Novel Closed-Form 2-D Green's Function of Shielded Layered Media And Its Use in Transmission Lines Inductance Extraction

Abstract

New closed-form expression for quasi-static 2-D Green's function of fully-shielded layered medium is proposed. Along the vertical direction of the medium stratification the spectrum of the Green's function can be obtained through the 1-D ordinary differential equation and expressed as pole-residual form. This rational function representation of the spectrum allows to evaluate space domain Green's function in layered medium shielded from top and bottom with horizontal ground planes in a closed-form. This closed-form expression allows to analytically add up contributions from infinite number of source images with respect to the vertical side walls of the rectangular enclosure, hence, producing the new closed-form expression for the 2-D Green's function of rectangular enclosure vertically filled with multilayered medium. Availability of such Green's functions enable construction of integral equation based magneto-quasi-static and electro-quasi-static 2-D extractors. Such 2-D magneto-quasi-static extractor based on solution of Surface-Volume-Surface Electric Field Integral Equation (SVS-EFIE) for multi-conductor transmission lines (MTLs) situated in shielded layered media is demonstrated.