Air-cored transformers are definitely not the solution.
All ferromagnetic material will behave the same.

Are you saying that even a toroidal transformer won't work? I have just read some information and it says the operation frequency could be 20Hz-100khz. Also, as the frequency goes up the size of the transformer decreases.

 

Are you saying that even a toroidal transformer won't work?

No. Never said that.
whoever said that they would work to 100kHz exaggerating.
1kHz for one designed for 50Hz power, about 18kHz for one designed for audio.