Everywhere that you find information about transformers, it says "make sure that you know what you do, these things can kill you".
Well, I thought I knew, but I still managed to mess up. I didn't get killed, but I learned a bit about transformers and rectifiers.
Let me explain.
There are two basic ways of turning an AC voltage into a DC voltage. One uses a half wave rectifier, the second a full wave rectifier.
The difference is that the half way rectifier only uses the positive part of the voltage swing, whereas the full wave rectifier uses both parts by magically reflecting the negative part. The full wave rectifier requires a few extra diodes but gives a smoother DC voltage (or at least one that requires a smaller smoothing capacitor and is more efficient).
Then there are two basic transformer configurations - single and dual secondary. When the two outputs of the secondary are of equal voltage, and the "bottom" of one is connected to the "top" of the next, we call it a centre-tap transformer. This kind of transformer is often used if you want a dual voltage output, for example +15V and -15V for audio circuits.
Here is how the different transformers may be connected for a single output voltage.
First off, a single secondary, half wave rectified configuration:
Here, the lower pin of the secondary is connected to ground, and the top is connected to a smoothing cap through a power diode.
Then we have the single secondary, full wave rectified configuration:
Here, none of the secondary output pins are connected to ground. Instead, they are connected to the top and bottom of a diode bridge rectifier. Then, one of the other rectifier junctions is connected to the smoothing cap, and the last one is connected to ground.
Now, if we have a centre-tap transformer, we get to use a little trick:
Instead of using four diodes, we get away with two. Ground is connected to the centre tap.
So what if we want a dual (positive and negative) output from a centre-tap transformer? Well, just duplicate the circuit, but turn the diodes the other way around for the second half.
This looks suspiciously like the full wave rectifier for the single secondary transformer, but there is a crucial difference!
Instead of connecting the last pole of the diode bridge to ground, it is used as the point where we tap the negative voltage/connect the smoothing cap for the negative voltage.
This may seem obvious, but when I tried to use a centre-tap transformer for a single output voltage, I didn't think this part trough. I left the four diodes in and connected both the last pole of the diode bridge AND the centre-tap to ground. This immediately blew the input fuses (luckily I was using fuses) and it is easy to see why: With the diodes in place there is a direct short (well, through the diodes anyway) between the negative half wave and ground, which drew a large current.
As for my circuit design - the fact that I both have a three pin input with one pin connected to ground, and room for four diodes in the bridge rectifier, means I can use both a centre-tap and single secondary transformer - as long as I do not connect the diodes when connecting the centre tap.