On finding the optimal number of decoupling capacitors by minimizing the equivalent inductance of the PCB PDN

PCB-PDN design remains a challenge with the reducing noise margins. One aspect of PDN design is finding the number of decoupling capacitors required for each power rail. As more capacitors are added, the mid frequency equivalent inductance in the impedance of the PCB-PDN converges to a minimum value for each placement pattern. This convergence is studied for different placement patterns to find the least number of capacitors required to satisfy a certain convergence criteria. A first principle method is used resonant cavity model for the analysis.