Coupled 2D Telegrapher's equations for PDN analysis

Abstract

Governing partial differential equations are derived for multiple parallel plane structure in frequency-domain. The equations can be considered as an extension of broadband equations derived earlier for one pair of planes and as an extension of well-known 2D Telegrapher's equations originally derived for analysis of narrow-band microwave planar circuits. The broadband equations have appropriate high and low frequency asymptotes and are suitable for analysis of power delivery networks (PDN) with multiple parallel planes at frequencies from DC to multi-gigahertz frequency range. Derived equations are validated with results of 3D electromagnetic analysis and with published measured data.