Mesh-sensitivity based decoupling capacitor sizing and placement for power delivery networks

With the present day demand for low power ICs, Power Integrity (PI) for packages and printed circuit boards (PCBs) have become a design necessity. Several classes of analysis tools for PI, 2.5D and 3D, are commercially available. However, the design tools for obtaining optimal decoupling capacitor sizing and placement are limited to stochastic techniques based on evolutionary optimization methods that require a large number of expensive forward Electromagnetics solutions for convergence. In this work, a fast and efficient mesh-sensitivity based decoupling capacitor sizing and placement approach is proposed. Such a formulation serves two goals : (i) highlighting the relative impact of decoupling capacitors placed at different regions of the layout and (ii) utilizing this analytical sensitivity information in a gradient based Sequential Quadratic Programming (SQP) method for achieving an optimized PDN. The Adjoint Variable Method (AVM), facilitates analytical sensitivity calculation of multiple decoupling capacitors using one single forward solution, making this approach feasible and efficient.