A new algorithm for the wide-band analysis of arbitrarily shaped planar circuits

An algorithm for the wideband analysis of the two-dimensional model of a planar circuit is described. The planar circuit is considered to be enclosed in a regularly shaped (rectangular or circular) resonator, and the electric and magnetic fields are derived from the Green´s functions of this resonator by integrating over the periphery of the circuit not coinciding with the regular shape. The special form used for the Green´s functions makes it possible to derive the Z-parameters in a special form, similar to Foster´s series, but converging much more rapidly. The calculation requires the determination of a reduced number of resonances of the planar circuit, which are obtained by an integral equation approach leading to a linear eigenvalue problem. The algorithm was implemented in an efficient computer-aided design (CAD) routine, named ANAPLAN, which is briefly described