Numerical Evaluation of the Green's functions for Arbitrarily Shaped Enclosures

Abstract

Abstract-In this paper, a new spatial method has been implemented for the efficient calculation of the mixed potential Green's functions associated to electrical sources, when they are placed inside arbitrarily-shaped cylindrical cavities. The technique consists of placing electric dipole images and charges outside the cavity, imposing, at discrete points of the metallic wall, the appropriate boundary conditions for the potentials. Results show that the numerical convergence is attained fast. The cut-off frequencies and potential patterns for a trapezium-shaped waveguide are compared to those obtained by a standard finite elements technique, showing excellent agreement. Furthermore, a printed planar filter shielded in a square cavity has been analyzed with the new Green's functions, showing the practical value of the new theory.

Practical Implementation of the Spatial Images Technique for the Analysis of Shielded Multilayered Printed Circuits

“…The strength and orientation of the images are then computed so the proper boundary conditions are satisfied at discrete points of the metallic wall. The details of the formulation for arbitrarily shaped cavities employing free-space Green's functions can be found in [3]. However, for the analysis of completely closed enclosures, the bottom and top covers of the cavity must be included in the formulation.…”

“…In this paper, we have combined the original technique described in [3] with the multilayered media Green's functions in the spatial domain formulated through the Sommerfeld transformation. This has allowed us to study real multilayered printed circuits shielded in cavities of complex shapes.…”

“…The method was modified in order to analyze complex-shaped cylindrical cavities, defined with linear segments, in [3]. The idea of the method is to use charge and dipole images outside the cavity to enforce the proper boundary conditions for the potentials.…”

“…The boundary conditions are imposed at discrete points along the cavity wall, and thus, the technique proposed should be considered as an approximation to the real cavity modeling. To do that, the free-space Green's function was employed in [3]. In this paper, we incorporate the multilayered media Green's functions formulated as Sommerfeld integrals [4] in order to study real closed multilayered cavities including top and bottom covers.…”

“…This idea was first proposed in [2] in the context of circular cylindrical cavities. In this paper, we combine the same idea with the formulation presented in [3] to analyze circuits printed in convex cavities.…”