any transformer will work on multiple frequencies though??
There's no frequency term in inductance.
In principle if you build a transformer with sufficient inductance it'll work at any frequency.
What you run into is practical limits of the iron core at low and high frequencies.
First - inductance is flux linkages per ampere. So a lot of inductance implies a lot of flux.
Iron can only carry in the range of 1 or two webers per square meter
so a highly inductive transformer implies a physically large core.
Fortunately, there is a frequency term in inductive reactance
ohms = 2pi X freq X inductance
so at reasonably high frequency a practical transformer needs only modest inductance hence a reasonable sized core.
In early days of AC power they used 20 hz but soon realized 60 hz allowed them to use smaller iron cores.
At higher frequencies you run into the next problem - heating inside the iron core.
The magnetic flux induces current in the iron core which heats it by simple ohmic loss.
To combat that they make the cores out of thin sheets, laminations, to break up the induced current into long flat loops. That makes the core current take a longer path, through more of the iron which lowers its amplitude hence less heating.
The higher the frequency the thinner the laminations need to be. That's because the induced currents want to flow in circles , so they make the laminations thinner than the diameter of the circle. Higher frequency = smaller circle so thinner lamination.
I have seen power transformers that are rated from 50 to 440 hertz operation.
They have thinner laminations than plain 60 hz transformers, so they can go to clear up to 440 hz.
They have thicker cores, ie more of those thin iron laminations, than would be needed for 440 hz operation . That's so they'll have enough inductance to go clear down to 50 hz.
that's the very basic fundamental idea.
i think what confuses people about transformers is the idea of flux
and voltage being derivative of flux.
Further we are introduced to them as if all they ever handle is sinewaves .
In reality the sinewave is a special case.
Transformers should be taught as inductors in close proximity.
It is a useful thought experiment to pass a triangle wave current through a itransformer primary , instead of a sinewave current, and observe voltage induced in secondary.
Read up on volt-second integral and volts-per-hertz protection , it'll help you work the flux in your head.
old jim
jim