Stable Broadband Finite Element Parasitic Extraction and Sensitivity Analysis

Parasitic extraction is a powerful tool in the design process of electronic components, specifically as part of workflows that check electromagnetic compatibility. It enables to capture parasitic effects in field simulation and to embed them as lumped parameters in subsequent circuit simulations together with the functional elements of the design. This thesis develops a broadband parasitic extraction method capable of the automatic treatment of multi-port models of arbitrary conductor geometry without requiring any significant manual user interaction. It applies the finite element method to the differential form of Maxwell's equations, which makes it more flexible than established integral equation approaches with respect to spatial discretization and the handling of inhomogeneous material parameters. The method is capable of both the extraction of the impedance matrix using a full-wave system as a universal description of a model's parasitics, and the extraction of individual resistances, inductances and capacitances with quasistatic approximations. The inherent low-frequency instability of finite element solutions of Maxwell's equations is successfully alleviated by applying a state-of-the-art discretization scheme, that is based on a decomposition of the Sobolev space of curl-conforming functions. Beyond the mere assessment of a design, sensitivity analysis provides the basis for shape optimization. The stable parasitic extraction is used to improve an existing sensitivity analysis method with respect to efficiency, robustness and applicability. Furthermore, a low-frequency stable approach to include the extracted frequency-dependent parasitics in transient circuit simulations utilizing the vector fitting method is investigated. The parasitic extraction method is verified with both analytical results, and measurement results of a common-mode choke