# Electronic Circuits and Projects Forum

1. ## Copper losses of the transformer and current density

Hi all,

How to calculate the current density of the transformer ?

I have calculated the copper wire size according to the skin depth formula i.e..,

where f = 1000Hz, Voltage = 565 , Current 175A

Skin depth = 6.6/Sqrt (f) Cm^2 = 0.208 Cm^2

wire area = Pi * skin depth^2 = 13.69 mm^2

from the above wire area i have selected the AWG 6 wire dimensions.

%Primary Resistance Rp
Rp = MLT*Np*Cr*1e-6;

I was wondered to ask you that how to calculate the secondary side wire area and AWG wire for the secondary side.

2. Transformer are usually designed to trade off wire loss and core loss to be about equal contribution.

For a transformer the heat generated is bled off very slowly so you have to be careful of total lost wattage which on the wiring loss includes the total length of wire within the winding, not just cross sectional area.

#6 does seem small for 175 amps. It's about 0.4 ohms per 1000 feet at d.c. For 565 volts I assume the total wire length is pretty significant to losses.

This site has comprehensive design explaination.

3. It's been a long time since I really looked at the phenomena, but I don't believe that current density is at unity until you get to that depth, then dropping to zero. I expect that it is a logarithmic decline as you go into the wire, starting from the first micron.

As such, you don't want to choose a wire whose diameter falls is anywhere close to the skin depth number. Far better is to be a fraction of that number. Then use multiple strands to carry the current.

This is a common practice in high frequency transformers and inductors, where "Litz wire" is often used. Google that and read the wikipedia article on the subject. For your frequency, you don't need to use the fine stranding (some as small as 40awg) often used in litz wire, but probably something in the 18 to 12 awg might be good.

4. Hi ,

Thanks for the feebback. Actually I am designing for 100KW output power as a step down transformer. My aim is to design the transformer output current more than 10KA at secondary side.

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