Multiport PDN Optimization With the Newton–Hessian Minimization Method

TLDR: In this paper, an optimization algorithm using the Hessian minimization method, based on the Newton iteration, is proposed to evaluate the effectiveness of the placement of multiple decoupling capacitors on a power/ground plane pair.

Abstract: This article proposes an optimization algorithm using the Hessian minimization method, based on the Newton iteration, to evaluate the effectiveness of the placement of multiple decoupling capacitors on a power/ground plane pair. The exact effective decoupling regions are obtained using the Newton iteration method for each decoupling capacitor. The impedance of the IC port is lower than the target impedance no matter where the decoupling capacitor is placed in this region. To optimize specific capacitor placements in this region, the Newton iteration, based on the Hessian matrix, is used to determine the location where the impedance of the IC port is minimized at the antiresonant frequency of the plane pair. This placement optimization algorithm allows for a decoupling design method that can also be applied to a PDN with multiple decoupling capacitors for multiple IC ports. Compared with the method of random selection from within the effective decoupling area, the method proposed here requires fewer decoupling capacitors and less computational time.