Understanding 110/220V Transformers and Designing Linear 24V 3A DC Power Supply

[likephysics]

I can't figure out how those 110/220v transformer work. Like the ones in cell phone chargers.
Say for example, if the primary voltage is 110v, the secondary will be 24v. But if the primary is connected to 220v, the secondary should be 48v.
Are the stages after the secondary designed for up to 48v?
These are the ones without 110v/220v select switch like in the back of a desktop PC SMPS.

I am trying to design a linear 24V, 3A DC power supply. I couldn't find a small enough transformer. Everything I found was big(toroidal - 10cm dia and 5cm height) and heavy(1Kg).
But the transformers in DC adapters like laptop have small form factor.

 

[MATLABdude]

I think they're designed with a switchmode supply after the transformer (which can deal with a large range of input voltages) or are pure solid state designs (without big transformers). In either case, I don't think you can go linear, unless you're willing to deal with a lot of power dissipation (a 7805 can be connected to up to 30V input, but it gets awfully toasty if you start drawing even modest amounts of current from it).

 

[Adjuster]

Yes, such things as laptop power supplies which have large power outputs for their size normally use switch-mode techniques.

Switched-mode design makes it practical to design for a wide input voltage range without the very large power loss which would be inherent in a linear design. If you think about it, a 110V to 220V input linear design could have no more than 50% efficiency at 220V, actually less when you allow for transformer and rectifier losses.

It is usual to rectify the line input directly without a transformer. The necessary isolation from the mains is normally achieved using a transformer fed by the switcher. Now for the clever bit - that isolating transformer works at kilohertz frequencies, much higher than the 50Hz or 60Hz line frequency. This allows it to be far smaller and lighter.