Transformer Voltage Question

Question

If I have an AC source outputting, theoretically, 10 volts AC at 1 kHz, then if I connected this ac source to a transformer with a ratio of 1:10 for primary coils to secondary coils, then connected the output coil to a primary coil on a second transformer with a 1:10 ratio, then connected the secondary coil of this transformer to the primary coil of a third transformer with the same ratio, would I get an increase in voltage of 1:1000? For context, I am trying to make an arc lighter so current doesn't really matter to me. I just need to increase the voltage by a very large amount.

Answer 1

The 1:10 transformer that is designed for the 10 volt source would be unsuitable as the transformer for the 2nd stage and wholly unsuitable for the third stage.

All transformers have to magnetize their cores in order to set-up the mechanism for transferring energy from primary to secondary. The associated magnetization current needs to be sourced by the input supply; it provides the means for correct transformer operation but, that current does not produce output energy at the secondary. It's a necessary current that can be quite high if large cores are to be avoided.

So, what you really need to do is design a single transformer that has a primary winding that doesn't have too low a magnetization inductance then, wind a secondary that has 1000 times as many turns as the primary.

But, what about three cascaded transformers...

Having a reasonably high magnetization inductance might mean (for example) 10 turns on the primary to handle (say) an input voltage of 10 volts RMS. But, a transformer suited for 10 volts on the primary will be wholly unsuitable for operation at 100 volts unless many more primary turns are wound.

So, say you wound a 2nd stage transformer with 100 turns on the primary; the primary inductance would be 100 times higher (a good thing) but, it needs to handle 10 times the voltage hence, the 2nd stage transformer magnetization current would be one-tenth of that seen by the 1st stage transformer.

That sounds good however, once you consider that the 2nd stage magnetization current will be ten times bigger into the 1st stage transformer you can see that these currents are stacking up in equal measures and, of course, the primary source has to supply this enlarged magnetization current.

With three cascaded transformers with respective primaries of 10, 100 and 1000 turns you get three times that magnetization current drawn into the primary of the first transformer and, all transformers are necessarily different in design and performance. Three times the design work.

This makes no sense.

Surely it makes absolutely more sense to wind a single transformer with a primary of 10 turns and, a secondary of 10000 turns.

would I get an increase in voltage of 1:1000?

No, not by a long way if you assume all transformers are the same. Put your efforts into designing one transformer with a suitable secondary winding and forget the daft idea of using three transformers.

Answer 2

Yes, in principle, and there would be some losses so you won't get N^3 quite, even with no load.

The transformer that could reliably accept 1kVAC @1kHz and gives you 10kVAC would be quite different than a well-designed transformer that accepts 10VAC @1kHz and gives you 100VAC. The number of turns, the insulation etc. would be quite different.

Answer 3

Yes, daisy-chaining transformers like that can, in theory, achieve large step-up voltages. The problem is that there will be losses at each stage, and at the very end when the voltage is high, the insulation will fail.

What you’re trying to make is much more easily done using a flyback approach, with a single high-step ratio transformer. That’s how those little plasma arc lighters work, which are making easily over 10kV from a 3V battery.