We have looked closely at the theory behind bypass capacitor self resonant behavior and have published some conclusions in our landmark paper in 2000 entitled "ESR and Bypass Cap Self-Resonant Behavior, How to Select Bypass Caps." These conclusions include:

1. As ESR goes down, the troughs get deeper and the peaks get higher.

2. The minimum impedance value is not necessarily ESR (or ESR/n, where n is the number of identical parallel capacitors); it can be lower than that!

3. The impedance minimums are not necessarily at the self resonant points of the bypass capacitors.

4. For a given number of capacitors, better results can be obtained from more capacitor values, with moderate ESRs, spread over a range than with with a smaller set of capacitor values, with very low ESRs, at even well-chosen specific self resonant frequencies.

The theoretical calculations for the impedance response of a large number of parallel RLC circuits of different values can be quite complex. We wrote our own program to help with this.

A description and mini-operator's manual for the program (in *.pdf form) is available here. 

The calculator program itself is described here.

For information regarding a license for the full version of the program, look here.