2.2 The semi-analytical approach based on EMI source multipole macro modeling

A semi-analytical approach for the simulation of EMC emissions from complex devices, PCBs, and ICs utilizes a multipole macro modeling of the radiation from subsystems [31]. The method describes the emissions from a subsystem (i.e PCB trace, IC) by a multipole expansion with spherical base functions of the Helmholtz equation. The multipole moments are obtained by three-dimensional full wave simulations for layout elements or by near field measurements for ICs. For the consideration of an enclosure, the multipoles are used as excitations in a three-dimensional full wave simulation. This simulation has to consider the external device environment, such as external cabling and scattering objects. This is a drawback for the optimization of devices, because resonances from external structures, which cannot be changed by the design are included in the simulation results and have to be distinguished from the device behavior. The external environment has to be simulated for every optimization design change.
The domain separation method presented in this work enables the device to be optimized independently of the external environment and the emissions to be investigated in different environments. Only one simulation per external environment is necessary.
Another problem of the multipole expansion method is the modeling of ICs. A measurement based modeling as presented by [31] needs a prototype device and a test board. The emissions depend on the software coding and the external circuitry [6][8]. Even if all necessary data of the IC could be obtained by simulations, it would be difficult to generate a port controlled multipole model. There are currently no IC multipole models in the literature, which consider all dependencies generally.
The method presented here utilizes established network simulation and an analytical description of the common mode coupling to the enclosure, which enables quick modeling.

C. Poschalko: The Simulation of Emission from Printed Circuit Boards under a Metallic Cover