In a voltage regulator circuit, how do you calculate which capacitors are placed before and after the regulator?
For example, if I'm pulling 50mA from a 5VDC regulator(L78M05) with a 9V input, how do I determine which caps are going to give me the least amount of ripple?
There is a wide latitude. In a big enough design where I'm using various size caps already, I usually use 10 µF on the input of such a regulator and 1 µF on the output. You can get away with a lot less, but there is little harm to having more, especially on the input where more is better from the regulator point of view.
The cap values have little to do with current, since for a ideal regulator and battery the voltages on them would not change. The purpose is to make the lines look low impedance at frequencies high enough that the active circuitry can't handle. The output cap is also part of the feedback loop of the regulator, and different regulators have different requirements. A 7805 will be fine with 1 µF ceramic close to its output pins. Other regulators may have specific requirements, including some minimum ESR for some of the older low-dropout types.
So the real answer is to read the datasheet and make sure you meet all the input and output cap requirements.
The larger the capacitor, the less the ripple. As an analogy, think of the capacitor as a water storage tank. The larger the water tank, the less impact drawing water from it will have on the water level. The ocean is an effectively infinite capacitor, so when water leaves the ocean, the water level doesn't change hardly at all. Also, you can see from the equation that the higher the load resistance, the less ripple. That's pretty obvious because the higher the resistance, the less current it will draw.
But obviously, you can't just throw in a massive capacitor. You should read the datasheet for your regulator to see what it suggests.
