An Arnoldi Algorithm for Power-Delivery Networks With Variable Dielectric Constant and Loss Tangent

The tracking-sensitivity algorithm is an efficient method to calculate the changes in the network matrix of a circuit, when a global parameter, such as temperature, is continuously varied. In this paper, we apply the concept of tracking sensitivity on the frequency-domain simulation of power-delivery networks (PDNs) in chip packages and printed circuit boards. The global variable we consider is the complex permittivity of the dielectric. We present a methodology to calculate the change in the PDN impedance due to a variation in the dielectric constant, loss tangent, or both. This information is useful not only to understand any deviations between simulations and measurements, but also to understand the impact of the variability of these dielectric properties on the performance of the PDN. Using the tracking-sensitivity algorithm, we can efficiently recalculate the impedance matrix after changing a global parameter. The classical tracking-sensitivity algorithm was based on a power series expansion. This paper presents a more accurate approach based on the block Arnoldi algorithm.