As I understand, a pair 0.1uF and 4.7 or 10uF are the standard size used as the decoupling cap between power and ground. My question is:
What type and kind (Ceramic and or electrolytic and other types, etc) the 0.1uF and 4.7 or 10uF decoupling capacitors should be in order to provide the best electrical performance to minimize ringing. Please advice and thank you in advance

 

For the .1 uF, monolithic ceramic types are good for a low impedance path. The larger cap may be tantalum or electrolytic. Tantalums are usually smaller, but more expensive. Get a voltage rating of at least twice the supply voltage.

 

More about decoupling capacitors than is decent: http://www.planetanalog.com/showArticle.jhtml?articleID=199905522

This may be the best information available on the subject.

Something not shown in these fine papers is the perils of using a large ceramic cap (2.2 uF, for example) in place of an electrolytic or tantalum. Due to the low ESR and ESL these modern big ceramics provide great decoupling, but the same low ESR means they have a very high Q and can form resonant circuits with the self-inductance of PCB tracks and wiring, to the extent that hot-plugging the power supply can put a spike of 2X the PSU voltage into your circuit, which is often enough to destroy it. The trick here is to add extra damping, either with a series resistor before the whole circuit (1 ohm is a good start), or with an ordinary electrolytic in parallel with the ceramic. In the latter case, it's the high ESR of the electrolytic that provides the damping.

 

Oops posted wrong link; still pretty good info, but here's the best:

http://www.techonline.com/learning/techpaper/206800493

 

I found it impossible to register to receive the pdf file.
It rejected any password I submitted to register.
Nothing pleased it. long, short, mixed numbers and letters

 

Is the circuit on a solderless breadboard or a printed circuit?

What voltage levels and switching frequency?

There is resistance/inductance/capacitance in the wires between the power supply and the IC. What decoupling capacitors do is electrically "move" the power supply closer to the IC.

The RC Time constant of the impedance of the circuit between IC and power supply, and the decoupling cap should be at least the fastest rise-time of the output signal. Typically, 0.1uF works well if applied across the ICs in the circuit. If there is still ringing, a 1-10uF electrolytic is added in parallel with the 0.1uF ceramic to "recharge" the ceramic faster than the power supply. Due to their high ESR, Electroylitics alone typically are not capable of supplying current as fast as ceramics, which is why both are used. Essentially, it is impedance matching, and exact math gets ugly. The danger, as stated above, is accidentally creating an RLC oscillator. This can be avoided by having the bypass/decoupling caps on every IC on the board, and with PC Boards, use thicker traces for the supply lines.