Piezo transformers are dirt cheap.

I've never heard of these before, so thank you for making me aware of them, they are very cool.

Unfortunately I'm unable to find any examples of them used outside of voltage-multiplying circuits in obsolete electronics.

There's nothing special about the transformer in SMPS other than it's size which is due to the high frequency.

The other problem they create, then, is high frequency noise which must be filtered out. Some cheaper adapters just dump the noise back into the mains and cause problems for _other_ devices.

Come to think of it there's a decent chance it's a /different/ adapter somewhere on his system that's causing the problem and not the size or capacity of the products native adapter.

> the transformer in SMPS other than it's size which is due to the high frequency

There absolutely is. The core material is not iron, it is a material specifically engineered for the purpose. There's a very specific size gap between the two halves of the core. There's an extra sense coil for the feedback circuit.

It depends on the switching frequency, and not all SMPS run at a high enough frequency to justify ferrite. On top of that ferrite is effectively just iron in a ceramic.

The gap is controlled by the cross section of the core but also contributes to EMI. The sizing concerns are typically related to the latter problem.

An SMPS can easily use an external feedback circuit and may do so for certain types of applications. For mass manufactured low current applications you can often buy them with one integrated.

If you aren't fussed about galvanic isolation there are many SMPS topologies that don't use transformers. Cheapest step down converter would be a simple buck regulator - no transformer needed!