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I am trying to get general idea of what size of cross-sectional area I would need on a toroidal core to use it as a step-down transformer of a given power rating.

I am aware that the answer depends on frequency. I'm told that as frequency increases, the core-size can decrease and still transfer a given amount of power.

Note: It might be worth noting that I have a very specific need for a transformer in which primary impedance is completely irrelevant. I know most power step-down transformers have a high impedance primary winding to reduce no-load current. But in my case, I am going to use the absolute minimum number of primary windings, because a no-load condition will never occur. My step-down transformer will always be assumed to be 100% loaded. So I want to know how to figure out how big of a toroid I need in order to transfer a given amount of power at a given frequency or frequency range.

As a matter of example, how I would figure out much power the following toroid can transfer when operated at 260 Hz: Amico Toroid Ferrite on Amazon

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But in my case, I am going to use the absolute minimum number of primary windings, because a no-load condition will never occur.

Not a good idea. Core saturation is of primary (no pun intended) importance in any transformer application. Flux density causes saturation and, flux density depends on magnetic field strength, H. H is measured in ampere turns per metre and the amps depends on primary voltage applied and operating frequency. Higher frequencies means lower currents because the magnetization current is inductive in nature.

When the secondary is unloaded, the primary impedance is governed by operating frequency, core dimensions, core permeability and turns-squared. Double the turns and you quadruple the inductance and, for a given primary voltage and frequency, the off-load current reduces by one quarter.

If you double the turns and quarter the current then H has halved and so has peak flux density and therefore saturation potential is also halved.

Irrespective of the load current, the magnetization current will flow regardless. Core saturation is not dependent on load currents flowing in the primary. You are completely mistaken if you think core saturation depends on load current. Load current ampere-turns in the primary are perfectly cancelled by load current ampere-turns in the secondary. This is a fact.

A particular example might be a mag current of only 70mA superimposed on a primary load current of 1A - naive intuition tells you that the load current of 1A dominates and causes saturation. Knowledge and experience tell you otherwise.

So, if you want to design a toroid to run at 260 Hz, work out what the primary inductance is, calculate the current, work out H and look at the BH curve for the transformer core to see if things are going saturate magnetically. If Amazon can't supply that info then look for a transformer that has a data sheet.

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