How to calculate power of unknowm transformer

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Hmmm… I'm going to confess early on: of magnetics I know not much beyond what I remember from UC physics 1. (Which is to say, not much!)

But I kind of thought that VA scaling would have to scale linearly with the mass of energized iron. (Which comes directly from the idea that magnetic energization of the core material (and free space, were it not there) is the coupling between windings.)...

GoatGuy

Well... not really.

Rated power is usually a thermal limit. I calculated earlier the exact theoretical dependency (and written to the forum), but didn't memorize it. Given everithing is similar, an N times bigger (in linear dimensions) transformer is rated between N^3 and N^4 higher power. Maybe exactly N^3.5, if I remember correctly. The false approximation of N^4 can be deduced from constant current density (which is a false approximation, but for small variation the error is acceptable). I will not do this now, because nobody cares and hard to draw equations here. Magnetisation losses and apparent energy is negligible regarding nominal power of a regular 50...60 Hz power transformer over 1...4 VA. N^5 approximation is based on constant normalised drop.

The problem is: there are many different kinds of transformers, with very different core shape, quality (iron and insulator quality), and fill factor. To measure everithing: generally impossible or very hard. Problem No2: ambient temperature and convection efficiency affects allowable dissipation. Problem No3: many users (amplifier builders different from ClassA) don't really care about thermal limit, but drop limit, however they don't know these things exist.

My solution is (instead of quesstimating 5 or 6 unknown factors) measuring the ohmic resistance of primary winding, estimating allowable power dissipation (based on surface area, geometry, and allowable temperature rise), and calculating primary current from Power and elevated (+25% because of temperature rise) resistance. Iprimary=sqrt(Pd/(2.5*R)).

(2.5 instead of 1.25, because primary and secondary power loss are additive, and approximately the same. If the trafo is built or used asymmetrical, then other factor must be used according to secondary strength.)

This is the minimal set of parameters one can calculate rated current of an unknown, in-hand transformer, and in every other methods these parameters are also there, just hidden and ignored.
 
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So If I have a small open EI trafo 120 Input, secondaries 52VCT with ~18mmx18mm core (dimension of core is 50x42x18mm) I get about 10VA with Jim Faheys guesstimate. It appears to be about the same size as a marked 15VA transformer, so it seems reasonable.

PAFis estimate using the above 10VA and a coil winding resistance of 34ohms gives something like 0.34A primary current.

Pd= dissipated Power.
Iprimary=sqrt(Pd/(2.5*R))=sqrt(~3W/85ohm)=0.19A
 
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