This IC is a switch cap charge pump the can source up to 50mA and can generate a negative supply from positve supply or can function as a voltage doubler. This thing is tough as nails and operates at 100KHz (easy to filter and above the audio range). It is over 90% efficient and requires two caps and maybe some diodes. I use it all the time for generation of dual supplies and doubled supplies for op amp circuits and high side nmos fet gate switching voltages. Check out the example circuits below. This IC solves all kinds of headaches with the addition of three or four parts to your circuit.

This covers the basic equations for noise and more advanced analysis  but it distills down most of the analysis into good rules of thumb.

https://circuitsaladdotcom.files.wordpress.com/2012/09/noise-in-amps.pdf

The highlights include:

every 1K orf resistance adds 4nV/Hz noise.

noise adds as the sum of squares… so – larger sources dominate and large gain in the first stage minimizes noise contribution in later stages

Source impedance needs to be considered in  terms of its effect on op map current noise( often ignored)

This is not a riddle but a painful reminder of  how un-ideal a capacitor can perform  in real world circuit conditions.  I measured the capacitance and Q factor for these capacitors shown below on a Agilent 4263B LCR meter, using 100Hz and 100Khz frequencies.

From left to right the capacitors in the picture are:

1000uF electrolytic,                     .01uF ceramic,                      10uF ceramic,                       .1uF tantalum

At 100Hz the results are as one might expect :   1007 uF, Q of 7     .014, Q of 100       8.6 uF , Q of 36       .104, Q of 80

The large electrolytic has a pretty low Q though indicating already at 100Hz its performance is starting to suffer

At 100Khz  things get really interesting : The 1000uF is now -.1 uF which is actually an inductor! The .01uF is .0098uF and the Q has gone down to 35. The nominal 10 uF(8.6) is now 8.2uF- not bad but the Q is down to 3. Finally the .1uF tantalum is now a .05uF with a Q of 1.2.

So even with this modest change in frequency, we can see capacitance starts to decrease as stray inductance becomes more of an effect. Also all of the capacitors start to become more lossy( low Q).

The bottom line here, especially with regard to decoupling, one large cap will not work well in most applications. One may have to use a combination of different type and value capacitors to achieve intended results.