[Eli5] Why do amplifiers require both a preamp and Poweramp stage?

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That is, if the preamp amplifies the instrument signal, why is a poweramp necessary at all?

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Preamps make very quiet things louder very cleanly. Power amps make things very loud, but if you only used a power amp you would end up with a loud sound with a lot of noise.

Imagine you had a picture of a stamp and you wanted to put it into an overhead projector. If you put a low-res image straight into the projector and made it huge it would look terrible.
But if you used a good scanner to get a larger, clean high resolution image of the stamp first, then pass it to the projector, it would look a LOT better.

In general, pre-amps are used to take very faint signals – such as those from microphones – up to line level, where it can be transmitted short distances, have signal processing applied, etc.

Power amplifiers are used to drive speakers – the actual mechanical device producing the sound – and take the line level sound and amplify it enough to do so.

Amplifiers are not perfect. In an amplifier there are factors and constraints at play other than just amplification, such as distortion/fidelity, energy consumption, input and output impedances, frequency response (not that relevant in audio I guess)… So different amplifiers are optimized for different situations.

Fidelity and energy consumption for example are usually directly contradicting requirements (measures to improve one, make the other worse) (talking about amplifier classes here). Among other differences then, the preamp is a higher fidelity, less energy efficient amplifier, outputting a signal better suited for simple processing (filtering and other effects) (the low efficiency is not grave because the signal is low power), while the power amp is lower fidelity, but is more energy efficient, suitable for driving the speaker loudly with high power signals.