Frequency response analysis (FRA) is a method which is used to detect mechanical faults in transformers. The FRA response of a transformer is determined by its geometry and material properties, and it can be considered as the transformer’s fingerprint. If there are any mechanical changes in the transformer, for example if the windings are moved or distorted, its fingerprint will also be changed so, theoretically, mechanical changes in the transformer can be detected with FRA. The purpose of this thesis is to partly create a simple model for the ferromagnetic material in the transformer core, and partly to investigate the high frequency part of the FRA response of the transformer winding. To be able to realize these goals, two different models are developed separately from each other. The first one is a time- and frequency domain complex permeability model for the ferromagnetic core material, and the second one is a time- and frequency domain winding model based on lumped circuits, in which the discretization is made finer and finer in three steps. Capacitances and inductances in the circuit are calculated with use of analytical expressions derived from approximated geometrical parameters. The developed core material model and winding model are then implemented in MATLAB separately, using state space analysis for the winding model, to simulate the time- and frequency response. The simulations are then compared to measurements to verify the correctness of the models. Measurements were performed on a magnetic material and on a winding, and were compared with obtained results from the models. It was found that the model developed for the core material predicts the behavior of the magnetic field for frequencies higher than 100 Hz, and that the model for the winding predicts the FRA response of the winding for frequencies up to 20 MHz.

In this work, a modeling approach is delineated and described in detail; predominantly done in the time domain from low frequency, DC, to high frequencies, 100 MHz. Commercially available computer aided design tools will be used to determine the propagation path in a given structure. Next, an integrated transmission-line filter — fabricated using planar processing technologies — is modeled to accurately predict the EMI characteristics of the system. A method was derived to model the filter's performance in the time-domain while accurately depicting the highly frequency dependant transmission-line properties. A system model of a power factor correction (PFC) boost converter was completed by using active device models for diodes, MOSFETs, and the gate driver. In addition, equivalent circuits were used to characterize high frequency impedances of the passive components. A PFC boost converter was built and used to validate the model. The PFC operated at a peak output power of 1 kW, switching at 400 kHz, with a universal input ranging from 90-270 VRMS with unity power factor. The time-domain and EMI frequency spectrum waveforms are experimentally measured and agree very well with the simulated values; within 5 dB for EMI. The transmission-line filter was also manufactured for model verification, and it is tested for the first time with an operating converter: a PFC at 50 W output and 50 VDC input. The small signal characteristics match the model very well. In addition, impedance interactions between the filter, the converter, and the EMI measurement set-up are discussed, evaluated, measured, and improved to minimize undesired resonances and increase low-frequency EMI attenuation. Experimentally measured attenuation provided by the filter in the range from 100 kHz to 100 MHz was 20-50 dBμV. The simulation also shows a similar attenuation, with the exception of one key resonance not seen in the simulation. / Master of Science

La modélisation numérique des réseaux de câbles est devenue une étape indispensable dans la phase de conception d’un projet afin de prédire les disfonctionnements dans les moyens de transport issus de l’augmentation des couplages électromagnétiques. La majorité des modèles repose sur des méthodes analytiques, qui sont certes rapides en comparaison avec les méthodes numériques 3D, mais en contrepartie sont limitées aux basses fréquences et aux géométries uniformes. De plus, des hypothèses concernant les conditions aux limites des conducteurs, comme les plans de masse infinis, sont souvent appliqués dans le but d’obtenir des formules analytiques simples C’est dans ce contexte, que nous avons envisagé l’amélioration de ces modèles en réduisant ces simplifications et ces hypothèses imposées au départ. A cet égard, nous avons développé dans un premier temps un modèle de ligne de transmission filaire qui consiste à prendre en compte les pertes par rayonnement en haute fréquence, la longueur finie et la géométrie non uniforme. Lors de cette étude, nous avons utilisé la théorie des lignes et deux méthodes numériques en l’occurrence les méthodes PEEC et TLST. Nous avons démontré pour le cas des risers que les coefficients de la méthode PEEC peuvent être obtenus analytiquement. Concernant notre deuxième axe de recherche, on s’est intéressé à la modélisation des conduits métalliques notamment les plans de masse finis et les goulottes. Ces derniers ont été modélisés avec un ensemble de câbles. Une étude expérimentale a été menée sur les effets induits par la goulotte sur la propagation des ondes électromagnétiques. Finalement, les résultats de nos modèles ont été validés expérimentalement avec des mesures. Une attention particulière a été portée sur l’effet des extrémités des lignes de transmission. / Considering the increasing awareness of the EM coupling issues inside aircraft and automotive engines, numerical modeling of cable harness networks is currently one of the most important steps in the design process of an engineering project. Most of the relevant softwares that deals with the cable topology simulation relies on the well-known analytical models such as the multiconductor transmission line theory. These techniques are better than the fullwave ones regarding the time calculation and the memory requirement. However, they are available only in the low frequency range because of the assumptions taken into account such as the uniform geometry and the infinite length of the wires. To overcome these restrictions and improve the existing solutions, we come up with a new high frequency model which is based on the transmission line theory and two numerical methods: PEEC and TLST. To keep the analytical approach of our model, we managed to get the analytical expressions of the PEEC’s partial elements. In this thesis, we were also interested by the cable raceways and cable trays. First of all, we developed a raceway model based on transmission line wires. Comparing our results with the FDTD ones, we noticed some differences especially in the high frequency range when the wire ends with the risers. Through an experimental study, we explained the behavior and the impact of these cables trays on the EM wave propagation. Finally, the results of our models have been validated with the measurements. Thanks to these experiments, we highlighted the fact that the termination of a wire has an important impact on the wave propagation.