Broadband Macromodels for Retarded Partial Element Equivalent Circuit (rPEEC) Method

The partial element equivalent circuit (PEEC) method is, nowadays, widely used in electromagnetic compatibility and signal integrity problems in both the time and frequency domains. Similar to other integral-equation-based techniques, its time domain implementation may suffer from late time instabilities, especially when considering delays [(Lp,P,R,tau)PEEC] (rPEEC). The cause of the instabilities may be either the numerical technique used for the time integration or problems created by the discrete representation of the electromagnetic continuous problem. In this paper, we concentrate on the latter and show that frequency dispersion plays an important role and must be taken into account in order to preserve accuracy and mitigate instabilities issues. An enhanced formulation of the PEEC method is presented that is based on a more accurate computation of partial elements describing the electric and magnetic field couplings; broadband macromodels are generated incorporating the frequency dependence of such elements, thus, allowing us to obtain better stability properties of the resulting (Lp,P,R,tau)PEEC model. The proposed equivalent circuits resemble those of the standard PEEC formulation but are able to capture the dispersion that, when neglected, might contribute to inaccuracies and late time instabilities