The Differential Pair: Amplify the Difference, Drop the Common
Widen the input difference and tip the tail current to one side
The two branches in the figure share one tail current at the bottom. As you widen the input difference vdiff = v+ − v−, the density of current dots in each branch changes. When the difference is 0, the current splits equally left and right, but when one input rises, current crowds into that branch and the differential output drawn as a bar grows accordingly.
A pair sharing a tail current
A differential stage ties together the sources (or emitters) of two identically made transistors and hangs one tail current source below them that draws a constant current. The total current the two branches can share is always set by this tail current. So when one branch takes more, the other takes exactly that much less. All the two inputs decide is how to divide this fixed total between left and right.
It amplifies the difference: current steers
When one input v+ rises above the other input v−, that transistor turns on harder and pulls more of the tail current, and the current in the opposite branch drops by the same amount. With equal load resistors on the two branches, the branch with more current drops more voltage across its resistor and the branch with less current drops less, so the difference between the two outputs widens in proportion to the input difference. Measured between the two outputs, this differential gain is Ad = gm Rd, the same form as the common-source amplifier. The proportional range is only near the center, though. Once the difference exceeds a few tens of millivolts, nearly all of the tail current moves to one side and the output saturates.
It rejects the common: CMRR
Now suppose both inputs rise together by the same amount. Their difference stays 0, so there is no reason to tip the current either way. On top of that, the tail current source below holds the total constant, so each branch still carries half, and the differential output does not budge. Common signals that ride equally on both inputs, such as noise, temperature drift, and supply ripple, are filtered out this way. The differential gain divided by the common-mode gain is the common-mode rejection ratio, CMRR, and larger is better. A real tail current source is not perfect and the two transistors are never identical, so a little of the common signal leaks through; CMRR is therefore a finite value, usually written in decibels, not infinity. This ability to amplify only the difference cleanly is why this pair serves as the input stage of every op-amp.
Back to the first screen
When the two inputs were equal, the tail current split equally left and right and the differential output was 0. When you raised one input, current crowded into that branch and the output widened in proportion to the difference; as the difference grew, all the current moved to one side and the output stopped growing. The key is the single tail current tied below. Because the total is always constant, whatever one side takes the other gives up, and that tilt is the differential output. When both inputs rise together, there is no difference to tip the current and the total stays the same, so the output does not change. The large gain of the op-amp you meet next starts in this pair, which amplifies the difference and discards what is common.
What comes next
Stack several stages of the large differential gain this stage creates, and you get the open-loop gain of an op-amp, a gain close to infinite. But that gain is not free. The next unit takes up the reality that an op-amp's gain falls as frequency rises, and the gain-bandwidth product (GBW), which says that gain times bandwidth stays constant.