Power transformer ratings and cross-sectional area.

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I think there is an empirical formula that relates the power transformer's power ratings to it's cross-sectional area in cm^2, could someone please remind me that formula?

It's an empirical and approximative one, not exact.
The power in VA of a conventional 50Hz transformer can be crudely estimated by squaring the cross-section expressed in cm². Give or take 25%, depending on the quality of the iron, filling ratio, margins, etc
A = core area in sq in or a = core area in sq cm
VA = 31 * A^2 for flux @ 1T
VA = 0.75 * a^2 for flux @ 1T
If you choose a different flux, you just change the VA in direct proportion.
core 3cm * 4cm
a= 12 sq cm
Flux = 0.7T
VA ~ 0.7 * 0.75 * [3*4]^2 = 75VA

I suppose you are meaning for so called wasteless cores.Are these formulas valid for c-cores or let's say double c-cores.I think that the size of window and the length of the core play a key role also,considering the constant flux.Are there any other formulas particularly aimed for c-cores regarding their different shapes?

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Andrew T gave some advice, but you would need to know the particular core-geometry those formulars are intended to use with.
I have seen (over?)simplified formulas on the web (sorry, I dont remember where I stumbled over them) that at least take core area and window area into account.
I would look fore specific data in one of the many core manufactures catalogs.
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If I have a core with unobtainable data I just measure all dimensions and calculate area of core and window, average the magnetic path length. I then use the OPT calculator the DIY member Yvesm has kindly provided. I plug in the cores data and, depending on the application, choose either a suitable current density or a suitable regulation percentage. All you need, except temperature rise, can be simulated. Temperature is what usually sets the powerlimit.
If used in a enclosure cramped with other "heathers" and/or heath sensitive parts nearby then I usually use the very conservative rating of 10mW/sqr cm averaged over the total surface area.
This will ensure the transformer runs cool and anything nearby will be happy too.
Manufacturers may use 25-50mW/sqarecm (or even higher), but that is theyr choice...
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Can anybody help me with the formulas?
Or simply suggest where I should search for the answer?

Hi Yugo,
If you look at Andrew formula that for flux @ 1T
If you have different core of course you need to change the flux density to suit the core you have. @ 1T i guess it for E I core.
The key is you must know the core can be use @ what flux density.
Once you know that you can start your trafo build.
See this http://www.diyaudio.com/forums/power-supplies/200849-iron-core-transformer-formula.html but I'm not finish anything yet hehe... :D

plot the Iprimary vs Primary supply voltage.

You will see when the Iprimary starts to become excessive.
That should be a good clue to what number of turns are required for your worst case supply voltage.
Then you could work back to determine the Limiting Flux for that core.

Is this feasible?
Thank you very much for your replies.
The problem began when I salvaged some transformers from an old colour Grundig TVs which had very interesting C cores and bobbins without side sheets similar what Lundahl transformers are winded.I hope the link John and instruction Andrew recommend will help me to calculate the right power for those cores.

Best regards,
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Can you explain the procedure for us?

The core must have as little airgap as possible and a winding with a known number of turns on it. Use a variac to feed the coil. Start at some low voltage and measure voltage and current. Take notes and calculate the impedance. Increase the voltage stepwise and caculate the impedances. With increased voltage the impedance will increase until it reaches a maximum. This is the point where the core has the highest impedance. Now divide this voltage with the known turns and you have the V/turn that givs the highest impedance/turn
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