain is transconductance times load resistor.

On your ownCMRR = Ad / ?

CMRR is the differential gain over the common-mode gain.

Back to the first screen

When the two inputs were equal, the tail current split evenly and the differential output was zero. As you raised one input, the current steered to that branch and the output widened in proportion to the difference. The secret is the single tail current tied below. The sum is always constant, so what one branch takes the other gives up, and that tilt is the differential output. Yet when both inputs rise together, there is no difference to steer by and the sum is fixed, so the output stays put. This pair, which amplifies only the difference and drops the common, is the input stage where the enormous gain of the op-amp we meet next begins.

A differential pair is two matched transistors sharing a tail current. The difference of the two inputs, vdiff = v+ − v−, steers the tail current to one side, making a differential output vod = Ad·vdiff (Ad = gm Rd). Conversely, a common signal in which both inputs move together is rejected, because the tail current source holds the sum constant and the output does not change. The ratio of differential to common-mode gain is the CMRR, and this "amplify only the difference" is the input stage of every op-amp.

What comes next

Stacking the large differential gain of the diff pair across several stages gives the nearly infinite open-loop gain of an op-amp. But that gain is not free. The next unit looks at the reality that an op-amp’s gain falls as frequency rises, and at the gain-bandwidth product (GBW), where the product of gain and bandwidth stays constant.