1. I have searched and it is not clear if the center tap on the secondary side of the transformer should be left floating? Some articles suggest it should be connected to mains earth/ground?
This mainly depends on the transformer and only after that comes if you like supplies with grounded outputs. If you let it float the transformer needs to be rated for use in class II appliances (double / reinforced insulation). You'll find that information sometimes on the nameplate of the transformer or you can see that it's a doubly insulated transformer (separate coil chambers, insulation to core etc.). If unsure, ground it.
2. A few websites have suggested there are potential problems with unbalanced current flow in the secondary side of the transformer between say +15V and the center tap and the center tap and -15V in this case. How big of an issue is this potentially?
Irrelevant.
3. The transformer has no datasheet except for a sticker that reads input: 240v,50HZ AC, output 15-0-15v AC, 3 AMP Max. I presume this current rating refers to the secondary side of the transformer and the transformer should be able to deliver at least 2 amps of current?
Depends on what kind of current you mean. If you mean DC after rectification you need to apply a "correction factor", so for a bridge rectifier you need to divide the current by 1.5 to 2, i.e. you can expect it to deliver about 1.5-2 A DC continuously. You
can pull out more current, but that leads to higher losses in the transformer and that might dissipate to much heat in the transformer. Personally I'd see 2 A already on the high side. 1.5 A would be a more conservative approach.
Re. cap rating: Unominal *
1.1 * 1.41 *
idle factor = required cap W.V. rating
1.1 => 10 % over voltage
idle factor => up to 1.6 for very small transformers, down to 1.0x for large ones. For a medium sized transformer like yours probably 1.2, maybe 1.3.
I'd use 35 V caps.
Re. filter cap size: 1000 µF / A usually works out nice for a regulated supply, gives ~15-20 % ripple (depends on various things), which is a good trade off between transformer losses and usable current output.
Various other stuff:
- Always use dual-pole switches for mains.
- A MOV (varistor) in parallel with the transformer primary is always a good idea.
- Bridge rectifiers should be over-dimensioned generously.
- Having a small RC snubber across the secondaries (say, 100..220 ? + 100 nF) can help with some strange effects (ringing when the rectifiers switch).
- Some people also prefer to put small caps across the rectifier diodes (again about 100 nF, or smaller) to avoid HF ringing and similar issues.
- Secondary side MOVs or Zeners are sometimes seen, but don't make much sense IMHO.
- Polyfuses on the secondary OTOH are handy.
- Oh, don't forget to fuse mains, preferably with a nice power entry module (IEC socket + fuse holder + optionally a switch and/or EMI filter).
- Isolate all mains-carrying parts nicely (shrink tube).
- Don't use bell wire for mains ; use proper wire rated for 300+ V working voltage.
- Ground all metal parts nicely, and use green/yellow striped wire for that.
- Don't ground case parts and other stuff just be screwing them together ; always use a (preferable crimped) PE wire running from a central "PE distribution screw" to all metal case parts.