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You don't mention what voltage (variable or otherwise) you want, so we can't really help until you give more info - but generally a 20A PSU is likely to be large, heavy, and expensive.
You might also mention what it's for feeding, it can be relevent to the design.
There are numerous 20 amp and greater power supplies described in American Radio Relay League (ARRL) handbooks and publications. Input is 120/240 vac, 60 hz and output is usually 13.8 vdc (or 28 vdc on occasion). Many are linear though there is at least one 40 amp switcher described. I would expect similar info to be found in UK publications as well as others. It's pretty common for amateur radio operators to need 20 amp supplies as much of today's equipment is based on 13.8 vdc input.
Take 3 PC power supplies and connect 5V outputs in series.
You will get nice 15V, 35-50Amp power supply.
Use 2 or 3 high current diodes to drop the voltage to 13.2-13.9VDC
or change feedback divider ratio in each PSU to drop each of the
outputs to some 4.5VDC for example. That would make for
3*4.5V=13.5V - without use of diodes.
I get used computer PSU for $5 - $10 (Canadian) if working or
for free if repair is needed (still - free parts). I don't think there is
a cheaper way to get so much power (regulated!).
You can also look for Tenma or B+K benchtop PSU for 12VDC,
they cost ca. $300-400 and come with current and voltmeter etc.
You can visit linear technology's website and download their SwitcherCAD software. It walks you through the calculations and steps in designing a switch mode power supply.
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