Technical memorandum. Rapidly converging expressions of dyadic green's functions for parallel-plate transmission line

The four dyadic Green's functions of electric and magnetic type for the parallel-plate transmission line are considered. From the expression of the dyadic Green's impedance in the form of a full modal expansion, two terms, diverging at the source point, are extracted and expressed in closed form. The first term represents the quasi-static approximation of the dyadic impedance and coincides with its irrotational part which contains the dominant singularity; the second term represents the lowfrequency approximation of the solenoidal part of the Green's impedance and is singular too. The remaining modal series, which represents a dyadic finite at the source point takes into account wave propagation and converges rapidly everywhere, even when the observation and the source points are very close to each other. Similar expressions are found for the other dyadic Green's functions.