Electromagnetic modelling of planar circuits in bounded layered media

Printed circuits in bounded media encompass a wide range of practical structures such as discontinuities in waveguides, planar circuits embedded in shielded multilayered media or even two-dimensional printed periodic structures. The Electromagnetic (EM) modeling of printed circuits in layered bounded media is performed via an Integral Equation (IE) technique. Green's functions (GFs) are specially defined to satisfy both the Boundary Conditions (BCs) imposed by the layered media and by the transverse boundary enclosing the entire structure. Finally, a system of IEs on the equivalent sources can be solved numerically by means of the Method of Moments (MoM). Each of the problems enumerated above has already been solved by other authors using IE-MoM techniques. Nevertheless, our formulation introduces a unified approach applicable to all the aforementioned problems. Due to the symmetry presented by a bounded layered media, the GF problem can be reduced into a two-dimensional transverse boundary problem and a one-dimensional transmission line problem in the normal direction. Both problems can be treated independently. This thesis proposes and fully develops an efficient technique that encompasses different laterally bounded multilayered problems with a seamless transition between them. The method is based on a modal representation of the transverse boundary problem and on the expansion of the equivalent surface currents by zero-curl & constant-charge Basis Functions (BFs). It offers a unified and versatile approach that, on one hand eliminates redundancy in the formulation and on the other hand simplifies each particular problem to the evaluation of constant coefficients or basic line integrals. Analytical solutions can be found for the combination of linear subsectional basis functions in rectangular and circular Perfect Electric Conductor (PEC) boundaries as well as for periodic lattices. This thesis then solves the problem of transmission line model in the longitudinal direction by proposing an efficient algorithm that guarantees numerical stability under a variety of known critical conditions where other already known formulations fail. In addition, it introduces alternate equivalent expressions of this formulation that allow new interpretations of the problem. Due to its practical interest, the method is applied for the EM modeling of multilayered boxed printed circuits. This motivated the implementation of a dedicated software tool for the efficient analysis of these topologies including losses. Extensive numerical experiments have been carried out to assess the validity of the aforementioned theory and some properties of test-structures (losses, mesh, etc).

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