## Project

# Spherical Wave Based Macromodelling for EMC/EMI System Analysis

Nowadays, full-wave electromagnetic simulation tools are widely used in antenna design, and their employment in the assessment of electronic designs with respect to ElectroMagnetic Compatibility (EMC) has increased significantly over the past years, owing to an exponential increase in the integration of functionality and the clock rates of new designs. However, several developers are still rather reserved about their engagement to embrace the use of full-wave simulations. This trend can be attributed to four factors: (i) the investment cost of a full-wave simulation package, (ii) the expertise of R&D engineers, (iii) the limited availability of component models due to conflicts with confidentiality, and (iv) the computational cost of full-wave simulations. Due to the inherent complexity in today’s electronic designs and their clock rates, often dedicated computing servers are indispensable to manage the run-time and computational resources of full-wave simulations. In this thesis, we therefore aim to develop a macromodelling technique, focussed at system-level EMC analysis, which is independent of any full-wave solver, which has a very low computational cost, and which bears close resemblance to the topology of circuit simulators.

We obtain these goals by employing a Generalized Scattering matrix (GS-matrix) formulation based on a Spherical Wave Expansion (SWE) of the electromagnetic fields radiated by a Device Under Test (DUT). To derive efficiently such models, a new technique based on a reduction to Chebyshev polynomials is described, which allows one to compute models in optimal time with very high accuracy. In the scope of system-level EMC analysis, two new truncation criteria are formulated, either applicable to fields sampled in the near-field region of a DUT or to fields sampled in the far-field region of a DUT. Based on these truncation criteria, it is observed that in order to accurately model radiated fields close to a DUT, high-order SWEs are indispensable. Models which have been obtained using this approach are gathered in a common model library, which is accessible to a custom GS-matrix based simulation engine. This simulation tool is designed analogous to a circuit simulation topology, and thus allows its users to compute full-wave interactions between multiple DUTs by ‘plug-and-play’ with models available in a component library. Consequently, the presented framework also fits into existing circuit solvers, and significantly increases the accuracy of these solvers by taking into account full-wave phenomena. The additional background computations which form the core of the GS-matrix based simulation tool are optimized by observing that the necessary operators acting on SWEs are sparse. Additionally, it has been observed that the number of spherical waves needed to accurately compute interactions between multiple GS-matrix instances only forms a subpart of the number of spherical waves needed to accurately represent the fields radiated by a DUT in its near-field region. In combination with numerous additional optimizations, full-wave simulations run in the order of seconds on a simple home laptop. To further show the computational efficiency of the proposed simulation tool, support has been added for a cylindrical scan of a DUT by an antenna. This setup, often corresponding to more than one thousand full-wave simulations, only takes up about one minute on a simple laptop.

In using the developed simulation tool, we have encountered that in certain cases multiple reflections between DUTs can compromise its accuracy. However, deriving the scattering parameters for incident spherical waves is not straightforward due to the lack of support for spherical wave excitations in most full-wave simulation tools. Therefore, we have derived an alternative approach based on plane wave illuminations. An appropriate linear combination of plane wave illuminations allows us to mimic, to a sufficient degree of accuracy, arbitrary spherical wave excitations. We have validated this approach by comparing scattered field patterns for arbitrary incident plane waves to full-wave simulations. Subsequently, we have applied the scattering parameters for incident spherical waves in simulations where multiple reflections between DUTs play a significant role. Finally, the simulation tool is extended to support an infinite perfectly conducting plane underneath DUTs. Depending on the distance of the DUTs above this conducting plane, an approach based on mirroring fields sampled on a hemispherical surface or an alternative ‘image theory’ is applied. We have, however, encountered inaccuracies in the computations when image theory is applied. These inaccuracies are attributed to forward scattering of fields reflected by the conducting plane. Nevertheless, using the knowledge of the scattering parameters for incident spherical waves, the deviation due to forward scattering of the reflected fields is tackled in a straightforward manner, and we have subsequently observed a very good correspondence between the GS-matrix simulation tool and a full-wave simulation.

We have thus, in summary, developed a numerically stable and efficient circuit based topology that can be employed to study a wide range of system-level EMC problems. Several realistic applications are discussed to validate the proposed methodology.