Co-simulation of distributive and lumped systems using the discontinuous Galerkin time domain finite element method

The signal integrity and power integrity analysis of 3D integrated circuits or other EMC/EMI systems usually separate the lumped circuit modeling and the distributive system modeling. However, due to the high density of integration, it is not proper to separate them in the modeling process anymore. In this paper, a hybrid electromagnetics (EM)-circuit simulator is proposed for incorporating multiport lumped circuit networks through their admittance matrices into the discontinuous Galerkin time-domain finite element method (DGTDFEM). The admittance matrix in the Laplace-domain can be derived analytically or obtained from network parameters such as S-parameters in the frequency domain. To convert frequency dependent S-parameters into the admittance matrix in the Laplace-domain, the vector fitting technique is employed to facilitate the mapping process. The computational domain of interest is split into two subdomains. One is the EM-part solved by the DGTDFEM, another is the circuit-part modeled by the basic I - V relationships in the time domain. The proposed method is valid for both linear and non-linear lumped components. And it is useful for subsystems with either measured data or equivalent circuit models. Benchmarks are provided to demonstrate the validity of the proposed method.