Electromagnetic Modelling of Planar Circuits Embedded in Laterally Shielded Multilayered Media

Abstract

Multilayered media with printed circuits embedded between their dielectric layers are one of the most successful technologies for manufacturing planar structures with a very promising performance-to-price ratio. These planar structures include many different geometries ranging from cavity-backed microstrip antennas through Frequency Selective Surfaces (FSS) and photonic band-gap structures, to shielded printed circuits and ultra-wide-band slot-line microwave filters. The electromagnetic characteristics of such structures can be modeled with a wide range of numerical techniques. In recent years we have witnessed a remarkable progress in developing numerical solvers specialized in analyzing specific electromagnetic problems including the Integral Equation technique (IE) solved by the Method of Moments (MoM) which has proven to be very robust and efficient in the framework of partially open or shielded planar structures. As a part of this study an efficient CAD tool was developed based on the IE formulation and implemented in the context of the MoM technique. It includes a rigorous mathematical formulation of the electromagnetic problem which automatically incorporates the effects of the metallic shield (cavity) and the multilayered substrate which supports different layers of metallization (interfaces). A comprehensive study has been carried out to point out the convergence of the proposed algorithm along with a detailed validation, verification and benchmarking plan. The tool is developed in such a way that is capable of working with a hybrid mesh (combination of both rectangular and triangular cells) which gives it a great flexibility in analyzing any arbitrarily-shaped embedded circuitry. To enhance the overall performance of the algorithm, symmetry options have been formulated and implemented. These additional features have shown to dramatically reduce the computational and temporal requirements and thus expand the range of microwave devices which can be efficiently analyzed by the software, such as filters based on waveguide structures and FSSs. Other enhancement techniques have been envisaged based on selective MoM matrix member calculation which successfully reduce the number of unknowns in large microstrip layouts while maintaining an acceptable accuracy. Mathematical formulations are developed to provide the capability of handling lumped ports (representing coaxial-line feeds) and waveguide excitations. The implementation of combined ports in the framework of planar multilayered structures is shown to be practically useful in analyzing systems that have both waveguide connections and planar circuitries in their structure as it enables the application of highly specialized algorithms in the analysis of each part of the system and subsequent communication of the network characterizations at the ports' interfaces. This approach has considerably enhanced the overall performance of the analysis tool by reducing the computation time and memory requirements to a great extent.