Determining appropriate frequency when winding a transformer

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While not directly audio related, I was hoping to get some help, as my problem refers more to general audio design rather than anything specific.

I need to wind some low power transformers (the load will be in the 10s of milliwatts) for a project involving nixie tubes and dekatrons. These will convert 110Vac to the voltage needed to be fed into the tubes (~170v for nixie tubes, 350-400v for the dekatron).

My question is this: I have read that transformers are designed for some minimum frequency, given a transformer I have wound, how can I determine whether or not my transformer has a low enough minimum frequency for safe use with 5/60Hz mains.

I've read this article: Transformers Part 1 - Beginners' Guide to Electronics
which does a good job of explaining the problem - the issue is that at too low a freqency, the flux density will be more than the core (in my case a small-ish ferrite toroid) can handle. Also it mentions that more windings will decrease the density.

If I wind the transformer in such a way that the flux density is too great for the core to handle (too few windings?), will I be able to see it somehow with an oscilloscope? will there be some obvious change to the waveform? Is this even something I need to worry about with a step up transformer?

Please note: I don't have details about the cores I'm using, they are salvaged, so probably only an experimental method will be useful to me (as I don't know the magnetic characteristics of the cores).

Thanks for the help!
If the flux is too great you will get core saturation, which means that the inductance will drop. This means that too much current will be taken so the primary winding will get hot.

I would strongly recommend that you don't try to wind your own mains transformer primary. There are/were kits available which give you a professionally wound safe primary on half a bobbin, together with the appropriate iron. You then wind whatever secondaries you need on the other half and assemble the whole thing.

Oops I didn't spot that you had ferrites. Quite unsuitable, as Pieter says.
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It can't be done

Okay, in the it can't be done department, I've been cutting up 400 W PC power supplies for spare parts, since they blow up once a year. The latest goes straight from the IEC socket and the 120-240 switch to a toroid transformer, green core, 7/8" outside diameter. It has 28 turns on one side. I presume it is the 240-120 mains frequency transformer. If it can't be done, how did they do it? I'm hoping to use it as a 120-60 transformer at mains frequency to produce 85 VDC for a hammond organ, that is producing 100VDC now from a 420V winding and tube rectifier.
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after helpful comments and additional research, I believe I will probably build a simple flyback dc-dc converter with a 555 timer. This should permit me to comfortably use the small-ish toroid since the 555 will be oscillating in the 10s of kHz.

Most of the guides I've read are pretty non-specific about their home-built transformer, and suggest monkeying around with it to get the output characteristics you want. This makes me think that with the frequencies common to 555 flybacks, my core will be well under saturation.

I'll try playing around with the scope and a function generator and see if I can detect when the transformer becomes saturated (obvious changes in waveform). Does anyone have any experience with what I should look for in the signal as the core becomes saturated? Should I take measurements across the secondary or elsewhere?

Thanks again
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