There is a falacy in using gigantic capacitors to hold up the average voltage and it is related to conduction angle of the rectifiers.
http://www-personal.engin.umd.umich.edu/~fmeral/CIRCUITS/05*Unit%205/Diode%20Rectifiers.pdf
Bottom line: If the conduction angle is very short, the rectifiers have to deliver the total energy in a short period of time. The current goes way up! Of course, the transformer also sees the high peak current and drops its output voltage.
I wonder why anybody wants to go through the anguish of trying to build a PSU when they are dirt cheap:
https://www.banggood.com/DPS3003-32V-3A-Buck-Adjustable-DC-Constant-Voltage-Power-Supply-Module-Integrated-Voltmeter-Ammeter-p-1062475.htmlHere's another thread re: DIY power supplies (among other things):
https://www.eevblog.com/forum/beginners/cheap-oscilloscopes-and-psus/It's real easy to build PSUs based on the 7805,7905,7812 etc. But these are fixed voltage with built-in current limiting. Unfortunately, the current limiting can't be set down to a really low number like 100 mA.
The LM317 is a better approach for adjustable supplies but current limiting may take a 2d 317.
Overall, you will wind up with a bunch of op amps around a current loop and voltage loop all working to drive a pass transistor.
Search around this site and the rest of the Internet. There are a lot of projects and none of them are simple. Adjustable current limiting is a bit hard to do.
Here's one approach to creating a PSU with current limit. It is a lightweight PS though, it only delivers 1.5A 0..26V. But it does serve to show the complexity of a PSU with adjustable voltage and current limiting.
http://dangerousprototypes.com/blog/2014/04/27/app-note-simple-current-limiting-power-supply/Where does the 3A requirement come from? Is it just copied from a catalog? I can't imagine building up a breadboard that needed even 1A, much less 3A. If I needed more than 3A, I would probably use a purpose bought fixed PS or a set of batteries. In my corner of the sandbox, 100 mA is a lot!
I do like the idea of adjustable current limiting when I bring up a new project. It kind of keeps the smoke inside the chips.
For fixed voltages, a PC PS works well. It won't have adjustable current limiting so it is more useful for things like motors. It also provides very high current so the smoke will leak out in a great big hurry!
Add a connector:
https://www.sparkfun.com/products/12867Here's a teardown video of the Rigol DP832. Ignore the UI components and the CPU/networking and you still have a bunch of parts involved in a 3 output supply.