Construction and applications of the Dirichlet-to-Neumann operator in transmission line modeling

The Dirichlet-to-Neumann (DtN) operator is a useful tool in the characterization of interconnect structures. In combination with the Method of Moments, it can be used for the calculation of the per-unit length transmission line parameters of multi-conductor interconnections, or to directly determine the internal impedance of conductors. This paper presents a new and fast calculation method for the DtN boundary operator in the important case of rectangular structures, based on the superposition of parallel-plate waveguide modes. Especially for its non-differential form, some numerical issues need to be addressed. It is further explained how the DtN operator can be determined for composite geometries. The theory is illustrated with some numerical examples.