Model Order Reduction Approach for PCB Structures based on Semi-discretized Darwin Model using FEM

The generation of reduced order models describing the input-output behavior of linear quasi-stationary electromagnetic field problems coupled with lumped elements is of particular interest, for example, in the field of electromagnetic compatibility (EMC) investigations such as conducted emission predictions for printed circuit boards (PCB). Therefore, this article proposes the construction of a linear differential-algebraic equation (DAE) using the semi-discretization of a linear Darwin model with finite elements, whereby the Darwin model is an approximation of the full set of Maxwell's equations incorporating resistive, inductive and capacitive effects. This linear DAE has the advantages that it enables the application of various linear model order reduction (MOR) techniques and that the full and reduced order model (ROM) can be easily coupled with lumped elements. The pro-posed approach is applied to a realistic linear 4-layer PCB layout incorporating 4 linear components implemented with prescribed material parameter as well as an external linear discrete resistor resulting in a linear DAE with a single input voltage and a single output current. Applying the rational Krylov MOR method leads to a ROM with satisfying broadband approximation and a high compression ratio regarding the degrees of freedom (DOF).