# Transformer core maximum power

so i am an EE undergrad, and i am wondering if and how exactly does a transformer core limit its power capacity. From my understanding, the rated power of a transformer is due to the current carrying capacity of its windings. As far as the core is concerned, the magnetic flux is pretty constant, and maximum (close to saturation) when the transformer is open circuited. Also core loses are more or less constant with respect to the load. Am i correct? So for example will a transformer with superconducting windings have near infinite power capacity?

I got confused, because i remember a while back i ordered a transformer for a power supply and when discussing the power rating with the guy , he said something like(for eg i wanted a 160va transformer) "we have 150va and 200va cores".

From my understanding, the rated power of a transformer is due to the current carrying capacity of its windings.

That's not far off the truth. Copper loss plays a big part in how much power can be transferred to the load. Bigger transformers inevitably produce more magnetization inductance for fewer primary turns so, a bigger transformer needn't have as many turns - this needs to be also considered. Fewer turns means fewer losses in the windings. Leakage inductance is also proportionally reduced when dealing with bigger cores too.

As far as the core is concerned, the magnetic flux is pretty constant, and maximum (close to saturation) when the transformer is open circuited.

That's very true. Flux in the core is maximum when load is minimum and gets slightly smaller as load increases (much to the distress of people who think they know how transformers work LOL). It gets slightly smaller because the primary leakage inductance and resistance drop more supply voltage as load increases: -

Xm in the picture above is the inductance that creates the flux in the core and if there is high primary current (Ip) then Rp and Xp drop more volts leading to a slightly lower voltage on Xm.

So for example will a transformer with superconducting windings have near infinite power capacity?

No, because Xp and Xs will not tend to follow Rp and Rs towards zero.

• But then why do larger transformers need larger cores? Nov 20, 2014 at 0:40
• @user19955 I think I covered that in my 1st paragraph but if you need more info just ask. Nov 20, 2014 at 8:07
• Yeah i didnt quite get that, can you explain it a little better? Nov 20, 2014 at 12:04
• A bigger core means more inductance per turn. More inductance per turn means you can use fewer turns on the primary and secondary. Fewer turns means less power loss. Less power loss means a higher power transformer. Bottom line with transformers is that Xm is a pain in the butt and you have to make it substantial or you end up with high VA drawn on no-load and the power companies don't like that. Big cores means fewer turns to achieve same Xm. Nov 20, 2014 at 12:09

The power limit isn't referring to losses or efficiency. It is referring to the point at which the core saturates. Under load, there is still a point where the core saturates, and so no more power can be transferred using the magnetic field.

This power handling capacity is proportional to the amount of iron in the core, and so the power rating is roughly proportional to its weight.

• But why does the core saturate at higher currents? Nov 19, 2014 at 18:16
• Because the permeability of the core material isn't linear. There comes a point where you keep increasing current but the flux through the core material barely changes.
– Eric
Nov 19, 2014 at 18:56
• But AFAIK the core flux remains basically constant. The increased secondary current produces an increase in the secondary Mmf which in turn causes the primary current and mmf to rise in order to keep the net flux constant. Nov 19, 2014 at 19:33
• @user19955 as per your original beliefs in your question, the core doesn't saturate more as load current increases. Nov 19, 2014 at 20:17