EM propagation through the loss substrate interconnect

One typical way of studying the EM propagation through some medium is treating the transmission medium as the sub-circuit and then using simple circuit theory to do the simulation. Efficient parameter extraction of per-unit length LRCG matrices for multilayer multiconductor transmission interconnects is presented here. Two separate solvers do the extraction. For the LR extraction, the boundary element method is used to solve the full wave integral equations and 2D fast multilayer Green´s function is used to capture the substrate coupling and ground plane effects; conduction mode basis functions are used to efficiently capture the skin effect and proximity effect. For the CG extraction. the boundary spectral method is applied to solve the differential equation. The substrate coupling effects that impact on CG are extracted by enforcing continuity conditions across different dielectric interfaces and the voltage condition on conductor surfaces. After frequency-dependent RLCG matrices are extracted, a robust rational function fitting algorithm generate lumped interconnect models via Gaussian quadrature.