I've noticed that certain types of capacitors seem to be used more commonly in certain applications. I've got a few over-sized 1uf PET caps that are a little too large for the application I originally got them for, and I should have enough spares to build this power supply design. On the other hand, I've never seen anyone use anything but electrolytic caps in power supplies (and in general nothing but PET and other plastic capacitors for audio use, other than a handful of tantalum capacitors). Would it be OK? I'm feeding it off a switch mode power supply, and I'd like to get as clean an output as possible.
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The main things that you need to look at when selecting capacitors for a power supply is the voltage rating of the capacitor, if it needs to be polarized, and the equivalent series resistance.
The datasheet of the IC that you are using will specify what value of capacitor you need and many times will specify the actual type of capacitor required.
Electrolytic Caps are polarized which doesn't work well for AC signal, but is the cheapest way to get a high value capacitance, which is why they are used a lot in power supplies.
So, in short, yes, any cap should work OK as long as you are in the allowable voltage range.