No. I had this custom made by a transformer maker. Unless he screwed up.
Why (and how) are you getting custom-made transformers when you don't even know how they work?
Actually the reality is quite the opposite. I ask a direct question (even the title says transformer physics) and get a page of irrelevant, tangential questions about arduinos and discrete circuitry, which, is why I don't tend to give great quantities of detail so as not to invite wasted time and effort. And at what point did I deny the laws of physics? By your own admission, frequency and duty "change" flux, something I theorized earlier in my posts. Change it how? You mean increase it? As in further saturation of the steel? Does that not produce more power, which is a commodity flexibly expressed as either voltage or current? My question was about when such tweaks cease to produce a positive return, assuming that the time constant of the transformer becomes a bottleneck at extreme duties, be they small or large, or when the frequency is so high it doesn't allow the magnetic field to grow and collapse fully. You would seem to be contradicting yourself if your short answer is, no and your long answer is, both parameters change the flux. I happen to believe that changing these parameters does increase voltage. TINA seems to agree with me as well. Forgive me for not putting blind faith in computer models however, and seeking confirmation here. Rather than chiming in on page 2 to tell me to STFU, you should go back a page and see how I was repeating myself over and over to try to end the conversation rather than perpetuate it. But then maybe my interpersonal skills are no match for the convoluted way in which people interpret questions these days.
Rant much? People here can barely understand what you're trying to do, let alone if it's even sensible to do that.
The rectification is nothing but a capacitor in my case. Just a big-ass capacitor and that's it.
For example, it's obvious from this that you don't even know what rectification means. Capacitors don't rectify. That's what diodes do.
My whole premise is that the core is designed not fully saturated so I know it can be saturated further. This extra "power" ought to be able to be expressed as voltage in theory, should it not?
What "theory"? Pulling words out of your butt is not a theory. Why do you think the core isn't being fully saturated? More likely it's designed to be right on the edge of or a little over the saturation point, because if there's room that means a bigger core which takes more material to build. You might not have much room to go up.
A transformer's output voltage is COMEPLETELY determined by the primary voltage multiplied by the turns ratio. That is an absolute limit. If you want more voltage out of the secondary, the ONLY thing you can do is increase the voltage applied to the primary. Changing frequency will not increase your output voltage. Changing the duty cycle will not increase your output voltage. This was pointed out to you in literally the first response.
I happen to believe that changing these parameters does increase voltage.
"What you believe" means nothing. You are wrong.
Here is a high level description of the physics of a transformer. When magnetic flux changes in a coil, it induces a voltage. Conversely, when voltage is applied to a coil is causes a change in flux. Specifically, a continuous voltage will cause a continuous, linear increase in flux that will theoretically continue forever. In reality parasitic resistance and saturation will get in the way of that. The exact relationship of the voltage to that change is determined by the core geometry and material, as well as the number of turns (more turns = slower changing flux).
That ramping flux is also applied to the secondary of the transformer, which induces a voltage across it. In a mirror of what happened to the primary coil, the voltage across the secondary is determined by how much the flux is changing. Since they have the same core geometry, the what's left to determine the voltage is the turns (more turns = more voltage).
Changing the transformer's frequency will not change the rate of flux change, since that is determined by the value of the voltage and not how quickly the voltage changes. Changing duty cycle can only decrease the output voltage, since straying off of a 50% duty cycle gives it more time at one level to drift into saturation. Since you're not changing the actual level of the primary voltage, it doesn't increase the output voltage.
You're at risk of killing yourself with mains level power here. I hope you are taking more precautions than you think are necessary.