Hello there,
I agree that the first thing to do is to look at the system and see if anything is wrong with it first before attempting to modify anything. Modification should only be an option when everything else is working the way it should.
In case everything is working ok, then there are various rules that are often used to select the required capacitor value based on the desired ripple voltage or the percent ripple voltage. However, most of them will be at best, wrong.
The problem is that capacitors are not God-like devices that can take any voltage you throw at them, they are quite limited not only by VOLTAGE but also by CURRENT, just like most other electronic devices. That being so, this means that we must also pay attention to the current through the capacitor.
Understanding the current however is not as simple as understanding the voltage (ripple). That's because there is a lot of variation among applications. And that's because applications differ as to the source impedance as well as other things like diode selection. Because i found that there was so much misunderstanding about this i did an in depth analysis a couple years back to find out just what was going on.
What i found out was that the CURRENT wave shape was different for different circuits. That meant the difference between having a near sine to something more like a pulse, and just about anything in between. With low source impedance we get nearly a pulse, and with high source impedance we get nearly a half sine. There is a bit more variation than that, but that gives you an idea what to expect. I found that the only way to analyze the behavior was to use the expected source impedance and also the model of the diode. It is believed however that the model of the diode might be generalized to other current levels assuming the right diode was selected for the higher power rectifiers.
What this in turn means is that the ripple CURRENT is also of importance. We might select a capacitor that would perform nicely for ripple voltage, but might burn up when used in the actual application.
Just to look at one quick formula, the capacitor is often modeled as a pure capacitance with equation:
dv=i*dt/C
So we simply solve for C:
C=i*dt/dv
and that gives us the basis for the capacitance C.
Another rule of thumb is simply 3000uf per amp of DC current at 60Hz with a full wave rectifier.
But with higher power circuits, the ripple current also has to be looked at. This means we might have to do a few tests to try to determine what the source impedance is and estimate the current through the capacitor. Then we might use more than one cap so we get several in parallel. The current peak would be roughly:
vCpeak=(Vpeak-Vnominal)/R
where R is the source resistance. Unfortunately if there is any series source inductance this complicates the calculation such that we'd have to know that too. Wall warts often have this source inductance which reduces the peak current somewhat and also helps with the smoothing effect. What this means then is that the best way is probably to select a few capacitors and connect them to the supply, then measure the ripple current through each one. That will give at least some estimate what is needed to properly perform the function of ripple voltage smoothing while at the same time being able to handle the ripple current. This might actually have to be done at several times during the day just to make sure the line impedance doesnt get stiffer at some times in the day than others.
I'll see what else i can find too.