Finite Element Parasitic Extraction and Sensitivity Analysis in Industry
Parasitic extraction is a key technique in electromagnetic compatibility analysis. It enables to extract the parasitic resistances, inductances, and capacitances from a CAD model, and thereby to asses the performance of the design in a joint circuit simulation in combination with its functional circuit elements. A sensitivity analysis of the parasitic elements with respect to geometry changes of the model forms the basis of gradient based optimizations.
A recent publication lays out an impedance computation method suitable for parasitic extraction, that was developed in a cooperation between Robert Bosch GmbH and TU Darmstadt. It is based on the finite element method (FEM) and thus in some aspects more flexible than many traditional extraction methods based on the method of moments. However, the process of solving Maxwell’s equations in frequency domain with the FEM is notorious for stability issues at low frequencies. The extraction method therefore employs the low-frequency stabilization approach of Eller et al. to ensure a stable impedance computation from the DC point to the high frequency regime. This stabilization is based on splitting the space of curl-conforming trial and test functions into tree subspaces: a space of functions with non-vanishing curl and two different spaces of gradient fields, one covering the conducting subdomain and one for the remainder of the computational domain.
An efficient sensitivity analysis approach based on this stable impedance computation method has recently been presented at the EMF 2021 conference. Furthermore, a technique to consider frequency-dependent parasitic elements in transient circuit simulations via vector fitting is being prepared for a conference publication.