What are +12V Rails?

It depends precisely on the construction of the PSU, but in basic terms I think it means that once the mains power is converted to DC and then stepped down, it is then split in to separate supplies, which are individually regulated by regulation circuitry.

A multiple rail PSU is mains AC -> mains DC -> 12V DC
-> 12V DC
-> 12V DC
... and so on.

This is why each rail has a certain capacity. A single rail PSU is simply a straight conversion: mains AC -> mains DC -> 12V DC. However, if I am not wrong, the 12V line must be much more stiffly regulated than having multiple 12V lines, in order to cope with the loads.

Many argue that ultimately, a PSU has only one rail anyway - the mains, since this is the ultimate source of supply for the PSU, and therefore a multiple-rail PSU is a waste of time. PP&C held this argument for a long time.

I suppose some supplies are what I'd call "true multi-rail", and create the rails at the earliest possible stage (rectification?), but I've not heard of such units.

EDIT:

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They simply supply power to those components that need 12V power - hard drives, CPUs, and graphics cards.

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The number of rails, in my opinion, is largely irrelevant. What's more important is how much current each one is capable of delivering (edit: and how well the voltages are maintained under load). Wattage is the result of Volts multiplied by Amps, so if your 12V rail can deliver 50A, then that's 12V * 50A = 600W.

Now add up the Wattages of the components in your system and see what it comes to. Then go to a website that does decent PSU reviews, and pick a unit. HardOCP and Tom's Hardware are two that I know of that use decent equipment and methodology to stress a PSU.

Or better yet, post the specs of your proposed system here, and we'll help you pick a unit.

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No no no. Nearly all PSUs have one 12V source. There is one 12V output on the transformer. It then goes through rectification (AC -> DC), where it is then filtered. After that is where the difference comes in most single and multi-rail units. In a multi rail unit there is a circuit called an OCP. It groups together sets of connectors (a rail), and sets a limit as to how much current can be drawn through that set of connectors. There is no divided up current, no trapped power. The power will go to where it is needed, but no more than a set amount to any one set of connectors.

You are correct that in almost all real world circumstances, it will be difficult to see a difference between properly designed single and multi-rail units. The three best reviewers ATM are [H], jonnyGURU and hardwaresecrets.com. jonnyGURU's forums in particular are a great source of PSU info. There is much to be learned there, particularly this sticky about 12V rails: http://www.jonnyguru.com/forums/showthread.php?t=3990

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SPRC is good too....

As shinji2k hinted that there are a few PSUs with actual dual +12v rails (Corsair 1000HX, TT 1000w, Enermax Galaxy) but those are the minority. I don't think you'll see many of those designs in the future anymore since DC-DC is becoming popular.

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They've got a nice setup but I am not a huge fan of resistive loads. I also have to question some of their ripple results.

edit: Looking at their most recent reviews they seem to have gotten ripple/noise measurements under control.

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No, first the mains is converted to DC with a bridge rectifier. Then it goes through switching transistors where the DC is converted to high frequency AC. Then it is put through the transformer which outputs 12V and 5V AC in the most common designs. Then it is sent through a rectifier to switch it back to DC and then the 3.3V is regulated off of the 5V (or some combination, there are many ways to get the 3.3V and 5V lines included DC-DC for both of them).

The most important aspect of a computer PSU is that it is a switched-mode power supply (SMPS). The lower the frequency of AC, the larger the transformer you need. At 50/60 Hz, the transformer needed in a linear PSU will be unfeasibly large and expensive. If you up the frequency to say the mHz range the transformer can be much smaller, that is the basis for these types of power supplies.