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.

中文翻译：

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牛顿-黑森最小化方法进行多端口PDN优化

本文提出了一种基于牛顿迭代法的使用Hessian最小化方法的优化算法，以评估在电源/接地层对上多个去耦电容器的放置效果。对于每个去耦电容器，使用牛顿迭代法可以获得确切的有效去耦区域。无论在该区域中放置去耦电容器如何，IC端口的阻抗都低于目标阻抗。为了优化该区域中特定的电容器放置，基于Hessian矩阵的牛顿迭代法用于确定在平面对的反谐振频率下IC端口的阻抗最小的位置。这种布局优化算法允许采用一种去耦设计方法，该方法也可以应用于具有用于多个IC端口的多个去耦电容器的PDN。与从有效去耦区域内随机选择的方法相比，此处提出的方法需要更少的去耦电容器和更少的计算时间。