The fundamental question is why we actually need caps in the first place..The topic is actually rather complicated and I wrote this all off the top of my head... so here goes...
Technically if you had a regulator in the centre of PCB, and chips placed all the way around it, the voltage regulation would be pretty stable. In some cases that is even enough. In the old days, datasheets used to say you only needed the caps if the part was further away than 5 inches from the regulator.
Unfortunately regulators are generally linear regulators which are very sluggish to react to current demand. In such cases, manufacturers recommend something like 1uF "stability capacitor".
The problem is with high-speed digital circuits, is that when there is a increase in current demand, the voltage will actually start to drop on the regulator, and sometime later, the regulator will start increase its voltage output to maintain the correct voltage level. Unfortunately while the regulator is increasing voltage, if the load then totally turns off, the voltage regulator will actually overshoot and if it is supposed to be maintaining 5V, it could easily overshoot to 5.5V.
If there just happened to be another high current demand at that moment in time as a voltage regulator is trying to increase the voltage, the load will start to decrease the voltage once again... And you basically end up with supply rail bouncing up and down which can vary a volt higher or lower than the proper voltage level. So this "stability capacitor" acts as a reservoir for the regulator for the peak current demand.
So once you have this setup, you pretty much almost do not need any additional capacitors.... BUT....
The problem starts to come into play (and is actually always been a problem) is what is called as the impedance of the power rails. The longer supply rails to any particular chip, the higher the impedances to the regulator. This is basically where the voltage will start bouncing up and down as previously discussed. So generally we place capacitors close to the IC's as possible so that these capacitors become in effect, temporary power supplies for each IC on the board. The regulator is basically a "top up power supply" for those capacitors.
The impedance of the power rails becomes more and more of a problem the higher the frequency becomes. The minute inductances on PCB traces in the high MHz range will have a impedance which limits the peak power performance once again. So generally we place capacitors next to IC's power pins in order for the voltage to remain stable.
Of course if we were talking of 100MHz+ ranges, then we are really getting into RF type PCB designs and layouts, where manufacturers may likely suggest something like 1nF per power pin on the IC. Which of course makes sense. But generally we are not running at extreme speeds like that and the load on the regulator will likely remain pretty much constant (not like we are switching several amps on and off at 100MHz speeds for example).
While on the subject of capacitors, this is a huge topic in its own right. Back in the old days we generally all understand that we need 100nF across each chip.. But we have to also remember PCBs could be a foot square and generally power hungry TTL chips. Those 100nF caps were generally physically big, so using higher values were generally work out worse is the packages were physically larger, and the "reaction times" were larger, so if you fitted 1uF caps across that particular board instead of 100nF caps, then you could actually make things worse.
However with modern systems, the physical size of a 1uF to 100nF capacitor is pretty much identical. Of course if you were really pushing high MHZ speeds, then every fraction of a millimetre in packet sizes would probably count. But not really for the stuff that we are working with.
So generally what we can do, as if we have a regulator relatively close by, we would put something like 1uF on its input and output to keep that stable. Then if the IC to be powered is only like a inch away, the impedance of that power rail is likely going to be pretty low, that we almost do not need any capacitors on the IC itself.
In many cases we could pretty much just get away with placing a 10uF 0805 the centre of the IC, and just run all the power rails for that IC direct to that capacitor. While some people may frown upon such a high value, the physical package size is not really much larger than a 100nF. But really the major limiting factor is the physical length of the PCB traces themselves. This pretty much makes the size and value of the capacitor almost irrelevant, Because the major contributing factor is the PCB traces themselves.
So what I do is, place a 0805, or 1206 10uF in the centre of the chip for the bulk capacitance, and run the IC power rails to that capacitor. Then what should really be done is diagnostics on that IC on its power rails to make sure that everything looks reasonably stable. If it is not, then we can place some smaller 0805's closer to the power pins. Generally we could just have 4 smaller caps each side of the IC. Then we can run power pin on the device to its own capacitor close to the power pins.. Those will of course be fed from the larger 10uF in the centre.
So if a particular IC as something like 20 power pins, in most cases there is little use in actually placing 20 capacitors around that chip. I have even seen in the past, where manufacturers have done exactly that, but they had extreme difficulty with the PCB routing, so any advantage they would have gained by having all the capacitors, was trashed by ending up with several inches of copper linking them all together. In that case, they would have been a lot better just to have one larger capacitor in the centre, and just use top and bottom layer to connect all the power pins together.
What I always strongly recommend is having solid copper for power rails and gnd rails. I have been stung by this in the past...
For example, the highlighted red area is my gnd connection. Keeping this solid is what needs to be done for good PCB layout..

- cpu.jpg (64.62 KiB) Viewed 4471 times
If we actually did this instead...

- cpu2.jpg (56.82 KiB) Viewed 4471 times
This is actually extremely bad and will cause a lot greater issue than any capacitors which may or may not be added.
In a previous design, I basically made that mistake above, and I ended up with 2 volts difference at each end of that gnd trace! This is what happens when you are getting into MHz ranges. Notice I have a capacitor side of the CPU. This is as good as things can realistically get.
So while people are contemplating how many capacitors may or may not be needed, this is actually not the question to be asking. Good PCB layout will have a much higher advantage over capacitors used. Capacitors are of course important in keeping power supply impedance is low, but the PCB itself is the main contributing factor of issues, not capacitors.
So generally, if you have good PCB layout, you are pretty much onto a winner of a design right from the start. We do of course need capacitors, how many really depends on each specific application. If we were really pushing the MHz boundaries, then yes we may need 20 physically small capacitors on each power pin. But for the projects that we are working on, one capacitor under each IC is probably all that is needed. Or if any designer wanted to add more capacitors, then add one at each corner (or side) of the chip which needs multiple power pins.
I have been placing 1uF - 10uF 0805/1206 caps on my boards which run at 40MHz. I have 2 caps on my CPU board above, because that is where the power pins are. I could have easily placed a single 0805 in the centre, and I have even done this on previous boards. But of course, physical constraints are also a factor, also ease of assembly etc.. If I went and placed a third capacitor in the centre, that is the point where it becomes pointless.
There are always trade-offs to be made in any design. Capacitors are of course thing to have, but if we are going to cut of the board with multiple capacitors, we really have to be careful that we are not increasing the track lengths feeding those capacitors, as any advantage of extra capacitors, can be undone by all the extra copper length!
Food for thought...