An interpolated spatial images method for the analysis of multilayered shielded microwave circuits

Abstract

In this paper, an efficient interpolation method is presented in order to compute the Green’s function associated to electrical sources, when they are placed inside cylindrical cavities. The interpolation scheme is formulated in the frame of the spatial images technique recently developed. The original idea was to calculate, for every location of a point electric source, the complex values of the electric dipole and charge images, placed outside the cavity, to impose the appropriate boundary conditions for the potentials. In order to considerably reduce the computational cost of the original technique, a simple interpolation method is proposed to obtain the complex values of the images for any source location. To do that, a rectangular spatial subdivision inside the cavity is proposed. Each new sub-region is controlled by means of the exact images values obtained when the source is placed at the four corners of the region. The key idea is to use a bilinear interpolation to obtain the images complex values when the source is located anywhere inside this sub-region. The interpolated images provide the Green’s functions of the new source positions fast, and with high accuracy. This new approach can be directly applied to analyze printed planar filters. Two examples with CPU time comparisons are provided, showing the high accuracy and computational gain achieved with the technique just derived.