Re: Transformer design
I designed a few transformers for some project a few years back. Basically its quite simple, though I don't have the formula's on top of my head. I've a few tidbits that I remembered that can make your design life a lot simpler.
Firstly, the core is the most crucial part of the transformer. Normally stacked silicon steel sheets are used with appropriate thickness related to the total power.
There is something called flux saturation after which the core no longer behaves as a transformer and shorts out the whole thing. IIRC, it is around 1.6 Tesla for very high quality laminates at line frequency. So your operating flux must be something lower than this plus safety margin.
You'll first work out the number of turns on the primary side, obviously. So with the selected flux density and the primary side voltage and frequency you can determine the number of turns there by turns/volt parameters.
Now the funny part is that the core size is simply a matter of accomodating the required number of turns of all the windings(primary, secondary,teritiary etc) at their respective wire guages.
All the above is rather crude and half-baked descriptions of typical line-frequency transformer design. But for a real efficient and reliable design you need to consulte some good references on that matter. Happy designing.