Okay i noticed someone wanting to make a transformerless power supply, and he has a microwave oven transformer with a removed secondary. It couldn't be easier to wind yourself a 1:1 transformer using a microwave transformer. They often have a large core, and require less turns to operate correctly. They may require as much as 200-300turns, which is a half an hour worths of work, having the right materials and skills. Okay so how it's done? You take a simple insulated wire and wind 10-15 turns for the secondary. You take a measurement of the output voltage. In this case we have 12V by winding 15 turns. So now we determine the winding ratio by dividing the primary voltage to the secondary. You can work with either the peak value or the RMS value it doesn't matter. Let's choose the peak value here. So our winding ratio is 320:12=26.66. Now that we know that, we just multiply the winding ratio by the windings of the secondary which we made (15). So 26.66*15=400. So you need to make 400 turns to turn the transformer into a 1:1 isolation transformer. If you want a different voltage, for instance let's say 50V. Then you divide 50 to the voltage we got from the 15turns (12V). 50:12=4.16. Now we take that number and multiply it by the turns of the secondary (15). 4.16*15=62.4, so after 62.4 turns you get 50V of output. Now you have to determine how much current can the wires safely pass, and with that the VA rating of the new transformer. The formula is d=0.02*SQRT(I) where I is in mA and d in mm. So if you want 5A at the primary (around 1kW of energy) the wire should be d=0.02*sqrt(5000) 1.41mm. Accounting for active resistance and the slight skin effect, choose a wire 5-10% thicker. So the ideal wire for the secondary is 1.5mm. For lower voltages for the secondary like the 50V example keep in mind that the current of the secondary will be raised as much times as the voltage is reduced, so if you have 5A at the primary you'll have around 21A at the secondary, (5A*4.16) so the wire thickness for the secondary should be d=0.02*sqrt(21000)=2.89mm. Again applying the 5-10% rule the wire should approximately be 3mm. You have to comply with the physical dimensions of the windows in which you'll wind the windings, so always keep that in mind too. Now lastly you need to calculate the VA rating of the transformer. Most of the times and especially for single phase/high power the formula is the same as for Watts. So VA=V*I VA=220*5=1100VA. With that you've finished designing your transformer and you can start building it. Take care, though because this still works at mains potential and it's dangerous if the given precautions are not used.
P.S. If you want to build a transformer from scratch, with just having the wires and the core, the calculations are a bit difficult and vary from core to core, and from power rating to power rating.
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