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Registered Member #33
Joined: Sat Feb 04 2006, 01:31PM
Location: Norway
Posts: 971
I think the resonant frequency might be a problem.
You have 4 sections, with an estimated 15 layers of 50 turns, according to an earlier post. This makes the total around 3000 turns, and for 75kV output, that's 25V/turn. Ferrite cores are normally limited by core loss, but since the run times are going to be short and the core is oil-cooled, you can run it close to saturation. The saturation flux density for normal ferrite materials is around 0.4T. The diameter of a typical flyback core limb is around 16mm, giving a total core cross-sectional area of around 2cm^2.
Plugging these numbers into transformer design equations tells us that the minimum frequency you can run it at and still get enough output voltage is ~80kHz. If your transformer ends up with a lower resonant frequency than this, you will hit core saturation before you get enough output voltage.
This is a problem, because your 3000-turn coil will almost certainly have a much lower resonant frequency than this. In this thread, jpsmith123 describes a transformer he made that had 420 turns, and the output voltage started dropping off above 16kHz. The segmented pie winding will have a lower self-capacitance for a given number of turns, but running your transformer with 7 times as many turns at 5 times that frequency is not really realistic.
Or, to put it in different terms, if we assume an Al value of 2uH/n^2, which seems to be typical for flyback core-sized UU core sets, the total inductance of the secondary is 18 henries. To keep the resonant frequency above 80kHz, the stray capacitance has to be less than 220 femtofarads.
This is why you never see high frequency transformers for very high AC voltages, it just doesn't work too well.
You could make it the way they make DC flybacks, with multiple pie-wound sections and diodes between them, or a full diode bridge for each "pie" if you want fullwave rectification. This way, each section doesn't see the inductance and capacitance of the other sections. You would probably need a bit more than four sections though, to get the resonance frequency high enough.
I'm not trying to rain on your parade, I'm just telling you that what you're trying to do is not going to work, to hopefully save you from wasting time winding a transformer that will only be usable as a paperweight.
Registered Member #152
Joined: Sun Feb 12 2006, 03:36PM
Location: Czech Rep.
Posts: 3384
Anders: the L in the resonant frequency is determined by the leakage (and series if any) inductance if driven from a low impedance source (eg. a bridge), so the actual transformer/system resonant frequency depends on the series-L parameters and is much higher than the secondary-core self resonant frequency.
Registered Member #33
Joined: Sat Feb 04 2006, 01:31PM
Location: Norway
Posts: 971
Thanks for the correction, Dr. kV. If I understand you right, the Fres is determined by the series/leakage inductance and the reflected secondary capacitance. That makes sense.
My main point is still valid though, for a slightly different reason. The reflected capacitance is going to be very high, due to the high step-up ratio and the leakage inductance is also hard to keep down in a transformer made for such a high voltage.
The reflected capacitance is the secondary self-capacitance multiplied by the square of the turns ratio. The primary number of turns can't be too high either, because then the step-up ratio becomes impractically low. Let's say you go for 10 primary turns, that makes the step-up ratio 1:300 if you have 3000 secondary turns. This means that the stray capacitance of the secondary is multiplied by 300^2 = 90 000, so even 10pF of secondary capacitance will appear as 900nF on the primary. This means that the resonant frequency will be quite low.
It might be possible to use a series capacitor to cancel out some of the leakage inductance, not sure if that would work.
In any case, making this work is going to be a lot harder than just using a lower step-up ratio transformer and a multiplier (if it's even possible). Insulating 75kV at 80kHz is not easy, members here have tried making lower voltage lower frequency transformers, and have run into these exact problems.
I would love to be proven wrong though, and the whole thing might be a valuable learning exercise even if it doesn't work, I just want to warn you beforehand that this has a very high chance of not working, so that you know what to expect.
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