Perfectly clear. Thanks Joe.
The only thing I'm left wondering is regards to the signal flow. What happens if you have a signal passing through two components with the same interface e.g. a CD player with a built-in DAC connected to an external DAC, or an integrated amp connected with powered (amp) speakers? Does the signal then get double-converted, and /or get double amplified?
No. Take your example of a CD player with an internal DAC, which is also connected to an external DAC. (This could NOT happen over the same interface. An analog interface (post-DAC) cannot simultaneously double as a digital interface (pre-DAC).) You could have the analog outputs from the CD player connected to an amplifier, and the digital output from the CD player running to a DAC which would then also be connected to a (different) amplifier. This means there are now two analog signals, one from each DAC. You could amplify one or the other, or both. You can't re-convert an analog signal by passing it through a DAC again; it's a one-way transformation. (To go the other way, you need an analog-digital converter, or ADC.)
Double amplification is not possible, really. I suppose you *could* run an amplified signal into the analog inputs of an amp, and it could work -- maybe (I am not sure and I would be scared to try it). But only the last amp before the speakers (i.e., the amp that's actually connected to the speakers) actually powers the speakers and therefore determines the overall power.
Let me just run through some terminology on the end-to-end solution here. This has already been done by s44 and joetekubi, but maybe I can clarify.
You start with a digital signal. This comes from your CPU. This digital signal needs to be converted to an analog signal by a DAC. This analog signal is called a "low-level" signal because it is not very powerful. It is powerful enough to power tiny speakers or headphones, or to carry a signal from one component to another; but not to power normal speakers. The low-level analog signal needs to be amplified in order to power speakers. Once amplified, it becomes a "high-level" analog signal, and it is only useful for powering speakers. (As I said above, it's *possible* that you could connect it into the low-level inputs of an amp or other component, but I think it would probably damage those inputs.)
So, in schematic form.... signals will be in (), devices will be in []
[PC]-> (digital signal) -> [DAC] -> (analog low-level signal) -> [amp] -> (analog high-level signal) -> [speakers]
The (digital signal) is carried by an optical or coaxial digital cable.
The (analog low-level signal) is probably carried by multiple RCA cables or a single 1/8" headphone jack type cable.
The (analog high-level signal) is carried by a two-conductor speaker wire.
The (analog low-level signal) is most susceptible to RF interference. The (digital signal) is impervious, and the (analog high-level signal) is very resistant to interference.
Now, each of the devices above does one thing, and one thing only. A [DAC] accepts a digital signal, and it cannot act upon an analog signal; and it outputs an analog low-level signal. An [amp] accepts an analog low-level signal, and it cannot act upon any other kind of signal (although many [amp]s have [DAC]s built-in, I'm still counting each as a separate device even though they may reside within the same physical object); and it outputs an analog high-level signal. [Speakers] accept only high-level analog signals.
Now not all of these devices will be standalone devices as in the schematic. To give some examples:
The [DAC] could be integrated into the [PC], thus keeping the (digital signal) wholly internal to the [PC]. And the [amp] could be integrated into the [speakers], thus keeping the (analog high-level signal) wholly within the [speakers]. Or there are even [speakers] with a built-in [amp] AND [DAC], thus crunching 3 devices into one physical object. And of course it is common for the [amp] to have a built-in [DAC], thus eliminating the analog low-level signal. I don't think I've ever seen a decent [amp] nor [speakers] that could really be built-in to a [PC], though (although of course laptops have tiny speakers and amps), so we're looking at a minimum of two devices here... although if you wanted to fabricate a monster PC case with built-in high-quality speakers and an amp, I'm sure you could (although it would likely end up weighing over 100lbs and it would be quite a bit bigger than most PC's).
Now, to add a couple of more terms.
An integrated amp includes a power [amp] and a pre-amp. Nowadays a pre-amp pretty much means a device that can switch among input sources, so you could have a CD player, a PC, and a DVD player all plugged into one pre-amp, and push a button on the pre-amp to choose which one you want to listen to. Pre-amps usually have built-in [DAC]s nowadays too, but strictly speaking, a pre-amp will be analog and the [DAC] will be considered a separate device in the signal path. A receiver is simply an integrated amp with a built-in radio tuner. Strictly speaking, a pre-amp is mostly for convenience in switching sources (although a pre-amp is required for listening to vinyl records with a standard record player). If you just have one source, the pre-amp is not required, and you can plug the source directly into the amp.