Cascaded equal transformers

Question

Lets say I have several identical transfomers 1:10 voltage ratio. I connect them in sequence expecting to get 1:100 voltage ratio.

This will not work because of impedance missmatch, when first transformer high inductance coil tries to feed into low inductance coil of the second transformer.

For it to work as naively expected second transformer needs to have 100 times the inductance in every coil. But this quickly becomes impractical, as required inductance grows.

So the question is, can this 'cascaded equal transformers' work, if impedance is corrected by other means? Ideally by adding a capacitor. Even at the cost of higher current that this capacitor would create.

Bonus question: what is this topic called, so that I can read a bit more about it?

Answer 1

This will not work because of impedance missmatch

The problem is not quite impedance mismatch, but core saturation.

For a given magnetic core, and for a given frequency and a given primary voltage, the primary of a transformer needs a certain minimum number of turns to prevent core saturation.

Say your transformer has a 120VAC, 60Hz primary, and a 1200VAC secondary. Suppose further, that the core for that transformer needs 120 turns on the primary to prevent core saturation, and in fact has 120 turns on the primary. And finally, suppose you actually feed the first transformer with 120VAC. The first transformer in the cascade will work, but the second transformer will not, it will saturate. The second transformer's input voltage is 1200VAC, but it's primary was only wound for a 120VAC input, i.e. 120 turns. However, it needs 1200 turns to prevent saturation. That is your problem.

If you started with a sufficiently small voltage, you could cascade a fixed number of identical transformers together without saturating the core of any of them. For example, if you had 3 transformers with primaries rated at 120VAC, and a turns ratio of 1:10, then if your initial voltage is 1.2VAC, you could cascade these three transformers together. The first would have 1.2VAC primary and 12VAC secondary. The second would have 12VAC primary and 120VAC secondary. The third would have 120VAC primary and 1200 VAC secondary. But then you can go no further, unless you use a different transformer.

can this 'cascaded equal transformers' work, if impedance is corrected by other means? Ideally by adding a capacitor.

No. Adding a capacitor will not alter the fact that the secondary of one of the transformers will have a higher voltage than the primary of the following transformer can handle. You cannot cascade identical step-up transformers in this way without eventually saturating the core of one of the transformers.

Answer 2

It will work.

An ideal (and even reasonably good one) will transform the V & I at one winding in to N*V and I/N at the other winding. No (little) energy is stored in an ideal (practical) transformer, and there is no such thing as an impedance match for transformers.

In practice, the leakage inductance of the transformer will mean that when one is loaded by the other, the full N* voltage won't appear, and the magnetizing inductance of the 2nd transformer will provide some (small) loading on the 2nd.

In addition, winding resistances will become 10* more important in the 1st transformer, causing additional losses.

In summary -- ideal transformers will work 'perfectly', and practical ones will work quite well, but with some losses.