2.1.2 Frequency domain methods

Frequency domain methods obtain a solution for one frequency at one simulation. Therefore, multiple simulations have to be performed to obtain a broad band solution. However, fast frequency sweep interpolation techniques have been developed for efficient broad band simulations [22]. Therefore, the main restriction for the frequency domain methods consists of the model size determined by the number of unknowns. Methods with volume discretization, such as, for instance, the finite element method (FEM) or the finite difference frequency domain method (FDFD) are generally based on sparse matrices, which enable models to be solved with significantly more unknowns than methods with dense matrices, like the classical method of moments. However, sparse matrix methods are also not capable of handling complex PCBs inside a metallic enclosure. For example, the interposer simulation of [10] was meshed cubically with 594.000.000 mesh nodes. Assuming a mesh size reduction by a factor 5 by tetrahedral meshing, the remaining 118.800.000 mesh nodes would require about 5.7e9 nonzero elements to be handled in a sparse matrix, with a memory requirement of about 91GByte. Methods, that require only surface discretization, such as the standard MoM, the boundary element method (BEM), or the PEEC method may be used to avoid the meshing of the surrounding space [23]. However, these methods are initially based on dense matrices and, therefore, require significantly more memory and a larger simulation time. Thus, none of these methods is capable of handling a complex PCB under a metallic enclosure cover.

Recent developments of three-dimensional full wave simulation methods are fast multipole methods used to simulate electrically large scattering and enclosure shielding models [24][25]
[26][27][28]. The MLFMM drastically reduces the memory cost for field integral equation solutions to O(N logN), where N is the number of unknowns. In comparison, a standard MoM algorithm requires O(N²) memory. However, this memory reduction is feasible solely on electrically large models, because the MLFMM uses only propagating plane waves and therefore succumbs to a severe numerical instability, when dealing with interactions of source and observer points which are closer than approximately one wavelength. The recently developed NSPWMLFMA which is numerically stable in the near field region, is however based on dense matrices [26]. Therefore, it is not suitable for PCB, slim enclosure, and IC package simulations with dense structures in the near field region.
This work presents an efficient simulation method for the cavity field between a PCB ground plane and a metallic enclosure cover, which is parallel to the ground plane at an electrically short distance. The interface of the cavity field to the external environment of the device is given by the open slots at the cavity boundaries. A new domain separation approach by port interfaces and a PMC boundary condition at the slot surfaces enables the separate simulation of the internal and the external field with different methods. The internal field can be calculated with the efficient cavity model, while the external environment can be simulated with any three-dimensional full wave method which is able to handle a PMC boundary condition and excitation current ports. The fast multipole method provides a powerful opportunity for this external device environment simulation, because recent developments by [28] enable a coupling with network simulations.

The mentioned examples, based on recently published manuscripts, indicate that there is actually no single method capable of handling the whole device EMC simulation. Every method has some constraints which limit the usable model size, frequency range or domain. Combining different methods provides an efficient solution to overcome this problem. The cavity model of this work handles the internal enclosure simulation with maximum efficiency by analytical or two-dimensional numerical methods. The external environment (i.e. a cable harness) may be modeled by existing efficient methods for this purpose. An efficient approach for the modeling of the emissions from cable harnesses was published in [29][30].

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