would it be possible design any psu without any electrolytic capacitors?

[chris_leyson]

I once designed a 6W 48V to 5V converter with nothing but X7R ceramic caps on the primary and secondary side. It was designed to run in an 85C+ environment 24 hours a day and I didn't want to use electrolyics. Doable but expensive.

[chris_leyson]

It was DC so I guess it doesn't count 

[SiliconWizard]

Whereas it's certainly relatively easy (if a bit expensive) for a DC/DC converter, as was mentioned earlier, PS from single-phase mains for anything but very low power are much trickier, and unless you're ready to design something ridiculously expensive and bulky, it's often a compromise with the power factor (which in turn may make it not compliant with current regulations.)

[David Hess]

An active PFC stage is a great way to lower the required input bulk capacitance by increasing the conduction angle however using it this way compromises the power factor.

You can get the best of both worlds using an active capacitor multiplier -- essentially, use a smaller capacitor at a higher ripple fraction, by application of a synchronous buck converter (controlled to act as, I think, a step-up transformer relative to a virtual midpoint).

In combination with poled ceramics (e.g. Ceralink), this enables record low volumes (e.g. Google Little Box inverter from some years ago).

I have never had to take advantage of it but for a given size of capacitor, doubling the working voltage while halving the capacitance doubles the energy storage (0.5CV^2).  So stepping the AC input voltage up further allows for a physically smaller input capacitor but also requires handling a higher ripple voltage.

A couple years ago I looked into this for SSD power loss protection and while it would work, it is not necessary because the energy density of existing non-super capacitors is sufficient for SSDs and in some you can see a bank of solid tantalum capacitors just for this purpose.

[schmitt trigger]

A rotary converter?
https://www.nycsubway.org/wiki/Rotary_Converter_Power_Technology

Now seriously, like others have mentioned, it is feasible but impractical because of size and cost constraints.

[larrybl]

I have a 28 VAC 6A Center taped Xformer with a bridge rectifier, works great for testing 12 VDC things like 12V Solenoid's, 12V electric clutch, 12V incandescent lamps, No caps involved.

The normal charging system on a Garden Tractor consists of a stator and either a regulator or single diode to provide power to drive electric clutch and charge the battery.