Gab wrote:
The problem : How do I choose the right reservoir and smoothing capacitors size, and resistor size ?
You start by assessing your chosen power transformer. You are using a line isolation transformer. This type of transformer is built and rated for 360º secondary conduction. When you run any type of rectification bridge from these, conduction angle is a major concern. You will have to derate the current available roughly proportional to conduction angle to avoid overheating the transformer core and windings. So first, always use a full wave bridge or doubler, and second, choose the smallest first capacitor you can (conversant with the desired ripple) to maximize conduction angle in the secondary. Then worry about ripple reduction afterward.
Gab wrote:
I would like to Have the least voltage drop possible, so chokes are out of the equation (they also cost a lot and they aren’t that easy to find)
This makes no sense to me. Chokes typically give the lowest voltage drop verses filtering and are relatively cheap. For example, the Triad C-14X (6H, 200mA, 150Ω) is available for $15.48 from Mouser and the C-24X (1H, 240mA, 50Ω) is only $9.78. I would hardly call these options "expensive". Especially given the level of filtering provided when coupled with a reasonably size capacitor.
Gab wrote:
I think i’ll buy two 470uf 250v electrolytics for the doubler. Psu designer « suggested » 220uf for the reservoir cap and filter cap.
Again, be very careful of the conduction angle. Isolation transformers are not rated for pulsed loads. Too large a first capacitor and you will burn up your transformer even at nominal loads.