Answering my own question here:
As Andy Aka pointed out, transformers function at any input voltage, even voltages well below the minimum spec voltage. If the physics don't impose a limit, then how do manufacturers calculate the minimum voltage on their transformers?
I went and talked to a few FAE contacts I know and asked them how they calculated their minimum voltage ratings. Interestingly, no one had the same answer. It seems every company has a different method of qualifying their transformers, which confirms what Andy Aka was pointing out.
One of the most detailed answer said something along these lines (paraphrasing a lot here):
The minimum input voltage is calculated in function of the highest input currents and longest duty cycles which maintain the output voltage within its desired range.
There's a corollary to the statement above
The minimum input voltage calculation is dependent on the power supply topology which the transformer is intended to operate.
That is to say, the minimum voltage is calculated for a specific SMPS topology.
Using this method for calculating numbers, if I wound a transformer to operate in a flyback power supply, I would:
- Figure the required output voltage and current, select the appropriate wire size for the output, and wind the output.
- Figure out the input voltage range I want to support.
- Run a simulation to see what the input current becomes for the highest duty cycle.
- If the input current is too high, either change my output voltage/current requirements, or increase the minimum input voltage. Otherwise, select the appropriate wire size and wind the input.
This is just one method of calculating the minimum input voltage. As I said before, every FAE I talked with had a different method (some didn't even know).