Electronic – Transformer voltage rating vs open-circuit voltage: what’s the typical load assumed for the voltage rating

Switching an inductor may make it work like a boost converter, and thus temporarily generate a higher voltage.

One way of making sure that the input voltage to the LM338 converter is no higher than allowed, is to wire a high-wattage (between 600W and 5 kW) TVS diode with an appropriate clamping max voltage biased against the input voltage and ground.

Also, if you're switching on the measured/actual output voltage, then you can get into oscillation. It would be safer to switch on "desired" output voltage, and let the regulator make sure it gets there. You could perhaps feed the bias voltage from the regulator ADJ into your microcontroller with a resistive divider to achieve this. Or you could just use a comparator with a pre-set trip point to drive/un-drive the relay.

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.