In my electronics class, we just saw the principles of a linear regulator (like the LM140L or uA78LXX). But I didn't understand why we are controlling a common collector with the differential amplifier. If we use a common emitter or common base, we will have a really big gain…
Can you help me to understand that little thing?
Besides the excellent answer by Neil_UK, I'll add another point of view.
The differential amplifier (a.k.a. the error amplifier) is the stage that provides the "signal processing" needed to keep the output voltage at the required level. The CC stage, a.k.a. emitter follower, acts as a buffer, i.e. a power stage that doesn't provide voltage amplification, but only handles the required power needed by the load (you should know that an emitter follower is called like that because the emitter voltage "follows" the voltage at the base).
In other words, the CC stage provides current amplification: it sources all the current needed by the load (within certain limits) keeping the same voltage level provided by the previous differential amplifier.
When you're designing a feedback circuit, you don't necessarily need the biggest gain from each component in the loop, just sufficient gain. More important than gain is stability. A good way to design an unstable system is to have several high gain stages, each rolling off at a similar frequency.
In the case of the old style regulators, enough gain comes from the differential amplifier. The common collector stage is fast, it has no Miller capacitance, which makes it easier to concentrate all the stabilisation efforts into the differential amplifier. But they are expensive in terms of a high minimum voltage drop across the part. 3v wasted was OK with 15v rails, but looks pretty sick with 5v and 3.3v rails.
Newer style LDO (low dropout regulators) do use a PNP common collector stage as the output device. They need a more complicated amplifier stage before them. Read the datasheet carefully before you use one, some are unstable into the 'wrong' sort of output capacitor (ceramic).
