Spherical Wave Based Macromodels for Efficient System-Level EMC Analysis in Circuit Simulators Part II: Optimized Calculation of DUT–DUT Interactions

In this second part of two papers, the framework presented in Part I is extended with optimized routines that enable one to evaluate interactions between several devices under test (DUTs) through free space inside a circuit simulator environment, aimed at efficient system-level electromagnetic compatibility (EMC) analysis. Using a generalized scattering matrix formulation and an extensive understanding of the underlying theory of spherical wave expansions (SWEs), it is shown that the presented routines only add negligible computational cost to traditional scattering parameter simulations. The latter is obtained on the one hand by optimally truncating SWE based macromodels as described in Part I and on the other hand by observing that both near- and far-field interactions are only determined by a subset of parameters in the models. Therefore, this paper derives guidelines on the number of parameters needed to assure accurate simulations and validates them using two applications: 1) computing the radiated coupling between two DUTs; and 2) extending the first example in order to simulate efficiently a cylindrical scan of a DUT by an arbitrary measurement antenna.