Volume Rooftop Basis Functions in Shielded Layered Media

Infinitely thin planar circuits are often represented with rooftop basis functions. These basis functions use a sheet of surface current over the area of a subsection and are overlapped to generate a piece-wise linear representation of the actual surface current. This paper extends rooftop functions to volume current. Volume current rooftop subsections are overlapped in a similar fashion to represent the volume current flowing in a thick conductor. Layered media enclosed in a rectangular shielding conductor is assumed. This allows fast and numerically exact evaluation of the Green's function with the resulting method of moments reaction integrals evaluated analytically, rather than numerically. Use of volume rooftops results in faster high accuracy analysis of planar circuits composed of thick metal, especially for lines with a high aspect ratio cross-section.