In a transformer, why are both coils apart from each other? Wouldn’t make more sense to have the ferrite core (tube shape), wind the primary coil around that and then wind the secondary coil on top of the primary? So that the magnetic fields are as close to each other as possible?
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I’m not sure I understand your proposed solution, but the ferrite core guides the magnetic flux, there are very few losses, and both circuits are perfectly electrically insulated from each other. How would your solution be an improvement?