Çoklu dikey iletkenli düzlemsel geometriler için verimli elektromagnetik simülasyon algoritmasının geliştirilmesi

ABSTRACT An efficient electromagnetic simulation algorithm, which is based on the solution of mixed-potential integral equation (MPIE) via the method of moments (MoM), is presented for the analysis of general planar geometries with multiple vertical metallizations. Although the algorithm itself is the main contribution of this thesis, there have been two additional contributions in the steps towards this goal. These contributions are in the form of thor ough investigation of the two subtopics leading to the main algorithm, namely, closed-form Green's functions and MoM matrix entries. Since the closed-form Green's functions are employed in and the vital part of the al gorithm presented in this thesis, the steps of getting these Green's functions are critically reviewed, not only for the sake of completeness, but also for clarifying some misunderstand ings in the derivation, and the limitations of the method. As it is well-known, the derivation of the closed-form Green's functions begins with the approximation of the spectral-domain Green's functions by complex exponentials, and continues with applying the Sommerfeld identity to cast these approximated spectral-domain Green's functions into the space do main in closed forms. During the last decade, several questions have been raised on the mathematical validity of some steps in the derivation, and remedies have been proposed. These questions can be categorized under the topics of branch point contributions, the ef fect of quasi-static terms, and the contributions of the surface wave poles to the closed-form Green's functions. The potential problems of the derivation of the closed-form Green's func tions, with a priority given to the topics addressed in the literature, have been discussed in detail, and demonstrated that some are due to misunderstandings, some due to numerical errors interpreted as physical errors, and the others are the mere limitations of the method. The numerical technique employed in this work for the analysis of planar geometries is based on the solution of MPIE using the spatial-domain MoM in conjunction with the closed-form Green's functions. The introduction of closed-form Green's functions into the MoM formulation has already resulted in a significant computational improvement for the ivanalysis of planar geometries. However, in cases of vertical metallization, the computational efficiency of the method cannot be improved by simply casting the Green's functions in closed forms, which is due to some difficulties encountered in incorporating the closed-form Green's functions into the MoM formulation for such geometries. In this work, a solution to circumvent these difficulties is proposed, and it is demonstrated that multiple vertical conductors can be efficiently modelled and incorporated into the simulation algorithm, pro vided all vertical metallization have the same dependence in the vertical direction. The results obtained from the algorithm proposed in this thesis are compared to those obtained from commercially available software and experiments. Keywords: Green's functions, DCIM, Pull- wave EM analysis, Method of Moments, 3-D Planarly Layered Media, Vertical Conductors