Capacitors can be complicated!
Hey there Paul,
Be careful taking advice from forums. I am frequently amazed at what folks sometimes say. I noticed that "kchriste" has his act together, so there's some good advice for you.
The link provided by kchriste for the Full Wave Rectifier is very good. The link provided to the electrolytic capacitor datasheet also is quite excellent. I'm not sure you will get all the answers you need from just these links, so keep on asking!
Bt the way, electronic and electrical units of measure used to be abbreviated differently than they are today. Once upon a time, "microfarads" were abbreviated "mfd" and sometimes "mf" -- and picofarads were abbreviated "mmfd" or "mmf." Nowadays, we use "µF" or "uF" to indicate the same thing. Occasionally, one sees "nF" which means nanofarad; 1.nF is equal to 0.001uF or 1000pF. Personally, I wish everyone would stick to uF and pF! If you see "mf" or "mF," then you cannot be 100% certain; however, the likely intended meaning was microfarad ("µF"). The "F" is capitalized because it is derived from a person name (Faraday). The "u" is really a Greek "µ" but no one cares.
I've done advanced research and development in component engineering and the reliability of electronic systems. So let me help you with a couple of points.
First of all, you DO want an electrolytic capacitor for power supply applications like these (called a filter capacitor or smoothing capacitor, etc.). If you are following the good published plans for something like this, the parts list should be clear about the type of capacitor you need.
Large-valued capacitors like these generally have a spec for ESR (equivalent series resistance) in ohms. When a current flows though a capacitor the ESR value helps to predict the internal heating that results. Too many amps through too many ohms means too many watts of heat is being generated within the capacitor. And, yep, they can explode because of this. However, it is not a beginner's task to predict how much heat a device can take.
The "ripple current" in power supply applications refers to combination of the current "rushing" into the capacitor (at one point in time) from the rectifier plus the current draining out of the capacitor into the load (at another point in time). This can be confusing to talk about. Lets just say this: Your "smoothing" capacitor needs to be large enough (in uF) so the ripple VOLTAGE meets your needs.
If you look at the voltage on the capacitor with no load attached yet, you should see approximately NO ripple. (This requires an AC Voltmeter or an Oscilloscope.) But when you attach the load, the ripple appears. The load "keeps trying" to drain all of the charge out of the capacitor, thereby causing the voltage on the capacitor to drop. Some number of milliseconds later, the voltage has dropped far enough so that the rectifier will "kick in" and start raising the voltage back up again. During this time, the rectifier supplies current both to the load AND to the capacitor. This is only one of the reasons why the current rating of the diode must be greater than the load current.
Choosing larger and larger values for capacitance will allow more and more current to flow into the capacitor -- and more current to flow into the load -- without allowing the voltage to droop down as far as a "smaller" capacitor.
There's a lot more to this, actually. Many factors like the transformer must be considered. I saw one product where the engineer designed-in a giant capacitor to keep the ripple down, but something exploded everytime he turned it on (either the cap or a diode)! He was using a super high performance cap called a Tantalum Electrolytic and other hi perf components. Sure, if the product didn't explode right when he turned it on, it would last forever because there was virtually no ripple even with the load attached. But, there is a special situation when the power first turns-on: the voltage in the capacitor has to ramp-up from ZERO. This causes a one-time in-rush of current MUCH larger than the ripple current -- enough to blow something up. In that product, we switched the large tantalum for a small one (why we needed this would be off topic here), but then also added a large-valued aluminum electrolytic cap to do most of the smoothing work. Normally, a BFC (big fat capacitor) is all that is needed, and rarely does one need to use anything but the usual aluminum electrolytic for this. Sometimes, two filter caps and a resistor are used in a Pi Network for really good smoothing -- that's a good way to make things work well and not cost too much.
So, how does one design one of these supplies? Most engineers worry about this less than you would think. Generally, if the RIPPLE VOLTAGE IS LOW ENOUGH, you are filtering enough. In an audio application, for example, you can hear a buzz if the ripple voltage is too high. Larger caps (more uF) may bring down the ripple voltage, and the ripple current with it, but they also INCREASE the startup in-rush current.
My advice is this: when you build projects from plans, stick to the plans -- unless you know both the math and the component engineering issues involved. Also, if you can choose between this kind of DC supply circuit (sometimes called a linear DC supply) and a so-called "switching supply," you should use the switching supply instead. They are MUCH, MUCH more difficult to design, and sometimes they can be unreliable when not designed right. But, they are Greener: they are way more efficient and emit much less heat. They, too, require filter caps, and filter chokes as well.
When you hear about using ceramics instead of electrolytics, the discussion usually involves COUPLING capacitors. These caps allow signals (which are AC) to pass though them without letting the DC voltage go on the other side as well. If the cap is too small (lower uF), then some lower frequencies might not pass though because they are too "close" to DC (0Hz). On the other hand, bigger caps (more uF) may have undesirable properties that distort the signal. In most circuits these coupling caps are so small (0.001uF to 0.1uF) that ceramic or polystyrene or polypropylene [or whatever] are used. They don't even make electrolytics that small. Most of these [non-electrolytic] caps have few issues with "undesirable properties." In certain applications, however, an idealistic cap is hard to find. This often happens, for example, in the loudspeaker circuit of audio applications; especially in the "crossover networks." This is one common place where "non-polar electrolytic" capacitors ("NP") are used. Making an NP by putting two polar electrolytics back-to-back is controversial, but it is common advice. I say, don't do it. Insofar as power supply caps are concerned, you should NEVER use NPs or put polar electrolytics back-to-back. A backwards-installed polar electrolytic capacitor WILL EXPLODE EVERYTIME!
Not only do we engineers sometimes have disagreements among ourselves, but there is the whole world of Audiophiles out there, and their beliefs frequently defy explanation in engineering terms. If you really want to launch a war on the web, then unlease the Audiophile dogs. I am both an engineer and an Audiophile, so I have had to defend both sides. None of this should come up, however, when we talk about DC supply filter caps.
Good Luck!