Review of computational electromagnetics in electromagnetic compatibility applications

Abstract

This review addresses the use of computational electromagnetics (CEM) in solving electromagnetic compatibility (EMC) problems. Issues such as, multi scale modelling, the use of macro-models, time-domain and frequency-domain models, the use of structured and un-structured meshes and modelling will be addressed to give a broad overview of the state of the art and future prospects in this challenging area. Numerical modelling for EMC faces several challenges. Unlike in other areas such machines, antennas and microwaves, where studies are required over a narrow bandwidth, EMC requires complete system characterization over a wide band of frequencies, at least up to 6 GHz. This range far exceeds, in most cases, the operational frequency range of equipment, and thus is not well understood by designers and not subject to well defined design rules intended to ensure normal equipment operation. Computational tools therefore have to be designed for broadband operation and in most cases are formulated in the time domain. Over such a wide frequency range it is inevitable that some geometrical features will be comparable to the wavelength and other much smaller (multi-scale problems). This imposes severe demands on modelling and computation and it requires innovative approaches such as the use of macro-models (also known as embedded models or in-cell models) so that irrespective of the electrical size of features a mesh is maintained at a spatial resolution of the order of λ/10, where λ is the wavelength at the highest frequency of interest. The development of these macro-models is a crucial area of current interest. Examples of macro-models required in EMC studies are for thin wires, wire bundles, fine perforations etc. A further problem brought about by the very wide frequency of interest is that material properties cannot be assumed constant and frequency dependence (or even non-linearity) must be accounted for to some extent. This requires the embedding of complex frequency-dependent material properties into time-domain codes. Also the current interest in new artificial materials (various composites, meta-material, nano-materials) requires sophisticated modelling developments to include the essential physics and at the same time retain simplicity, efficiency and accuracy required for good design. More often than not hybrid models are required where parts of the model space are described by solutions to Maxwell's equations (full-field models) and other parts by embedded macro-models based either on physical models (e.g. quasi-static or other analytical local solutions) or behavioural models (e.g. IBIS) or interfaces to lumped circuit solvers such as SPICE. Into this mix must be added the possibility of using full-field solvers based on either integral or differential formulation of Maxwell's equations or even ray optics methods. Modellers have attempted to accommodate all these features and also configure the mesh for optimum model descriptions with some success. A very challenging area here is the efficient incorporation of unstructured meshes in full-field time domain models. In the complex geometrical configurations encountered in realistic EMC problems it is important to be able to locate features, such as cables, in their actual locations which may not coincide with mesh points. Similar requirements apply for the accurate description of curved boundaries where the need is to avoid staircase approximations. These requirements inevitably lead to unstructured meshes which however can impose severe constraints on the maximum time-step and thus increase enormously computation time. A lot of work has been done in recent years on increasing computational efficiency in hybrid meshes which consist of a mix of structured and un structured domains suitably interfaced to maintain maximum accuracy and efficiency. This important work for EMC simulation will continue into the future. Finally, in all the work described above it has been implicitly assumed that a problem is fully defined and that models and computational resources are brought together to address it. This is an example of a deterministic calculation and as already pointed out it is very challenging. However, to complicate matters further, one has to keep in mind that in EMC problems in particular, many aspects of the problem are not fully defined. Examples are, the position of an individual wire inside a bundle, the route of a wire bundle relative to the chassis of a car or the skin of an aircraft, the electrical properties of many materials etc. In such cases it is important to develop stochastic models where from a few simulations it is possible to obtain the response of system (mean and higher moments) given the probability distribution of certain input parameters. In the full presentation mention will be made of progress in all these areas and the likely direction of future research, so that CEM can be applied efficiently in practical system-wide EMC studies.