Broadband Finite-Element Impedance Computation for Parasitic Extraction

Parasitic extraction is a powerful tool in the design process of electromechanical devices, specifically as part of workflows that ensure electromagnetic compatibility. A novel scheme to extract impedances from CAD device models, suitable for a finite element implementation, is derived from Maxwell's equations in differential form. It provides a foundation for parasitic extraction across a broad frequency range and is able to handle inhomogeneous permittivities and permeabilities, making it more flexible than existing integral equation approaches. The approach allows for the automatic treatment of multi-port models of arbitrary conductor geometry without requiring any significant manual user interference. This is achieved by computing a special source current density from its given divergence on chosen terminal surfaces, subsequently using this current density to compute the electric field, and finally calculating the impedance via a scalar potential. A mandatory low-frequency stabilization scheme is outlined, facilitating the finite element implementation. Two useful quasistatic approximations and the advantageous special case of perfect electric conductors are treated theoretically. The magnetoquasistatic approximation is validated against an analytical model in a numerical experiment. Moreover, the intrinsic capability of the method to treat inhomogeneous permittivities and permeabilities is demonstrated with a simple capacitor-coil model including dielectric and magnetic core materials.