@Easy peasy Thanks for correcting that. I stated just the saturation issue of Bmax in the single equation that is just the first check. If you only run the transformer briefly than this is an OK approach. For transformers that operate for longer periods of time or continuously, then a lower value of Bmax should be used. So adjusting the Bmax value for the power supply operating duty cycle (maybe continuous) and how much cooling may be done by moving air is the next step. But that gets back to some of your early posts about having to build and test, and we're still building up experience on how to determine those values.
And chosing core size also works into that one equation, in my attached sample I have the ETD49, ETD59 and E65 cores that are 'convenient' for use on this existing project with its peculiar existing case size and 6 channel control system along with our supply of existing fixtures and bobbins.
Using Bmax of 300uT, 700 volts, 115kHz and a 45% duty cycle, the minimum turns using the spreadsheet for E65, ETD59 and ETD49 calculates to 17.2, 24.8 and 43.7 primary turns. This would determine what the magnetizing inductance and current would end up being, which is what Andrew originally asked. As these calculated numbers require more turns in a smaller transformer core, this is where 'current capacity' of the core starts to be looked at when the combined primary and secondary turns have to be fit into the different windows and then all the proximity effects from the multiple layers have to be accounted for.
In our recent transformer we designed for Bmax at core saturation and 40 amps of average output current at 72 volts. For less turns in a bigger window the E65 core is what we picked. It turns out that at 30amps after running for 45 minutes, the core material heats up enough that even though the temperatures are still not hot enough to be alarming, the rate of temperature rise went from decelerating over time to suddenly increasing over time. So this makes your point about preventing excessive heating in the core by using a lower Bmax. If I'd tracked the duty cycle of that experiment, I could quickly come up with a Bmax value with the tool as a data point for that run time, and by doing this over and over would generate a table for that specific core and winding configuration.
For full disclosure, we didn't design this transformer, someone much smarter than us designed it and informed us we'd have to build and test it to find out its true capacity. Luckily this was not a customer project, but us building a replacement part for existing equipment with a low operational duty cycle, so we get to learn on the job. I applied the 'one equation' afterwards and because of all the research and experimentation, the 'one equation' now connects dots for me. I'm hoping others can pick up on this if they are new to the subject.
If you are interested on the testing I did on this system, here is a
shared google drive link where I was trying to recruit some collaborators on the facebook Power Supply Design Group
Dave